mathematics curriculum grades 7-8 · 2009-12-14 · 8th grade pre-algebra curriculum 156 8th grade...

Flemington-Raritan Regional School District Flemington, New Jersey

Mathematics Curriculum Grades 7-8

Gregory Nolan, Superintendent Daniel Bland, Assistant Superintendent Sandra Pollock, Mathematics Supervisor

Kristen Campbell Susan Hubert

Donna Jablonski Sherry Kodidek Melissa Neuman

Elizabeth Roll Jackie Schorr Jennifer Tobin

Council of Instruction Review Date: November 9, 2009 BOE Curriculum Committee Review Date: November 4, 2009 Board of Education Approval Date: December 7, 2009

Flemington-Raritan Regional Schools Mathematics Curriculum

Grades 7-8

Table of Contents

Mission Statement 1

Philosophy 2

2004 New Jersey Core Curriculum Content Standards 4

Program Description 5

Calculator Philosophy 7

Grade 7 Curriculum 9

7th Grade Interdisciplinary Connections 10

7th Grade Math Curriculum 18

7th Grade Algebra IA Curriculum 63

7th Grade Algebra IB Curriculum 107

Grade 8 Curriculum 147


8th Grade Pre-Algebra Curriculum 156

8th Grade Algebra IB Curriculum 205

8th Grade Advanced Algebra Curriculum 247

8th Grade Algebra II Curriculum 292

Flemington-Raritan Regional Schools

Mathematics Curriculum

Grades 7-8

District Mission Statement

The Flemington-Raritan Regional School District, a caring and proactive district, in partnership with the community, will provide each student with:

• A sound educational foundation, • The guidance to strive for his/her full potential, and • The inspiration to become a lifelong learner and a responsible,

productive citizen in an ever-changing global society.

1



Philosophy

The Grades 7-8 Mathematics Curriculum is based on the belief that all students can learn mathematics. The mathematics program develops each child’s mathematical reasoning in understanding the big ideas (concepts) of mathematics. The program sets high benchmarks and expectations for students to effectively express mathematical content, process, and skills through verbal and written communication. The use of technological tools is a vital component of the program, not only to enhance the understanding of concepts, but an important tool used in the adult world to access and analyze real world data. In accordance with the above beliefs, the program includes a comprehensive range of content in a variety of contexts. The program integrates skills, concepts, and applications based on the 2004 New Jersey Core Curriculum Content Standards for Mathematics, providing each student the opportunity to become an active participant in his/her mathematical education. Students explore the beauty of mathematics with confidence, with the aim to become a generation of mathematically literate adults. The grades 7-8 mathematics program is built on developmentally appropriate practice for middle school students:

• All students can learn and understand mathematics; • Students construct their own meaning based on prior experience; • Learning occurs in social situations; • Learning is tied to contextual, real-world situations; • Learning involves numerous strategies involving higher order thinking

skills. Students continually reflect on the following question: “Does this make sense?”

2



The 21st Century Learning and Thinking Skills are an integral part of the 7-8 mathematics program including:

• Critical Thinking and Problem Solving Skills • Communication Skills • Creativity and Innovation Skills • Collaboration Skills • Information and Media Literacy Skills • Contextual Learning Skills

3



2004 New Jersey Core Curriculum Content Standards – Mathematics

The 2004 New Jersey Core Curriculum Content Standards contain Specific Cumulative Progress Indicators for each grade and the Mathematics Curriculum for grades 7 and 8 reflects the relevant cumulative progress indicators for grades 7, 8 and, where appropriate, grade 12. There are five standards altogether, each of which has a number of lettered strands. These standards and their associated strands, are enumerated below:

4.1 Number and Numerical Operations A. Number Sense B. Numerical Operations C. Estimation 4.2 Geometry and Measurement A. Geometric Properties B. Transforming Shapes C. Coordinate Geometry D. Units of Measure E. Measuring Geometric Objects 4.3 Patterns and Algebra A. Patterns B. Functions and Relationships C. Modeling D. Procedures 4.4 Data Analysis, Probability, and Discrete Mathematics A. Data Analysis (Statistics) B. Probability C. Discrete Mathematics -- Systematic Listing and Counting D. Discrete Mathematics -- Vertex-Edge Graphs and Algorithms 4.5 Mathematical Processes A. Problem Solving B. Communication C. Connections D. Reasoning E. Representation F. Technology

4



Program Description

The curriculum emphasizes a balance between hands-on, inquiry-based problem solving, and traditional mathematical computation and arithmetic. Teachers focus on making connections between facts and fostering new understanding in students, and tailor their teaching strategies to student responses, encouraging students to analyze, interpret, and predict information. Teachers also rely heavily on open-ended questions and promote extensive dialogue among students through cooperative learning strategies.

Assessments consist of teacher-created quizzes, tests, teacher observations, student responses, student projects, student daily work, district wide and state wide testing as well as the Hunterdon Central High School placement exams. In practice, assessment is ongoing and serves to provide feedback to students and to inform instruction. Teachers use a variety of assessment techniques, both quantitative and qualitative, to assess student development in the areas of mathematical conceptual understanding, mathematical procedures, and mathematical process. Multiple choice, short answer, and open-ended responses requiring written explanations are all components of the ongoing assessments in the classroom.

In grades 7 and 8, all students are grouped homogeneously by ability and achievement in mathematics. Various district wide tests, teacher recommendation, and student performance are considered when placing students for mathematics. Mathematics textbooks, support materials, and teacher instruction are modified according to the different needs of students in order for students to meet the New Jersey Core Curriculum Standards for each grade level. Continual assessment and reflection upon student work and achievement drives instruction. All student data, performance and achievement are constantly monitored in order to move students forward to their fullest mathematical potential. Placements procedures include not only student ability and achievement in concepts and computation, but also the ability to work independently at an accelerated pace.

5



Grades 7-8

The following textbooks are used in grades 7 and 8 mathematics classes at J.P. Case Middle School:

Level Textbook Grade 7 7th Grade Math McDougal Littell Course 2 Holt Course 2 (Special Education) Algebra IA Discovering Algebra (first half) Algebra IB Discovering Algebra (second half) Grade 8 Pre-Algebra McDougal Littell Course 3 Holt Course 3 (Special Education) Algebra IB Discovering Algebra (second half) Advanced Algebra Discovering Advanced Algebra Algebra II McDougal Littell Algebra 2

6



Calculator Philosophy

The J.P. Case Middle School mathematics program believes that calculators are a vital component of the mathematics program. The following rationale from Texas Instruments covers many of the advantages of using calculators, as outlined by the NCTM and the 2004 New Jersey Core Curriculum Standards. Calculators are valuable educational tools that allow students to reach a higher level of mathematical power and understanding. By reducing the time that, in the past, was spent on performing tedious paper-and-pencil arithmetic and algebraic algorithms, calculator use today allows students and teachers to spend more time developing mathematical understanding, reasoning, number sense, and applications. They afford students learning tools that complement, but do not replace, mental and paper-and-pencil skills, and they expand students’ ability to solve problems by providing multiple solution techniques. Calculator technology allows students who would ordinarily be frustrated or bored by tedious manipulations to have access to the real mathematics itself, thus gaining a higher level of mathematical understanding, rather than giving up. The fact is, calculators are better tools to do some of the computations and manipulations that were once done with paper and pencil. In the past, paper and pencil were the only tools available. Appropriate use of technology and associated pedagogy will get more students thinking and reasoning mathematically. Thus more students will develop useful mathematical understanding and mathematical power. Despite all of their benefits and capabilities, calculators will never be able to replace the human mind when it comes to knowing how to read and understand a problem situation, writing an appropriate equation for the problem, choosing which operations to use to solve the problem, correctly interpreting the solution displayed on the calculator, and determining the appropriateness of the answer. Calculators are only as effective as the information students enter into them. Calculators, in conjunction with mental, paper-and-pencil, and estimation skills when appropriate, comprise the tools to help students work through the computations and manipulations necessary for solving problems. Calculators are like computer word processors to English students. Computer word processors do not “create” essays but they

7

do facilitate the creation of an essay. Calculators do not “understand” mathematics but they do facilitate the understanding of mathematics. Despite all of their capabilities, however, they will never replace the important, complex thought processes of which only humans are capable.

8

7th Grade Curriculum

9

Flemington Raritan School District


Grades 7-8

7th Grade Interdisciplinary Connections

Standard Subject Learning Experience

4.1.A.2. Demonstrate a sense of the relative magnitudes

of numbers.

Science

Social Studies

Parts per Billion Lab

Population of the Middle Ages

4.1.A.3. Understand and use ratios, rates, proportions,

and percents (including percents greater than 100 and

less than 1) in a variety of situations.

Social Studies Junior Scholatic Magazines

4.1.B. 1. Use and explain procedures for performing

calculations with integers and all number types named

above with: Pencil-and-paper; Mental math; Calculator.

Science Labs throughout the year

4.1.C.1. Use equivalent representations of numbers such

as fractions, decimals, and percents to facilitate

estimation.

All Disciplines Discussions, labs all year long

4.2.A.2. Understand and apply the concept of similarity:

Using proportions to find missing measures; Scale

drawings; Models of 3D objects.

Art

Social Studies

Scale Drawings, Polygon Project

Reading a map, identifying landmarks on a

map




Grades 7-8



4.2.B.1. Understand and apply transformations: Finding

the image, given the pre-image, and vice-versa; Finding

the image, given the pre-image, and vice-versa;

Sequence of transformations needed to map one figure

onto another; Reflections, rotations, and translations

result in images congruent to the pre-image; Dilations

(stretching/shrinking) result in images similar to the pre-

image.

Art Tessellations, Transformations

4.2.C.1. Use coordinates in four quadrants to represent

geometric concepts.

Social Studies Map Reading

4.2.D.1. Solve problems requiring calculations that

involve different units of measurement within a

measurement system (e.g., 4’3” plus 7’10” equals 12’1”).

Science

Social Studies

Art

Labs, Metric system use

Reading a scale on a map

Making a scale drawing

4.2.E.1. Develop and apply strategies for finding

perimeter and area: Geometric figures made by

combining triangles, rectangles and circles or parts of

circles; Estimation of area using grids of various sizes.

Social Studies iSearch, population density




Grades 7-8



4.3.A.1. Recognize, describe, extend, and create patterns

involving whole numbers, rational numbers, and

integers: Descriptions using tables, verbal and symbolic

rules, graphs, simple equations or expressions; Finite

and infinite sequences; Arithmetic sequences (i.e.,

sequences generated by repeated addition of a fixed

number, positive or negative); Geometric sequences (i.e.,

sequences generated by repeated multiplication by a

fixed positive ratio, greater than 1 or less than 1).

Social Studies iSearch data gathering

4.3.C.1. Analyze functional relationships to explain how

a change in one quantity can result in a change in

another, using pictures, graphs, charts, and equations.

Science Volume and Density labs

Motion and Sound labs

4.3.C.2. Use patterns, relations, symbolic algebra, and

linear functions to model situations: Using

manipulatives, tables, graphs, verbal rules, algebraic

expressions/equations/inequalities; Growth situations,

such as population growth and compound interest, using

recursive (e.g., NOW- NEXT) formulas (cf. science

standards and social studies standards).

Science Volume and Density labs

Motion and Sound labs




Grades 7-8



4.3.D.2. Solve simple linear equations informally and

graphically: Multi-step, integer coefficients only

(although answers may not be integers); Using paper-

and-pencil, calculators, graphing calculators,

spreadsheets, and other technology.

Science Motion and Sound unit

Volume and Density unit

4.4.A.1. Select and use appropriate representations for

sets of data, and measures of central tendency (mean,

median, and mode): Type of display most appropriate

for given data; Box-and-whisker plot, upper quartile,

lower quartile; Scatter plot; Calculators and computer

used to record and process information.

Social Studies

Discovering Algebra

iSearch Paper

Use of Statistics to compare gender equality,

life expectancy, zoology, election results,

deomgraphics, penny data

4.4.A.2. Make inferences and formulate and evaluate

arguments based on displays and analysis of data.

Science Lab write-ups

Daily Discussions in Social Studies and

Science

4.4.B.1. Interpret probabilities as ratios, percents, and

decimals.

Science Probability of weather occurring

4.4.B.3. Estimate probabilities and make predictions

based on experimental and theoretical probabilities.

Economics Insurance Industry




Grades 7-8



4.4.C.1. Apply the multiplication principle of counting:

Permutations: ordered situations with replacement (e.g.,

number of possible license plates) vs. ordered situations

without replacement (e.g., number of possible slates of 3

class officers from a 23 student class).

Social Studies Population increases and license plate

number, area codes, phone numbers

(availability)

4.4.C.2. Explore counting problems involving Venn

diagrams with three attributes.

Language Arts Venn Diagrams - compare and contrast

4.5.A.2. Solve problems that arise in mathematics and in

other contexts: Open-ended problems; Non-routine

problems; Problems with multiple solutions; Problems

that can be solved in several ways.

Language Arts Reading Skills

4.5.A.6. Distinguish relevant from irrelevant

information, and identify missing information.

Language Arts Reading Skills

4.5.B.1. Use communication to organize and clarify

mathematical thinking: Reading and writing;

Discussion, listening, and questioning.

Language Arts Grammar Usage, Paragraph Construction

Skills




Grades 7-8



4.5.B.2. Communicate mathematical thinking coherently

and clearly to peers, teachers, and others, both orally

and in writing.

Language Arts Grammar Usage, Paragraph Construction

Skills

4.5.B.3. Analyze and evaluate the mathematical thinking

and strategies of others.

Language Arts Peer editing

4.5.C.3. Recognize that mathematics is used in a variety

of contexts outside of mathematics.

Science

Social Studies

Art

Computer Applications

Cooking and Sewing

Physics Formulas, graphs, tables

Statistics

Transformations, perspectives, scale

drawing, computer aided design

Marble maze

Measuring Ingredients, Measuring material

4.5.C.4. Apply mathematics in practical situations and

in other disciplines.

Science

Social Studies

Art

Computer Applications

Cooking and Sewing

Physics Formulas, graphs, tables

Statistics

Transformations, perspectives, scale

drawing, computer aided design

Marble maze

Measuring Ingredients, Measuring material




Grades 7-8



4.5.D.2. Use reasoning to support their mathematical

conclusions and problem solutions.

Language Arts Persuasive writing, supporting their ideas

4.5.D.5. Make and investigate mathematical conjectures:

Counterexamples as a means of disproving conjectures;

Verifying conjectures using informal reasoning or

proofs.

Science Scientific Method

4.5.D.6. Evaluate examples of mathematical reasoning

and determine whether they are valid.

Science Scientific Method

4.5.E.1. Create and use representations to organize,

record, and communicate mathematical ideas: Concrete

representations (e.g., base-ten blocks or algebra tiles);

Pictorial representations (e.g., diagrams, charts, or

tables); Symbolic representations (e.g., a formula);

Graphical representations (e.g., a line graph).

Science

Social Studies

Gathering Data from Labs

Graph Population over time

4.5.E.3. Use representations to model and interpret

physical, social, and mathematical phenomena.

See 4.4 Standards




Grades 7-8



4.5.F.1. Use technology to gather, analyze, and

communicate mathematical information.

Science

Social Studies

Labs, temperature probes, sound waves,

light refraction

iSearch

4.5.F.2. Use computer spreadsheets, software, and

graphing utilities to organize and display quantitative

information.

Computers

4.5.F.6. Use computer-based laboratory technology for

mathematical applications in the sciences.

Science Long run value


7th Grade Math Curriculum

18

A. Number Sense

· How do mathematical ideas interconnect and build on one another to produce a coherent whole?

· How can we compare and contrast numbers?

· How can counting, measuring, or labeling help to make sense of the world around us?

Resources

Essential Questions :

1. Extend understanding of the number system

by constructing meanings for the following

(unless otherwise noted, all indicators for

grade 7 pertain to these sets of numbers as

well): Rational numbers; Percents; Whole

numbers with exponents.

Interactive Student Line-Up

Games

Geometer’s Sketchpad- Lesson

Links

Newspaper Coupons

McDougal Littell Chapter 2,4,6,9

Pre-Algebra With Pizzazz!!

Math With Pizzazz! Books C-E

Developing Skills in Algebra One,

Book A

Holt Chapter 1,2,3*


3. Understand and use ratios, rates,

proportions, and percents (including percents

greater than 100 and less than 1) in a variety

of situations.

Knowledge/Skills/Understanding Learning Experiences


Grades 7-8

McDougal Littell Chapter 8,9

Pre-Algebra With Pizzazz!


Holt Chapter 5,6*




Holt Chapter 1,2,3*

2. Demonstrate a sense of the relative

magnitudes of numbers.

Number Line Graphing

Comparing Bar Graphs

Spend $1000/sec, How long to

spend a trillion dollars?

Calculator Use

Standard 4.1 Number and Numerical Operations

Teacher Observation

Test/Quiz

Do Now

Teacher Observation

Test/Quiz

Do Now

Teacher Observation

Test/Quiz

Do Now

Dilations, Reductions

Similarity Lab

Sales Tax

Newspaper Coupons

Grades

Real World Problems

Assessments

4.1.A 7th Grade Math 19

A. Number Sense




Resources





Grades 7-8


Assessments

McDougal Littell Chapter 2,4,6

Pre-Algebra With Pizzazz

Math With Pizzazz Books C-E

Holt Chapter 2*




Developing Skills in Algebra One,

Book A

Holt Chapter 2*

4. Compare and order numbers of all named

types.

Teacher Observation

Test/Quiz

Do Now

Interactive Student Line-Up

Graphing Ordered Pairs

Measures of Center

I Have-Who Has Game

White Board Activities

Teacher-Generated Questions

Daily Use of Common Fractions,

Decimal and Percents

Coupons

5. Use whole numbers, fractions, decimals, and

percents to represent equivalent forms of the

same number.

Teacher Observation

Test/Quiz

Do Now


A. Number Sense




Resources





Grades 7-8


Assessments

Teacher Observation

Test/Quiz

Do Now

Teacher will emphasize the

difference through class

discussion and practice

problems

6. Understand that all fractions can be

represented as repeating or terminating

decimals.




White Board Activities


Daily Use of Common Fractions,

Decimal and Percents

Coupons


· What makes a computational strategy both effective and efficient?

· How do operations affect numbers?

· How do mathematical representations reflect the needs of society across cultures?

Resources

Teacher Observation

Do Now

Test/Quiz

Use of Graphing Calculator

Minute Math*


Geometer’s Sketchpad Lesson

Links

Mad Minute

Holt Chapter 2,3*

Teacher Observation

Do Now

Test/Quiz

Minute Math*

Geometer’s Sketchpad-Lesson

Links


Teacher-Created Worksheets

3. Understand and apply the standard

algebraic order of operations, including

appropriate use of parentheses.

McDougal Littell Chapter 1

Discovering Algebra Chapter 4

Holt Chapter 1*

Teacher Observation

Do Now

Test/Quiz

Minute Math*

Geometer’s Sketchpad

Discovering Algebra 4.1


2. Use exponentiation to find whole number

powers of numbers.

1. Use and explain procedures for performing

calculations with integers and all number

types named above with: Pencil-and-paper;

Mental math; Calculator.


Holt Chapter 1*



Grades 7-8

Assessments

B. Numerical Operations




4.1.B 7th Grade Math 22

C. Estimation

· How can we decide when to use an exact answer and when to use an estimate?

ResourcesKnowledge/Skills/Understanding Learning Experiences Assessments

1. Use equivalent representations of numbers

such as fractions, decimals, and percents to

facilitate estimation.

McDougal Littell Chapter

1,2,4,5,6,9

Pgs 736-737 in Student Text

Teacher Edition A2

Holt Chapter 2,3*

Daily Warm-Ups

Everyday Use of Numbers


Teacher Observation

Test/Quiz

Do Now



Grades 7-8



4.1.C 7th Grade Math 23

Standard 4.2 Geometry and Geometrical Properties

· How can spatial relationships be described by careful use of geometric language?

· How do geometric relationships help to solve problems and/or make sense of phenomena?

Resources

2. Understand and apply the concept of

similarity: Using proportions to find missing

measures; Scale drawings; Models of 3D

objects.


Math with Pizzazz! Books C-E

Pre-Algebra with Pizzazz!

Holt Chapter 5,6,10*

Similarity Lab

Graphing Calculators

Flagpole Measurement by using

shadow of pole and student

Math Cartoons

Teacher Observation

Test/Quiz

Do Now

Warm-up Exercises

Knowledge/Skills/Understanding Learning Experiences Assessments

1. Understand and apply properties of

polygons: Quadrilaterals, including squares,

rectangles, parallelograms, trapezoids,

rhombi; Regular polygons.




Holt Chapter 8*

Geoboards

White Boards

Communicators*

Polygon Name Projects

Teacher Observation

Test/Quiz

Do Now

Warm-up Exercises



Grades 7-8


A. Geometric Properties








Grades 7-8



3. Use logic and reasoning to make and

support conjectures about geometric objects.




Holt Chapter 8,9*


Question of Same Perimeter,

What is the Maximum Area?

Give closed properties, have

class draw shape. If class has

different shapes, ask for more

properties. Discuss necessary

properties and subsets.

Teacher Observation

Test/Quiz

Do Now

Warm-up Exercises



· What situations can be analyzed using transformations and symmetries?

Resources



Grades 7-8

1. Understand and apply transformations:

Finding the image, given the pre-image, and

vice-versa; Sequence of transformations

needed to map one figure onto another;

Reflections, rotations, and translations result

in images congruent to the pre-image;

Dilations (stretching/shrinking) result in

images similar to the pre-image.




Holt Chapter 8*

White Boards – Class Graphing

Activities

Can You Transform? Game

Communicators*

Hands-on rotations*

See 4.2 C

Teacher Observation

Quiz/Test

Do Now

Daily Warm-up



B. Transforming Shapes



· How can geometric/algebraic relationships best be represented and verified?

