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Mathematics – Grade 8Unit of Study: Number, Operations, and Algebraic Thinking

First Grading Period – Week 1- 2 (8 days) CURRICULUM OVERVIEWBig Idea Unit Rationale

Knowing how to use different operations, and the correct order of those operations, makes it possible for students to solve many problems with real world applications. Understanding the relationships between tables, graphs, and equations allows students to apply mathematics to everyday situations.

Students should understand that: choosing the appropriate operation is vital to solving real world problems. using graphs, tables, and equations will allow for making predictions and solving

problems such as comparing purchase prices. data can be represented in a variety of forms (table, graph, equation, and verbal

description) and some forms provide a better understanding of the data than others.Essential Questions Guiding Questions

What would happen if there was not an agreed upon order of operations to use in solving problems?

How can using tables, graphs, and equations help you make good decisions about everyday situations?

√How do you know what operation to use in solving a problem?

√How can tables, graphs, and equations help in solving problems?

√How can you get the same information from a table, graph, or equation?

TEKS TEKS Specificity - Intended Outcome

Con

cept

s

8.2 Number, operations, and quantitative reasoning. The student selects and uses appropriate operations to solve problems and justify solutions. The student is expected to:

8.2(B) use appropriate operations to solve problems involving rational numbers in problem situations.

8.4 Patterns, relationships, and algebraic thinking. The student makes connections among various representations of a numerical relationship. The student is expected to:

8.4(A) generate a different representation of data given another representation of data (such as a table, graph, equation, or verbal description)

8.5 Patterns, relationships, and algebraic thinking. The student uses graphs, tables, and algebraic representations to make predictions, and solve problems. The student is expected to:

8.5(A) predict, find, and justify solutions to application problems using appropriate tables, graphs, and algebraic equations

” I CAN” statements highlighted in yellow and italicized should be displayed for students.

I can: choose the right operation to solve problems (8.2B). solve problems using tables, graphs, and equations (8.5A). make a table from a graph or an equation (8.4A).

8.14 Underlying processes and mathematical tools. The student applies Grade 8 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. The student is expected to:

(A) identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics

(B) use a problem solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness

I can: work problems that apply to everyday situations (8.14A). solve problems (8.14B). use the Guess and Check Strategy to solve problems (8.14C). explain mathematical ideas using words, pictures, objects, and symbols (8.15A). explain my answers to problems (8.16B).

SAISD © 2010-11 – First Grading Period Mathematics Grade 8 of 43

Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.

Skill

s(C) select and develop an appropriate problem-solving strategy from a variety of

different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem.8.15 Underlying processes and mathematical tools. The student communicates

about Grade 8 mathematics through informal and mathematical language, representations, and models. The student is expected to:

(A) communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebra mathematical models.8.16 Underlying processes and mathematical tools. The student uses logical

reasoning to make conjectures and verify conclusions. The student is expected to:

(B) validate his/her conclusions using mathematical properties and relationships. ELPS

1. Learning Strategies(C) use strategic learning techniques such as concept mapping, drawing, memorizing, comparing, contrasting, and reviewing to acquire basic and grade-level vocabulary;(E) internalize new basic and academic language by using and reusing it in meaningful ways in speaking and writing activities that build concept and language attainment;

2. Listening(C) learn new language structures, expressions, and basic and academic vocabulary heard during classroom instruction and interactions;(D) monitor understanding of spoken language during classroom instruction and interactions and seek clarification as needed;

3. Speaking(D) speak using grade-level content area vocabulary in context to internalize new English words and build academic language proficiency;(E) share information in cooperative learning interactions;

4. Reading(C) develop basic sight vocabulary, derive meaning of environmental print, and comprehend English vocabulary and language structures used routinely in written classroom materials(K) demonstrate English comprehension and expand reading skills by employing analytical skills such as evaluating written information and performing critical analyses commensurate with content area and grade-level needs

5. Writing(B) write using newly acquired basic vocabulary and content-based grade-level vocabulary;(G) narrate, describe, and explain with increasing specificity and detail to fulfill content area writing needs as more English is acquired

Evidence of LearningAt least 80% of the time, students will demonstrate on paper that they can:1. use addition, subtraction, multiplication and division to solve problems involving rational numbers.2. represent numeric data in a variety of forms including tables, graphs, algebraic expressions and written or oral descriptions.3. use tables, graphs, and/or equations to predict, find, and justify solutions to problems.4. use the Guess and Check Strategy to solve problems.



Essential Pre-Requisite SkillsGrade 6 use addition and subtraction to solve problems involving fractions and decimals

(6.2B) use multiplication and division of whole numbers to solve problems including

situations involving equivalent ratios and rates (6.2C) use order of operations to simplify whole number expressions (without exponents) in

problem solving situations (6.2D) use tables of data to generate formulas representing relationships involving

perimeter, area, volume of a rectangular prism, etc. (6.4B) formulate equations from problem situations described by linear relationships (6.5A)

Grade 7 use addition, subtraction, multiplication, and division to solve problems involving

fractions and decimals (7.2B) simplify numerical expressions involving order of operations and exponents (7.2E) generate formulas involving unit conversions, perimeter, area, circumference,

volume, and scaling (7.4A)



Mathematics – Grade 8Unit of Study: Number, Operations, and Algebraic Thinking

First Grading Period – Week 1- 2 (8 days) CURRICULUM GUIDE

The Teaching and Learning PlanInstructional Model & Teacher Directions

The teacher will…Assessment for Learning

so students can…. ResourcesGo over beginning of Year Procedures and expectations to include course syllabus.Have students draw a clock in their journals and label 12:00, 3:00, 6:00 and 9:00. Have students find a person to be their working partner throughout the grading period for each time, beginning with 12:00. Students should have four different partners.Days 1-8:Step 1: Problem Solving: Begin days 1-8 with problem solving for 10 minutes per day. Use the following experiences from the Lane County Mathematics Project. The identified problems will be teacher directed for the purposes of building a background in problem solving strategies.

Problem Solving Strategy: Day 1: Students write in journals (see lesson for Day 1 below) Day 2: Guess and Check: Week 1 – Day 1 Day 3: Guess and Check: Week 1 – Day 2 Day 4: Guess and Check: Week 1 – Day 3 Day 5: Guess and Check: Week 1 – Day 4 Day 6: Guess and Check: Week 1 – Day 5 Day 7: Students create their own Guess and Check Problems Day 8: Students create their own Guess and Check Problems

Step 1: Problem Solving use math journals to write about their

method/s of problem solving – what works for them (Day 1).

use the strategies of Guessing and Checking and Looking for a Pattern to solve problems (8.14C) (Days 2-6).

use math journals to write their own problems that can be solved using the Guess and Check Strategy.

solve other students’ problems (Days 7&8).

Step 1: Problem Solving Lane County Mathematics Project

– Guess and Check (Grade 8) – pp. 7-10

Student math journals – students need a spiral notebook for daily journal entries.

Collect math journals at least one time/week to respond to students problem solving strategies (graded assignment at least once per week)

Day 1: Mathematics Autobiography Prepare a short “Mathematics Autobiography” of your experience with

mathematics. Read your autobiography to the class as a way of introduction and to model for students what they will be writing in their journals. This journal writing experience will provide you with a general overview of your class and students’ attitudes and experiences about mathematics.

Day 1: Mathematics Autobiography

Students will write their personal mathematics autobiography in their math journals.

Day 1: Mathematics Autobiography teacher prepared autobiography student journals

Day 2: Animated Math- www.classzone.com Step 1: Problem Solving (see beginning of Unit)Step 2: Interactive Learning

You will need a laptop and LCD projector for this activity. Once laptop and LCD projector are connected, launch Internet Explorer. Type

the web address: www.classzone.com Locate Chapter 1 and Animated Math Activity: Order of Operations. Review order of operations by engaging the students in the Animated Math

Activity – Chapter 1 – Order of Operations

Step 2: Interactive Learning Students will create and evaluate

expressions using appropriate order of operations by interacting with the animated math display. Students will solve problems presented in Animated Math Activity in their journals or notebooks.

Step 2: Interactive Learningwww.classzone.com



http://www.classzone.com/



Step 3: Visual Learning and Practice As the students follow along in the book, the teacher will read the problem

“Visiting an Aquarium” pg. 8. Use Think-Pair-Share Activity to guide students to solving problem on pg.8.

As students work, the teacher will circulate and notice the various ways that students are solving the problem.

When the students have found a solution to the problem, invite 2 or 3 different student pairs to share their strategy and solution. Ask for other solutions and/or strategies that may be different from what was presented.

Direct student’s attention to Example 3 – page 9 – “Using a Verbal Model.” Make sure that the students understand the relationship between the words and the numbers as they substitute the values.

Ask the students to write a Verbal Model for question #7 p. 9, and to find the solution.

Ask all students to complete problem 38 – page 11. Assign problem 39, page 11, to those students who finish quickly and

understand the previous problems. Create small groups of students (4-5 per group) who need additional assistance and take time to provide assistance for each group.

Step 3: Visual Learning and Practice Students will use appropriate operations to

solve problems (8.2B). Students communicate mathematical ideas

and language as demonstrated by the way they explain their solutions (8.15A).

Students will work together with partners solving the problems and talking about the methods which they chose to use.