Resources

Teacher Observation

Test/Quiz

Do Now

Daily Warm-ups

2. Use a coordinate grid to model and quantify

transformations (e.g., translate right 4 units).




Holt Chapter 8*


Can You Transform? Game

Communicators*

Coordinate plane white boards

Give coordinates for a figure,

then give new coordinates and

have students express in

algebraic terms. Ex (x,y)= (x+3,y-

2) or (x,y) = (3x,2y) which

preserve the shape

Teacher Observation

Test/Quiz

Do Now

Daily Warm-ups

Assessments

1. Use coordinates in four quadrants to

represent geometric concepts.




Holt Chapter 4, 8*

White Boards – Graphing Points


Communicators*

Coordinate plane white boards

Geoboards



Grades 7-8


C. Coordinate Geometry



· How can measurements be used to solve problems?

Resources

1. Solve problems requiring calculations that

involve different units of measurement within

a measurement system (e.g., 4’3” plus 7’10”

equals 12’1”).


NJ ASK Coach



Holt Chapter 1,5*

2. Select and use appropriate units and tools to

measure quantities to the degree of precision

needed in a particular problem-solving

situation.

Knowledge/Skills/Understanding

Teacher Observation

Test/Quiz

Do Now

Daily Warm-ups

Measuring Length in the

Classroom

Measuring Student Heights

3. Recognize that all measurements of

continuous quantities are approximations.

McDougal Littell Chapter 10-12



Holt Chapter 5,9*


Measuring Lines

Constructing Graphs

Real-World Examples

Teacher Observation

Test/Quiz

Do Now

Daily Warm-ups

Assessments

Teacher Observation

Test/Quiz

Do Now

Daily Warm-ups




Holt Chapter 9*

Various Investigations

On-Going Class Discussions

Geometer’s Sketchpad – Lesson

Link



Grades 7-8

D. Units of Measurement

Learning Experiences

4.2.D 7th Grade Math 28



Resources

2. Recognize that the volume of a pyramid or

cone is one-third of the volume of the prism or

cylinder with the same base and height (e.g.,

use rice to compare volumes of figures with

same base and height).




Pages 750-751 in Student Text

Teacher Edition A16

Holt Chapter 10*

Use 3-D objects to

demonstrate with water

Teacher Observation

Quiz/Test

Do Now

Daily Warm-up


1. Develop and apply strategies for finding

perimeter and area: Geometric figures made

by combining triangles, rectangles and circles

or parts of circles; Estimation of area using

grids of various sizes.




Holt Chapter 8,9,10*

Pattern Blocks

Same Perimeter, Maximum Area

Problems

Use Geoboards*

Physically measuring objects

around room*

Find the value of pi by

measuring circumference and

diameter of circular objects*

Teacher Observation

Quiz/Test

Do Now

Daily Warm-up



Grades 7-8


E. Measuring Geometric Objects

4.2.E 7th Grade Math 29

· How can change be best represented mathematically?

Resources

Teacher Observation

Quiz/Test

Do Now

Daily Warm-up

Standard 4.3 Patterns and Algebra

Assessments


A. Patterns


· How can patterns, relations, and functions be used as tools to best describe and

help explain real – life situations?



Grades 7-8

1. Recognize, describe, extend, and create

patterns involving whole numbers, rational

numbers, and integers: Descriptions using

tables, verbal and symbolic rules, graphs,

simple equations or expressions; Finite and

infinite sequences; Generating sequences by

using calculators to repeatedly apply a

formula.


Holt Chapter 1,2*

Geometer’s Sketchpad-to graph

patterns

Use of Graphing Calculators

Teacher-Created Problems

Flashlight and Bridge

Locker Problem

Dot patterns that involve a

recursive routine. Students write

the recursive routine and then it's

explicit formula expressing the

number of dots as a function of

the term number.

Use a line-up to explore

patterns*


· How are patterns of change related to the behavior of functions?


B. Functions and Relationships

1. Graph functions, and understand and

describe their general behavior: Equations

involving two variables.



Holt Chapter 1,4*


Cartesian Cartoons

Input/Output tables


Links

Teacher Observation

Quiz/Test

Do Now

Daily Warm-up



Grades 7-8



4.3.B 7th Grade Math

31

· How can mathematical models be used to describe physical relationships?

· How can physical models be used to clarify mathematical relationships?

Resources Assessments

Input/Output Tables

Geometer’s Sketchpad –Lesson

Links

Population Growth Activity

Lesson Investigation 1.6

Teacher Observation

Quiz/Test

Do Now

Daily Warm-up

Graphing Lines-Describing the

Relationship


Measures of Center

Teacher Observation

Quiz/Test

Do Now

Daily Warm-up

1. Analyze functional relationships to explain

how a change in one quantity can result in a

change in another, using pictures, graphs,

charts, and equations.


NJ ASK Coach

TinkerPlots

Holt Chapter 4*

2. Use patterns, relations, symbolic algebra,

and linear functions to model situations: Using

manipulatives, tables, graphs, verbal rules,

algebraic expressions/equations/inequalities;

Growth situations, such as population growth

and compound interest, using recursive (e.g.,

NOW- NEXT) formulas (cf. science standards

and social studies standards).


C. Modeling


Discovering Algebra - 1.6

Holt Chapter 4*



Grades 7-8




· What makes an algebraic algorithm both effective and efficient?

Resources


Discovering Algebra Chapter 4.1


Holt Chapter 1,2*


Graphing/Scientific Calculator

Use

Teacher Observation

Quiz/Test

Do Now

Daily Warm-up

2. Solve simple linear equations informally

and graphically: Multi-step, integer

coefficients only (although answers may not be

integers); Using paper-and-pencil, calculators,

graphing calculators, spreadsheets, and other

technology.




Holt Chapter 12*

Working Backwards Tables

Hands on Equations Balance

Graphing Calculator Use

Teacher Observation

Quiz/Test

Do Now

Daily Warm-up

3. Create, evaluate, and simplify algebraic

expressions involving variables: Order of

operations, including appropriate use of

parentheses; Substitution of a number for a

variable.



1. Use graphing techniques on a number line:

Absolute value; Arithmetic operations

represented by vectors (arrows) (e.g., “-3 + 6”

is “left 3, right 6”)



Holt Chapter 2*

Geometer's Sketchpad-Lesson

Links

Teacher Observation

Quiz/Test

Do Now

Daily Warm-up



Grades 7-8


D. Procedures



Resources





Grades 7-8


D. Procedures

4. Understand and apply the properties of

operations, numbers, equations, and

inequalities: Additive inverse; Multiplicative

inverse.


Discovering Algebra 4.2/4.3

Holt Chapter 1*

Lesson Investigation 4.2/4.3

Hands on Equations Balance

Teacher Observation

Quiz/Test

Do Now

Daily Warm-up


Resources

2. Make inferences and formulate and

evaluate arguments based on displays and

analysis of data.


Student Pages 758-7579

TE A24


Holt Chapter 7*

Penny Data Investigation

Layer Various graphs on the

same number line

TinkerPlots Prepared Data

Teacher Observation

Quiz/Test

Do Now

Daily Warm-up



1. Select and use appropriate representations

for sets of data, and measures of central

tendency (mean, median, and mode): Type of

display most appropriate for given data; Box-

and-whisker plot, upper quartile, lower

quartile; Scatter plot; Calculators and

computer used to record and process

information.


Student Pages 756-757

TE A22


Holt Chapter 7*

Tinkerplots Prepared Data

Geometer's Sketchpad - Lesson

Links

Penny Data Investigation

Class Line-up to find the five

number summary


Teacher Observation

Quiz/Test

Do Now

Daily Warm-up

· How can the collection, organization, interpretation, and display of data be used to answer

questions?



Grades 7-8

A. Data Analysis

Standard 4.4 Data Analysis, Probability and Discrete Mathematics


Resources

2. Model situations involving probability with

simulations (using spinners, dice, calculators

and computers) and theoretical models:

Frequency, relative frequency.


Connected Mathematics “What Do

You Expect?”

Holt Chapter 11*

"What Do You Expect?"

Investigations


Teacher Observation

Quiz/Test

Do Now

Daily Warm-up

3. Estimate probabilities and make predictions

based on experimental and theoretical

probabilities.



You Expect?”

Holt Chapter 11*


Investigations

Graph Class results as well as

group results, have students

compare/contrast results.

Teacher Observation

Quiz/Test

Do Now

Daily Warm-up



1. Interpret probabilities as ratios, percents,

and decimals.



You Expect?”

Holt Chapter 11*


Hands on Simulation -Rolling

Die, M & M's, Spinners

Teacher Observation

Quiz/Test

Do Now

Daily Warm-up

· How can experimental and theoretical probabilities be used to make predictions or draw

conclusions?



Grades 7-8

B. Probability



Resources




conclusions?



Grades 7-8

B. Probability


4. Play and analyze probability-based games,

and discuss the concepts of fairness and

expected value.



You Expect?”

Holt Chapter 11*


Investigations

Game Discussions

Candy land vs. Chutes and

Ladders

Design own "Zark" Game

Teacher Observation

Quiz/Test

Do Now

Daily Warm-up


· What counting strategy works best here?

Resources

3. Apply techniques of systematic listing,

counting, and reasoning in a variety of

different contexts.


Connected Mathematics "What Do

You Expect?"

NJ ASK Coach

Holt Chapter 11*


Investigations

Teacher Observation

Quiz/Test

Do Now

Daily Warm-up

1. Apply the multiplication principle of

counting: Permutations: ordered situations

with replacement (e.g., number of possible

license plates) vs. ordered situations without

replacement (e.g., number of possible slates of

3 class officers from a 23 student class).


NJ ASK Coach

Holt Chapter 11*

Winning the Lottery

License Plate Combinations

Teacher Observation

Quiz/Test

Do Now

Daily Warm-up

2. Explore counting problems involving Venn



Student Edition Pg 790

NJ ASK Coach

Holt Chapter 11*

Card Probabilities

Mutually Exclusive Events

Discussion of Overlap of Events

Teacher Observation

Quiz/Test

Do Now

Daily Warm-up


· How can attributes be used to classify data/objects?

· What is the best way to solve this?




Grades 7-8

C. Systematic Listing and Counting



· How can algorithmic thinking be used to solve problems?

Resources



1. Use vertex-edge graphs to represent and

find solutions to practical problems: Finding

the shortest network connecting specified

sites; Finding the shortest route on a map

from one site to another; Finding the shortest

circuit on a map that makes a tour of specified

sites.

Student Edition pg 744-745

TE A10

Rutgers Prepared Activities Teacher Observation

Quiz/Test

Do Now

Daily Warm-up

· How can visual tools such as networks (vertex-edge graphs) be used to answer questions?



Grades 7-8

D. Vertex-Edge Graphs and Algorithms



Resources



Grades 7-8

Standard 4.5 Mathematical Processes

A. Problem SolvingEssential Questions :

· How will learning to “think” mathematically enable us to make a life, make a living,

and make a difference?

· How does the use of technology enable us to have a deeper understanding of

mathematics?


1. Learn mathematics through problem

solving, inquiry, and discovery.

McDougal Littell Chapters 1-13

Menu Problems (Middle School

Math Teacher)

NCTM Navigations Series

Van De Walle

Connected Mathematics

Holt Chapters 1-12*

Direct Instruction

Investigations

Collaborative/Cooperative

Learning

Written Explanations

Student Directed Discussions

Written Test/Quiz

Written Explanation

Open-ended Questions

Teacher Observation

2. Solve problems that arise in mathematics

and in other contexts: Open-ended problems;

Non-routine problems; Problems with

multiple solutions; Problems that can be

solved in several ways.



Math Teacher)


Van De Walle


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Written Test/Quiz

Written Explanation


Teacher Observation

4.5.A 7th Grade Math

40

Resources



Grades 7-8






mathematics?


3. Select and apply a variety of appropriate

problem-solving strategies (e.g., “try a simpler

problem” or “make a diagram”) to solve

problems.



Math Teacher)


Van De Walle


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Written Test/Quiz

Written Explanation


Teacher Observation

4. Pose problems of various types and levels of

difficulty.



Math Teacher)


Van De Walle


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Written Test/Quiz

Written Explanation


Teacher Observation


41

Resources



Grades 7-8






mathematics?


5. Monitor their progress and reflect on the

process of their problem solving activity.



Math Teacher)


Van De Walle


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Written Test/Quiz

Written Explanation


Teacher Observation

6. Distinguish relevant from irrelevant




Math Teacher)


Van De Walle


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Written Test/Quiz

Written Explanation


Teacher Observation


42

Resources

Do Now

Quiz/Test

Teacher Observation

Open-Ended Questions



Math Teacher)


Van De Walle


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Do Now

Quiz/Test

Teacher Observation


2. Communicate mathematical thinking

coherently and clearly to peers, teachers, and

others, both orally and in writing.



Math Teacher)


Van De Walle


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning







mathematics?


1. Use communication to organize and clarify





Grades 7-8


B. Communication


Resources





mathematics?




Grades 7-8


B. Communication

3. Analyze and evaluate the mathematical

thinking and strategies of others.

4. Use the language of mathematics to express

mathematical ideas precisely.



Math Teacher)


Van De Walle


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Do Now

Quiz/Test

Teacher Observation




Math Teacher)


Van De Walle


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Do Now

Quiz/Test

Teacher Observation



Resources



Grades 7-8


C. ConnectionsEssential Questions :


and make a difference?· How does the use of technology enable us to have a deeper understanding of

mathematics?


1. Recognize recurring themes across

mathematical domains (e.g., patterns in

number, algebra, and geometry).



Math Teacher)


Van De Walle


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Do Now

Quiz/Test

Teacher Observation

Learnia


2. Use connections among mathematical ideas

to explain concepts (e.g., two linear equations

have a unique solution because the lines they

represent intersect at a single point).



Math Teacher)


Van De Walle


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Do Now

Quiz/Test

Teacher Observation

Learnia


4.5.C 7th Grade Math

45

Resources



Grades 7-8





mathematics?


3. Recognize that mathematics is used in a

variety of contexts outside of mathematics.



Math Teacher)


Van De Walle


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Do Now

Quiz/Test

Teacher Observation

Learnia


4. Apply mathematics in practical situations

and in other disciplines.



Math Teacher)


Van De Walle


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Do Now

Quiz/Test

Teacher Observation

Learnia



46

Resources



Grades 7-8





mathematics?


5. Trace the development of mathematical

concepts over time and across cultures (cf.

world languages and social studies standards).



Math Teacher)


Van De Walle


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Do Now

Quiz/Test

Teacher Observation

Learnia


6. Understand how mathematical ideas

interconnect and build on one another to

produce a coherent whole.



Math Teacher)


Van De Walle


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Do Now

Quiz/Test

Teacher Observation

Learnia



47

Resources



Grades 7-8


D. ReasoningEssential Questions :




mathematics?


1. Recognize that mathematical facts,

procedures, and claims must be justified.



Math Teacher)


Van De Walle


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Written Test/Quiz

Written Explanation


Teacher Observation

2. Use reasoning to support their

mathematical conclusions and problem

solutions.



Math Teacher)


Van De Walle


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Written Test/Quiz

Written Explanation


Teacher Observation


Resources



Grades 7-8






mathematics?


3. Select and use various types of reasoning

and methods of proof.



Math Teacher)


Van De Walle


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Written Test/Quiz

Written Explanation


Teacher Observation

4. Rely on reasoning, rather than answer keys,

teachers, or peers, to check the correctness of

their problem solutions.



Math Teacher)


Van De Walle


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Written Test/Quiz

Written Explanation


Teacher Observation


Resources



Grades 7-8






mathematics?


5. Make and investigate mathematical

conjectures: Counterexamples as a means of

disproving conjectures; Verifying conjectures

using informal reasoning or proofs.



Math Teacher)


Van De Walle


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Written Test/Quiz

Written Explanation


Teacher Observation

6. Evaluate examples of mathematical

reasoning and determine whether they are

valid.



Math Teacher)


Van De Walle


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Written Test/Quiz

Written Explanation


Teacher Observation


Resources



Grades 7-8




Math Teacher)


Van De Walle


Holt Chapters 1-12*

E. Representations

1. Create and use representations to organize,

record, and communicate mathematical ideas:

Concrete representations (e.g., base-ten blocks

or algebra tiles); Pictorial representations

(e.g., diagrams, charts, or tables); Symbolic

representations (e.g., a formula); Graphical

representations (e.g., a line graph).



Math Teacher)


Van De Walle


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Do Now

Quiz/Test

Teacher Observation


2. Select, apply, and translate among

mathematical representations to solve

problems.

Direct Instruction

Investigations


Learning



Do Now

Quiz/Test

Teacher Observation






mathematics?


4.5.E 7th Grade Math

51

Resources



Grades 7-8


E. Representations Essential Questions :




mathematics?


3. Use representations to model and interpret

physical, social, and mathematical

phenomena.



Math Teacher)


Van De Walle


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Do Now

Quiz/Test

Teacher Observation


4.5.E 7th Grade Math

52

Resources



Grades 7-8


F. TechnologyEssential Questions :




mathematics?

1. Use technology to gather, analyze, and




Math Teacher)


Van De Walle


TinkerPlots


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Do Now

Quiz/Test

Teacher Observation


2. Use computer spreadsheets, software, and

graphing utilities to organize and display

quantitative information.



Math Teacher)


Van De Walle


TinkerPlots


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Do Now

Quiz/Test

Teacher Observation


4.5.F 7th Grade Math

53

Resources



Grades 7-8






mathematics?

3. Use graphing calculators and computer

software to investigate properties of functions

and their graphs.



Math Teacher)


Van De Walle


TinkerPlots


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Do Now

Quiz/Test

Teacher Observation


4. Use calculators as problem-solving tools

(e.g., to explore patterns, to validate solutions).



Math Teacher)


Van De Walle


TinkerPlots


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Do Now

Quiz/Test

Teacher Observation



54

Resources



Grades 7-8






mathematics?

5. Use computer software to make and verify

conjectures about geometric objects.



Math Teacher)


Van De Walle


TinkerPlots


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Do Now

Quiz/Test

Teacher Observation



55

Resources



Grades 7-8






mathematics?

6. Use computer-based laboratory technology

for mathematical applications in the sciences.



Math Teacher)


Van De Walle


TinkerPlots


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Do Now

Quiz/Test

Teacher Observation



56

14 5 11

Mid-Year Benchmark

Assessment

1

12 10

Integers 6 12

1

122

Percents

Number of Blocks

9 11 6 11

9

Data Analysis and

Statistics

3 15 7 13

Number Sense, Patterns

and Algebraic Thinking

1 6 3

Pacing Guide

UnitMcDougall Littell Mathematics

Course 2 ChaptersNumber of Blocks

Holt Mathematics Course

2 Chapters



Grades 7-8

7th Grade Math

Equations, Inequalities and

Functions

7 8

Ratios and Proportions 8

7th Grade Math Pacing Guide

57

Number of Blocks

Pacing Guide

UnitMcDougall Littell Mathematics

Course 2 ChaptersNumber of Blocks

Holt Mathematics Course

2 Chapters



Grades 7-8

7th Grade Math

6

Geometric Figures 10 6 8

Discrete Math 1 1

Probability 13


7 11


Venn Diagrams with three

attributes

End-of-the-Year

Benchmark Assessment

1 1

6

Measurement and Area 11 5 9

2 2

Surface Area and Volume 12 1 10 2

5

7th Grade Math Pacing Guide

58

UCSMP Transitions Lesson Masters A and B Zal Usiskin Scott, Foresman 1995

Algebra Out Loud Pat Mower, PhD Jossey Bass 2003

Impact Mathematics Course 1 Glencoe 2003

New Jersey ASK Coach Jerome Kaplan Ed.D Triumph Learning 2005

Question Quest Level C Paul Lawrence LL Teach, Inc. 2002

Pre-Algebra with Pizzazz! Steve & Janis Marcy McGraw Hill 2002

Middle School Math with Pizzazz- Books A-E Steve & Janis Marcy McGraw Hill 2002

Developing Skills in Algebra One - Books A

and B

Harold and Loretta Taylor Dale Seymour Publications 1984

Algebra with Pizzazz! Steve & Janis Marcy McGraw Hill 2002

Title of Resource Author(s) Publisher Copyright

McDougall Littell Course 2

and all related resources (differentiation

including ELL)

Larson, Boswell, Kanold & Stiff McDougal Littell 2008



Grades 7-8

7th Grade Math

Resources

Holt Mathematics Course 2 and all related

resources (differentiation including ELL)

Bennett, Burger, Chard, Jackson,

Kennedy, Renfro, Scheer & Waits

Holt, Rinehart and Winston 2007

7th Grade Resources

59




Grades 7-8

7th Grade Math

Resources

1998

2003

Algebra Puzzles & Problems

Algebra Teacher's Activities Kit

Greenes/Findell

Judith & Robert Muschla

Creative Publications

Jossey Bass

Tinker Plots Clifford Konold & Craig D. Miller Key Curriculum Press 2005

Geometer's Sketchpad 4 Nicholas Jackiw Key Curriculum Press 2006

UCSMP Algebra Lesson Masters A and B Zal Usiskin Scott, Foresman 1995

Explain It Lepore, Fleetwood & Hall Creative Publications 2001

ASK Workout

Differentiated Middle School Math

Jerome Kaplan Ed.D Triumph Learning

Exemplars

2008

Teaching Student-Centered Mathematics

Grades 5-8

Hands -On Algebra !

Daily Word Problems Grade 6

Middle School Collection: Geometry: Basic

Concepts, Geometry: Solids, Geometry:

Polygons, Pre-Algebra

John A. Van de Walle & LouAnn

H. Lovin

Frances M. Thompson

Amy Beth Tuttle, Wes Tuttle

D.W. Skrabanek

Pearson Education

The Center for Applied Research

Education

Evan-Moor Publishers

Steck-Vaugh Company

2006

1998

2001

2000

7th Grade Resources

60




Grades 7-8

7th Grade Math

Resources

Middle Grade Math Minutes

Mathematical Reasoning Through Verbal

Analysis Book 2

Doug Stoffel

Warren Hill & Ronald Edwards

Creative Teaching Press

Critical Thinking Books &

Software

2000

1991

Measuring Up to the NJ Core Curriculum

Content Standards

Kenneth Owens Peoples Publishing Group 2003

NCTM Navigation Series: Probability, Data

Analysis, Geometry

8-Step Model Drawing

Bright, Frierson Jr., Tarr,

Thomas, Brewer, McClain,

Mooney, Pugalee, Frykholm,

Johnson, Slovin, Malloy, Preston

Bob Hogan & Char Forsten

The National Council of

Teachers of Mathematics

Crystal Spring Books

2003

2007

Geometry Activities for Middle School

Students

Shape Makers: Developing Geometric

Reasoning in Middle School

What Do You Expect?

Strategies for Success in Mathematics: Level

G

Key Curriculum Press

Key Curriculum Press

Dale Seymour Publications

Steck-Vaugh Company

Wyatt, Lawrence, Foletta

Michael T. Battista

Lappan, Fey, Fitzgerald, Friel

and Phillips

Weisenfeld, Coultas, Swalm

2003

2004

1998

1999

7th Grade Resources

61




Grades 7-8

7th Grade Math

Resources

Curriculum and Evaluation Standards for

School Mathematics Addenda Series Grades 5-

8

Geddes, Zawojewski, Reys,

Phillips, Curcio, Bezuk



1992

7th Grade Resources

62

Algebra 1A Math Curriculum

63

A. Number Sense



· How can counting, measuring or labeling help to make sense of the world around us?

Resources



Grades 7-8








well): Rational numbers; Percents;

Exponents; Roots; Absolute Values; Numbers

represented in scientific notation

Discovering Algebra Chapter 2, 4

UCSMP Transitions

Investigate decimal patterns

using a calculator

Lesson Investigations

Direct Instruction

Do Now

Quiz/Test

Teacher Observation



Elementary and Middle School

Math Chapter 26

Number line graphing

Lesson Investigations throughout

the textbook

On-going




of situations.

Discovering Algebra Chapter 2, 3 Lesson Investigations 2.2, 2.3,

3.1, 3.2, 3.3

Similarity Lab

Do Now

Quiz/Test

Class discussion

Teacher Observation

4.1.A 7th Algebra 1A 64

A. Number Sense



· How can counting, measuring or labeling help to make sense of the world around us?

Resources



Grades 7-8




Teacher-created review

Calculator Activities

I have . . . who has

6. Recognize that repeating decimals

correspond to fractions and determine their

fractional equivalents .

Discovering Algebra Chapter 2 Lesson Investigation 2.1

Calculator Activities

Do Now

Quiz/Test

Class discussion

Teacher Observation


types.

Van De Walle Chapter 24 Student Line-Up Student Line Up



same number.

UCSMP Transitions Lesson

Masters

National Council of Teachers of

Mathematics, Developing Number

Sense





Resources



Grades 7-8



Lesson Investigations 2.2, 2.3 Teacher Observation

Discussion of Lesson

Investigation results

Do Now




calculations involving addition, subtraction,

multiplication, division, and exponentiation

with integers and all number types named

above with: Pencil-and-paper; Mental math;

Calculator.

Teacher-created problems

Math With Pizzazz! Book E


Algebra with Pizzazz!

Mental Math Warm-Ups Do Now

Quiz/Test

Teacher Observation


powers of numbers.


Developing Skills in Algebra One –

Book A

Review as needed Quiz

3. Solve problems involving proportions and

percents.


4.1.B 7th Algebra 1A 66




Resources



Grades 7-8


B. Numerical OperationsEssential Questions :









Lesson Investigation 4.1 Do Now

Teacher Observation

Quiz/Test


C. Estimation


Resources



Grades 7-8







Various Lesson Investigations

Daily discussions

Daily problems


Do Now

Teacher Observation

2. Recognize the limitations of estimation and

assess the amount of error resulting from

estimation.

Various Lesson Investigations

Daily discussions

Daily problems On-going

4.1.C 7th Algebra 1A 68




Resources



Grades 7-8







rhombi; Regular polygons

Navigations Series – Geometry


Geoboard exploration

Manipulatives

Do Now

Teacher Observation




objects.


Van De Walle pg 365-366


Measure shadow of flagpole and

person to determine height

Quiz/Test

Do Now

Teacher Observation





Direct Instruction


Teacher Observation




Resources



Grades 7-8













Masters

Worksheets

Navigation Series – Geometry

Geometry in the Middle Grades


Van De Walle pg 371

NJ ASK Coach

Manipulatives

Give coordinates for a figure,

then give new coordinates and




preserve the shape

Do Now

Quiz/Test

Teacher Observation




Resources

Do Now

Quiz/Test

Teacher Observation



Grades 7-8





NJ ASK Coach

Teacher-made materials

Graphing Calculator

Give coordinates for a figure

then, give new coordinates and




preserve the shape

Do Now

Quiz/Test

Teacher Observation




• Slope of a line

Discovering Algebra Chapter 4, 5



NJ ASK Coach


Book C

Lesson Investigations 4.4, 4.6,

4.7, 5.1, 5.2

Working Cooperatively

Graphing Calculator work




Resources



Grades 7-8







equals 12’1”).

Discovering Algebra Chapter 2, 3 Lesson Investigations 2.3, 3.2 Do Now

Teacher-Created problems

Quiz/Test

Teacher Observation


Investigation

2. Use approximate equivalents between

standard and metric systems to estimate

measurements (e.g., kilometers is about 3

miles).


UCSMP Transitions Chapter 3

Lesson Investigations 2.3, 3.2 Do Now


Quiz/Test

Teacher Observation


Investigation

4.2.D 7th Algebra 1A 72



Resources



Grades 7-8




Various Lesson Investigations Do Now


Quiz/Test

Teacher Observation


Investigation

3. Recognize that the degree of precision

needed in calculations depends on how the

results will be used and the instruments used

to generate the measurements.

On-going class discussions Various Lesson Investigations Do Now


Quiz/Test

Teacher Observation


Investigation




situation.

On-going class discussions Various Lesson Investigations Do Now


Quiz/Test

Teacher Observation


Investigation



On-going class discussions




Resources



Grades 7-8




6. Solve problems that involve compound

measurement units, such as speed (miles per

hour), air pressure (pounds per square inch),

and population density (persons per square

mile).




Direct Instruction

Dimensional Analysis

Do Now


Quiz/Test

Teacher Observation


Investigation




Resources


Learnia

Do Now



Grades 7-8








Van De Walle Chapter 19



Math with Pizzazz! Book D


NJ Ask Coach

Direct Instruction Teacher-created problems

Learnia

Do Now






grids of various sizes.

Van De Walle Chapter 19



Math with Pizzazz! Book D


Investigations

4.2.E 7th Algebra 1A 75


Resources



Grades 7-8


A. Patterns Essential Questions :









infinite sequences; Arithmetic sequences;

Geometric sequences; Generating sequences

by using calculators to repeatedly apply a

formula.

Discovering Algebra Chapter 4 Direct Instruction


4.6

Modeling

Graphing Calculators

Do Now

Quiz/Test

Teacher Observation


Investigations



Resources



Grades 7-8


B. Functions and RelationshipsEssential Questions :




involving two variables; Equations involving

two variables; Rates of change (informal

notion of slope).

Discovering Algebra Chapter 4, 5 Direct Instruction


4.7, 5.1, 5.2, 5.3

Do Now

Quiz/Test

Teacher Observation


Investigations




Resources

Direct Instruction

Modeling throughout lessons


4.4, 4.6, 4.7, 5.1, 5.2, 5.3

Teacher observation


Investigations



Grades 7-8


C. Modeling



concrete materials (manipulatives), tables,

graphs, verbal rules, algebraic expressions/

equations/ inequalities; Growth situations,

such as population growth and compound

interest, using recursive (e.g., NOW-NEXT)

formulas (cf. science standards and social

studies standards).

Discovering Algebra Chapter 3, 4, 5 Direct Instruction

Modeling throughout lessons


4.4, 4.6, 4.7, 5.1, 5.2, 5.3

Do Now

Quiz/Test

Teacher Observation


Investigations







Discovering Algebra Chapter 3, 4, 5



Resources



Grades 7-8


D. Procedures Essential Questions :





is “left 3, right 6”)


Transitions Chapter 5



Direct Instruction


Link

Do Now

Quiz/Test

Teacher Observation

2. Solve simple linear equations informally,

graphically, and using formal algebraic

methods:

Multi-step, integer coefficients only (although

answers may not be integers) Simple literal

equations (e.g., A = lw) Using paper-and-

pencil, calculators, graphing calculators,


Discovering Algebra Chapter 2, 3, 4 Direct Instruction

Graphing Calculator

Do Now

Quiz/Test

Teacher Observation

4.3.D 7th Algebra 1A

79


Resources



Grades 7-8




Direct Instruction


Graphing Calculator

Do Now

Quiz/Test

Teacher Observation




inverse; Addition and multiplication

properties of equality.




Book A

Direct Instruction

Graphing Calculator

Do Now

Quiz/Test

Teacher Observation




parentheses; Distributive property;

Substitution of a number for a variable;

Translation of a verbal phrase or sentence into

an algebraic expression, equation, or

inequality, and vice versa.



4.3.D 7th Algebra 1A

80

Resources



Grades 7-8

A. Data Analysis




questions?









information; Finding the median and mean

(weighted average) using frequency data;

Effect of additional data on measures of

central tendency.


More Practice with Your Skills

TinkerPlots

Direct Instruction

Graphing Calculator

Lesson Investigations 1.1-1.7

Class Discussion

Do Now

Graphing Calculator

Quiz/Test

Teacher Observation


Investigation



analysis of data sets.


More Practice with Your Skills

TinkerPlots

Direct Instruction

Graphing Calculator

Lesson Investigations 1.1-1.7

Class Discussion

Do Now

Graphing Calculator

Quiz/Test

Teacher Observation


Investigation


Resources



Grades 7-8

A. Data Analysis




questions?


3. Estimate lines of best fit and use them to

interpolate within the range of the data.

Discovering Algebra Chapter 5 Lesson Investigation 5.3

Class Discussion

Do Now

Graphing Calculator

Quiz/Test

Teacher Observation


Investigation


Resources

Do Now

Quiz/Test

Teacher Observation



Grades 7-8

B. Probability


Lesson Investigations 2.6, 2.7

Experiments from Connected

Mathematics “What Do You

Expect?"

Do Now

Quiz/Test

Teacher Observation



conclusions?



and decimals.



You Expect?"

Math with Pizzazz! Book E





Expect?"







You Expect?"






Expect?"

Do Now

Quiz/Test

Teacher Observation



probabilities.



You Expect?"



4.4.B 7th Algebra 1A

83

Resources



Grades 7-8

B. Probability




conclusions?




expected value.


You Expect?"





Expect?"

Do Now

Quiz/Test

Teacher Observation


84


Resources



Grades 7-8



Problems from UCSMP

Transitions Textbook and

UCSMP Algebra

Venn Diagrams

Teacher Observation

Quiz/Test







different contexts.

UCSMP Transitions Textbook

Math Counts


Mathematics Dealing with Data and

Chance Standards

Find number of ways to arrange

batters

Teacher Observation

Quiz/Test



with replacement vs. ordered situations

without replacement.

UCSMP Algebra Textbook

Math Counts



You Expect?”

NJ ASK Coach



Expect?”

Counting Trees

Teacher Observation

Quiz/Test



UCSMP Transitions Textbook


Mathematics Dealing with Data and

Chance Standards

NJ ASK Coach



Resources



Grades 7-8






1. Use vertex-edge graphs to represent and

find solutions to practical problems: Finding

the shortest network connecting specified

sites; Finding the shortest route on a map

from one site to another; Finding the shortest

circuit on a map that makes a tour of specified

sites.

Teacher-created materials

Pgs 744-745 McDougal Littell

Rutgers prepared worksheets

Write a tour guide with map

Teacher-Created

worksheets

Tour Guide Project


Resources



Grades 7-8






mathematics?




Discovering Algebra Chapters 1-5

Math Counts

NCTM Navigation Series



Mathematics

Question Quest Level C

Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation







Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation

4.5.A 7th Algebra 1A

87

Resources



Grades 7-8






mathematics?





problems.


Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation


difficulty.


Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation


88

Resources



Grades 7-8






mathematics?





Math Counts




Mathematics

Question Test Level C

Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation

6. Distinguish relevant from irrelevant



Math Counts

Navigation Series



Mathematics


Direct Instruction



Learning


Open-Ended Question

Written Test/Quiz

Written Explanation


Teacher Observation


89

Resources



Grades 7-8


B. CommunicationEssential Questions :



mathematics?






Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation





Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation


90

Resources



Grades 7-8





mathematics?





Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation




Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation


91

Resources



Grades 7-8





mathematics?






Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation






Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation


Resources



Grades 7-8





mathematics?





Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation




Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation


Resources



Grades 7-8





mathematics?






Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation





Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation


Resources



Grades 7-8






mathematics?





Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation



solutions.


Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation


Resources



Grades 7-8






mathematics?





Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation





Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation


Resources



Grades 7-8






mathematics?







Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation



valid.


Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation


Resources

E. Representations



Grades 7-8


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Journaling

Teacher Observation





mathematics?










Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Journaling

Teacher Observation



problems.


Math Counts




Mathematics


4.5.E 7th Algebra 1A

98

Resources

E. Representations



Grades 7-8






mathematics?




phenomena.


Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Journaling

Teacher Observation

4.5.E 7th Algebra 1A

99

Resources



Grades 7-8






mathematics?





Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation





Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation

4.5.F 7th Algebra 1A

100

Resources



Grades 7-8






mathematics?




and their graphs.


Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation




Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation


101

Resources



Grades 7-8






mathematics?





Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation




Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation


102



Grades 7-8

7th Grade Algebra 1A

Pacing Guide

UnitDiscovering Algebra

ChapterNumber of Blocks

Data Exploration

1 15

Proportional Reasoning

2 14

Variations and Graphs

3 14

Linear Equations

4 15

Slope and Fitting a Line to Data

5 14

Probability

2

"What Do You Expect ?"

12

Geometry

Math with Pizzazz

Pre-Algebra with Pizzazz

5

7th Grade Algebra 1A Pacing Guide 103



Grades 7-8


Resources


Discovering Algebra An Investigative

Approach

Jerald Murdock, Ellen Kamischke,

Eric Kamischke

Key Curriculum Press 2002


and B

Harold and Loretta Taylor Dale Seymour Pulbications 1984


LL Teach, Inc. 2002


Middle School Math with Pizzazz- Books A-E Steve & Janis Marcy McGraw Hill 2002

Algebra Out Loud Pat Mower, Phd Jossey Bass 2003


Question Quest Level C Paul Lawrence




7th Grade Algebra 1A Resources

104



Grades 7-8


Resources



Algebra Puzzles & Problems Greenes/Findell Creative Publications 1998

Algebra Teacher's Activities Kit Judith & Robert Muschla Jossey Bass 2003


ASK Workout Jerome Kaplan Ed.D Triumph Learning 2008

Differentiated Middle School Math Exemplars


Grades 5-8


H. Lovin

Pearson Education 2006

NCTM Navigation Series: Probability, Data

Analysis, Geometry

Bright, Frierson Jr., Tarr,

Thomas, Brewer, McClain,

Mooney, Pugalee, Frykholm,

Johnson, Sloving, Malloy,



2003

Hands -On Algebra ! Frances M. Thompson The Center for Applied Research

Education

1998


Students

Wyatt, Lawrence, Foletta Key Curriculum Press 2004



Michael T. Battista Key Curriculum Press 2003


105



Grades 7-8


Resources


What Do You Expect? Lappan, Fey, Fitzgerald, Friel

and Phillips

Dale Seymour Pulbications 1998


G

Weisenfeld, Coultas, Swalm Steck-Vaugh Company 1999



8

Geddes, Zawojewski, Reys,

Phillips, Curcio, Bezuk



1992


106

Algebra 1B Math Curriculum

107




Resources



Grades 7-8



A. Number Sense








represented in scientific notation

Discovering Algebra Chapter 7.1, 8,

9, 10

Math Counts

Teacher-created

worksheets/problems

Investigate decimal patterns

using a calculator

Applicable Problems

Recursive Routines

Through the use of geometry of

squares and cubes

Applicable Lesson Investigations

Direct Instruction

Cooperative student exploration

of “undoing” operations of

functions

Teacher-created review

examples

Do Now

Quiz/Test

Teacher Observation

Class Discussions





Mathematics, Developing Number

Sense

Spend national debt at a given

rate-how long?

4.1.A 7th Algebra 1B 108




Resources



Grades 7-8



A. Number Sense





of situations.

Math Counts

Real-world examples

Problem solving

Collaborative discussions

Do Now

Quiz/Test

Class discussion

Teacher Observation


types.

UCSMP Transitions Chapter 12 Graphing on a number line



same number.


UCSMP Algebra

Spiral of right triangles –

Pythagorean Theorem





Resources



Grades 7-8



Lesson Investigations Teacher Observation


Investigation results

Do Now








Calculator.

Developing Skills in Algebra One

Book A & B

Mental Math Warm-Ups

Do Now

Use Applications

Do Now

Quiz/Test

Teacher Observation

2. Find cube roots of numbers and understand

the inverse nature of powers and roots.



Finding the length of the edge of

a cube knowing volume

Do Now

Quiz/Test

Teacher Observation


percents.


Math Counts

4.1.B 7th Algebra 1B 110




Resources



Grades 7-8




4. Understand and apply the laws of exponents

to simplify expressions involving numbers and

variables raised to powers.



Book B



7.6, 7.7

Skittle Activity

U.S. Census Activity

Do Now

Quiz/Test

Teacher Observation


C. Estimation


Resources



Grades 7-8




1. Estimate square and cube roots of numbers. Teacher-Created Problems

Discovering Algebra 10.8

Lesson Investigation 10.8 Mental Practice

Calculator Teacher

Observation



estimation.


Mathematics – Data Analysis and

Statistics Addenda series

Physically measure lengths and

discuss why disparities occur

when using π or 3.14 for surface

area and volumes (cones and

cylinders)

Measure/Justify

4.1.C 7th Algebra 1B

112




Resources



Grades 7-8




1. Understand and apply the Pythagorean

Theorem.

Navigating through Geometry 9-12



Math Counts

Real-world application problems Do Now

Teacher Observation




objects.




Manipulatives

Quiz/Test

Do Now

Teacher Observation






Direct Instruction Teacher Observation

4.2.A 7th Algebra 1B

113



Resources



Grades 7-8













Masters

UCSMP Transitions Chapter 8


Discovering Algebra Chapters 9 &

11


Use calculator to compare

graphs of equations that involve

transformations


Do Now

Quiz/Test

Coordinate grid drawings

Teacher Observation

4.2.B 7th Algebra 1B

114



Resources



Grades 7-8




1. Use coordinate geometry to represent and

verify properties of lines.

• Finding the intersection of two lines

• Lines with the same slope are parallel

• Lines that are perpendicular have slopes

whose product is -1

Discovering Algebra Chapter 6 &

11


More Practice with Yours Skills



6.3

Graphing Calculator work

Applications in coordinate

geometry

Do Now

Quiz/Test

Teacher Observation

4.2.C 7th Algebra 1B 115



Resources



Grades 7-8




1. Use appropriate equivalents between



miles)

Discovering Algebra Chapters 6-11 Appropriate use throughout


Do Now


Quiz/Test

Teacher Observation


Investigation







Do Now


Quiz/Test

Teacher Observation


Investigation




situation.



Do Now


Quiz/Test

Teacher Observation


Investigation

4.2.D 7th Algebra 1B

116



Resources



Grades 7-8








Do Now


Quiz/Test

Teacher Observation


Investigation





mile).



Do Now


Quiz/Test

Teacher Observation


Investigation


117



Resources



Grades 7-8





perimeter and area: Impact of a dilation on

the perimeter and area of a 2-dimensional

figure.


Math Counts


Cooperative Investigations Learnia

NJ ASK Coach

2. Develop and apply strategies and formulas

for finding the volume of a three-dimensional

figure.


Math Counts



NJ ASK Coach

3. Impact of a dilation on the volume of a

three-dimensional figure.


Math Counts



NJ ASK Coach

4. Use formulas to find the volume of a sphere. Geometer’s Sketchpad

Math Counts



NJ ASK Coach



cylinder with the same base and height


Math Counts



NJ ASK Coach

4.2.E 7th Algebra 1B 118


Resources



Grades 7-8


A. Patterns Essential Questions :









infinite sequences; Arithmetic sequences (i.e.,

sequences generated by repeated addition of a

fixed number, positive or negative); Geometric

sequences (i.e., sequences generated by

repeated multiplication by a fixed positive

ratio, greater than 1 or less than 1);

Generating sequences by using calculators to

repeatedly apply a formula.



Navigating through Algebra Grades

9-12


7.7

Given terms in a pattern,

describe patterns in words

Recursive investigations

Real-world problem solving

U.S. Census Activity

Do Now

Quiz/Test

Teacher Observation


119


Resources

Direct Instruction

Lesson Investigation

Real-world problems

Lesson Investigations from

Chapter 8

Do Now

Quiz/Test

Teacher Observation



Grades 7-8



2. Recognize and describe the difference

between linear and exponential growth, using

tables, graphs, and equations.

Discovering Algebra Chapter 7 Lesson Investigations 7.1, 7.2,

7.7

Skittle Activity

Do Now

Quiz/Test

Teacher Observation






involving two variables; Equations involving

two variables; Rates of change (informal

notion of slope).



120



Resources

Direct Instruction


8.4, 8.5, 8.7

Teacher observation

Do Now

Quiz/Test



Grades 7-8


C. Modeling







interest, using recursive (e.g., NOW-NEXT)

formulas (cf. science standards and social

studies standards).