Step 3: Visual Learning and Practice McDougal Littell – pp. 8, 9, 11

Step 4: Differentiate/AssessmentOn Level Learners:

Assign problem 40 (page 11) and problems 9, 10, and 11 (page 12). Provide calculators for students who have this stated as either a 504 or IEP

Accommodation. Write the Essential Questions below on board for the “writing prompt”. Have

each student spend a few minutes writing their responses to each question in their Journal. Make sure to collect Journals and provide feedback.

√Ask students how they know what operation to use when solving problems?

What would happen if there was not an agreed upon order of operations to use in solving problems?Struggling Learners:

McDougal Littell Course 3 Activity Generator- Investigation 1.2-Activity A. The teacher should work with small groups of students as they evaluate the steps that need to be followed in order to obtain the correct value.

Advanced Learners: McDougal Littell Course 3 Activity Generator – Investigation 1.2 – Activity C.

Students should work with a partner to complete the activity.

Suggested Homework/Independent Practice: Page 11 problems 36, 41, 42, 43, 44; computational practice problems 13 – 18 page 10.

Step 4: Differentiate/Assessment Students will use appropriate operations to

solve problems (8.2B). Students will communicate mathematical

ideas and language (8.15A).

Step 4: Differentiate/Assessment McDougal Littell – pages 11,

12(graded assignment) McDougal Littell Course 3 Activity

Generator

Days 3 & 4: Variables and Patterns; Investigation 1 This lesson will take 2 days to complete.Day 3Step 1: Problem Solving (see beginning of Unit)Step 2: Interactive learning:

Ask the students to read silently, pages 5&6 of Investigation 1. Have students summarize what they read by writing their thoughts in their journal.

Step 2: Interactive Learning

Students will answer the questions in their journals to activate thinking.

Students will share their responses.

Step 2 Interactive Learning Connected Mathematics Project

(CMP) Variables and Patterns Investigation 1 pp 5-14 Student math journals



http://www.saisd.net/dept/math/index2.php?option=com_docman&task=doc_view&gid=270&Itemid=9

Students will write in their math journals to respond to “Think about this!” questions on page 6.

Ask for volunteers to share their journal entries, by reading to the whole group.Step 3: Visual Learning and Practice:

Groups of 4- Have students stand in one line. Allow each student to draw a card from a regular deck (arrange cards in advance and label tables). Student takes card to labeled table, to form groups of 4. Students will complete problem 1.1, in groups of 4 – gathering information about the number of jumping jacks they can do every 10 seconds. Each group will assign roles: time keeper, recorder, materials manager, and task manager.

Once activity is complete, have students complete problem 1.1 Follow-up questions, by writing responses in journals.

Review the process of making a graph – page 7 (1.2) Before students leave class, ask the following question:

√How can tables, graphs, and equations help in solving problems?

Suggested Homework: Students use data collected to make graph (1.2 A)

Step 3: Visual Learning and Practice:

Students will work in groups of 4 to create tables to represent the data collected (8.4A).

Students will create a written explanation of the data represented in the table (8.4A).

Students will create a graph from data in table (8.4A).

Step 3 Visual Learning and Practice Connected Mathematics Project


Other materials needed: chart paper stop watches markers Deck of Cards

Day 4Step 1: Problem Solving (see beginning of Unit)Step 3: Visual Learning and Practice (continued)

Students will respond to 1.2B in the math journals. Discuss as a class the relationship between the number of jumping jacks and time.

Display on chart paper a graph with the corresponding table. Answer the question in 1.2 follow-up. Students should answer the problems individually prior to having a class discussion.

Step 3: Visual Learning and Practice (cont.) Students will work with a partner to generate

a graph given the data in table form (8.4A). Students will communicate mathematical

ideas by explaining the relationships between the tables and graphs (8.15A).

Step 3 Visual Learning and Practice Connected Mathematics Project


Step 4: Differentiate/Assessment:On Level Learners:

ACE questions # 2, 3, 5, 6 (students choose 2 of the 4) Students could be given extra credit if they choose to complete all 4 Students should work with a partner to complete the problems Teacher can now work with individuals who are having a difficult time creating

the graphs and/or tables. Prior to dismissing the students, have students answer the following question in

their journal:

√ How can tables, graphs, and equations help in solving problems?


Struggling Learners: Work with small groups of students on any of the unassigned ACE questions in

the Connected Mathematics Variables and Patterns book.

Advanced Learners:

Step 4: Differentiate/Assessment Students will apply mathematics to everyday

experiences as they answer the ACE questions (8.14A).

Students are generating various representations of data (8.4A).

Step 4 Differentiate/Assessment Connected Mathematics Project

(CMP) Variables and Patterns Investigation 1 pp 5-14 Ace Questions (graded

assignment) Student math journals



Connected Mathematics Variables and Patterns – pages 17 and 35. Students will work together in small groups (3-4) to answer the questions posed in Mathematical Reflections.

Suggested Homework: ACE questions 7&8. (graded assignment)Day 5& 6 Variables and Patterns Investigation 3 This lesson will take 2 days to complete.Day 5Step 1: Problem Solving (see beginning of Unit)Step 2: Interactive learning

Have students partner with their 3:00 partner. Ask the students to read with their partner page 36 – Investigation 3. As students are reading, the teacher should be circulating around the room

listening to the students read and redirecting when needed.

Students respond to the “Think about this!” questions by writing solutions in their math journals.

Ask for volunteers to share their responses to the questions and to model thinking where appropriate (i.e. writing samples on board, chart paper)

Step 2: Interactive learning Students will communicate mathematically

by responding in math journals to questions.

Step 2: Interactive Learning Connected Mathematics Project


Step 3: Visual Learning and Practice Have someone read section 3.1 aloud, while the other students follow along in

their books. Ask the students questions about the table and graph, in order to make certain that the students understand the information presented in both representations. For example, ask the student to look at the table and identify how much it would cost to rent bikes for 35 people. By looking at the graph, about how much would it cost if 28 people rented bikes? Model solutions by solving on board for whole group.

Have the whole group read, silently, the questions posed for Problem 3.1. Have students select their 3:00 partners to answer Problem 3.1 follow-up

questions, while the teacher circulates and assists students as they are answering the questions.

Read aloud section 3.2, while students follow along in their books. Have students work with the same partner to answer the questions in problem

3.2 A, B, C. Have student pairs write their responses on paper, while the teacher circulates around the room, working with individuals who are in need of extra assistance.

Suggested Homework: ACE question # 1 and 2 page 42. Differentiate homework according to student needs and abilities.

Step 3: Visual Learning and Practice Students make connections between the

graphs and table of given data (8.4A). Students make predictions to application

problems using graphs and tables (8.5A).

Step 3: Visual Learning and Practice Connected Mathematics Project


Day 6Step 1: Problem Solving (see beginning of Unit)Step 3: Visual Learning and Practice (continued)

Complete problem 3.3 page 39-40, by writing responses on notebook paper or in journals

Step 3: Visual Learning and Practice Students make connections between the

graphs and table of given data (8.4A). Students make predictions to application

Step 3: Visual Learning and Practice Connected Mathematics Project

(CMP) Variables and Patterns Investigation 3 pp 36-46



Call on volunteers to provide solutions for problem 3.3 and 3.3 Follow-up. Have the whole class read and discuss problem 3.4. Model solutions by writing

examples on board. Assign students to work individually to complete questions A-D, Problem 3.4 As the students work, the teacher will circulate and provide assistance and

direction where needed.

problems using graphs and tables (8.5A). Student math journals

Step 4: Differentiate/Assessment:On Level Learners:

ACE questions #4 and 5 pp 43-44. Any incomplete work should be finished as homework.

√ How can tables, graphs, and equations help in solving problems?


Struggling Learners: Work with small groups of students on any of the unassigned ACE questions on

pp. 43-44, in the Connected Mathematics Variables and Patterns book.

Advanced Learners: Connected Mathematics Variables and Patterns – pages 17 and 35. Place a

chart on board or overhead indicating group names, so that students know their assigned groups (3-4). Have groups work to answer the questions posed in Mathematical Reflections.

Step 4: Differentiate/Assessment make predictions to application problems

using graphs and tables (8.5A) use appropriate operations to solve

problems (8.2B)

Step 4: Differentiate/Assessment Connected Mathematics Project

(CMP) Variables and Patterns Investigation 3 pp 36-46 Ace Questions (graded

assignment) Student math journals

Day 7 McDougal Little Chapter 1 – Section 1.3Step 1: Problem Solving (see beginning of Unit)Step 2: Interactive Learning:

Prepare the computer and LCD projector for this lesson. Display the Mountain Climbing Substitution Race from www.classzone.com.

Chapter 1 Interactive math. Each student should have paper and pencil in order to evaluate the expressions

as they play the game. Students will take turns evaluating expressions.

After playing the Mountain Climbing Race for 3-5 minutes, ask students to write in their journals the process for evaluating expressions with a variable.

As for volunteers to share their responses

Step 2: Interactive learning Students will review the process of

evaluating an expression with variables by playing the Mountain Climbing Substitution Race Game.

Students will write and evaluate expressions in math journals as the game is being played.

Students will communicate mathematically as they explain the process for evaluating expressions with a variable (8.15A).