Discovering Algebra Chapter 7 Lesson Investigations 7.1, 7.7

Direct Instruction

Do Now

Quiz/Test

Teacher Observation










Resources



Grades 7-8





Absolute value.

Discovering Algebra Chapter 9 Direct Instruction


Do Now

Quiz/Test

Teacher Observation



methods: Multi-step, integer coefficients only

(although answers may not be integers);

Absolute value; Compound inequalities;

Rational expressions; Using paper-and-pencil,

calculators, graphing calculators,


Discovering Algebra Chapters 5 &

6

Teacher-created material

Direct Instruction


Do Now

Quiz/Test

Teacher Observation

3. Solve systems of equations:

• Graphically

• Algebraic methods



Book B

Direct Instruction


Graphing Calculator

Do Now

Quiz/Test

Teacher Observation

Teacher-Created materials


122


Resources



Grades 7-8




Direct instruction Do Now

Quiz/Test

Teacher Observation


6. Evaluate and simplify algebraic

expressions:

• Add and subtract polynomials

• Multiply a polynomial by a monomial or

binomial

• Divide a polynomial by a binomial

• Use laws of exponents



Books B-D


Direct Instruction

Algebra Tiles

Do Now

Quiz/Test

Teacher Observation


4. Factor polynomials Discovering Algebra Chapter 10


Book B

Direct Instruction

Algebra Tiles

Do Now

Quiz/Test

Teacher Observation

5. Rational Expressions

• Add and Subtract

• Multiply and Divide


Book D



123

Resources



Grades 7-8

A. Data Analysis




questions?




tendency (mean, median, and mode); Finding

the median and mean (weighted average)

using frequency data; Effect of additional data

on measures of central tendency.

Math Counts Graphing Calculator


Class Discussion


Graphing Calculator

Teacher Observation




Navigation through Data Analysis

Grades 6-8


Prediction

Using graphing calculator to

show two statistical graphs at the

same time to compare various

statistical averages

Graphing Calculator

Teacher Observation




TinkerPlots

Internet Resources


Class Discussion

Internet Resources

TinkerPlots Activities

Do Now

Graphing Calculator

Quiz/Test

Teacher Observation


Investigation


Resources



Grades 7-8

B. Probability




conclusions?


1. Determine probabilities of compound

events.


You Expect?"

USCMP Transitions

Manipulatives

Use of collaborative

investigations


2. Explore the probabilities of conditional

events.


You Expect?"

USCMP Transitions

Manipulatives

Use of collaborative

investigations






Dealing with Data and Chance –


Mathematics Addenda Series

Navigating through Data and

Chance Grades 6-8

Graphing calculator probability

simulation programs

Teacher observation

Written explanation of how

the two ideas are related in

given situations



probabilities.

Dealing with Data and Chance –


Mathematics Addenda Series

Navigating through Data and

Chance Grades 6-8

Graphing calculator probability

simulation programs

Investigation write-up


Resources



Grades 7-8

B. Probability




conclusions?




expected value.


You Expect?"

Math Counts

Analyze size of sections on dart

boards for area versus

probability

Investigation write-up



Resources



Grades 7-8



Direct Instruction

Manipulatives

Investigations

Textbook-generated

quizzes and tests







different contexts.

Math Counts


You Expect?”

Direct Instruction

Manipulatives

Investigations

Textbook-generated

quizzes and tests






3 class officers from a 23 student class).

Math Counts


You Expect?”

UCSMP Algebra

Direct Instruction

Manipulatives

Investigations

Textbook-generated

quizzes and tests



Math Counts


You Expect?”



Resources



Grades 7-8






1. Use vertex-edge graphs and algorithmic

thinking to represent and find solutions to

practical problems: Finding the shortest

network connecting specified sites; Finding a

minimal route that includes every street (e.g.,

for trash pick-up); Finding the shortest route

on a map from one site to another; Finding the

shortest circuit on a map that makes a tour of

specified sites.

Rutgers workshop on Discrete

Mathematics


Rutgers prepared worksheets

Write a tour guide with map

Teacher-Created

worksheets

Teacher-created quiz

Tour Guide Project

4.4.D 7th Algebra 1B 128

Resources



Grades 7-8






mathematics?





Website Standards

www.nctm.org

Connected Math Series


TinkerPlots

Math Counts

Brainstorming

Journaling

Classroom Discussion

Predictions







Question Quest level C

Teacher-Created Materials



Tinkerplots

Math Counts

Students analyze each others

written responses

Share solution methods



129

Resources



Grades 7-8






mathematics?


Brainstorming

Journaling


Predictions





problems.

Math Counts




TinkerPlots

Brainstorming

Journaling


Predictions



difficulty.

Math Counts




TinkerPlots


130

Resources



Grades 7-8






mathematics?




New Jersey Frameworks


Mathematics: Curriculum and

Evaluation Standards for School

Mathematics


Mathematics

Strategies for Success Level G

Brainstorming

Journaling


Predictions



131

Resources



Grades 7-8






mathematics?









Mathematics


Mathematics


Brainstorming

Journaling


Predictions









Mathematics


Mathematics


Brainstorming

Journaling


Predictions



132

Resources



Grades 7-8






mathematics?








Mathematics


Mathematics


Brainstorming

Journaling


Predictions








Mathematics


Mathematics


Brainstorming

Journaling


Predictions



133

Resources



Grades 7-8






mathematics?









Mathematics


Mathematics


Brainstorming

Journaling


Predictions










Mathematics


Mathematics


Brainstorming

Journaling


Predictions



Resources



Grades 7-8






mathematics?








Mathematics


Mathematics


Brainstorming

Journaling


Predictions








Mathematics


Mathematics


Brainstorming

Journaling


Predictions



Resources



Grades 7-8






mathematics?









Mathematics


Mathematics


Brainstorming

Journaling


Predictions

Class Discussions








Mathematics


Mathematics


Brainstorming

Journaling


Predictions

Class Discussions


Resources



Grades 7-8






mathematics?








Mathematics


Mathematics


Give examples and

counterexamples




solutions.





Mathematics


Mathematics


Brainstorming

Journaling


Predictions



Resources



Grades 7-8






mathematics?








Mathematics


Mathematics


Share methods

Students analyze each others’

responses









Mathematics


Mathematics


Estimations and predictions Written Explanations


Resources



Grades 7-8






mathematics?










Mathematics


Mathematics


Test x ^2 > x for all real

numbers




valid.





Mathematics


Mathematics


Brainstorming

Journaling


Predictions



Resources



Grades 7-8


E. Representations

Brainstorming

Journaling







mathematics?










Math Counts

Algebra Out Loud

Navigating Algebra grades 9-12

Use algebra tiles to show

multiplication of polynomials

Use tables to find algebraic

functions relating quantities

Use area formula and graphing

calculator to predict maximum

area

Graphs




problems.


Math Counts

Algebra Out Loud


4.5.E 7th Algebra 1B

140

Resources



Grades 7-8


E. Representations Essential Questions :




mathematics?




phenomena.


Math Counts

Algebra Out Loud


Brainstorming

Journaling



4.5.E 7th Algebra 1B

141

Resources



Grades 7-8






mathematics?





Geometer's Sketchpad

Use graphing calculator or

computer to compare various

ways of finding “Line of best fit”







Compare two teams batting

averages using various graphical

representations




and their graphs.



Graph rational expressions and

discuss asymptotes


4.5.F 7th Algebra 1B

142

Resources



Grades 7-8






mathematics?





Developing Number Sense

Addenda series National Council of


Discover patterns from positive

to negative through investigation

with graphing calculator






Test Triangle Similarity

Theorem




Core math textbooks

Various workbooks


Use CBL’s to collect data on

motion sensor or temperature

and analyze for algebraic

patterns


4.5.F 7th Algebra 1B

143



Grades 7-8

7th Grade Algebra 1B

Pacing Guide

UnitDiscovering Algebra

ChapterNumber of Blocks

Linear Equations 5 8

Graphing, Slope, and Writing the Equation of

a Line

5 8

Systems of Equations and Inequalities 6 10

Exponents and Exponential Models 7 12

Functions 8 10

Transformations 9 11

Polynomials Developing Skills in Algebra

One Books A-D

7

Radicals Developing Skills in Algebra

One Books A-D

6

Quadratics 10 12

Rational Expressions Developing Skills in Algebra

One Books A-D

4

7th Grade Algebra 1B Pacing Guide 144



Grades 7-8


Resources


Discovering Algebra An Investigative

Approach

Jerald Murdock, Ellen Kamischke,

Eric Kamischke



and B

Harold and Loretta Taylor Dale Seymour Publications 1984


LL Teach, Inc. 2002


Algebra Out Loud Pat Mower, PhD Jossey Bass 2003


Question Quest Level C Paul Lawrence





Algebra Puzzles & Problems Greenes/Findell Creative Publications 1998

7th Grade Algebra 1B Resources

145



Grades 7-8


Resources


Algebra Teacher's Activities Kit Judith & Robert Muschla Jossey Bass 2003


ASK Workout Jerome Kaplan Ed.D Triumph Learning 2008

Hands -On Algebra ! Frances M. Thompson The Center for Applied Research

Education

1998


Grades 5-8


H. Lovin

Pearson Education 2006


NCTM Navigation Series: Algebra Burke, Erickson, Lott, Obert The National Council of


2001


G

Weisenfeld, Coultas, Swalm Steck-Vaugh Company 1999


Students

Wyatt, Lawrence, Foletta Key Curriculum Press 2004



Michael T. Battista



12

Burrill The National Council of


1992

7th Grade Algebra 1B Resources

146

8th Grade Curriculum

147

4.1.B.1. Use and explain procedures for performing


multiplication, division, and exponentiation with

integers and all number types named above with: Pencil-

and-paper; Mental math; Calculator.

Science Wave activity

4.1.A.2. Demonstrate a sense of the relative magnitudes

of numbers.

Science

Social Studies

Astronomy Unit

Holocaust Unit - visual representation of

numbers

4.1.A.5. Use computer software to make and verify


Technology Creating models



Grades 7 - 8

Standard Subject


Learning Experience

4.1.A.1. Extend understanding of the number system by

constructing meanings for the following (unless

otherwise noted, all indicators for grade 8 pertain to

these sets of numbers as well): Rational numbers;

Percents; Exponents; Roots; Absolute Values; Numbers

represented in scientific notation.

Science Astronomy Unit

4.1.A.3. Understand and use ratios, rates, proportions,

and percents (including percents greater than 100 and

less than 1) in a variety of situations.

Science

Music

Art

Cooking

Genetics - Punnet Squares

Chemistry

Notes (1/4,1/16)

Scale Drawing

Recipes




Grades 7 - 8

Standard Subject


Learning Experience

4.2.A.1. Understand and apply concepts involving lines,

angles, and planes: Complementary and supplementary

angles; Vertical angles; Bisectors and perpendicular

bisectors; Parallel, perpendicular, and intersecting

planes; Intersection of plane with cube, cylinder, cone,

and sphere.

Sewing Creating quilts

4.2.A.4. Understand and apply the concept of similarity:

Using proportions to find missing measures; Scale

drawings; Models of 3D objects.

Technology

Art

Creating Models

Scale drawings, creating lables for cans

4.2.A.3. Understand and apply properties of polygons:

Quadrilaterals, including squares, rectangles,

parallelograms, trapezoids, rhombi; Regular polygons;

Sum of measures of interior angles of a polygon; Which

polygons can be used alone to generate a tessellation and

why.

4.1.B.4. Solve problems involving proportions and

percents.


4.1.C.2. Use equivalent representations of numbers such

as fractions, decimals, and percents to facilitate

estimation.


Art Polygon project and tessellations

4.1.C.3. Recognize the limitations of estimation and

assess the amount of error resulting from estimation.





Grades 7 - 8

Standard Subject


Learning Experience

4.2.B.1. Understand and apply transformations: Finding

the image, given the pre-image, and vice-versa;

Sequence of transformations needed to map one figure

onto another; Reflections, rotations, and translations

result in images congruent to the pre-image; Dilations

(stretching/shrinking) result in images similar to the pre-

image.

Art Reflections and rotations

Science On-going through science labs, metric

system

4.2.C.1. Use coordinates in four quadrants to represent

geometric concepts.

Social Studies Reading a map

4.2.D.2. Use approximate equivalents between standard

and metric systems to estimate measurements (e.g.,

kilometers is about 3 miles).

Science Ongoing through science labs, metric

system

4.2.D.1. Solve problems requiring calculations that

involve different units of measurement within a

measurement system (e.g., 4’3” plus 7’10” equals 12’1”).

4.2.E.1. Develop and apply strategies for finding

perimeter and area: Geometric figures made by

combining triangles, rectangles and circles or parts of

circles; Estimation of area using grids of various sizes;

Impact of a dilation on the perimeter and area of a 2-

dimensional figure; Impact of a dilation on the

perimeter and area of a 2-dimensional figure.

Sewing

Art

Creating a quilt

Polygon project




Grades 7 - 8

Standard Subject


Learning Experience

Science Half-life lab

4.3.C.2. Use patterns, relations, symbolic algebra, and

linear functions to model situations: Using concrete

materials (manipulatives), tables, graphs, verbal rules,

algebraic expressions/ equations/ inequalities; Growth

situations, such as population growth and compound

interest, using recursive formulas.

Social Studies Population growth

4.3.B.1. Graph functions, and understand and describe

their general behavior: Equations involving two

variables; Rates of change (informal notion of slope).

4.3.C.1. Analyze functional relationships to explain how

a change in one quantity can result in a change in

another, using pictures, graphs, charts, and equations.


4.3.B.2. Recognize and describe the difference between

linear and exponential growth, using tables, graphs, and

equations.

Social Studies Population growth, immigration information




Grades 7 - 8

Standard Subject


Learning Experience

Social Studies

Science

Current events

Environmental unit

4.3.D.2. Solve simple linear equations informally,

graphically, and using formal algebraic methods:

Multi-step, integer coefficients only (although answers

may not be integers) Simple literal equations (e.g., A =

lw) Using paper-and-pencil, calculators, graphing

calculators, spreadsheets, and other technology.

Science Equation balancing in chemistry

Social Studies Current events

4.4.A.2. Make inferences and formulate and evaluate

arguments based on displays and analysis of data sets.

Social Studies Data analysis from graphs

4.4.A.1. Select and use appropriate representations for

sets of data, and measures of central tendency (mean,

median, and mode): Type of display most appropriate

for given data; Box-and-whisker plot, upper quartile,

lower quartile; Scatter plot; Calculators and computer

used to record and process information; Finding the

median and mean (weighted average) using frequency

data; Effect of additional data on measures of central

tendency.

4.4.A.3. Estimate lines of best fit and use them to


Science Half-life graphs

4.4.A.4. Use surveys and sampling techniques to

generate data and draw conclusions about large groups.




Grades 7 - 8

Standard Subject


Learning Experience

Reading skills

Physical Education

4.4.D.1. Use vertex-edge graphs and algorithmic

thinking to represent and find solutions to practical

problems: Finding the shortest network connecting

specified sites; Finding a minimal route that includes

every street; Finding the shortest route on a map from

one site to another; Finding the shortest circuit on a

map that makes a tour of specified sites; Limitations of

computers.

Science

Social Studies

Circuit labs

Shortest route on a map

4.5.A.2. Solve problems that arise in mathematics and in

other contexts: Open-ended problems; Non-routine

problems; Problems with multiple solutions; Problems

that can be solved in several ways.

Language Arts

Fairness of games

4.4.C.3. Apply techniques of systematic listing, counting,

and reasoning in a variety of different contexts.

All disciplines Discussions throughout

4.4.B.6. Play and analyze probability-based games and

discuss the concepts of fairness and expected value.

All disciplines Discussions throughout4.5.A.4. Pose problems of various types and levels of

difficulty.

4.5.A.5. Monitor their progress and reflect on the






Grades 7 - 8

Standard Subject


Learning Experience

4.5.B.1. Use communication to organize and clarify



Language Arts Ongoing throughout

Ongoing throughout

Scientific method


4.5.C.4. Apply mathematics in practical situations and

in other disciplines.


4.5.D.3. Select and use various types of reasoning and

methods of proof.

Discussions and persuasive essays

4.5.C.3. Recognize that mathematics is used in a variety

of contexts outside of mathematics.

4.5.C.5. Trace the development of mathematical

concepts over time and across cultures.

Social Studies

World Languages

Discussions throughout

Discussions throughout

4.5.B.2. Communicate mathematical thinking coherently

and clearly to peers, teachers, and others, both orally

and in writing.

Science


Language Arts

4.5.D.5. Make and investigate mathematical conjectures:

Counterexamples as a means of disproving conjectures;

Verifying conjectures using informal reasoning or

proofs.

Science

4.5.D.4. Rely on reasoning, rather than answer keys,

teachers, or peers, to check the correctness of their

problem solutions.




Grades 7 - 8

Standard Subject


Learning Experience

Science Scientific method

4.5.E.1. Create and use representations to organize,

record, and communicate mathematical ideas: Concrete

representations (e.g., base-ten blocks or algebra tiles);

Pictorial representations (e.g., diagrams, charts, or

tables); Symbolic representations (e.g., a formula);

Graphical representations (e.g., a line graph).

Science Data collection from labs

Creating excel spreadsheets

4.5.F.5. Use computer software to make and verify


Technology Creating models

4.5.F.2. Use computer spreadsheets, software, and

graphing utilities to organize and display quantitative

information.

4.5.D.6. Evaluate examples of mathematical reasoning

and determine whether they are valid.

Software Applications


Pre-Algebra Curriculum

156

A. Number Sense

· How can problems in the real world be solved with Mathematics?

· How can estimation be useful to us to reason out solutions to problems?


Resources







represented in scientific notation.

- Students calculate relative

change in quantity

- Number line in classroom

- Students use calculators to

work with numbers with more

than 10 digits

McDougal Littell

7.3 - 7.7 (Rational Numbers)

1.4, 4.6, 4.7 (Exponents)

9.1 (Roots)

2.1 (Absolute Value)

4.8 (Scientific Notation)

_______________________

Holt

Ch. 6 (Rational Numbers)

4.1 - 4.3 (Exponents)

4.5 - 4.6 (Roots)

1.3 (Absolute Value)

4.4 (Scientific Notation)



Students discuss why

numbers are easier to

compare when written in

scientific notation


Assessments




Grades 7 - 8

4.1.A 8th Grade Pre-Algebra 157

A. Number Sense




Resources




Assessments




Grades 7 - 8


types.

McDougal Littell

2.1 - 2.5

_______________________

Holt

2.3 - 2.5



- Geometer's Sketchpad

- Activity to show integers on a

number line

- Students use real world data to

discover relationships of

numbers

Do Now

Written assessments

Teacher Observation

Do Now

Written assessments

Teacher Observation

Do Now

Written assessments

Teacher Observation

Ongoing in all investigations

McDougal Littell

7.1 - 7.7, 8.8

_______________________

Holt

5.1 - 5.4, 5.5

McDougal Littell

2.1, 5.5

_______________________

Holt

2.2




of situations.


A. Number Sense




Resources




Assessments




Grades 7 - 8

McDougal Littell

4.3, 4.5, 5.1 - 5.7, 7.3 - 7.7

_______________________

Holt

6.1 - 6.6

Do Now

Written assessments

Teacher Observation



Classwork Activity/Accuracy

of Student work

7. Construct meanings for common irrational

numbers, such as pi (π) and the square root of

two.

McDougal Littell

9.2

_______________________

Holt

4.5 - 4.6

Students explore irrational

numbers through Pythagorean's

Theorem

Classwork Activity/Accuracy

of Student work



fractional equivalents:

5/7 = 0.714285714285...

= 0.714285

McDougal Littell

5.5

_______________________

Holt

2.1 - 2.6

Calculator Exploration






Resources

Do Now

Written assessments

Teacher Observation

Technology exploration

Do Now

Written assessments

Teacher Observation






Calculator.

McDougal Littell

2.2 - 2.5

_________________________

Holt

1.4 - 1.6

3. Find square and cube roots of numbers and

understand the inverse nature of powers and

roots.

McDougal Littell

9.1

_________________________

Holt

4.5 - 4.6


powers of numbers.


McDougal Littell

4.6 - 4.8

_________________________

Holt

4.1 - 4.4


Do Now

Written assessments

Teacher Observation



AssessmentsLearning ExperiencesKnowledge/Skills/Understanding






Calculator.




Grades 7 - 8

4.1.B 8th Grade Pre-Algebra 160




Resources



AssessmentsLearning ExperiencesKnowledge/Skills/Understanding




Grades 7 - 8




McDougal Littell

1.2

_________________________

Holt

1.1

Do Now

Written assessments

Teacher Observation



percents.

Do Now

Written assessments

Teacher Observation

McDougal Littell

7.2 - 7.7

_________________________

Holt

5.1, 5.4, 6.2 - 6.6

Solving real world problems


C. Estimation




Resources




Grades 7 - 8




1. Estimate square and cube roots of numbers. NJ Frameworks Students use the multiplication

function to perform successive

approximations to find

acceptable values for several

square roots (the square roots of

2, 3, 7, 19 and the cube roots of

10 and 100)

Do Now

Written assessments

Teacher Observation




McDougal Littell

7.4

_______________________

Holt

6.1

Ongoing through investigations Do Now

Written assessments

Teacher Observation

4.1.C 8th Grade Pre-Algebra 162

C. Estimation




Resources




Grades 7 - 8






estimation.

NJ Frameworks Students make estimates of the

number of times things happen in

a lifetime and compare

estimations to referenced

materials

Do Now

Written assessments

Teacher Observation


· How can knowledge of geometric properties help in problem solving situations?

· How can coordinate grid systems help us analyze situations?


Resources


Flemington Raritan School DistrictFlemington Raritan School District



Grades 7 - 8



Theorem.

McDougal Littell

9.3 - 9.4

_______________________

Holt

4.8

- Using manipulatives


· How does the mathematics of geometry enable us to wonder and understand our natural

and physical world?

Do Now

Written assessments

Teacher Observation


1. Understand and apply concepts involving

lines, angles, and planes: Complementary and

supplementary angles; Vertical angles;

Bisectors and perpendicular bisectors;

Parallel, perpendicular, and intersecting

planes; Intersection of plane with cube,

cylinder, cone, and sphere.

McDougal Littell

8.1 - 8.2

_______________________

Holt

7.1 - 7.2

Geometer's Sketchpad Do Now

Written assessments

Teacher Observation





Resources





Grades 7 - 8



and physical world?


- Direct instruction

- Using manipulatives

McDougal Littell

8.8

_______________________

Holt

5.5

Use proportions to investigate

real world problems

Do Now

Written assessments

Teacher Observation




rhombi; Regular polygons; Sum of measures

of interior angles of a polygon; Which

polygons can be used alone to generate a

tessellation and why.

McDougal Littell

8.3 - 8.4

_______________________

Holt

7.4




objects.

Do Now

Written assessments

Teacher Observation





Resources





Grades 7 - 8



and physical world?




McDougal Littell

Ch. 8

_______________________

Holt

Ch. 7

Ongoing through Geometry

Investigations

Do Now

Written assessments

Teacher Observation






Do Now

Written assessments

Teacher Observation










McDougal Littell

8.6 - 8.8

_______________________

Holt

7.7

- Exploring through Geometer's

Sketchpad

- Rotation art activity

Students describe sizes,

positions, orientation of

shapes such as flips, slides,

turns, and scaling



and physical world?


2. Use iterative procedures to generate

geometric patterns: Fractals (e.g., the Koch

Snowflake); Self-similarity; Construction of

initial stages; Patterns in successive stages

(e.g., number of triangles in each stage of

Sierpinski’s Triangle).

NJ Frameworks - Students explore shapes with

tangrams

- Students build a Sierpinski's

Triangle





Grades 7 - 8





Resources


Assessments


and physical world?



Grades 7 - 8

Essential Questions : Essential Questions :





McDougal Littell

2.8

_______________________

Holt

7.5

Students explore properties of

shapes in a coordinate system

Do Now

Written assessments

Teacher Observation



McDougal Littell

8.7

_______________________

Holt

7.7

Students will perform

transformations on a coordinate

grid

Do Now

Written assessments

Teacher Observation






Resources



Accuracy of student work

Assessments


and physical world?


Do Now

Written assessments

Teacher Observation

Students plan a new Olympics by

renaming standard events in

different measurement units





equals 12’1”).





Students develop a project, for

example, scale drawing of an

apartment floor plan


McDougal Littell

7.1

_______________________

Holt

5.2

Using real life examples




miles).

NJ Frameworks

NJ Frameworks

Ongoing with all measurement

activities



Grades 7 - 8

Students reflect on close they

are to degree of accuracy and

how it affects results

4.2.D 8th Grade Pre-Algebra 169




Resources



Assessments


and physical world?


Learning ExperiencesKnowledge/Skills/Understanding



Grades 7 - 8

Students are asked to find the

height of a tall tree if the

height of a small tree is

known






mile).

Teacher created materials

Various workbooks

Students will use their

knowledge of mathematics to

plan and carry out scientific

experimentation

Reflection on results of

student created experiments


Various workbooks




Various workbooks

Using real life examples Do Now

Written assessments

Teacher Observation




situation.









Grades 7 - 8







McDougal Littell

10.7

_______________________

Holt

8.6

Teacher demonstration with

manipulatives

Do Now

Written assessments

Teacher Observation





grids of various sizes; Impact of a dilation on


figure; Impact of a dilation on the perimeter

and area of a 2-dimensional figure.

McDougal Littell

1.6, 10.1 - 10.2

_______________________

Holt

8.1 - 8.3

Students investigate the

relationship between perimeter

and area

Do Now

Written assessments

Teacher Observation



and physical world?

4.2.E 8th Grade Pre-Algebra 171








Grades 7 - 8




and physical world?

4. Use formulas to find the volume and surface

area of a sphere.

McDougal Littell

10.7

_______________________

Holt

8.9

Students will evaluate problems Do Now

Written assessments

Teacher Observation


for finding the surface area and volume of a

three-dimensional figure: Volume —prism,

cone, pyramid; Surface area —prism

(triangular or rectangular base), pyramid

(triangular or rectangular base); Impact of a

dilation on the surface area and volume of a


McDougal Littell

10.4 - 10.7

_______________________

Holt

8.5 - 8.8

Students investigate the nets of

three dimensional figures

Students build models and

explain how changes in

surface area and volume are

impacted as lengths are

changed



Resources

McDougal Littell

11.1

_______________________

Holt

13.1 - 13.3

- Direct Instruction




Grades 7 - 8









formula.

Do Now

Written assessments

Teacher Observation


Assessments


Knowledge/Skills/UnderstandingKnowledge/Skills/Understanding Learning Experiences




A. Patterns



Resources





Grades 7 - 8











McDougal Littell

11.6

_______________________

Holt

13.4 - 13.5

Cooperative Learning Activities Do Now

Written assessments

Teacher Observation



involving two variables; Rates of change

(informal notion of slope).

McDougal Littell

11.3 - 11.7

_______________________

Holt

13.4 - 13.7

Technology Exploration Do Now

Written assessments

Teacher Observation



Resources



Grades 7 - 8


C. Modeling Essential Questions :

Assessments















Various workbooks

Ongoing through all

investigations

Do Now

Written assessments

Teacher Observation

Technology exploration Do Now

Written assessments

Teacher Observation





McDougal Littell

11.6

_______________________

Holt

12.2



Resources



Grades 7 - 8



methods:


answers may not be integers) Simple literal

equations (e.g., A = lw) Using paper-and-

pencil, calculators, graphing calculators,


Assessments


help explain real-life situations?








is “left 3, right 6”).

McDougal Littell

2.1

_______________________

Holt

1.3

Number Line in classroom

McDougal Littell

3.1 - 3.4, 6.1 - 6.4

_______________________

Holt

11.2


- Real world problem solving

Do Now

Written assessments

Teacher Observation

Do Now

Written assessments

Teacher Observation



Resources



Grades 7 - 8

Assessments







Do Now

Written assessments

Teacher Observation

McDougal Littell

3.6 - 3.7, 6.5

_______________________

Holt

11.4

Direct Instruction Do Now

Written assessments

Teacher Observation

3. Solve simple linear inequalities.




parentheses; Distributive property;

Substitution of a number for a variable;

Translation of a verbal phrase or sentence into

an algebraic expression, equation, or

inequality, and vice versa.

McDougal Littell

1.3, 2.6, 2.7

_______________________

Holt

11.1

Applied throughout

investigations



Resources



Grades 7 - 8

Assessments










inverse; Addition and multiplication

properties of equality; Addition and

multiplication properties of inequalities.

McDougal Littell

3.1 - 3.4

_______________________

Holt

1.7 - 1.8


Written assessments

Teacher Observation



Resources



Grades 7 - 8

Graphing project


· How can classifying help me in organizing data to solve problems?

A. Data Analysis


· How can experimental and theoretical probability be used to make predictions or draw

conclusions?

· How can statistics help us to understand real world situations?












central tendency.

McDougal Littell

5.8, 12.1 - 12.3

_______________________

Holt

9.3 -9.4, 9.8

Real world problem solving



Resources



Grades 7 - 8



A. Data Analysis



conclusions?



McDougal Littell

5.8, 12.1 - 12.3

_______________________

Holt

9.3 -9.4, 9.8

Do Now

Written assessments

Teacher Observation


Student project



McDougal Littell

11.2

_______________________

Holt

12.7

Real world problem solving Students produce a scatterplot

to determine line of best fit




4. Use surveys and sampling techniques to

generate data and draw conclusions about

large groups.

Teacher created material

Various worbooks







Grades 7 - 8


B. Probability



conclusions?


McDougal Littell

12.8

_______________________

Holt

10.5

Stations in classroom Results from stations

McDougal Littell

7.8, 12.7

_______________________

Holt

10.1

Cooperative Learning activities Do Now

Written assessments

Teacher Observation


events.


events (e.g., if there are seven marbles in a

bag, three red and four green, what is the

probability that two marbles picked from the

bag, without replacement, are both red).

McDougal Littell

12.7 - 12.8

_______________________

Holt

10.5




and decimals.






Grades 7 - 8


B. Probability



conclusions?



6. Play and analyze probability-based games


expected value.


_______________________

Holt

Ch. 10 ending activity

Cooperative Learning activities Do Now

Written assessments

Teacher Observation





McDougal Littell

12.7 - 12.8

_______________________

Holt

10.4




probabilities.

McDougal Littell

7.8

_______________________

Holt

10.2, 10.4


Written assessments

Teacher Observation



Resources



Grades 7 - 8






Learning Experiences Assessments



with replacement vs. ordered situations

without replacement; Factorial notation;

Concept of combinations.

McDougal Littell

12.4 - 12.6

_______________________

Holt

10.8 - 10.9


- Ice cream activity

Student projects


conclusions?



Various workbooks Direct instruction Do Now

Written assessments

Teacher Observation



different contexts.

McDougal Littell

12.4

_______________________

Holt

10.8

Ongoing throughout

investigations

Do Now

Written assessments

Teacher Observation




Resources



Grades 7 - 8







conclusions?






minimal route that includes every street;

Finding the shortest route on a map from one

site to another; Finding the shortest circuit on

a map that makes a tour of specified sites;

Limitations of computers.

NJ Frameworks - Students explore common

discrete mathematical models,

explore their properties, and

design them for specific

situations

- Students devise, describe, and

test algorithms for solving

optimization and search options

Do Now

Written assessments

Teacher Observation



Resources



Grades 7 - 8


mathematics?



A. Problem Solving






McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks

Incorporated throughout

investigations

Do Now

Written assessments

Teacher Observation






McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks


investigations

Do Now

Written assessments

Teacher Observation




problems.

McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks


investigations

Do Now

Written assessments

Teacher Observation



Resources



Grades 7 - 8


mathematics?



A. Problem Solving





difficulty.

McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks


investigations

Do Now

Written assessments

Teacher Observation



McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks


investigations

Do Now

Written assessments

Teacher Observation



Resources


mathematics?




Grades 7 - 8



B. Communication







McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks


investigations

Do Now

Written assessments

Teacher Observation


investigations

Do Now

Written assessments

Teacher Observation




McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks

Assessments



McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks


investigations

Do Now

Written assessments

Teacher Observation



Resources


mathematics?




Grades 7 - 8



B. Communication



Knowledge/Skills/Understanding Assessments



McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks


investigations

Do Now

Written assessments

Teacher Observation



Resources



Grades 7 - 8


mathematics?



C. Connections







McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks


investigations

Do Now

Written assessments

Teacher Observation





McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks


investigations

Do Now

Written assessments

Teacher Observation



McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks


investigations

Do Now

Written assessments

Teacher Observation



Resources



Grades 7 - 8


mathematics?



C. Connections





investigations

Do Now

Written assessments

Teacher Observation




McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks


investigations

Do Now

Written assessments

Teacher Observation



McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks


investigations

Do Now

Written assessments

Teacher Observation



McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks



Resources



Grades 7 - 8


mathematics?



D. Reasoning






McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks


investigations

Do Now

Written assessments

Teacher Observation



solutions.

McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks


investigations

Do Now

Written assessments

Teacher Observation



McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks


investigations

Do Now

Written assessments

Teacher Observation



Resources



Grades 7 - 8


mathematics?



D. Reasoning





investigations

Do Now

Written assessments

Teacher Observation



valid.

McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks


investigations

Do Now

Written assessments

Teacher Observation




McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks


investigations

Do Now

Written assessments

Teacher Observation





McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks



Resources



Grades 7 - 8


mathematics?



E. Representations











McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks


investigations

Do Now

Written assessments

Teacher Observation



problems.

McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks


investigations

Do Now

Written assessments

Teacher Observation



Resources



Grades 7 - 8


mathematics?



E. Representations






phenomena.

McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks


investigations

Do Now

Written assessments

Teacher Observation



Resources



Grades 7 - 8


mathematics?



F. Technology






McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks

- Technology exploration


Do Now

Written assessments

Teacher Observation




McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks



Do Now

Written assessments

Teacher Observation



and their graphs.

McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks



Do Now

Written assessments

Teacher Observation

4.5.F 8th Grade Pre-Algebra 195


Resources



Grades 7 - 8


mathematics?



F. Technology






Do Now

Written assessments

Teacher Observation

6. Use computer-bases laboratory technology


McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks


investigations

Do Now

Written assessments

Teacher Observation



McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks



Do Now

Written assessments

Teacher Observation



McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks

4.5.F 8th Grade Pre-Algebra 196

Algebra with Pizzazz! Steve and Janis Marcy

Fractions, Decimals, and Percents Joke

WorksheetsChristine A. Koers Nasco 2006

Algebra Joke Worksheets Christine A. Koers Nasco 2003

Geo Joke Worksheets Christine A. Koers

McGraw Hill 2002

Middle School Math with Pizzazz! Steve and Janis Marcy McGraw Hill 1989

Pre-Algebra with Pizzazz! Steve and Janis Marcy McGraw Hill 2002



Grades 7 - 8

2008

Author(s)

McDougall Littell Course 3


including ELL)

Ron Larson, Laurie Boswell,

Timothy D. Kanold, and Lee

Stiff

McDougal Littell

Holt Course 3: Pre-Algebra


including ELL)

Jeanine M. Bennett, Edward B.

Burger, David J. Chard, Audrey

L. Jackson, Paul A. Kennedy,

Freddie L. Renfro, Janet K.

Scheer, and Bert K. Waits

Holt, Reinhart and Winston

8th Grade Pre-Algebra

Title of ResourceTitle of Resource Publisher Copyright

Resources

2007

Pre-Algebra Joke Worksheets Christine A. Koers Nasco 2003

Nasco 2002

8th Grade Pre-Algebra Resources 197



Grades 7 - 8

Author(s)



Resources

Frank Schaffer Publications 2002

Teacher Created Resources Inc. 1999Pre-Algebra Brain Teasers Lorin Olschanski

Skills for Success - Algebra Theresa Kane McKell

The 100+ Series - Standard Based Math

Grades 7-8

Mary Lee Vivian and Margaret

Thomas

Frank Schaffer Publications 2003

Carson-Dellosa Publishing

Company, Inc.2003

1998

1996

1996

The 100+ Series - Pre-Algebra Grades 5-8Mary Lee Vivian and Margaret

ThomasFrank Schaffer Publications 2003

The 100+ Series - Intro to GeometryMary Lee Vivian and Margaret

Thomas

The 100+ Series - Math Grades 7-8Mary Lee Vivian and Margaret


The 100+ Series - Algebra Grades 5-8Mary Lee Vivian and Margaret


Jossey-Bass 2003Algebra Teacher's Activities Kit Judith and Gary Robert Muschla

Algebra Puzzlers

Pre-Algebra

Masterminds Riddle Math Series - Pre-Algebra

Theresa Kane McKell

Dawn Talluto Jacobi

Brenda Opie and Douglas

McAvinn

Frank Schaffer Publications

Kelley Wingate Publications

Incentive Publications Inc.




Grades 7 - 8

Author(s)



Resources

-------NJ Frameworkshttp://www.state.nj.us/education/

frameworks/math/index.html

Geometer's Sketchpad Nicholas Jackiw Key Curriculum Press 2006

Punchline Problem Solving Steve and Janis Marcy Marcy Mathworks 2006

Punchline Algebra Book A and Book B Steve and Janis Marcy Marcy Mathworks 2006

GEPA Success in Mathematics - Level H Richard Crowe Steck-Vaughn/Berrent Company 2000

Question Quest - Level D Mathematics Paul Lawrence LL Teach, Inc. 2002

Preparing for the New Jersey GEPA - Grade 8David J. Glatzer and Joyce

GlatzerAmsco School Publications, Inc. 2005

New Jersey ASK 8 Coach Jerome D. Kaplan Triumph Learning 2008

Adventures with Area Evelyn B. Christensen Nasco 2007

Quadrant Quandries Julie K. Cohen Nasco 2007

The Complete Book of Graphing Douglas C. McBroom J. Weston Walch Publisher 2001

Tinkerplots Clifford Konold, Craig D. Miller Key Curriculum Press 2005

New Jersey Department of

Education and Rutgers




Grades 7 - 8

Author(s)



Resources

Measuring Up - Grade 8 Michael Goodman People's Publishing Group 2003

Skills for Success - GeometryTiffany Moore and Jenae

Hawkins


Company, Inc.2007

Plotting Pictures Paula Rozell Dale Seymour Publications 1995

Algebra Puzzles Hank Garcia Creative Teaching Press 2006

Power Practice Geometry Pamela Jennett Creative Teaching Press 2007

Scratch Your Brain AlgebraDoug Brumbaugh and David

RockThe Critical Thinking Co. 2008

Algebra Practice Exercises Thomas E. Campbell

Power Practice Pre-Algebra Wendy Osterman Creative Teaching Press 2004

J. Weston Walch Publisher 1996


5

11

Integer Operations 2

-----



Grades 7 - 8

Ratio, Proportion, Percent 7

6

-----

Benchmark Assessment -

Midtem

Factors, Fractions, Exponents,

Rational Number Operations

-----

7


Pre-Test-----

Equations and Inequalities 3

10

McDougall Littell Mathematics

Course 3 Chapter

4,5

Number of Blocks


Unit

Pacing Guide

Variables and Expressions 1

8th Grade Pre-Algebra Pacing Guide 201



Grades 7 - 8

McDougall Littell Mathematics

Course 3 ChapterNumber of Blocks


Unit

Pacing Guide

Multi-Step Equations and

Inequalities5 7


Post-Test----- -----

5

Measurement, Area, Volume 10 6

6

Linear Equations and Graphs 12

Polygons and Transformations 8 10

4Real Numbers and Right

Triangles9

Data Analysis and Probability 11



Pre-Test-----

Holt Course 3 Chapter

2

Variables, Expressions, Integers 1

Ratios, Proportion, Similarity 5

Exponents, Square roots,

Pythagorean Theorem, and

Scientific Notation

Graphs, Functions, and

Sequences

4

10

-----

Number of Blocks

3



Grades 7 - 8

Unit


Pacing Guide

Percents

Fractions, Decimals, and

Percents

11

8

9

10

6 5


Holt Course 3 Chapter Number of Blocks



Grades 7 - 8

Unit


Pacing Guide

-----

Measurement, Area, and

Volume8


Midterm-----

Probability 10 7

Two Dimensional Geometry 7

4

12

Data and Statistics 9


Post-Test----- -----

5


Algebra 1B Curriculum

205

A. Number Sense




Resources




Grades 7 - 8


Do Now

Written assessments

Teacher Observation



Assessments




of situations.

Do Now

Written assessments

Teacher Observation

Do Now

Written assessments

Teacher Observation






Exponents; Roots; Absolute Values.

- Investigate decimal patterns

using a caluclator

- Class discussions

- Written explanations

- Recursive Routines

- Through the use of geometry

and squares and cubes


Discovering Algebra

Sections 7.3 - 7.6


Various workbooks



Ongoing through problems

- Problem Solving

- Collaborative discussions

- Brainstorming


Various workbooks

4.1.A 8th Grade Algebra 1B 206

A. Number Sense




Resources




Grades 7 - 8




Assessments



same number.


Various workbooks

Ongoing throughout problems

Spiral of Right Triangles

(Pythagorean Theorem)

Circle - develop pi from

circumference formula


Various workbooks

Do Now

Written assessments

Teacher Observation

Do Now

Written assessments

Teacher Observation

Do Now

Written assessments

Teacher Observation

Do Now

Written assessments

Teacher Observation



two.


types.




5/7 = 0.714285714285...

= 0.714285


Various workbooks

Graphing on a number line

Line-up in classroom

Use equations method


Various workbooks





Resources





powers of numbers.

Discovering Algebra

Sections 7.1 - 7.6

Do Now

Written assessments

Teacher Observation


3. Find square and cube roots of numbers and

understand their inverse relationships.


Grades 7 - 8


Do Now

Written assessments

Teacher Observation

Do Now

Written assessments

Teacher Observation

Finding the length of the edge of

a cube knowing the volume

Mental Math Warmups


Do Now

Written assessments

Teacher Observation

Knowledge/Skills/Understanding AssessmentsLearning Experiences






Calculator.


Do Now

Written assessments

Teacher Observation




- Real world problems


percents.

Teacher created packet of percents,

proportion, and interest

4.1.B 8th Grade Algebra 1B 208




Resources





Grades 7 - 8



Knowledge/Skills/Understanding AssessmentsLearning Experiences


Written assessments

Teacher Observation

Pattern investigation Do Now

Written assessments

Teacher Observation

6. Perform operations on matrices (Addition

and Subtraction, Scalar Multiplication,

Multiplication).

Discovering Algebra

Chapter 1 and 8





Discovering Algebra

Chapter 7


C. Estimation




Resources



estimation.

Teacher created problems

Various workbooks

Physically measure lengths and

discuss why disparities occur

Do Now

Written assessments

Teacher Observation





Various workbooks


Written assessments

Teacher Observation


1. Estimate cube roots of numbers. Teacher created problems

Various workbooks

Technology Exploration Do Now

Written assessments

Teacher Observation




Grades 7 - 8



4.1.C 8th Grade Algebra 1B 210




Resources


polygons.

Real world application problems Do Now

Written assessments

Teacher Observation

Assessments

Do Now

Written assessments

Teacher Observation

Exploration and Investigation Do Now

Written assessments

Teacher Observation




Various workbooks


Various workbooks

Direct instruction


Theorem.