Step 2: Interactive Learning www.classzone.com – Interactive

Math – Chapter 1 – Mountain Climbing Substitution Race

Step 3: Visual Learning and Practice: Discuss Examples 1, 3, and 4 on pp. 13-15. Students should discuss and answer the questions for the guided practice for

Example 1. After discussing Example 4, ask the students to complete the Guided Practice

(question 10) in math journal. Assign problems 38-43 pp 16 & 17. Students should work independently, and

then with a partner to compare their answers to the problems. The teacher should be working with small groups of students as needed and circulating to assist and check for understanding as the students work.

Step 3: Visual Learning and Practice: Students will generate expressions from

verbal descriptions in a problem situation (8.4A).

Working with partners students will share ideas and solutions to problems (8.2B).

Step 3: Visual Learning and Practice McDougal Littell Course 3 –

Chapter 1 - pp. 13-17





Step 4: Differentiate/AssessmentOn Level Learners:

Assign problems 44 – 48 for students to work independently. Assess for 80% mastery.

Struggling Learners: Work with students individually or in small groups who need additional

assistance. ELL students may need to make a list matching mathematical symbols with words. For example: more than (+) ; 3 times as much (3X).

Advanced Learners: Invite students to write similar problems of their own, demonstrating an

understanding of writing an expression for a verbal description.Before students leave the room, ask the following question:

√How do you know what operation to use in solving a problem?

Step 4: Differentiate/Assessment Students will generate expressions from

verbal descriptions of a problem situation (8.4A).

Step 4: Differentiate/Assessment McDougal Littell Course 3 -

Chapter 1 - p. 17 Problems 44-48 (graded

assignment )

Day 8 Assessment Variables and Patterns – pp 73 & 74 - Problem #1 McDougal Littell Assessment Book – p 10 - Problems 30 &31 Write the Essential Questions below on board for the “writing prompt”. Have

each student spend a few minutes writing their responses to each question in their Journal. Make sure to collect Journals and provide feedback.

What would happen if there was not an agreed upon order of operations to use in solving problems?


Students will use appropriate operations to solve problems involving rational numbers in problem situations (8.2B).

Students will generate a different representation of data given another representation of data (8.4A).

Students will predict, find, and justify solutions to application problems using tables, graphs, and algebraic equations (8.5A).

CMP – Variables and Patterns – pp 73, 74 ( graded assignment )

McDougal Littell Assessment Book – p 10 – problems #30-31(graded assignment )

Content Vocabulary: numerical expression evaluate order of operations variable variable expression

*Reference McDougal Littell Textbook for English-Spanish Glossary for ELL students.

TAKS Vocabulary: generate predict justify

Evidence of LearningFormative Mini Assessment TAKS/Benchmarks College-Readiness

Anticipated Skills for SAT/ACT/College Board



2. A chemist mixes 4 ⅔ ounces of Liquid A, 0.75 ounces of Liquid B, 2 ⅔ ounces of Liquid C, and 5.5 ounces of Liquid D in a beaker. How many ounces of liquid are in the mixture?(FMA 9/22/2008 TEKS 8.2B)

3. The Science Club is raising money by selling hot dogs for $1 each at football games. They spent $20on buns, frankfurters, and napkins. Create a table to show their possible profits.(FMA 9/22/2008 TEKS 8.4A)

1. Valerie is making charm bracelets for a craft sale. Each bracelet consists of a chain with a certain number of charms as shown in the table below.

11. A recipe for 12 waffles calls for 1 ½ cups of milk, 2 ¼ cups of flour, and 1 1/3 cups of other ingredients. How many cups of milk, flour, and other ingredients are needed to make 36 waffles?

A 20 1/3 cups B 15 ¼ cups C 12 ¼ cups D 5 1/12 cups

(April 2006 TAKS Test – TEKS 8.2B

8. A set of parentheses is missing from the expression below.

15 5 + 7 · 2 + 4Which of the following expressions has the parentheses in the correct place for the expression to equal 52?F 15 (5 + 7 · 2) + 4G (15 5 + 7) · 2 + 4



Cost of BraceletsNumber of

CharmsCost of Supplies3$96$159$2112$27Based on this information, how much does each charm cost and how much do the

chains cost?(FMA 9/22/2008 TEKS 8.5A)

H 15 (5 + 7 · 2 + 4)J 15 5 + 7 · (2 + 4)

(April 2006 TAKS Test – TEKS 8.16B)

3. The students in Mr. Lee’s science class are ordering the materials they will need for a science experiment. Each student will need a bag of plant seeds that costs $1.00 and a 6-plant tray that costs $2.50. If x represents the number of students in Mr. Lee’s science class, which equation can be used to find y, the amount in dollars spent by Mr. Lee’s students?A y =2.5x + 1B y =3.5xC y =x + 3.5

D y =x + 2.5(April 2006 TAKS Test – TEKS 8.4A)

21 A fast train, known as a bullet train, travels at an average speed of 163 miles per hour. The equation below shows the relationship between d, the number of miles the train travels, and t, the number of hours it travels.

d =163tWhat is the distance in miles the train will travel in 1 hour?Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value.

(2006 TAKS Test – TEKS 8.5A)A box of cereal contains 18 ¾ cups of cereal. At most,



Mathematics – Grade 8Unit of Study: Integers

First Grading Period – Weeks 3-4 (10 days) CURRICULUM OVERVIEWBig Idea Unit Rationale

The students will build an understanding of integers. These numbers have been experienced by students informally in their everyday world. Although students have intuitively used operations on integers to make sense of situations, they are now required to find more formal ways to add, subtract, multiply, and divide positive and negative numbers.

Students should understand that: positive and negative integers are useful for noting relative changes or values such

as temperature changes or lost yards on football plays understanding the problem and selecting the correct operation(s) necessary for

solving the problem are skills used in everyday life

Essential Questions Guiding Questions

Where are positive and negative integers used in everyday life?

Why is it important to have positive and negative integers in everyday life?

√How do I know when to use positive or negative integers?

√How are positive and negative integers alike and/or different?

√How do I name points on a coordinate graph?


Con

cept

s

8.1 Number, operation, and quantitative reasoning. The student understands that different forms of numbers are appropriate for different situations. The student is expected to:

8.1(A) compare and order rational numbers in various forms including integers, percents, and positive and negative fractions and decimals

8.2 Number, operation, and quantitative reasoning. The student selects and uses appropriate operations to solve problems and justify solutions. The student is expected to:

8.2(A) select appropriate operations to solve problems involving rational numbers and justify the selection

8.2(B) use appropriate operations to solve problems involving rational numbers in problem situations

8.2(C) evaluate a solution for reasonableness

8.7 Geometry and spatial reasoning. The student uses geometry to model and describe the physical world. The student is expected to:

8.7(D) locate and name points on a coordinate plane using ordered pairs of rational numbers


I can: put numbers in order from greatest to smallest when they are written as integers,

fractions, decimals, or percents(8.1A). use the correct operation to solve problems (8.2A, B). tell if an answer makes sense (8.2C). locate and name points on a coordinate plane(8.7D).


(A) identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics

I can: use mathematics to solve real-life problems (8.14A) solve problems using a problem solving process (8.14B) select and use different strategies to solve problems (8.14C) use the Look for a Pattern Strategy to solve problems (8.14C) explain mathematical ideas using words, pictures, objects, and symbols (8.15A)



Skill

s(B) use a problem solving model that incorporates understanding the problem,

making a plan, carrying out the plan, and evaluating the solution for reasonableness

(C) select and develop an appropriate problem-solving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem.8.17 Underlying processes and mathematical tools. The student communicates

about Grade 8 mathematics through informal and mathematical language, representations, and models. The student is expected to:

(A) communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebra mathematical models.

ELPS1. Learning Strategies(C) use strategic learning techniques such as concept mapping, drawing, memorizing, comparing, contrasting, and reviewing to acquire basic and grade-level vocabulary;(E) internalize new basic and academic language by using and reusing it in meaningful ways in speaking and writing activities that build concept and language attainment;2. Listening(C) learn new language structures, expressions, and basic and academic vocabulary heard during classroom instruction and interactions;(D) monitor understanding of spoken language during classroom instruction and interactions and seek clarification as needed;3. Speaking(D) speak using grade-level content area vocabulary in context to internalize new English words and build academic language proficiency;(E) share information in cooperative learning interactions;4. Reading(C) develop basic sight vocabulary, derive meaning of environmental print, and comprehend English vocabulary and language structures used routinely in written classroom materials(K) demonstrate English comprehension and expand reading skills by employing analytical skills such as evaluating written information and performing critical analyses commensurate with content area and grade-level needs5. Writing(B) write using newly acquired basic vocabulary and content-based grade-level vocabulary;(G) narrate, describe, and explain with increasing specificity and detail to fulfill content area writing needs as more English is acquired

Evidence of Learning

At least 80% of the time students will demonstrate on paper that they are able to:1. compare and order rational numbers in various forms including integers, percents, and positive and negative fractions and decimals2. select and use the appropriate operations to solve problems involving rational numbers3. locate and name points on a coordinate plane using ordered pairs of rational numbers

Essential Pre-requisite skillsGrade 6 compare and order non-negative rational numbers (6.1A) use addition and subtraction to solve problems involving fractions and decimals

(6.2B) use multiplication and division of whole numbers to solve problems including

situations involving equivalent ratios and rates (6.2C) locate and name points on a coordinate plane using ordered pairs of non-

negative rational numbers (6.7)

Grade 7 compare and order integers and positive rational numbers (7.1A) convert between fractions, decimals, whole numbers, and percents mentally, on paper, or

with a calculator (7.1B) use addition, subtraction, multiplication, and division to solve problems involving fractions

and decimals (7.2B) locate and name points on a coordinate plane using ordered pairs of integers (7.7A)



Mathematics – Grade 8Unit of Study: Integers

First Grading Period – Weeks 3-4 (10 days) CURRICULUM GUIDEThe Teaching and Learning Plan

Instructional Model & Teacher DirectionsThe teacher will…

Assessment for Learningso students can…. Resources

Days 1-8:Step 1: Problem Solving: Begin these days with problem solving for 10 minutes. Use the following experiences from the Lane County Mathematics Project. The identified problems will be teacher directed for the purposes of building a background in problem solving strategies.