Discovering Algebra

Chapter 11

Various workbooks

1. Understand and apply concepts involving

lines, angles, and planes: Complementary and

supplementary angles; Bisectors and

perpendicular bisectors; Parallel,

perpendicular, and intersecting planes;

Intersection of plane with cube, cylinder, cone,

and sphere.



and physical world?



Grades 7 - 8







Resources AssessmentsKnowledge/Skills/Understanding Learning Experiences



and physical world?



Grades 7 - 8






objects.





Various workbooks

Exploration and Investigation Do Now

Written assessments

Teacher Observation


Various workbooks

Cooperative Learning activity Do Now

Written assessments

Teacher Observation





Resources








Discovering Algebra

Chapter 0,1,2,3


Written assessments

Teacher Observation


















Discovering Algebra

Chapter 9 and 11

Use calculator to compare

graphs of equations that involve

transformations

Coordinate grid drawings

Teacher Observation




Grades 7 - 8



and physical world?






Resources



Grades 7 - 8




and physical world?

AssessmentsKnowledge/Skills/Understanding

C. Coordinate Geometry Essential Questions :



Discovering Algebra

Chapter 11

Direct Instruction Coordinate grid drawings

Teacher Observation



Discovering Algebra

Chapter 11

Determine if a quadrilateral is a

parallelogram or a rectangle

Do Now

Written assessments

Teacher Observation





Resources

Do Now

Written assessments

Teacher Observation





miles).

Discovering Algebra

Chapters 6 - 11

Ongoing in all investigations Do Now

Written assessments

Teacher Observation

Do Now

Written assessments

Teacher Observation

Assessments


and physical world?




Grades 7 - 8





the same system.

Discovering Algebra

Chapters 6 - 11






Discovering Algebra

Chapters 6 - 11

Students develop a project, for

example, scale drawing of an

apartment floor plan

4.2.D 8th Grade Algebra 1B 215




Resources


Assessments


and physical world?




Grades 7 - 8





Discovering Algebra

Chapters 6 - 11


Written assessments

Teacher Observation




situation.

Discovering Algebra

Chapters 6 - 11


Written assessments

Teacher Observation

Do Now

Written assessments

Teacher Observation



hour).

Discovering Algebra

Chapters 6 - 11






Resources

Do Now

Written assessments

Teacher Observation



cylinder with the same base and height.

Students investigate the

relationship between perimeter

and area



Grades 7 - 8



Various workbooks

Teacher demonstration with

manipulatives


Do Now

Written assessments

Teacher Observation





grids of various sizes; Impact of a dilation on


figure; Impact of a dilation on the perimeter

and area of a 2-dimensional figure.


Various workbooks


Various workbooks




and physical world?

4.2.E 8th Grade Algebra 1B 217




Resources



Grades 7 - 8






and physical world?










Various workbooks

Students investigate the nets of

three dimensional figures


area of a sphere.


Various workbooks

Students evaluate problems Do Now

Written assessments

Teacher Observation

Do Now

Written assessments

Teacher Observation



Resources

Do Now

Written assessments

Teacher Observation


Assessments






Discovering Algebra

Chapters 6 - 11


- Given terms in a pattern,

describe patterns in words




Grades 7 - 8

A. Patterns









formula.



Resources



involving two variables; Rates of change

(informal notion of slope).

Discovering Algebra

Chapters 5 - 6


- Discussion

Do Now

Written assessments

Teacher Observation




Discovering Algebra

Chapter 7


- Discussion

Do Now

Written assessments

Teacher Observation











Grades 7 - 8




Resources


and linear functions to model situations:

Growth situations, such as population growth

and compound interest, using recursive

formulas.



Grades 7 - 8


- Collaborative investigations

C. Modeling

Do Now

Written assessments

Teacher Observation

- Reasoning

- Discussions

Do Now

Written assessments

Teacher Observation








Discovering Algebra

Chapter 7







Discovering Algebra

Chapters 6 - 11



Resources

Discovering Algebra

Chapter 4



Written assessments

Teacher Observation

3. Solve systems og equations: graphically;

algebraic methods; using matrices.

Discovering Algebra

Chapter 6


Direct instruction

2. Solve linear equations and inequalities

informally, graphically, and using formal

algebraic methods:


answers may not be integers); absolute value;

compound inequalities; rational expressions;

using paper-and-pencil, calculators, graphing

calculators, spreadsheets, and other

technology.


Do Now

Written assessments

Teacher Observation





Grades 7 - 8

Discovering Algebra

Chapter 8


Direct instruction



Absolute value.

D. Procedures

Do Now

Written assessments

Teacher Observation





Resources






Grades 7 - 8


D. Procedures



6. Evaluate and simplify algebraic

expressions: add and subtract polynomials;

multiply a polunomial by a monomial or

binomial; divide a polynomial by a monomial;

use laws of exponents.

Discovering Algebra

Chapter 7


Various workbooks

Discovering Algebra

Chapter 10


- Algebra tiles

- Investigations

Do Now

Written assessments

Teacher Observation

5. Rational expressions: add and subtract;

mulitply and divide.


Various workbooks

Do Now

Written assessments

Teacher Observation

Direct instruction

Direct instruction

Do Now

Written assessments

Teacher Observation

4. Factor polynomials.



Resources

Discovering Algebra

Chapter 1




conclusions?




Discovering Algebra

Chapter 1


Real world problem solving Do Now

Written assessments

Teacher Observation


Assessments

Do Now

Written assessments

Teacher Observation



tendency (mean, median, and mode): Finding

the median and mean (weighted average)

using frequency data; Effect of additional data

on measures of central tendency.





Grades 7 - 8

Learning ExperiencesKnowledge/Skills/Understanding

A. Data Analysis




Resources

Discovering Algebra

Chapter 2



conclusions?







Discovering Algebra

Chapter 2


- Manipulatives

- Probability stations


- Manipulatives



Do Now

Written assessments

Teacher Observation

Do Now

Written assessments

Teacher Observation



Grades 7 - 8






Do Now

Written assessments

Teacher Observation


B. Probability



- Manipulatives




events.

Discovering Algebra

Chapter 2




Resources


conclusions?




Grades 7 - 8



B. Probability



Do Now

Written assessments

Teacher Observation

5. Play and analyze probability-based games


expected value.

Discovering Algebra

Chapter 2


- Manipulatives



Do Now

Written assessments

Teacher Observation



probabilities.

Discovering Algebra

Chapter 2


- Manipulatives





Resources



different contexts.

Discovering Algebra

Chapter 2


- Manipulatives


Do Now

Written assessments

Teacher Observation



Discovering Algebra

Chapter 2


- Manipulatives


Do Now

Written assessments

Teacher Observation





replacement.

Discovering Algebra

Chapter 2


- Manipulatives


Do Now

Written assessments

Teacher Observation


conclusions?








Standard 4.4 Data Analysis, Probability and Discrete MathematicsGrades 7 - 8


Resources









Limitations of computers (overwhelming the

capacity).

Teacher created materials - Students explore common

discrete mathematical models,

explore their properties, and

design them for specific

situations

- Students devise, describe, and

test algorithms for solving

optimization and search options

Do Now

Written assessments

Teacher Observation


conclusions?












Resources






Discovering Algebra

Chapters 6 - 11

Question Quest

Level D

Various workbooks

- Students analyze their own

written response compared to

teacher created examples

- Students analyze each other's

written responses

Do Now

Written assessments

Teacher Observation




Discovering Algebra

Chapters 6 - 11

Question Quest

Level D

Various workbooks

- Brainstorming

- Journaling

- Classroom discussion

- Predictions

Do Now

Written assessments

Teacher Observation


mathematics?







A. Problem Solving

Grades 7 - 8





mathematics?







A. Problem Solving

Grades 7 - 8


difficulty.

Discovering Algebra

Chapters 6 - 11

Question Quest

Level D

Various workbooks

- Brainstorming

- Journaling


- Predictions

Do Now

Written assessments

Teacher Observation


problem-solving strategies to solve problems.

Discovering Algebra

Chapters 6 - 11

Question Quest

Level D

Various workbooks

- Brainstorming

- Journaling


- Predictions

Do Now

Written assessments

Teacher Observation





mathematics?







A. Problem Solving

Grades 7 - 8



Discovering Algebra

Chapters 6 - 11

Question Quest

Level D

Various workbooks

- Brainstorming

- Journaling


- Predictions

Do Now

Written assessments

Teacher Observation



Resources



Discovering Algebra

Chapters 6 - 11


Various workbooks


investigations

Do Now

Written assessments

Teacher Observation



Grades 7 - 8


B. Communication




Discovering Algebra

Chapters 6 - 11


Various workbooks


investigations

Do Now

Written assessments

Teacher Observation


investigations

Do Now

Written assessments

Teacher Observation




Discovering Algebra

Chapters 6 - 11


Various workbooks


mathematics?



Assessments






Resources



Grades 7 - 8


B. Communication


mathematics?



Assessments






Discovering Algebra

Chapters 6 - 11


Various workbooks


investigations

Do Now

Written assessments

Teacher Observation



Resources

Do Now

Written assessments

Teacher Observation

Discovering Algebra

Chapters 6 - 11


Various workbooks


investigations

Do Now

Written assessments

Teacher Observation



Discovering Algebra

Chapters 6 - 11


Various workbooks


investigations





Do Now

Written assessments

Teacher Observation






mathematics?



C. Connections





Grades 7 - 8

Discovering Algebra

Chapters 6 - 11


Various workbooks


investigations





mathematics?



C. Connections





Grades 7 - 8



Discovering Algebra

Chapters 6 - 11


Various workbooks



Discovering Algebra

Chapters 6 - 11


Various workbooks


investigations

Do Now

Written assessments

Teacher Observation


investigations

Do Now

Written assessments

Teacher Observation

Do Now

Written assessments

Teacher Observation




Discovering Algebra

Chapters 6 - 11


Various workbooks


investigations



Resources

Do Now

Written assessments

Teacher Observation

Discovering Algebra

Chapters 6 - 11


Various workbooks


investigations

Do Now

Written assessments

Teacher Observation



Discovering Algebra

Chapters 6 - 11


Various workbooks


investigations




Do Now

Written assessments

Teacher Observation



solutions.


mathematics?



D. Reasoning





Grades 7 - 8

Discovering Algebra

Chapters 6 - 11


Various workbooks


investigations





mathematics?



D. Reasoning





Grades 7 - 8




Discovering Algebra

Chapters 6 - 11


Various workbooks





Discovering Algebra

Chapters 6 - 11


Various workbooks


investigations

Do Now

Written assessments

Teacher Observation


investigations

Do Now

Written assessments

Teacher Observation

Do Now

Written assessments

Teacher Observation



valid.

Discovering Algebra

Chapters 6 - 11


Various workbooks


investigations



Resources



problems.

Discovering Algebra

Chapters 6 - 11


Various workbooks


investigations

Do Now

Written assessments

Teacher Observation









Discovering Algebra

Chapters 6 - 11


Various workbooks


investigations

Do Now

Written assessments

Teacher Observation


mathematics?







E. Representations

Grades 7 - 8





mathematics?







E. Representations

Grades 7 - 8



phenomena.

Discovering Algebra

Chapters 6 - 11


Various workbooks


investigations

Do Now

Written assessments

Teacher Observation



Resources

Do Now

Written assessments

Teacher Observation

Discovering Algebra

Chapters 6 - 11


Various workbooks


investigations

Do Now

Written assessments

Teacher Observation



and their graphs.

Discovering Algebra

Chapters 6 - 11


Various workbooks


investigations




Do Now

Written assessments

Teacher Observation





mathematics?



F. Technology





Grades 7 - 8

Discovering Algebra

Chapters 6 - 11


Various workbooks


investigations

4.5.F 8th Grade Algebra 1B 240




mathematics?



F. Technology





Grades 7 - 8



Discovering Algebra

Chapters 6 - 11


Various workbooks



Discovering Algebra

Chapters 6 - 11


Various workbooks


investigations

Do Now

Written assessments

Teacher Observation


investigations

Do Now

Written assessments

Teacher Observation

Do Now

Written assessments

Teacher Observation

6. Use computer-bases laboratory technology


Discovering Algebra

Chapters 6 - 11


Various workbooks


investigations

4.5.F 8th Grade Algebra 1B 241




Resources

Grades 7 - 8

Title of Resource Publisher Copyright

Discovering AlgebraJerald Murdock, Ellen

Kamischke, and Eric KamischkeKey Curriculum Press 2002

Author(s)

Pre-Algebra with Pizzazz! Steve and Janis Marcy McGraw Hill 2002

Middle School Math with Pizzazz! Steve and Janis Marcy McGraw Hill 1989


Algebra with Pizzazz! Steve and Janis Marcy McGraw Hill 2002

Geo Joke Worksheets Christine A. Koers Nasco 2002

Pre-Algebra Joke Worksheets Christine A. Koers Nasco 2003

Algebra Teacher's Activities Kit Judith and Gary Robert Muschla Jossey-Bass 2003

Fractions, Decimals, and Percents Joke

WorksheetsChristine A. Koers Nasco 2006

The 100+ Series - Pre-AlgebraMary Lee Vivian and Margaret

ThomasMcGraw Hill 2003

The 100+ Series - AlgebraMary Lee Vivian and Margaret


8th Grade Algebra 1B Resources 242




Resources

Grades 7 - 8

Title of Resource Publisher CopyrightAuthor(s)


Company, Inc.

Teacher Created Resources Inc.


Kelley Wingate Publications

2003

1999

1998

1996

Skills for Success - Algebra

Pre-Algebra Brain Teasers

Algebra Puzzlers

Pre-Algebra

Theresa Kane McKell

Lorin Olschanski

Theresa Kane McKell

Dawn Talluto Jacobi

NJ Frameworkshttp://www.state.nj.us/education/f

rameworks/math/index.html

New Jersey Department of

Education and Rutgers-------

Masterminds Riddle Math Series - Pre-AlgebraBrenda Opie and Douglas

McAvinnIncentive Publications Inc. 1996



Punchline Algebra Book A and Book B Steve and Janis Marcy Marcy Mathworks 2006

Punchline Problem Solving Steve and Janis Marcy Marcy Mathworks 2006







Resources

Grades 7 - 8





Quadrant Quandries Julie K. Cohen Nasco 2007

Adventures with Area Evelyn B. Christensen Nasco 2007

Scratch Your Brain AlgebraDoug Brumbaugh and David

RockThe Critical Thinking Co. 2008


Developing Skills in Algebra 1: Book C Harold and Loretta Taylor Dale Seymour Publications 1984

Algebra Practice Exercises Thomas E. Campbell J. Weston Walch Publisher 1996

The Univeristy of Chicago School Mathematics

Project - AlgebraScott Foresman Harper Collins Publishers 1996

What's My Rule? (Using Problem Solving

Strategies Grades 6 - 12)Dave and Teddy Logothetti Dale Seymour Publications 1983

Geometry Reproducibles Sara Freeman Milliken Publishing Company 2004

Test Time Algebra Maureen Steddin J. Weston Walch Publisher 2003


-----

Polynomials

10 7

Linear Equations

5 16

Systems of Equations and Inequalities


a Line

Benchmark Assessment - Midterm

----- -----

Exponents and Exponential Models

7


Discovering AlgebraDiscovering Algebra

6 10

Pacing Guide



Grades 7 - 8

Unit Number of Blocks

Benchmark Assessment - Pretest -----

5 10

8



Discovering AlgebraDiscovering Algebra

Pacing Guide



Grades 7 - 8


Benchmark Assessment - Final

----- -----

13

Rational Expressions and Functions

9 4

Radicals

11 4

Quadratics

10


Advanced Algebra Curriculum

247

A. Number Sense





Grades 7 - 8





Assessments

Written assessments

Class discussions

Teacher observations

Do now

Written assessments

Teacher observation


Various Workbooks

Discovering Advanced Algebra

Chapter 1

Written classwork2. Demonstrate a sense of the relative


Resources





well): Roots of monomials, Variables in

exponents, Roots, Know the meaning on

square/cubic roots, Understand the inverse

relationship between powers and roots.

- Use of geometry connections

through squares and cubes



4.1.A 8th Grade Advanced Algebra 248

A. Number Sense





Grades 7 - 8





AssessmentsResourcesKnowledge/Skills/Understanding Learning Experiences

Do now

Written assessments

Teacher observation

Class discussion




of situations. Solving ratios and proportions

involving polynomials.


Various Workbooks



two. Prove the square root of two is irrational.

Teacher created mateirals Direct instruction

Do now

Written assessments

Teacher observation

Solving real world problems

Graphing on a number line4. Compare and order rational and irrational

numbers.


Various Workbooks

Do now

Written assessments

Teacher observation







2. Perform operations on Matrices. 2. Perform operations on Matrices. Discovering Advanced Algebra

Section 6.2

Do now

Written assessments

Teacher observation

Students investigate weekly

movement of rental cars between

cities and analyze results

- Various workbooks

- Teacher created materials

Do now

Written assessments

Teacher observation

- Mental Math classwork

worksheets

- Ongoing throughout

investigations

ResourcesKnowledge/Skills/Understanding AssessmentsLearning Experiences





above with: Mental math.



Grades 7 - 8



4.1.B 8th Grade Advanced Algebra 250

C. Estimation






estimation.

- Various workbooks

-Teacher created materials

Take results of experiments done

in class and make conclusions

for a larger/smaller group or

time.

Do now

Written assessments


Knowledge/Skills/Understanding Learning Experiences AssessmentsResources




Grades 7 - 8



4.1.C 8th Grade Advanced Algebra 251



Solve real world problems Do now

Written assessments

Teacher observation

Assessments


similarity using:

Models of 3D objects

Polynomials used sometimes as dimensions.



Various workbooks

- Use Geometer's Sketchpad to

investigate the effects of rotating

a triangle around a fixed point

- Cooperative learning activity

- Solve real world problems


3. Use geometric models to represent real

world situations and to solve problems.

Various workbooks Solve real world problems


and physical world?

Resources

Do now

Written assessments

Teacher observation

Do now

Written assessments

Teacher observation



Various workbooks







Grades 7 - 8





Grades 7 - 8

Knowledge/Skills/UnderstandingKnowledge/Skills/Understanding




needed to map one figure onto another.


Chapter 4, pg. 219


Various workbooks




Assessments

Do now

Written assessments


- Graphing activities


investigations

- Cooperative learning activities


and physical world?

Resources Learning Experiences


Do now

Written assessments










pgs. 9, 32-33, 369-397, 642

- Investigations


- Students investigate the

Mandelbot set.





Grades 7 - 8

Knowledge/Skills/UnderstandingKnowledge/Skills/Understanding




Assessments


and physical world?

Resources Learning Experiences



Direct instruction Do now

Written assessments


3. Determine whether two or more given

shapes can be used to generate a tessellation.


pg. 208





Students perform investigations Do now

Written assessments

Teacher observation



Grades 7 - 8

Do now

Written assessments

Teacher observation

AssessmentsResources


pgs. 129-130, 186-189, 455,

Chapter 4

Various workbooks



- Students investigate and

explore what happens to the

equation of a linear function

when they translate the graph of

a line

- Students use motion detectors,

graphing calculators, fathom

software to investigate parallel

lines



2. Show position and represent motion in the

coordinate plane using vectors.


pg. 455


1. Use coordinate geometry to represent and

verify properties of lines; distances between

two points; midpoint and slope of a line

segment; finding the intersection of two lines;

lines with the same slope are parallel; lines

that are perpendicular have slopes whose

product is -1.


and physical world?








Grades 7 - 8



C. Coordinate Geometry Essential Questions : Essential Questions :


and physical world?



polygons. Quadrilaterals, including squares,

rectangles, parallelograms, trapezoids and

rhombi; regular polygons; sum of measures of

interior angles of a polygon.

Various workbooks


- Solving real world problems


Do now

Written assessments

Teacher observation


support conjectures and geometric objects.

Various workbooks


Ongoing throughout

investigations

Do now

Written assessments

Teacher observation







needed in a particular problem solving

situation.

Various workbooks Direct instruction Do now

Written assessments

Teacher observation

2. Understand and use the concept of

significant digits.

Teacher created materials Direct instruction Do now

Written assessments

Teacher observation

Assessments


and physical world?

Knowledge/Skills/Understanding Learning ExperiencesResources




Grades 7 - 8



4.2.D 8th Grade Advanced Algebra 257








Grades 7 - 8

Do now

Written assessments

Teacher observation


perimeter and area:

Impact of a dilation on the perimeter and are

of a two dimensional figure.


pg. 309

Various workbooks

Students investigate using

models

Do now

Written assessments

Teacher observation

Class discussion








pg. 523

Various workbooks

-Students explore the volume of

cones and pyramids by

constructing

- Solve real world problems



and physical world?

4.2.E 8th Grade Advanced Algebra 258








Grades 7 - 8




and physical world?


area of a sphere.

Various workbooks


Direct Instruction Do now

Written assessments

Teacher observation









Various workbooks


- Cooperative learning

- Investigations

Do now

Written assessments

Teacher observation



Do now

Written assessments

Teacher observation


Assessments






1. Use models and algebraic formulas to

represent and analyze sequences and series:

Explicit formulas for nth terms, sums of finite

arithmetic series, sums of finite and infinite

geometric series, develop and informal notion

of limit, use inductive reasoning to form

generalizations.


pgs. 45-48, 114, 630, 637-640, 650-

651

- Students investigate, compare

and contrast formulas: three

recursive, three graphs, three

linear equations

- Students investigate arithmetic

number sequences and find the

partial sum formula



Grades 7 - 8

Resources

A. Patterns




2. Understand and perform transformations

on commonly used functions; translations,

reflections, dilations; effects on linear and

quadratic graphs of parameter changes in

equations.


pgs. 186, 188, 202, 309

Students investigate using a

graphing calculator what

happens to the equation of a

linear function when you

translate the graph of a line

Do now

Written assessments



Resources



1. Analyze and explain the general properties

and behavior of functions of one variable,

using appropriate graphing technologies:

Slope of a line or curve, domain and range,

intercepts, maximum/minimum, estimating

roots of an equation, intersecting points as

solutions of systems of equations, rates of

change.


pgs. 121-124, 151-152

Various workbooks

- Students use motion sensor to

calculate the speed of a balloon

rocket

- Cooperative learning graphing

activities

Do now

Written assessments





Grades 7 - 8








Resources






Grades 7 - 8




- Cooperative learning graphing

activities


- Graphing calculator

Do now

Written assessments


3. Understand and compare the properties of

classes of functions, including exponential,

polynomial, rational, and trigonometric

functions; linear vs. non-linear.

Various workbooks




- Students solve real world

problems to understand finite

differences/functions using

physical representations

- Students investigate cost of

living growth exponentially

Do now

Written assessments

Teacher observation


Chapter 5










Grades 7 - 8

Assessments

Do now

Written assessments

Teacher observation












Resources

Students investigate using

exponential functions to model

real world growth and decay

scenarios


Chapter 5






Grades 7 - 8

Assessments









- Cornering the Market

investigation: students simulate

what happens when a popular

new product enters the Market

- Students investigate the

breaking point of spaghetti

- Students use recursion to

explore loan balances and

payment opt

Cooperative learning activities

using the graphing calculator

Do now

Written assessments

Teacher observation

Do now

Teacher observation

3. Use functions to model real-world

phenomena and solve problems that involve

varying quantities: Linear, quadratic,

exponential, periodic (sine, cosine), and step

functions (e.g. price of mailing a first class

letter over the past 200 years), direct and

inverse variation, absolute value, expressions,

equations and inequalities, same function can

model variety of phenomena, growth/decay

and change in the natural world, application

in mathematics, biology, and economics

(including compound interest).

4. Analyze and describe how a change in an

independent variable leads to change in a

dependent one.


Chapter 5 pgs. 38-41, 52-54, 62-

63, 67-70, 178, 180, 185, 537







Grades 7 - 8

Assessments








Investigation on the Tower of

Hanoi.

Do now

Written assessments

Teacher observation

5. Convert recursive formulas to linear or

exponential functions (e.g. Tower of Hanoi

and doubling).


Chapter 1



1. Solve simple linear inequalities. Teacher created materials

Various workbooks


- Investigations through graphing

Do now

Written assessments

Teacher observation


Various workbooks


- Investigations using the

graphing calculator

- Geometer's Sketchpad activity

Do now

Written assessments

Teacher observation

2. Evaluate and simplify expressions, add and

subtract polynomials, multiply a polynomial

by a monomial or binomial, divide a

polynomial by a monomial.


pgs. 414 - 416

Various workbooks


using the algebra tiles

- Investigations using the column

method and area method

Do now

Written assessments

Teacher observation

3. Select and use appropriate methods to solve

equations and inequalities: Linear equations -

algebraically, Quadratic equations - factoring

(when the coefficient of x2 is 1) and using the

quadratic formula, All types of equations

using graphing, computer, and graphing

calculator techniques.






Resources




D. Procedures

Grades 7 - 8








Resources




D. Procedures

Grades 7 - 8

4. Judge the meaning, utility and

reasonableness of the results of symbol

manipulations, including those carried out by

technology.


Various workbooks

Investigations using the graphing

calculator

Do now

Written assessments

Teacher observation


- Cooperative learning activites

Do now

Written assessments

Teacher observation

5. Students perform arithmetic operations on

rational expressions.


Various workbooks



Do now

Written assessments

Teacher observation

Assessments

Teacher created problems based on

real world situations


pgs. 77 - 81, Chapter 13

Do now

Written assessments

Teacher observation

Projects


- Students investigate pulse rates

and practice making box plots

- Students analyze data about

backpacks and determine how

much the typical backpack

weighs

- Graphing calculator

investigations


using the graphing calculator











central tendency.






Grades 7 - 8


conclusions?

A. Data Analysis



ResourcesKnowledge/Skills/Understanding





AssessmentsLearning Experiences



Grades 7 - 8


conclusions?

A. Data Analysis



ResourcesKnowledge/Skills/Understanding



Investigations Do now

Written assessments

Teacher observation

Do now

Written assessments

Teacher observation

5. Evaluate the use of data in real world

context.

Various workbooks Cooperative learning activities Do now

Written assessments

Teacher observation

4. Use surveys and sampling techniques to

generate data and draw conclusions about

large groups.




pg. 131

Students investigate and extend

"The Wave" activity


pg. 128



Resources


events.

Do now

Written assessments

Teacher observation






and decimals.


pg. 687

"Dieing for a Four"

investigation: students conduct

and analyze playing a board

game in which they must roll a 4

on the die before taking the first

turn



conclusions?


Do now

Written assessments

Teacher observation






Do now

Written assessments

Teacher observation


pg. 672


Various Workbooks



Grades 7 - 8




B. Probability



Resources




conclusions?




Grades 7 - 8




B. Probability



expected value.


Do now

Written assessments

Teacher observation

Class discussion


used to solve real life problems





Do now

Written assessments

Teacher observation


pg. 659


Students will play a variety of

probability games

Do now

Written assessments

Teacher observation



probabilities.


Various workbooks

Students use the multiplication

rule for independent events and

calculate the theoretical

probability of rolling a sum of 6

with 2 dice









3 class officers from a 23 student class);

Factorial notation; Concept of combinations

(e.g., number of possible delegations of 3 out

of 23 students).


pgs. 694-698, 703- 707

Various workbooks

- Investigation when students

explore the placements of jigsaw

puzzle pieces to determine

placement possibilities

-Students determine the number of

handshakes in a social setting

- Students analyze a simulated

lottery game to determine

probability of winn

Do Now

Written assessments

Teacher observation



Various workbooks


Students use Venn diagrams to

solve problems

Do Now

Written assessments

Teacher observation


conclusions?




Grades 7 - 8









conclusions?




Grades 7 - 8







different contexts.

Various workbooks



Written assessments

Teacher observation












Limitations of computers.


Various workbooks

Cooperative learning activities Do now

Written assessments

Teacher observation


conclusions?




Grades 7 - 8













Chapters 1 - 13

Various workbooks


Ongoing through all

investigations, activities and

class discussions

Do now

Written assessments

Teacher observation




problems.


Chapters 1 - 13

Various workbooks


Ongoing through all


class discussions

Do now

Written assessments

Teacher observation





Chapters 1 - 13

Various workbooks


Ongoing through all


class discussions

Do now

Written assessments

Teacher observation

Resources



Grades 7 - 8


mathematics?



A. Problem Solving








Grades 7 - 8


mathematics?



A. Problem Solving




difficulty.


Chapters 1 - 13

Various workbooks


Ongoing through all


class discussions

Do now

Written assessments

Teacher observation




Chapters 1 - 13

Various workbooks


Ongoing through all


class discussions

Do now

Written assessments

Teacher observation



Resources




Chapters 1 - 13

Various workbooks


Ongoing through all


class discussions

Do now

Written assessments

Teacher observation

Ongoing through all


class discussions

Do now

Written assessments

Teacher observation







B. Communication

Grades 7 - 8


mathematics?






Chapters 1 - 13

Various workbooks


Ongoing through all


class discussions

Do now

Written assessments

Teacher observation





Chapters 1 - 13

Various workbooks





Resources







B. Communication

Grades 7 - 8


mathematics?

Learning Experiences AssessmentsKnowledge/Skills/Understanding




Chapters 1 - 13

Various workbooks


Ongoing through all


class discussions

Do now

Written assessments

Teacher observation







Do now

Written assessments

Teacher observation




Chapters 1 - 13

Various workbooks


Ongoing through all


class discussions

Do now

Written assessments

Teacher observation

Resources


Chapters 1 - 13

Various workbooks


Ongoing through all


class discussions


mathematics?







Chapters 1 - 13

Various workbooks


Ongoing through all


class discussions

Do now

Written assessments

Teacher observation




Grades 7 - 8




C. Connections



Learning Experiences AssessmentsResources


mathematics?





Grades 7 - 8




C. Connections

Do now

Written assessments

Teacher observation





Chapters 1 - 13

Various workbooks


Ongoing through all


class discussions

Do now

Written assessments

Teacher observation




Chapters 1 - 13

Various workbooks


Ongoing through all


class discussions




Chapters 1 - 13

Various workbooks


Ongoing through all


class discussions

Do now

Written assessments

Teacher observation






Do now

Written assessments

Teacher observation




Chapters 1 - 13

Various workbooks


Ongoing through all


class discussions

Do now

Written assessments

Teacher observation

Resources


Chapters 1 - 13

Various workbooks


Ongoing through all


class discussions


mathematics?




solutions.


Chapters 1 - 13

Various workbooks


Ongoing through all


class discussions

Do now

Written assessments

Teacher observation




Grades 7 - 8




D. Reasoning





mathematics?





Grades 7 - 8




D. Reasoning

Do now

Written assessments

Teacher observation



valid.


Chapters 1 - 13

Various workbooks


Ongoing through all


class discussions

Do now

Written assessments

Teacher observation





Chapters 1 - 13

Various workbooks


Ongoing through all


class discussions






Chapters 1 - 13

Various workbooks


Ongoing through all


class discussions

Do now

Written assessments

Teacher observation





problems.


Chapters 1 - 13

Various workbooks


Ongoing through all


class discussions

Do now

Written assessments

Teacher observation










Chapters 1 - 13

Various workbooks


Ongoing through all


class discussions

Do now

Written assessments

Teacher observation

Resources



Grades 7 - 8


mathematics?



E. Representations








Grades 7 - 8


mathematics?



E. Representations





phenomena.


Chapters 1 - 13

Various workbooks


Ongoing through all


class discussions

Do now

Written assessments

Teacher observation






Do now

Written assessments

Teacher observation



and their graphs.


Chapters 1 - 13

Various workbooks


Ongoing through all


class discussions

Do now

Written assessments

Teacher observation

Resources


Chapters 1 - 13

Various workbooks


Ongoing through all


class discussions


mathematics?






Chapters 1 - 13

Various workbooks


Ongoing through all


class discussions

Do now

Written assessments

Teacher observation




Grades 7 - 8




F. Technology

4.5.F 8th Grade Advanced Algebra 285




mathematics?





Grades 7 - 8




F. Technology

Do now

Written assessments

Teacher observation




Chapters 1 - 13

Various workbooks


Ongoing through all


class discussions

Do now

Written assessments

Teacher observation




Chapters 1 - 13

Various workbooks


Ongoing through all


class discussions




Chapters 1 - 13

Various workbooks


Ongoing through all


class discussions

Do now

Written assessments

Teacher observation

4.5.F 8th Grade Advanced Algebra 286

Algebra Warm-Ups Scott McFadden

Algebra Teacher's Activities Kit Judith and Gary Robert Muschla

Skills for Success - Algebra

Jossey-Bass 2003

Applying Algebra from A to Z Margaret Thomas Instructional Fair 1999

Dale Seymour 1987




Clever CountingLappan, Fey, Fitzgerald, Friel, and

PhillipsPrentice Hall 2002

GeometryMary Lee Vivian, Tammy Bohn-

Voepel, and Margaret ThomasMcGraw Hill 2003

Title of Resource Publisher Copyright

Discovering Advanced AlgebraJerald Murdock, Ellen and Eric

KamischkeKey Curriculum Press 2004

Author(s)

8th Grade Advanced Algebra



Resources

Grades 7 - 8

2004

1986

2003

Milliken

Houghton Mifflin


Company, Inc.Theresa Kane McKell

Geometry

Algebra

Sara Freeman

Dolciani, Brown, and Cole

8th Grade Advanced Algebra Resources 287





Resources

Grades 7 - 8

Preparing for the New Jersey GEPA - Grade 8 David J. Glatzer and Joyce Glatzer Amsco School Publications, Inc. 2005



Navigating through ProbabilityShaughnessy, Barrett, Billstein,

Kranendonk, and Peck


Teachers of Mathematics, Inc.2004

80 Activities to Make Basic Algebra Easier Robert S. Graflund Walch Publishing 2001


McGraw Hill 2003


GEPA Success in Mathematics Richard Crowe Steck-Vaughn/Berrent 2000

Algebra Puzzlers Theresa Kane McKell Frank Schaffer Publications 1998

Algebra IIChad Helgeson and Margaret


AlgebraMary Lee Vivian and Margaret

Thomas

Algebra and Trigonometry 1986Houghton MifflinDolciani, Sorgenfrey, Brown, and

Kane






Resources

Grades 7 - 8



Navigating through Data AnalysisBurrill, Franklin, Godbold, and

Young



Navigating through GeometryDay, Kelley, Krussel, Lott, and

Hirstein





Exponents and Exponential Models

5 8

Quadratics

7

Linear Equations

3 8

Systems of Equations and Inequalities

3, 6 5


a Line


Discovering Advanced AlgebraDiscovering Advanced Algebra



Grades 7 - 8

Unit

Pacing Guide

Number of Blocks

12

Polynomials

7 6

3 6

Functions

4, 5 4

8th Grade Advanced Algebra Pacing Guide 290


Discovering Advanced AlgebraDiscovering Advanced Algebra



Grades 7 - 8

Unit

Pacing Guide

Number of Blocks

Radical Expressions

4 8


----- -----


----- -----

Probability and Discrete Math

Other resources 7

Rational Expressions

9 11

8th Grade Advanced Algebra Pacing Guide 291

Algebra 2 Curriculum

292

A. Number Sense




Quiz 1.1-1.2, Unit Test 1


Algebra 2

pgs. 3, 4, 7, 17, 39, 58

2. Compare and order rational and irrational

numbers.

Written classwork

Students use linear equations to

solve real life problems such as

how much fuel a car consumes

over various distances

3. Develop conjectures and informal proofs of

properties of number systems and sets of

numbers.

Algebra 2

pgs. 5, 13, 19-24, 201

AssessmentsKnowledge/Skills/Understanding Learning Experiences

Quiz 1.1-1.2, Unit Test 11. Extend understanding of the number system

to all real numbers.

Students graph real numbers on a

number line and problem solve

using algebraic models

Algebra 2

pgs. 3, 5-6, 8, 14, 49-55, 58, 60,

401

Resources





Grades 7 - 8


4.1.A 8th Grade Algebra 2 293





4. Understand and apply the laws of exponents

to simplify expressions involving numbers

raised to powers.

Algebra 2

pgs. 323-328, 388, 401-404, 480,

483

Quiz 6.1-6.3, Unit Test 6,


Direct instruction

- Students use a graphing

calculator to perform matrix

operations


- Students use matrices to find

the number of calories burned

3. Perform operations on matrices.

· Addition and subtraction

· Scalar multiplication

Algebra 2

pgs. 200-206, 207, 209, 240

Graphing calculator

Quiz 1.1-1.2, Unit Test 1Algebra 2

pgs. 5-9, 13, 19-24, 58, 201


Quiz 6.1-6.3, Quiz 6.4-6.6,

Unit Test 6, Quiz 7.1-7.2,


2. Develop, apply, and explain methods for

solving problems involving rational and

negative exponents.





Algebra 2

pgs. 323-328, 345-350, 352-357,

401-413, 415-420, 437-442, 456

Ongoing throughout

investigations

1. Extend understanding and use of operations

to real numbers and algebraic procedures.



Grades 7 - 8

Students use exponents to solve

finding the per capita GDP of

Denmark

Learning ExperiencesResources

4.1.B 8th Grade Algebra 2 294

C. Estimation








Grades 7 - 8



Resources

3. Recognize the limitations of estimation,


estimation, and determine whether the error is

within tolerance limits.

Algebra 2

pg. 103

Students employ the skill of

estimation in prediction of

outcomes when solving real-life

mathematical problems

Teacher observation

Student solutions to practice

exercises

4.1.C 8th Grade Algebra 2 295







and physical world?


and physical world?



1. Draw perspective views of 3D objects on

isometric dot paper, given 2D representations

(e.g. nets or projective views).

Algebra 2

pgs. 194-195

Students write a system of linear

equations to model real-life

situations

Teacher observation


exercises



Grades 7 - 8








Grades 7 - 8

Resources


b. Outcome of extending iterative process

indefinitely

Algebra 2

pgs. 275-276, 482

Students use real-life problem

solving (e.g. finding the balance

of an account; using an

exponential model to study and

analyze endangered species)

Teacher observation

Whole class discussions of

examples


problems

1. Generate and analyze iterative geometric

patterns.

a. Fractals (e.g. Sierpinski's Triangle)


Students apply complex numbers

to fractal geometry

Teacher observation


exercises

Algebra 2

pgs. 274-276



and physical world?







and physical world?



Grades 7 - 8




AssessmentsKnowledge/Skills/Understanding Learning ExperiencesResources

1. Use coordinates in geometry to represent

and verify properties of lines.

a. Distance between two points

Algebra 2

pgs. 589-594, 642

Students derive the distance

formula


b. Midpoint and slope of a line segment Algebra 2

pgs. 75-78, 92, 590-594, 642

Students use the distance and

midpoint formulas in finding the

diameter of a broken dish




d. Lines with the same slope are parallel Algebra 2

pgs. 77-140, 143

Students examine systems with

many or no solutions



c. Finding the intersection of two lines Algebra 2

pgs. 139-146, 186

Students use linear systems to

solve the real-life problem of

choosing the least expensive

long distance phone system






and physical world?



Grades 7 - 8




AssessmentsKnowledge/Skills/Understanding Learning ExperiencesResources

e. Lines that are perpendicular have slopes

whose product is -1

Algebra 2

pgs. 77, 79-80, 89

Students examine and analyze

real-life examples of slope (e.g.

slope as a geometrical use; slope

as a rate of change)







Do Now

Written Assessments

Teacher Observation


Algebra 2

Chapters 1 - 10




equals 12’1”).


and physical world?



Grades 7 - 8








Resources

Appropriate use throughout

lessons

Do Now

Written Assessments

Teacher Observation




miles).

Algebra 2

Chapters 1 - 10


lessons

Do Now

Written Assessments

Teacher Observation

Algebra 2

Chapters 1 - 10


lessons

4.2.D 8th Grade Algebra 2 300






and physical world?



Grades 7 - 8




Resources

Do Now

Written Assessments

Teacher Observation


lessons

Do Now

Written Assessments

Teacher Observation


lessons

Do Now

Written Assessments

Teacher Observation


lessons




5/7 = 0.714285714285...

= 0.714285

Algebra 2

Chapters 1 - 10




situation.

Algebra 2

Chapters 1 - 10



Algebra 2

Chapters 1 - 10







and physical world?



Grades 7 - 8




Resources

Do Now

Written Assessments

Teacher Observation



two.

Algebra 2

Chapters 1 - 10


lessons







Grades 7 - 8

Teacher observation

Student solutions to class

exercises and homework

problems






b. Estimation of area, perimeter, volume, and

surface area.

Algebra 2

pgs. 28, 375

Cooperative learning Teacher observation


exercises and homework

problems


and physical world?

1. Use a variety of strategies to determine

perimeter and area of plane figures and

surface area and volume of 3D figures.

a. Finding which shape has minimal (or

maximal) area, perimeter, volume, or surface

area under given conditions using graphing

calculators, dynamic geometric software,

and/or spreadsheets.

Algebra 2

pg. 375

Graphing calculator

Students use the graph of

polynomial functions to solve

real-life problems such as

maximizing the volume of a box

4.2.E 8th Grade Algebra 2 303


Conclusions drawn from

activity

Student written explanations


1. Use models and algebraic formulas to

represent and analyze sequences and series.

a. Explicit formulas for nth terms.

Algebra 2

pgs. 659, 661, 656, 681

Students evaluate and write

recursive rules for sequences




Grades 7 - 8

Resources


Assessments

Class discussion of calculator

activity



2. Develop an informal notion of limit. Teacher created materials Investigation Cooperative activity

Class discussion

Do Nows

Teacher observation


exercises

Geometer's Sketchpad Geometer's Sketchpad

Students evaluate and write

recursive rules for sequences.

c. Sums of finite and infinite geometric series.

b. Sums of finite arithmetic series. Algebra 2

pg. 675



A. Patterns







Grades 7 - 8

Resources


Assessments





A. Patterns

Cooperative work/graphic

organizers

Unit Test 11

3. Use inductive reasoning to form

generalizations.

Algebra 2

pgs. 689-690

Students use mathematical

induction to prove statements

about all positive integers







Grades 7 - 8








Resources

1. Understand relations and functions and

select, convert flexibility among, and use

various representations for them, including

equations or inequalities, tables and graphs.

Algebra 2

pgs. 19, 41-43, 67, 72, 82-88, 108-

113, 114-121, 131-132, 139-146,

156-162, 249-255, 300-302, 306-

312, 314, 316, 331-332, 373-388,

390, 466, 475, 524, 601-608, 609-

614, 615-620, 643-644, 595-596

Graphing calculator

- Students use piecewise

functions to model real-life

quantities

- Students graph and solve

systems of linear equations and

linear inequalities

- Students write quadratic

functions given characteristics of

their graphs

- Students analyze the graph of a

polynomial function

- Students graph and write

equations of circles


equations of ellipses


equations of hyperbolas

Unit Test 1


Quiz 3.1-3.2, Quiz 3.4, Unit

Test 3

Quiz 5.1-5.3,Unit Test 5



Quiz 10.1-10.3, Quiz 10.4-

10.5, Unit Test 10







Grades 7 - 8








Resources

2. Analyze and explain the general properties

and behavior of functions of one variable,

using appropriate graphing technologies.

a. Slope of a line or curve

Algebra 2

pgs. 75-81

Students find slopes of lines and

classify parallel and

perpendicular lines

Teacher observation


problems

b. Domain and range Algebra 2

pg. 453

Students use a graphing

calculator to find and draw

statistical graphs (e.g. NBA foul

shooting percentages).