Problem Solving Strategy: Day 1: Look for a Pattern: Week 2 – Day 1 Day 2: Look for a Pattern: Week 2 – Day 2 Day 3: Look for a Pattern: Week 2 – Day 3 Day 4: Look for a Pattern: Week 2 – Day 4 Day 5: Look for a Pattern: Week 2 – Day 5 Day 6: Students create their own Look for a Pattern Problems Day 7: Students create their own Look for a Pattern Problems Day 8: Lane County Mathematics Project Page 55 – Patterns Day 9: Make a Systematic List: Week 3 – Day 1 Day 10: Make a Systematic List: Week 3 – Day 2

Step 1: Problem Solving learn and practice the strategies of looking for

patterns and making a systematic list in order to solve problems (8.14C) (Days 1-5, 9-10)

use math journals to write their own problems that can be solved using the Look for a Pattern Strategy. Students will be given the opportunity to solve other students’ problems. (Days 6&7)

Step 1: Problem Solving Lane County Mathematics Project –

Problem Solving in Mathematics – Grade 8

Student math journals – students need either a spiral notebook or a section in their binder for math journal.


Day 1Step 1: Problem Solving (see beginning of Unit)Step 2: Interactive LearningSet up the computer and LCD projector to access the following link: http://nlvm.usu.edu/en/NAV/frames_asid_122_g_2_t_1.html?open=instructions&from=category_g_2_t_1.html

Engage the students in a review of integer concepts learned in 7th grade by using the link to a game involving the use of integers to add up to zero.

Step 2: Interactive Learning Students will solve the puzzle presented by the

teacher (8.2A). Students will write down observations about any

patterns they observed about the integers that added up to zero (8.2A).

Step 2: Interactive Learninghttp://nlvm.usu.edu/en/NAV/frames_asid_122_g_2_t_1.html?open=instructions&from=category_g_2_t_1.htmlFor a copy of a student worksheet, follow this link: http://www.uen.org/Lessonplan/preview.cgi?LPid=19833 , Scroll down to find Activity 3- Circle Zero Directions and Student Worksheet.

Step 3: Visual Learning and Practice McDougal Littell Course 3 page 57 – Ask a student to read the paragraph at

the top of page 57 – Geography. Review with the students the terms integers, positive integers, and negative

integers. Discuss together Example 1. Ask the students to look at problems 1,2, and 3 on page 57. Students will

discuss with a partner the order of the integers from least to greatest. Ask a student to read the definition of absolute value on page 58. Read aloud as a class Example 2 on page 58. Reinforce the concept of

opposite numbers. Ask individual students to read each of the examples listed in Example 3. Students will answer questions 4 – 7 with partners. Ask random students to

explain their answers for each of the questions.

Step 3: Visual Learning and Practice Students will compare and order rational

numbers, including integers as they complete the problems. (8.1A)

Step 3: Visual Learning and Practice McDougal Littell Course 3 pp 57-58



http://www.uen.org/Lessonplan/preview.cgi?LPid=19833


http://nlvm.usu.edu/en/NAV/frames_asid_122_g_2_t_1.html?open=instructions&from=category_g_2_t_1.html





Step 4: Differentiate/AssessmentOn Level Learners: Students will create a poster or some type of visual display using words,

numbers and/or pictures that identifies the following concepts:1. comparing and ordering positive and negative integers2. the meaning of absolute value3. opposite numbers

Students will respond to the following questions in their math journals. Collect students’ journals and respond to their writing.

√How are positive and negative integers alike and/or different?(Marzano – Similarities/Differences)


Possible Homework Assignment: McDougal Littell Course 3 p. 60 # 41-47Struggling Learners: any unassigned problems in the practice and/or problem solving sections of

Chapter 2 sections 1,2,3,4,5,8 in the practice workbook http://www.uen.org/Lessonplan/preview.cgi?LPid=19833 – use this link to

access lessons using colored beans or chips to enhance the teaching of operations using positive and negative integers

Advanced Learners: ask students to design a game that involves operations with positive and

negative integers students create their own picture on a coordinate graph, indicating the

coordinate points and directions so that the picture could be replicated by another student

http://www.uen.org/Lessonplan/preview.cgi?LPid=19833 use this link for additional games and activities using positive and negative integers

Step 4: Differentiate/Assessment Students will compare and order rational

numbers, including integers (8.1A).

Step 4: Differentiate/Assessment McDougal Littell Course 3 pp 57-58 Posters or other type of visual

display (graded assignment)

Additional materials needed: Poster paper, markers and/or colored

pencils

This lesson will take 2 days to complete.Day 2Step 1: Problem Solving (see beginning of Unit)Step 2: Interactive Learning: Read aloud with the class the scenario of Jonah’s Sandwiches

(TE p34, SE p 16) Students should work with a partner to complete Jonah’s Sandwiches The teacher should be actively monitoring the groups of students, asking the

facilitation questions suggested in TE pp 32, 33.

Step 2: Interactive Learning; Students are working with partners selecting

appropriate operations to solve problems involving rational numbers (8.2B).

Students are selecting a appropriate problem solving strategy (8.14C)

Step 2: Interactive Learning Accelerated Curriculum for

Mathematics Grade 8 TAKS – Region IV – Teacher Edition pp 31-34 and Student Edition pp 16

Additional materials needed: metric rulers





Step 3: Visual Learning and Practice: Prepare the Operations Organizer (available in the Appendix) for each student.

TE pp 35, 36 Students will write formulas or procedures that they use in order to add,

subtract, multiply, and divide fractions and decimals. These procedures were introduced in 6th and 7th grades. Students may want to just use numbers to show examples of the procedures.

Provide the students with calculators as they work the problems presented on the transparency (TE p. 37) to verify or change their procedures they had written on their organizers.

Debrief Operations Organizer with the class using the facilitation questions to guide the discussion (TE p. 38- 40).

Step 3: Visual Learning and Practice: Students are working with partners to use

appropriate operations to solve problems involving rational numbers (8.2B).

Students will evaluate their procedures for adding, subtracting, multiplying, and dividing fractions and decimals for accuracy and reasonableness (8.2C).

Step 3: Visual Learning and Practice Accelerated Curriculum for

Mathematics Grade 8 TAKS – Region IV – Teacher Edition pp 35-37

Accelerated Curriculum for Mathematics Grade 8 TAKS – Region IV – Appendix – (found on the CD in back of book) to make copies of the Operations Organizer

Additonal materials: calculators Transparency TE p. 37

Day 3Step 4: Differentiate/Assessment Assign the Independent Practice questions 1-7 TE pp.40-43. As students work on the assignment, monitor individuals to assess which ones

are in need of additional assistance. Calculators need to be provided for those students whose IEP or 504

modifications indicate the use of a calculator.

Assign Rapid Reptiles (TE p. 44, SE p 230-22) to evaluate the students understanding of the TEKS addressed in the lesson.

Step 4: Differentiate/Assessment Students will work independently to demonstrate

their ability to select and use appropriate operations to solve problems involving rational number and justify the solutions (8.2 A,B,C)

Step 4: Differentiate/Assessment Accelerated Curriculum for

Mathematics Grade 8 TAKS – Region IV – Teacher Edition pp 40-44 and Student Edition pp 17-22

Independent Practice (graded assignment )

Day 4 Step 1: Problem Solving (see beginning of Unit)Step 2: Interactive Learning Students will complete the Activity 2.2 from the McDougal Littell Course 3

Activity Generator Allow students to work with partners as they complete the activity. Move around the room, checking with each group of students to see that they

understand the activity and are correctly using the number lines in order to model addition of positive and negative integers.

Ask for volunteers to answer the questions: How do you add positive integers and what is the sign of the sum? How do you add negative integers and what is the sign of the sum? How do you positive and negative integers and how do you know what the sign of the sum will be?

Step 2: Interactive Learning Students are working together to develop the

rules for adding positive and negative integers so they will be able to select appropriate operations to solve problems (8.2A).

Step 2: Interactive Learning McDougal Littell Course 3 Activity

Generator – Chapter 2 – Lesson 2.2- Adding Integers

Step 3: Visual Learning and Practice McDougal Littell Course 3 p.65 – Example 4. Read the School Fair problem

aloud and put the information on the overhead or the board. Don’t have the students looking at their books since the answer is given in the example.

Ask the students to determine how much money was raised and how they would figure out the solution.

Practice adding integers by completing problems 16 – 20 on page 66 – Students can work with partners and check with the partner to see that they are getting the correct solution.

Step 3: Visual Learning and Practice Students are working together to develop the

rules for adding positive and negative integers so they will be able to select appropriate operations to solve problems (8.2A).

Step 3: Visual Learning and Practice McDougal Littell Course 3 pp 65-66



Step 4: Differentiate/AssessmentOn Level Learners: Assign problems 48- 57 on pp 66 – 67Struggling Learners: Work in a small group with the students who are having trouble mastering the

concepts. Simplify the problems by providing easier numbers for the students to work with. Work problems 21-23 p. 66

Advanced Learners: Include problem # 58 in the assignment.

Students will be able to complete the problems for homework.

Prior to dismissing students, ask the following essential question for discussion.


Step 4: Differentiate/Assessment Students will use appropriate operations to solve

problems involving rational numbers in problem situations (8.2B).

Students will evaluate the solutions to problems for reasonableness (8.2C).

Students will identify and apply mathematics to everyday situations (8.14A).

Students will communicate mathematical ideas (8.15A).

Step 4: Differentiate/Assessment McDougal Littell Course 3 pp 66-67

(graded assignment)

Day 5Step 1: Problem Solving (see beginning of Unit)Step 2: Interactive Learning Instruct the students to copy the table on page 68, McDougal Littell Course 3

and to fill in the columns. Discuss with the students the patterns observed when finding the difference

and how the addition problems relate to the subtraction problems. Students should come to the conclusion that in subtracting integers they must add the opposite.

Ask the students to write an explanation of how to subtract integers in their journals.

Step 2: Interactive Learning work simple subtraction problems and by looking

at patterns establish a rule for subtraction of integers (8.14C)

journal write about the process for subtracting integers (8.15A)

Step 2: Interactive Learning McDougal Littell Course 3 p 68

Step 3: Visual Learning and Practice Discuss Examples 1-3 on page 69 with the students. Allow the students to choose 4 problems to work from page 70, problems #9-17

and 2 problems from #19-26 As students are working these problems, circulate and ask the students to

verbalize the steps they are following as they solve the subtraction problems.

Step 3: Visual Learning and Practice solving problems involving rational numbers

(8.2A)

Step 3: Visual Learning and Practice McDougal Littell Course 3 p 70

Step 4: Differentiate/AssessmentOn Level Learners: Assign problems 38 -42 pp 70, 71Struggling Learners: For students who are having a difficult time applying the rule of adding the

opposite in order to subtract, make a number line available.Advanced Learners: Additional interactive practice in subtracting integers is available by following

the link contained in Step 4 Resources.

Journal writing – Explain why you add an integer’s opposite when you are subtracting integers. Encourage the students to use words, pictures, numbers, and examples in their writing. Collect journals so that you can respond to the students’ writing and evaluate for misconceptions.

Possible Homework Assignment Page 72, problems 50 – 53

Step 4: Differentiate/Assessment use appropriate operations to solve problems

involving rational numbers in problem situations (8.2B)

evaluate solutions for reasonableness (8.2C)


(graded assignment) http://nlvm.usu.edu/en/NAV/

category_g_2_t_1.html - Use this link for additional practice in subtracting integers. Go to “Color Chips – Subtraction” for an interactive display of subtracting integers



http://nlvm.usu.edu/en/NAV/category_g_2_t_1.html

http://nlvm.usu.edu/en/NAV/category_g_2_t_1.html

Day 6Step 1: Problem Solving (see beginning of Unit)Step 2: Interactive Learning

Using calculators, ask the students to find the answers to a number of multiplication and division problems involving integers. For example -6x5; 6X27; -38X-21; 96x-4; -3x-8, -14/-2, 930/-3, -142/-4, etc. Gather the information from the students and record on the board or overhead. Ask the students to determine the rule for multiplying and dividing integers.

They should be able to see the pattern that when integers with like signs are multiplied or divided, the solution is positive and the product or quotient of two integers with different signs is negative.

Students should write in their journals their observations about multiplying and dividing integers.

Step 2: Interactive Learning Students work simple multiplication and division

problems and by looking at patterns establish a rule for multiplying and dividing integers (8.14C).

Students written in journals about the process of multiplying and dividing integers (8.15A).

Step 2: Interactive Learning teacher generated list of

multiplication and division problems chart paper, overhead, or board to

record information in a table so that students can see the patterns of answers when multiplying and/or dividing integers with the same or different signs

Step 3: Visual Learning and Practice Divide students into 2 groups by numbering 1, 2, 1, 2, etc. Group 1 will play Brain Game Multiplying Integers for approximately 10 minutes Group 2 will play Brain Game Dividing Integers for approximately 10 minutes Switch groups so that all students play both games – play the second round for

approximately 10 minutes

Step 3: Visual Learning and Practice Students play games to practice selecting

appropriate operations to solve problems involving rational numbers (8.2A).

Step 3: Visual Learning and Practice McDougal Littell Course 3 Activity

Generator – Chapter 2, Lesson 2.4 McDougal Littell Course 3 Activity

Generator – Chapter 2, Lesson 2.5

Additional materials needed: decks of cards copies of Brain Game cards for

dividing integersStep 4: Differentiate/AssessmentOn Level Learners: Assign problems 53 – 56, p 76 and 38 – 41 p 80 Monitor the students as they are working on the problems to assess for

weaknesses in applying the rules for multiplying and dividing integers.Struggling Learners: Work with small groups of students, modeling the thinking process used in

solving the problems. Encourage students to draw a picture of the problem situation prior to applying numbers.

Advanced Learners: Assign problems 57 and 58 (p 76) in addition the 53-56, and 42 p 80.

Ask the students to respond to the following questions before leaving class:

√How are positive and negative integers alike and/or different? (Marzano – Similarities and Differences)

Unfinished problems may be completed as homework

Step 4: Differentiate/Assessment Students use appropriate operations to solve

problems involving rational numbers in problem situations (8.2B).

Students communicate mathematical ideas (8.15A).

Step 4: Differentiate/Assessment McDougal Littell Course 3 pp 76 and

80 (graded assignment)



Day 7Step 1: Problem Solving (see beginning of Unit)Step 2: Interactive Learning Prepare the computer and LCD projector. Display the coordinate graphing activity from www.classzone.com Provide all students with a piece of graph paper so that they can record the

positions on the coordinate graph as one student is demonstrating with the computer

Journal writing – students should explain how to find coordinate points on a graph. Make sure that they include examples of all 4 coordinates in their journal entry

Step 2: Interactive Learning Students are actively participating in the location

of points on a coordinate plane using ordered pairs of rational numbers (8.7D).

Step 2: Interactive Learning www.classzone.com – McDougall

Littell Course 3 – Animations- Chapter 2: The Coordinate Plane

Step 3: Visual Learning and Practice Allow students to choose their partner for the activity, with the understanding

that off task behavior will result in loosing that privilege. Students will work with a partner to play the Brain Game – The Coordinate

Plane – McDougal Littell Course 3 Activity Generator – Chapter 2, Lesson 2.8 Students will need centimeter graph paper and a metric ruler in order to play

the game.

Step 3: Visual Learning and Practice Students are working with a partner playing a

game in which they will locate and name points on a coordinate plane using ordered pairs of rational numbers (8.7D).

Step 3: Visual Learning and Practice McDougal Littell Course 3 – Activity

Generator – Chapter 2, Lesson 2.8

Additional supplies necessary: Centimeter graph paper metric ruler

Step 4: Differentiate/AssessmentOn Level Learners: Assign problems 24-28 p 96, and problems 36 – 40 pp 97, 98 McDougal Littell

Course 3 Monitor the students closely to see that they are able to correctly identify the

points on the coordinate planeStruggling Learners: Work individually with these students as they complete the assignment.

Encourage them to draw a picture, reminding them which is the x coordinate, and which is y.

Advanced Learners: For students who finish quickly assign problems 42 and 44 on page 98

Put the following writing prompts on the board/overhead and ask students to respond in their journals. Collect the journals and respond to the student writing.


Why is it important to have positive and negative integers in everyday life?

Step 4: Differentiate/Assessment Students will apply locating and naming points

on a coordinate plane using ordered pairs of rational numbers in problem situations (8.7D).


(graded assignment)





Day 8Step 1: Problem Solving (see beginning of Unit)Assessment Chapter Test McDougal Littell Course 3 – page 107 problems 1-8, 17-24, 28-34

Students will demonstrate their mastery of comparing and ordering rational numbers in

various forms (8.1A). selecting appropriate operations to solve

problems involving rational numbers and justify the selections (8.2A).

using appropriate operations to solve problems involving rational numbers in problem situations (8.2B).

evaluating a solution for reasonableness(8.2C). locating and naming points on a coordinate

plane using ordered pairs of rational numbers (8.7D).

McDougal Littell Course 3 Chapter 2 Test – page 107 (graded assignment )

Day 9Step 1: Problem Solving (see beginning of Unit)Reteach/ExtendStruggling Learners: For those students who did not master the content as demonstrated on the

assessment, use the Chapter 2 Review Questions to remediate weaknesses. Work with students in small groups to provide individualized assistance to students

Use the Animations for Chapter 2 – www.classzone.com for additional remediation

On Level and/or Advanced Learners: For those students who have mastered the content as demonstrated on the

assessment, use the Pre-AP Copymaster, pages 323 and 324, McDougal Littell Course 3 Best Practices Toolkit. This is an assignment that could take the students 1-2 days to complete and extends the concepts learned in coordinate graphing.