Do Now

Teacher observation

Classwork activities







Grades 7 - 8








Resources

c. Intercepts Graphing calculator Students use the graphing

calculator to find the real

solution to equations (e.g.

quadratic equations, polynomial

equations, an equation with an

extraneous solution)

Teacher observation

Solutions to classwork and

homework exercises

d. Continuity Algebra 2

pgs. 271, 372, 439

Direct instruction Teacher observation

Solutions to classwork and

homework exercises

e. Maximum/minimum Algebra 2

pgs. 121, 372, 546

Graphing calculator

- Students use technology to find

quadratic models

- Students examine and analyze

turning points corresponding to

local minimum and maximum

values

- Students use rational functions

to find a local minimum

Do Now

Teacher observation


exercises







Grades 7 - 8








Resources

Students find and use the

discriminant of quadratic

equations

Student oral and written

solutions

3. Understand and perform transformations

on commonly used functions.

· Effects on linear and quadratic graphs of

parameter changes in equations

Algebra 2

pg. 293

i. Rate of change Algebra 2

pgs. 90

Graphing calculator


calculator to graph equations of

the form y=f(x)

Teacher observation

Student graphs

f. Estimating roots of equations. Algebra 2

pgs. 252, 290, 308, 374-375, 549

Graphing calculator

- Students use technology to

approximate zeros

- Students find the rational

zeroes of a polynomial function


g. Intersecting points as solutions of systems of

equations

Algebra 2

pgs. 146, 149, 154, 300

Graphing calculator Teacher observation

Student graphs







Grades 7 - 8








Resources

4. Understand and compare the properties of

classes of functions, including exponential,

polynomial, rational, and trigonometric

functions.

a. Linear vs. non-linear

Algebra 2

pgs. 19-22, 329-335, 465-471,

481-485, 509-516, 524-526, 595

Graphing calculator

- Students evaluate/graph

polynomial functions

- Students graph and use

exponential growth functions

- Students evaluate and graph

logistic growth functions


equations of parabolas




Direct instruction Teacher observation


examples

c. Increasing/decreasing on an interval Algebra 2

pgs. 374, 518

Graphing calculator activity Do Nows

Teacher observation

Students solutions to practice

exercises

b. Symmetry Algebra 2

pgs. 249, 595-596



Quiz 2.4-2.5

Unit Test 2

Quiz 9.1-9.3

Unit Test 9

Students use absolute value in

real-life situations (e.g. Path of a

golf ball; graph functions of the

path of sunlight)


Unit Test 1

Unit Test 2



Grades 7 - 8


C. Modeling





b. Direct and inverse variation

1. Use functions to model real-world

phenomena and solve problems that involve

varying quantities.

a. Linear, quadratic, exponential, periodic

(sine and cosine), and step functions (e.g.,

price of mailing a first class letter over the

past 200 years)

Algebra 2

pgs. 70, 115-121, 266, 361, 468-

471, 510, 512

Graphing calculator

Algebra 2

pgs. 94, 97-98, 534-539

c. Absolute value Algebra 2

pgs. 52-55, 121, 126-127

Graphing calculator

Resources

- Exploration


Unit Test 2

Quiz 8.1-8.3

Unit Test 8

Assessments

- Students write linear equations

- Students write direct variation

equations by analyzing real-life

mathematical models






Grades 7 - 8


C. Modeling






Students examine and analyze

models of exponential decay.

(e.g. Descending value of an

automobile.) Students analyze

models with power functions

Quiz 8.1-8.3

Unit Test 8

- Exploration


e. Same function can model a variety of

phenomena

Algebra 2

pgs. 284, 288, 294, 297, 300, 303,

519, 521

f. Growth/decay and change in the natural

world

Text pages: 325, 467-471, 476-479,

482, 509-516, 519

Graphing calculator

d. Expressions, equations and inequalities Algebra 2

pgs. 21, 27, 44, 46-47, 93, 110,

112-113, 158, 165, 169, 172, 294-

297, 300, 302-305, 325

- Exploration


Do Nows

Class discussion of examples

and exploration

Teacher observation

Unit Test 1, Unit Test 2

Quiz 3.3-3.4

Unit Test 3, Unit Test 5






Grades 7 - 8


C. Modeling






g. Applications in mathematics, biology, and

economics (including compound interest)

Algebra 2

pgs. 21, 24, 28, 78, 101, 254, 275,

277-278, 288, 325, 332, 391, 399,

410, 413, 417, 419, 433, 436, 468-

471, 482, 497, 521-522, 527, 535,

551, 559, 563, 572

Students solve real-life models

mathematically (e.g. Number of

households owning a VCR; US

GDP and logistic growth; focal

lengths)

Teacher observation

Student written work and

solutions to examples

Students evaluate functions in

real-life models (E.g. Domain

and range of the Piccard/Jones

balloon flight; Boston Marathon

finishers as related to age;

domain and range examining cap

sizes)

2. Analyze and describe how a change in an

independent variable leads to change in a

dependent one.

Teacher observation

Oral and written explanations

Algebra 2

pgs. 69-73



c. Divide a polynomial by a monomial Algebra 2

pgs. 556, 559

Direct instruction Quiz 9.4-9.6

Unit Test 9

b. Multiply a polynomial by a monomial or

binomial

Algebra 2

pgs. 251, 253-254, 338-343, 389


Unit Test 5

Quiz 6.1-6.3

Unit Test 6

Resources




D. Procedures

Grades 7 - 8






1. Evaluate and simplify expressions.

a. Add and subtract polynomials

Algebra 2

pgs. 338, 340-343, 389

Students use polynomials in real-

life situations (E.g. Finding net

farm income; finding total

revenue from the sale of

softbound books; ratio of heat

release to size of a long-distance

runner; value of gold mined in a

year)

Quiz 6.1-6.3

Unit Test 6



Resources




D. Procedures

Grades 7 - 8







- Exploration



Quiz 5.1-5.3, Quiz 5.4-5.6,

Unit Test 5



Quiz 10.1-10.3, Quiz 10.4-

10.5, Unit Test 10

b. Quadratic equations - factoring (when the

coefficient of x^2 is 1) and using the quadratic

formula

Algebra 2

pgs. 256-263, 281-283, 291-298,

314-316

Students factor with: special

patterns; monomials first;

finding zeros of a quadratic

function; solving quadratic

inequalities.

Quiz 5.1-5.3

Quiz 5.4-5.6

Unit Test 5

2. Select and use appropriate methods to solve

equations and inequalities.

a. Linear equations - algebraically

Algebra 2

pgs. 5, 19-24, 41-47, 139, 177-

183, 186-188, 201


Unit Test 1

Quiz 3.1-3.2

Unit Test 3

c. All types of equations using graphing,

computer, and graphing calculator techniques

Algebra 2

pgs. 69-70, 82-88, 131, 139-146,

170-176, 186, 188, 249-255, 291,

306-316, 331-332, 373-390, 466,

475, 524, 595-600, 601-608, 609-

614, 615-620, 643

Graphing calculator



Resources




D. Procedures

Grades 7 - 8






Teacher observation


3. Judge the meaning, utility, and

reasonableness of the results of symbol

manipulations, including those carried out by

technology.

Algebra 2

pgs. 25, 146, 149, 259, 271, 300,

360, 368, 372, 439

Incorporated in all real-life

models



b. Correlation coefficient Algebra 2

pgs. 100 - 105

Direct Instruction Quiz 2.4-2.5

Unit Test 2



A. Data Analysis


Assessments

1.Estimate or determine lines of best fit (or

curves of best fit if appropriate) with

technology, and use them to interpolate within

the range of data.

Algebra 2

pgs. 103, 107, 307-308, 311

Exploration Teacher observation

Discussion of exploration

Resources



2. Analyze data using technology, and use

statistical terminology to describe conclusions.

a. Measures of dispersion: variance, standard

deviation, outliers

Algebra 2

pgs. 453-454

Graphing calculator


calculator to find statistics and

draw statistical graphs (e.g. The

number of calories in a

sandwich)

Teacher observation



conclusions?







A. Data Analysis






conclusions?



c. Normal distribution (e.g., approximately

95% of the sample lies between two standard

deviations on either side of the mean)

Algebra 2

pg. 453-454

Exploration Teacher observation





2. Use concepts and formulas of area to

calculate geometric probabilities.



and computers) and theoretical models, and

solve problems using these models.

Various workbooks Cooperative learning

Algebra 2

pgs. 718 - 757


1. Calculate the expected value of a

probability based game, given the

probabilities and payoffs of the various

outcomes, and determine whether the game is

fair.

Algebra 2

pgs. 734 - 738, 708 - 709, 715 -

716, 724 - 725

Direct instruction Unit 12 Tests



Grades 7 - 8


B. Probability


Teacher observation



conclusions?


Students use area to find

probability

Unit 12 Tests







Grades 7 - 8


B. Probability



conclusions?


4. Determine probabilities in complex

situations.

a. Conditional events

Algebra 2

pgs. 732-733, 736



probabilities.

Algebra 2

pgs. 753-754

c. Dependent and independent events

b. Complementary events Algebra 2

pgs. 726

Algebra 2

pg. 736

Students explore randomly

selecting two cards from a

standard 52 count deck

Unit 12 Tests

Exploration Unit 12 Tests

Unit 12 TestsExploration

Unit 12 TestsStudents use two six-sided dice

to find the probability of a given

event







Grades 7 - 8


B. Probability



conclusions?


6. Understand and use the "law of numbers"

(that experimental results tend to approach

theoretical probabilities after a large number

of trials).

Algebra 2

pgs. 717, 757

Unit 12 TestsStudents use length (video

cassette recording-probability of

over-recording)




Direct instruction Unit 12 Test



Grades 7 - 8




Algebra 2

pgs. 701-752

Real world problem solving Unit 12 Test


conclusions?


1. Calculate combinations with replacement

and without replacement.

Algebra 2

pgs. 730-736


2. Apply the multiplication rule of counting in

complex situations, recognize the difference

between situations with replacement and

without replacement, and recognize the

difference between ordered and unordered

counting situations.

Algebra 2

pgs. 701-707, 756

Students use permutations to

count the number of ways an

event happens

Unit 12 Test

3. Justify solutions to counting problems.






Grades 7 - 8





conclusions?



Students use the binomial

theorem to discover the

relationship between Pascal's

triangle and the coefficients of a

binomial expansion

Unit 12 Test4. Recognize and explain relationships

involving combinations and Pascal's Triangle,

and apply those methods to situations

involving probability.

Algebra 2

pg. 701




- Exploration


Included in probability2. Explore strategies for making fair decisions.

a. Combining individual preferences into a

group decision (e.g., determining winner of a

election or selection process)

Various workbooks



Grades 7 - 8






thinking to represent and solve practical

problems.

· Circuits that include every edge in a graph

· Circuits that include every vertex in a graph

Various workbooks - Exploration


Teacher made tests


conclusions?







Grades 7 - 8






conclusions?


b. Determining how many Student Council

representatives each class gets when the

classes have unequal sizes (apportionment)

Teacher created resources Exploration Do Now







Grades 7 - 8


mathematics?



A. Problem Solving



Assessments



Algebra 2

pgs. 12, 21, 27, 33-39, 52, 60, 85,

93, 110, 141, 151, 258, 355, 361,

375, 533, 542

Incorporated in all mathematical

content.

Teacher observation


ResourcesKnowledge/Skills/Understanding Learning Experiences


and in other contexts.

a. Open-ended problems

Algebra 2

pgs. 46, 72, 105, 113, 154, 206,

269, 328


content

b. Non-routine problems Algebra 2

pgs. 170-176, 177-183, 229, 254-

255, 272, 279-280, 289, 312, 412,

533


content

c. Problems with multiple solutions

Teacher observation

Student written explanations

Unit Test 3

Quiz 5.5-5.6

Unit Test 5

Algebra 2

pgs. 140, 150, 179, 250-254, 272,

277-278, 550


content





Grades 7 - 8


mathematics?



A. Problem Solving




d. Problems that can be solved in several ways Incorporated in all mathematical

content




problems.

Algebra 2

pgs. 12, 21, 27, 33-39, 52, 60, 85,

93, 110, 141, 151, 258, 355, 361,

375, 533, 542


content.

Students use of problem

solving strategies in oral and

written work

Algebra 2

pgs. 82-83, 91, 148-154, 177-183,

186-187, 216-220, 230-235, 237-

238, 241-242, 282-288, 290-297,

353, 373

Quiz 2.1-2.3, Quiz 2.4-2.5,

Unit Test 2, Quiz 3.1-3.2,

Unit Test 3, Unit Test 4, Quiz

5.4-5.6, Unit Test 5


difficulty.

Algebra 2

pgs. Found throughout text. See,

for example, 46, 72, 105, 113, 154,

170-176, 177-183, 206, 229, 237-

238, 254-255, 269, 272, 279-280,

289, 312, 328, 412, 533, 639


content

Teacher observation


exercises





Grades 7 - 8


mathematics?



A. Problem Solving






Algebra 2

pgs. 2, 66, 138, 198, 248, 322,

400, 464, 532, 588


content

Continual student to student

feedback

Teacher to student feedback

Student self reflection





Grades 7 - 8

b. Discussion, listening, and questioning Algebra 2

pgs. 1, 49, 65, 82, 108, 137, 147,

195, 197, 222, 281, 321, 345, 379,

397


content


content



Assessments





mathematics?



mathematical thinking.

a. Reading and writing

Algebra 2

pgs. Found throughout the text.

See, for example, 2, 57, 129, 138,

185, 198, 239, 248, 313, 322, 387,

400, 421, 455, 464, 523, 532, 575,

588, 641

Teacher observation based on

whole class and small group

discussions

Student explanation and

mathematical reasoning in

written work

Resources





Grades 7 - 8



Assessments





mathematics?





Algebra 2

pgs. 1, 2, 47, 49, 57, 63, 65, 72,

82, 108, 129, 137, 138, 145, 147,

153, 185, 191, 195, 197, 198, 206,

222, 239, 248, 281, 305, 313, 321,

322, 345, 379, 387, 393, 397, 399,

400, 406, 421, 455, 463-465, 473,

507, 517, 523, 531-533, 560, 575,


content

Clarity of mathematical logic

in student oral and written

work

Teacher observation



Algebra 2

pgs. 153, 206, 266, 268, 305, 312,

350, 383


content

Student to student oral and

written work

Teacher observation





Grades 7 - 8



Assessments





mathematics?




Algebra 2

pgs. 6, 13, 21,28, 36, 44, 70, 78,

85, 94, 102, 110, 141, 151, 175,

180, 217, 226, 232, 259, 266, 276,

294, 302, 308, 347, 361, 368, 375,

386, 403, 410, 417, 425, 433, 440,

448, 468, 489, 495, 504, 512, 557,

570


content

Student use of mathematical

language in oral and written

work

Teacher observation



Integrated throughout problem

solving examples

Resources


mathematics?







Grades 7 - 8





Algebra 2

Chapters 1 - 10


solving examples


Do Nows

Teacher observation


C. Connections

Student written and oral work

Assessments



numbers, algebra, and geometry).



Algebra 2

pgs. 82-82, 91, 145, 213, 282-288,

290-297, 353


solving examples

Teacher observation


explanations

Algebra 2

pgs. 153, 206, 266, 268, 305, 312,

350, 383



Resources


mathematics?







Grades 7 - 8


C. Connections

Assessments

Art, music, economics, etc.,

history incorporated throughout

mathematical models, examples

and problem solving

Teacher observation; Student

use of abstract math models

to solve "science," "social

studies," "art" and "music"

models

Teacher observation

Class discussions



Algebra 2

pgs. 9, 16, 80, 87-88, 93, 105,

127, 133, 151, 161, 172-173, 183,

204, 212, 217, 220, 235, 254, 262,

263, 266, 268, 279, 284, 288, 296,

308, 327, 342, 347, 355, 405, 410,

412, 414, 428, 433, 435, 450, 451,

452, 459, 471, 472, 483, 495, 506, 5


solving examples



Algebra 2

pgs. 40, 89, 169, 236, 270, 351,

444, 499, 574



Resources


mathematics?







Grades 7 - 8


C. Connections

Assessments




Algebra 2

pgs. 57, 129, 185, 239, 313, 387,

455, 523, 575, 641


solving examples

Teacher observation


explanations




mathematics?

Teacher observation; Oral

and written explanations



content



Grades 7 - 8






content





Algebra 2

pgs. 396-397, 439, 504


content

Teacher observation; Student

oral and written work



solutions.

Algebra 2

pg. 439



Algebra 2

Chapters 1 - 10




Algebra 2

pgs. 101, 379, 439, 568


content






mathematics?




Grades 7 - 8






content


conjectures.

a. Counterexamples as a means of disproving

conjectures

Algebra 2

pgs. 565, 622


content

Teacher observation

Student oral and written work



valid.

Algebra 2

pg. 19


content



Teacher observation

Student oral and written work

b. Verifying conjectures using informal

reasoning or proofs

Algebra 2

pgs. 235, 439



Algebra 2

pgs. 25, 345


content


record, and communicate mathematical ideas.

a. Concrete representations (e.g., base-ten

blocks or algebra tiles)

c. Symbolic representations (e.g., a formula)

b. Pictorial representations (e.g., diagrams,

charts, or tables)

Algebra 2

pgs. 24, 28-29, 72, 266, 291, 440,

468, 482, 494, 589-590, 642


mathematics?





Algebra 2

pgs. 49, 99, 281, 421, 533, 622


content

Teacher observation


exercises

E. Representations



content

Teacher observation


exercises

Teacher observation


exercises



Grades 7 - 8




mathematics?





E. Representations




Grades 7 - 8

Algebra 2

pgs. 291, 304, 239, 448, 453, 473


content

Teacher observation


exercises

Algebra 2

pgs. 82-88, 91, 139-146, 148-154,

235


content

d. Graphical representations (e.g., a line

graph)

Teacher observation


exercises



phenomena.

Algebra 2

pgs. 25, 49, 99, 220, 281, 294,

297, 345, 421, 512, 533, 622


content

Teacher observation


exercises



problems.





Grades 7 - 8


mathematics?



F. Technology






Algebra 2

pgs. 25, 48, 90, 107, 121, 146,

154, 176, 207, 271, 290, 308, 337,

372, 382, 453-454, 500, 510, 546,

561, 608


content

Do Now

Written Assessments

Teacher Observation

Resources




Algebra 2

pgs. 18, 172, 234, 336


content

Do Now

Written Assessments

Teacher Observation



and their graphs.

Algebra 2

pgs. 90, 121, 146, 231, 254, 259,

265, 271, 304, 331, 336, 439, 482,

500, 596

Graphing calculator


content

Do Now

Written Assessments

Teacher Observation

4.5.F 8th Grade Algebra 2 339




Grades 7 - 8


mathematics?



F. Technology






Algebra 2

pgs. 48, 176, 224, 231-232, 234,

259, 265, 271, 283, 290, 372, 374-

376, 482, 546, 561, 563, 566, 569-

570, 608

Graphing calculator


content

Do Now

Written Assessments

Teacher Observation



Algebra 2

Chapters 1 - 10


content

Do Now

Written Assessments

Teacher Observation

4.5.F 8th Grade Algebra 2 340

Algebra Dolciani, Brown, and Cole Houghton Mifflin 1986

Geometry Sara Freeman Milliken 2004

Algebra Teacher's Activities Kit Judith and Gary Robert Muschla Jossey-Bass 2003

Algebra Warm-Ups Scott McFadden Dale Seymour 1987


Applying Algebra from A to Z Margaret Thomas Instructional Fair 1999



GeometryMary Lee Vivian, Tammy Bohn-

Voepel, and Margaret ThomasMcGraw Hill 2003

Clever CountingLappan, Fey, Fitzgerald, Friel,

and PhillipsPrentice Hall 2002

Algebra 2Ron Larson, Laurie Boswell,

Timothy Kanold, and Lee StiffMcDougall Littell 2001


8th Grade Algebra 2



Resources

Grades 7 - 8

Skills for Success - Algebra Theresa Kane McKellCarson-Dellosa Publishing

Company, Inc.2003

8th Grade Algebra 2 Resources 341


8th Grade Algebra 2



Resources

Grades 7 - 8

Algebra and Trigonometry

Algebra Puzzlers

Algebra

Dolciani, Sorgenfrey, Brown,

and Kane

Theresa Kane McKell

Mary Lee Vivian and Margaret

Thomas

Houghton Mifflin


McGraw Hill

1986

1998

2003

GEPA Success in Mathematics Richard Crowe Steck-Vaughn/Berrent 2000

Algebra IIChad Helgeson and Margaret




Navigating through ProbabilityShaughnessy, Barrett, Billstein,

Kranendonk, and Peck










8th Grade Algebra 2



Resources

Grades 7 - 8

Navigating through Data AnalysisBurrill, Franklin, Godbold, and

Young



Navigating through GeometryDay, Kelley, Krussel, Lott, and

Hirstein





Joke Worksheets for Algebra 2 and Precalculus Christine A. Koers NASCO 2002

Algebra 2 Word Problems Anita Harnadek The Critical Thinking Company 2001

Algebra 2Barbara Sandall and Melfried

OlsonMark Twain Media 2005

Algebra 2 Sara Freeman Milliken 2002


Powers, Roots, and Radicals7

5

9

Polynomials and Polynomial Function6 10


Grades 7 - 8

8th Grade Algebra 2

2

4

Quadratic Functions


4

Algebra 2

Pacing Guide

Matrices


Equations and Inequalities1 6

5

----- -----

Systems of Equations and Inequalities3


10

Linear Equations and Functions6

8th Grade Algebra 2 Pacing Guide 344


Grades 7 - 8

8th Grade Algebra 2


Algebra 2

Pacing Guide


9

Quadratic Relations and Conic Sections10 8

Exponential and Logarithmic Functions8 9

Rational Equations and Functions


----- -----

7

8th Grade Algebra 2 Pacing Guide 345

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