Students will demonstrate their mastery of comparing and ordering rational numbers in

various forms (8.1A). selecting appropriate operations to solve

problems involving rational numbers and justify the selections (8.2A).

using appropriate operations to solve problems involving rational numbers in problem situations (8.2B).

evaluating a solution for reasonableness(8.2C). locating and naming points on a coordinate

plane using ordered pairs of rational numbers (8.7D).

McDougal Littell Course 3 Chapter 2 Review pp 102-106 (graded assignment )

McDougal LIttell Course 3 – Best Practices Toolkit – Pre-AP copymaster page 323 and 324 (graded assignment)

Day 10Step 1: Problem Solving (see beginning of Unit) Continue with the reteach/extension lesson from the previous day if more time

is necessary. If the students have completed Day 9 assignments, then present The Bake

Sale Problem. This problem is on the Differentiated Best of Math Exemplars II Disk. Students should be working in groups of 3-4 in order to solve the problem.

Students will work in groups to: use appropriate operations to solve problems

involving rational numbers in problem situations (8.2B).

identify and apply mathematics to everyday experiences (8.14A).

use a problem solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness (8.14B).

select or develop an appropriate problem-solving strategy from a variety of different types (8.14C).

communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models (8.15A).

Differentiated Best of Math Exemplars II Disk – student and teacher copies are on the disk in PDF form.




Content Vocabulary: integers negative integers positive integers absolute value x-axis opposite

y-axis origin quadrant ordered pair x and y coordinates*Reference McDougal Littell Textbook for English-Spanish Glossary for ELL students.

TAKS Vocabulary: compare order evaluate locate name

Evidence of Learning

Formative Mini Assessments TAKS Benchmarks SAT/ACT/C College-ReadinessAnticipated Skills for College Board

1 The number of slices of pizza available, a, is proportional to the number of pizzas delivered, d. If this relationship can be described with the equation a = 8d, which statement is true?A There are 8 times as many slices as number of pizzas.B There are 8 times as many pizzas as number of slices.C There are 8 more slices than the number of pizzas.D There are 8 more pizzas than the number of slices.(FMA 11/8/2008 TEKS 8.2A)

(FMA 10/13/2008 TEKS 8.1A)

(TAKS 2004 – 8.2B)

7. When graphed in the (x,y) coordinate plane, at what point do the lines x + y = 5 and y = 7 intersect?

A. (–2,0) B. (–2,7) C. (0,7) D. (2,5) E. (5,7)

(ACT Sample Questions)

6. What is the largest possible product for 2 even integers whose sum is 34?

F. 64 G. 68 H. 120 J. 240 K. 288

(ACT Sample Questions)



http://www.actstudent.org/sampletest/math/math_03.html#math_06k%23math_06k

http://www.actstudent.org/sampletest/math/math_03.html#math_06j%23math_06j

http://www.actstudent.org/sampletest/math/math_03.html#math_06h%23math_06h

http://www.actstudent.org/sampletest/math/math_03.html#math_06g%23math_06g

http://www.actstudent.org/sampletest/math/math_03.html#math_06f%23math_06f

http://www.actstudent.org/sampletest/math/math_02.html#math_07e%23math_07e

http://www.actstudent.org/sampletest/math/math_02.html#math_07d%23math_07d

http://www.actstudent.org/sampletest/math/math_02.html#math_07c%23math_07c

http://www.actstudent.org/sampletest/math/math_02.html#math_07b%23math_07b

http://www.actstudent.org/sampletest/math/math_02.html#math_07a%23math_07a

TAKS 2006– 8.7D)



Mathematics – Grade 8Unit of Study: Fractions and Rational Numbers

First Grading Period – Weeks 5 – 6 (10 days) CURRICULUM OVERVIEWBig Idea Unit Rationale

In real-life problem situations, students can: compare and order rational numbers of various kinds choosing the appropriate form

to use simplify, compare, and order fractions add, subtract, multiply, and divide fractions and mixed numbers choose the appropriate operations with fractions and decimals

Students should understand that: various forms of rational numbers can be compared and ordered, for example:

comparing sports statistics it is helpful to approximate irrational numbers mentally or with a calculator so that we

can analyze the effects of weather or wind speed developing a benchmark is valuable when estimating with decimals, percents and

fractionsEssential Questions Guiding Questions

How do I decide which form of a number I should use in solving a problem?

In a problem situations, how will I know is an answer is reasonable?

√How do I arrange numbers in order from least to greatest or greatest to least?

√How can I change numbers from one form to the other?

√How do I know what operation to use to solve a problem?

√How would you explain that dividing a number by a fraction and multiplying by its reciprocal will produce the same result?


Con

cept

s

8.1 Numbers, operation, and quantitative reasoning. The student understands that different forms of numbers are appropriate for different situations. The student is expected to:

8.1(A) compare and order rational numbers in various forms including integers, percents, and positive and negative fractions and decimals;

8.1(B) select and use appropriate forms of rational numbers to solve real-life problems including those involving proportional relationships;

8.2 Numbers, operation, and quantitative reasoning. The selects and uses appropriate operations to solve problems and justify solutions. The student is expected to:

8.2(A) select appropriate operations to solve problems involving rational numbers and justify the selections;


I can: arrange positive and negative fractions, decimals, percents and integers in order

from least to greatest or greatest to least (TEKS 8.1A) choose the best form of a number to use in problem solving (TEKS 8.1B). use the right operation to solve a problem know if it makes sense(TEKS 8.2A).


8.14(A) identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics;

8.14(B) use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness;

I can: identify mathematics in everyday experiences, activities in and outside of school,

with other subjects and with other math topics (8.14A). apply mathematics in everyday experiences, activities in and outside of school, with

other subjects and with other math topics (8.14A). use a problem-solving model to solve problems (8.14B). select and use different strategies to solve problems (8.14C) choose the right tool or method to solve problems (8.14D) explain mathematical ideas using words, pictures, objects, and symbols (8.15A)



Skill

s8.14(C) select or develop an appropriate problem-solving strategy from a variety of

different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem; and

8.14(D) select tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation, and number sense to solve problems.

8.15 Underlying processes and mathematical tools. The student communicates about Grade 8 mathematics through informal and mathematical language, representations, and models. The student is expected to:

8.15(A) communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models; and


Evidence of LearningAt least 80% of the time, students will demonstrate on paper that they are able to:

1. compare and order fractions2. solve problems involving fractions and decimals3. select and use the appropriate operation(s) when solving problems4. solve real-life problems applying mathematical concepts and processes5. use a variety of strategies to solve meaningful, real-world problems6. clarify, justify and validate both the mathematics used to solve the problem and the reasonableness of the solution



Mathematics – Grade 8Unit of Study: Fractions and Rational Numbers

First Grading Period – Weeks 5 – 6 (10 days) CURRICULUM GUIDEEssential Pre-requisite Skills

Grade 6 Compare and order non-negative rational numbers (TEKS 6.1A). Generate equivalent forms of rational numbers to include whole numbers,

fractions and decimals (TEKS 6.1B). Use integers to represent real-life situations (TEKS 6.1C).Use addition and subtraction to solve problems with fractions and decimals (TEKS 6.2B).

Grade 7 Compare and order integers and positive rational numbers (TEKS 7.1A). Convert between fractions, decimals, whole numbers, and percents (TEKS 7.1B). Use addition, subtraction, multiplication and division to solve problems with fractions and

decimals (TEKS 7.2B). Select and use appropriate operations to solve problems and justify the selection (TEKS

7.2F). The Teaching and Learning Plan

Instructional Model & Teacher DirectionsThe teacher will…

Assessment for Learningso students can…. Resources

Days 1 – 9:Step 1: Problem Solving: Begin each day with problem solving for 10 minutes.Use the following experiences from the Lane County Mathematics Project . The identified problems will be teacher directed for the purposes of building a background in problem solving strategies.

Problem Solving Strategy: Day 1: Make a Systematic List: Week 3 – Day 3 Day 2: Make a Systematic List: Week 3 – Day 4 Day 3: Make a Systematic List: Week 3 – Day 5 Day 4: Make and Use a Drawing or Model: Week 4 – Day 1 Day 5: Make and Use a Drawing or Model: Week 4 – Day 2 Day 6: Make and Use a Drawing or Model: Week 4 – Day 3 Day 7: Make and Use a Drawing or Model: Week 4 – Day 4 Day 8: Make and Use a Drawing or Model: Week 4 – Day 5 Day 9: Students create their own Make and Use a Drawing/Model Problems

Step 1: Problem Solving use the strategies of making a systematic list

and making and using a model or drawing in order to solve problems (8.14C) (Days 1 – 8)

using math journals, students will write their own problems that can be solved using the make and use a drawing or model strategy. Students will be given the opportunity to solve other students’ problems. (Day 9)

Step 1: Problem Solving Lane County Mathematics Project –

Make a Systematic List (Grade 8) – pp. 19 – 22

Lane County Mathematics Project – Make and Use a Drawing or Model (Grade 8) pp. 28

Student math journals – students need either a spiral notebook or a section in their binder for math journal.


Day 1: McDougal Littell, 4.5 Comparing Fractions and Mixed Numbers, pp. 198-201 using the Activity Generator Course 3. Refer to the page numbers below for a detailed script of the lesson.

Step 1: Problem Solving (see beginning of Unit)Step 2: Interactive Learning Discuss fraction models at top of p. 198. Spend just a few minutes expanding

upon the lesson by having students compare other fractions using fraction pieces.

Using the Activity Generator – Course 3 – 4.5 Brain Game, display a transparency of the Brain Game: Comparing Fractions and Mixed Numbers practice exercises 1-8, so that these can be completed as a whole group. Answer questions and clarify as necessary.

**See the Teacher Note’s located at the bottom of this activity for preparation and materials. Step 3: Visual Learning and Practice Students will work in pairs to play the Brain Game. Monitor students to ensure they are converting correctly. If players do not

agree, have them compare two ways by writing the mixed number as an

Step 2: Interactive Learning Focus AND Motivate: Students will be

individually modeling fractions using fraction squares (8.14D).

Students have an opportunity to practice comparing fractions and mixed numbers by answering the practice questions of the Brain Game. (8.1A, 8.1B)

Step 3: Visual Learning and Practice Students will actively explore mathematical

concepts by playing the Brain Game in pairs. Students should be prepared to share their strategies with the class and in their journals. (8.14A, 8.14B, 8.15A)

Resources for Steps 2-4 can be found in the McDougal Littell Middle School Activity Generator Course 3 - Lesson 4.5 Brain Game: Comparing Fractions and Mixed Numbers



improper fraction and having them write the improper fraction as a mixed number.

Ask students how they are comparing numbers in this activity – by writing mixed numbers as improper fractions, writing improper fractions as mixed numbers or another method?

Step 4: Differentiate/AssessmentOn Level Learners: See Activity Management for differentiating. There are 3 different card sets for

different ability levels. Teacher will monitor students and/or work with small groups to provide

interventions for struggling students.

Journal Writing: p. 201 #40 Collect journals to respond to students’ writing. Include the following question in the journal writing:

√How do I arrange numbers in order from least to greatest or greatest to least?

Suggested Homework: pp. 200 - 201 #3 & 5, 9 & 11, 19 & 21, 38 & 39 (for visual learners, students can use a number line to order the fractions). Provide calculators for students who are struggling with calculations or who

have use of a calculator identified in their IEP or 504 plan.

Struggling Learners: Lesson 4.5, Section 2 Lesson 4Advanced Learners: Chapter 4 Section 5

Step 4: Differentiate/Assessment Students who are visual learners can use a

number line to order fractions. Students will work independently to complete the

suggested homework for additional skill and problem solving practice (8.1A).

Step 4: Differentiate/Assessment McDougal Littell Course 3, Lesson

4.5, p. 198 – 201 Student Journals Homework (graded assignment)

Other Materials Needed: square fraction pieces copies of fraction cards on cardstock

Day 2: McDougal Littell, 5.1 Fractions with Common Denominators, pp. 233-237 using the Activity Generator Course 2. Refer to the page numbers below for a detailed script of the lesson.*This lesson introduces a key concept when adding and subtracting fractions and applies rules for integers (see Ch.2 for review if needed) Step 1: Problem Solving (see beginning of Unit)Step 2: Interactive Learning Prepare the computer and LCD projector www.classzone.com – Course 3 – Lesson 5.1: The teacher will display the

PP for lesson 5.1 to students. Students should have their books open to page 233. Ask students to work problems on their own paper. Work through examples 1 & 3 only, using the Guided Practice as skill practice.

After Example 1, have students record in their notebooks how to rename a mixed number and when to rename it.

Using the Activity Generator – Course 2 – Lesson 5.2 Modeling Addition and Subtraction of Mixed Numbers, provide groups of 2-3 students with graph chart paper, rulers and markers. Provide each group with a copy of the activity and review the steps as a whole group. Answer questions and clarify if necessary.

Step 2: Interactive Learning Students have an opportunity to practice adding

and subtracting fractions with common denominators by working through the example problems as a class (8.1A, 8.2B)

Resources for Steps 2-4 can be found in the McDougal Littell Middle School Activity Generator Course 2 - Lesson 5.2 Modeling Addition and Subtraction of Mixed Numbers

Step 2: Interactive Learning www.classzone.com –PowerPoint

Presentations Course 3 Chapter 5, Examples 1 & 3.

McDougal Littell Course 3, Lesson 5.1, pp. 233-234





Step 3: Visual Learning and Practice Students continue to work in their groups to draw models of exercises 1-4 on

chart paper. Use questions 5 & 6 to facilitate a class discussion on mixed numbers.

Remind students that fully shaded squares can also have lines drawn inside to represent five fifths. A fully shaded square represents 1 whole number or 5/5 – this should help them learn to regroup numbers when they add and subtract.

Step 3: Visual Learning and Practice Now students will actively explore mathematical

concepts by working on drawing area models in small groups on chart paper to be displayed in the room. Students should be prepared to answer #5 & 6 and participate in a class discussion (8.14A, 8.14B, 8.15A)

Step 4: Differentiate/AssessmentOn Level Learners: McDougal Little p. 235 # 6-13Struggling Learners: Encourage struggling students to work an easier problem like drawing area

models for subtracting ¼ from ¾. Teacher will monitor students and/or work with small groups to provide

interventions for struggling students. Advanced Learners: p. 235 # 10 -17

Journal Writing: Describe how to add two mixed numbers without drawing an area model.

Suggested Homework: pp. 235-237 #18-20, 41 & 42. (graded assignment)

Step 4: Differentiate/Assessment Students can use the problem solving strategy of

working an easier problem to help them grasp the concept of mixed numbers (8.14C).

Students will work independently to complete the suggested homework for additional skill practice (8.1A).

Step 4: Differentiate/Assessment McDougal Littell, Lesson 5.1, p.

235-237 Student Journals

Other Materials Needed: graph chart paper rulers markers

Day 3: McDougal Littell, 5.2 Fractions with Different Denominators, pp. 238-242. Refer to the page numbers below for a detailed script of the lesson.Step 1: Problem Solving (see beginning of Unit)Step 2: Interactive Learning Ask students to develop a list of hobbies and activities that involve measuring

and computing with fractions. Prepare computer and LCD projector to access www.classzone.com –

Course 3 - Lesson 5.2: The teacher will display the PP for lesson 5.2 to students. Students should have their books open to page 238. Ask students to work problems on their own paper. As the students follow along in the book, read the Carpentry problem aloud. Work through examples 1 & 3 as a class, using the Guided Practice as skill practice.

Step 2: Interactive Learning Students will use prior knowledge to list activities

and hobbies that involve fractions (8.1A). Students have an opportunity to add and

subtract fractions with different denominators by working through the example problems as a class (8.1A, 8.2B)

Step 2: Interactive Learning www.classzone.com – PowerPoint

Presentations Course 3 - Chapter 5, Examples 1 & 3.

McDougal Littell – Course 3, Lesson 5.2, pp. 238-239

Step 3: Visual Learning and Practice: p. 241 #36, 37 & 39: As students work in pairs to solve #36, 37 & 39, the

teacher should actively monitor student work to ensure that the students are solving the problem properly. Have groups share their explanations with the class.

For #36, remind students to look at key words that will help them write an expression from the verbal description.

For #39, point out that an estimate may not answer the question since the exact answer is very close to 5 miles.

* These problems may also be assigned for homework if class time is not sufficient.

Assign problem 41, p. 201, to those students who finish quickly and understand the previous problems.


concepts by working on problem solving questions in pairs. Students should be prepared to share their explanations with the class either by discussion or with a visual representation on chart paper (8.14A, 8.14B, 8.15A)

Step 3: Visual Learning and Practice McDougal Littell, Lesson 5.2, p.

241





Step 4: Differentiate/Assessment See Best Practices Toolkit for suggestions on teaching this lesson to students

of different ability levels. Advanced Learners – see p. 287; Struggling Learners p. 57

Teacher will monitor students and/or work with small groups to provide interventions for struggling students.

Present the writing prompts for students to respond to using their math journals. Collect the journals to respond to the students’ writing.


In a problem situations, how will I know is an answer is reasonable?Journal Writing: p. 241 #42

Suggested Homework: pp. 240 #7-13 odd, 15-19 odd. Differentiate homework as needed, see p. 240 for guide.

Step 4: Differentiate/Assessment Students can use estimation to determine if their

answer is reasonable. Students will work independently to complete the

suggested homework for additional skill practice (8.1A).


240-241 Course 3 Best Practices Toolkit-

BPT (if needed) Student Journals

Day 4: McDougal Littell, 5.3 Multiplying Fractions, pp. 243-246 using the Activity Generator – Course 3 – Lesson 5.3 Brain Game. Refer to the page numbers below for a detailed script of the lesson.

Step 1: Problem Solving (see beginning of Unit)Step 2: Interactive Learning Ask students for suggestions as to how they might multiply 5 ½ by 3.

Encourage students to come up to the board/overhead. www.classzone.com – Lesson 5.3: The teacher will display the PP for lesson

5.3 to students. Students should have their books open to page 243. Ask students to work problems on their own paper. Work through examples 1 & 2 as a class, using the Guided Practice as skill practice.

Step 2: Interactive Learning: Encourage students to draw models that support

their answers to the Focus and Motivate question (8.14C).

Students have an opportunity to multiply fractions and mixed numbers by working through the example problems as a class (8.1B, 8.2B)


Presentations Course 3 Chapter 5, Examples 1 & 2.


Step 3: Visual Learning and Practice: 5.3 Brain Game – Multiplying Fractions: Students will work in pairs to play

the Brain Game and together can complete the practice problems. Encourage students to estimate the product of two cards before picking them. Ask students if they were surprised by the size of the product of the two cards

picked?**See the Teacher Note’s located at the bottom of this activity for preparation and materials.


concepts by playing the Brain Game – Multiplying Fractions in pairs.

Students should be prepared to share strategies or surprises that came about as a result of playing the game (8.14A, 8.14B, 8.15A).

Resources for Steps 3-4 can be found in the McDougal Littell Middle School Activity Generator Course 3 - Lesson 5.3 Brain Game – Multiplying Fractions

Step 4: Differentiate/AssessmentOn Level/Advanced Learners use all 36 cardsStruggling Students: use only the first 24 cards. allow more time for estimation. You may want to allow calculators as a way of

checking their answers.

Journal Writing: Have students answer the following question: “When you multiply two whole numbers, the product is larger than the factors. Is the product of two fractions larger than the fractions? Explain your reasoning.”

Prior to leaving the class, ask the students to orally respond to the following

Step 4: Differentiate/Assessment Students can take more time to estimate their

answers before picking their cards. Students can use all 36 cards for a more

challenging game. Students will work independently to complete the



245 Student Journals Homework Assignment (graded

assignment )

Other Materials Needed: Cardstock for deck of cards





questions:


In a problem situations, how will I know is an answer is reasonable?

Suggested Homework: pp. 245 #3-13 odd, 15-17 odd & 22. (graded assignment)Day 5: McDougal Littell, 5.4 Dividing Fractions, pp. 247-252. Refer to the page numbers below for a detailed script of the lesson.

Step 1: Problem Solving (see beginning of Unit)Step 2: Interactive Learning: Sketch 7/8 of a pizza on the board. Ask students how they would divide the

pizza into four equal pieces. Explain that 7/8 ÷ 4 models this situation. Activity – students use models to divide fractions. Have rulers available for

students to use if necessary. The Key Concept summarizes that you can use multiplication to solve problems

that involve division by a fraction. www.classzone.com – Lesson 5.4: The teacher will display the PP for lesson

5.4 to students. Students should have their books open to page 247. Ask students to work problems on their own paper. Work through examples 1-3 as a class, using the Guided Practice as skill practice.

In Exercise 2, remind students that the reciprocal of a negative number is a negative number. The opposite of a negative number is a positive number.

An Animated Math activity is available on-line for Example 4.

Step 2: Interactive Learning: Encourage students to draw models that support

their answers to the Focus and Motivate question (8.14C).

Students can use rulers to help visualize dividing fractions.

Students have an opportunity to divide fractions by fractions, whole numbers and mixed numbers by working through the example problems as a class (8.1B)


Presentations Chapter 5, Examples 1 – 4.

www.classzone.com – Animated Math Chapter 5, Penalty Shot

McDougal Littell, Lesson 5.4, pp. 247 – 249

Step 3: Visual Learning and Practice: p. 258-259 #55 & 56: As students work in pairs to solve #55 & 56, the teacher

should actively monitor student work to ensure that the students are solving the problem properly. Have groups share their explanations with the class.



concepts by working on problem solving questions in pairs.

Students should be prepared to share their explanations with the class either by discussion or with a visual representation on chart paper (8.14A, 8.14B, 8.15A)


251

Step 4: Differentiate/Assessment:Advanced Learners: Assign problem 60, p. 259, to those students who finish quickly and understand

the previous problems.

Struggling Learners: For students who have difficulty dividing fractions when the divisor or the

dividend is a whole number, suggest that they rewrite whole numbers as fractions.

Teacher will monitor students and/or work with small groups to provide interventions for struggling students.

Journal Writing: p. 251 #59.

Step 4: Differentiate/Assessment Students can practice rewriting whole numbers

as fractions. Students will work independently to complete the


Step 4: Differentiate/Assessment McDougal Littell, Lesson 5.4, pp.

249-251(graded assignment) Course 3 Best Practices Toolkit-







Ask students to respond to this question prior to leaving the class:


Suggested Homework: pp. 249-251 #3-7 odd, 27-31 odd, 37-41 odd & 58. (graded assignment) Day 6: McDougal Littell, 5.5 Fractions and Decimals, pp. 255 – 259. Refer to the page numbers below for a detailed script of the lesson.

Step 1: Problem Solving (see beginning of Unit)Step 2: Interactive Learning: Focus and Motivate: Have students name and give examples of all the

different groups of numbers they have studied so far. Choral read the opening of the lesson focusing on the highlighted vocabulary. www.classzone.com – Lesson 5.5: The teacher will display the PP for lesson

5.5 to students. Students should have their books open to page 255. Ask students to work problems on their own paper. Work through examples 1-3 only as a class, using the Guided Practice as skill practice.

Step 2: Interactive Learning: Students can display examples of different

groups of numbers in a Venn Diagram, table or other type of visual representation.

Students can use a number line to graph and order numbers (8.14D).

Students have an opportunity to write fractions as decimals and decimals as fractions in problem situations. (8.1A,B)


Presentations Chapter 5, Lesson 5 Examples 1 – 3.

McDougal Littell, Lesson 5.5, pp. 255-257

Step 3: Visual Learning and Practice: Explore/Summarize: p. 258-259 #57 & 58: As students work in pairs to solve

#57 & 58, the teacher should actively monitor student work to ensure that the students are solving the problem properly. Have groups share their explanations with the class.



concepts by working on problem solving questions in pairs.

Students should be prepared to share their explanations with the class either by discussion or with a visual representation on chart paper (8.14A, 8.14B, 8.15A).


258-259

Step 4: Differentiate/Assessment:Struggling learners: Encourage students to make a list in their notebooks of some common

fractions and their decimal equivalents. Advanced Learners: Assign problem 63, p. 259, to those students who finish quickly and understand

the previous problems

. Write the following question on board/overhead and have students respond in their math journals. Collect the journals to respond to the student writing.

How do I decide which form of a number I should use in solving a problem?

Suggested Homework: pp. 257- 258 #5 - 11 odd, 27, 29-33 odd. (graded assignment)

Step 4: Differentiate/Assessment Students can practice rewriting whole numbers

as fractions. Students will work independently to complete the


Step 4: Differentiate/Assessment McDougal Littell, Lesson 5.5, pp.







Days 7-9 : Accelerated Curriculum for Mathematics Grade 8 TAKS Unit 1 Lesson 1 Compare and Order Rational Numbers TE pp. 3-14. Refer to the page numbers below for each step for a detailed script of the lesson. This lesson should take approximately 3 days to complete.

Day 7

Step 1: Problem Solving (see beginning of Unit)Step 2: Interactive Learning pp. 4-6: The teacher will distribute pattern blocks to groups of 2 to 3 students.

Students are to complete Cover It worksheet, SE pp. 1-2 (Area Relationships of Pattern Blocks). Teacher should actively monitor student work and refer to page 4 for facilitation questions.

Journal Writing: Have the students answer the following topic: “Describe - in detail - the process you used to convert fractions, decimals and percents. Provide examples of how this process can help you solve real-life problems.” Prepare students for Explore activity on Day 8 by previewing the activity with

them.

Step 2: Interactive Learning Pairs of students will compare areas of the

pattern blocks which will lead to comparing and ordering integers, percents, and positive and negative fractions (8.1A).

Students will continue working in pairs to complete Cover It worksheet (Area Relationships of Pattern Blocks) and complete journal writing topic.

Steps 2-4: Accelerated Curriculum for

Mathematics Grade 8 TAKS (Region IV) TE pp. 3-17 and SE pp. 1-9

Accompanying CD for Accelerated Curriculum for Mathematics Grade 8 TAKS – Lesson 1 Compare and Order Rational Numbers

Step 2: Interactive Learning Teacher Edition (TE) pp. 3-6 Student Edition (SE) pp. 1-2

Day 8Step 3: Visual Learning and Practice Following Problem Solving Strategy, review previous day’s activity and answer

any questions students may still have before moving on.

Prepare index cards with a problem on one card, and the solution on another. Example: 62=? on one card and 36 on another card. Hand out the cards randomly to students. When they match the problem to the solution, they have found their partner. TE pp. 7-10: The teacher will distribute 1 paper clip and Rational Numbers

Spinners to each group. Students are to complete My Head is Spinning worksheet, SE p. 3-4.

Teacher should actively monitor student work and refer to TE, pp. 7-8 for facilitation questions.

Step 3: Visual Learning and Practice

Students will work with a partner to complete this activity. Explore/Summarize: Now students will actively

explore mathematical concepts by completing My Head is Spinning worksheet in pairs.

Step 3: Visual Learning and Practice Teacher Edition (TE) pp. 7-10, Student Edition (SE) pp. 3-4

Day 9Step 4: Differentiate/Assessment Teacher will distribute copies of the Mystery Fraction Sheet, SE p. 7, as an

assessment. Students may work in pairs or individually. As students complete the Mystery Fraction Sheet, distribute copies of TAKS

review questions, SE p. 8-9 for additional practice. Teacher will monitor students and/or work with small groups to provide

interventions for struggling students.

Suggested Homework/Independent Practice: The teacher will distribute copies of the Independent Practice, SE pp. 5-6, and assess for 80% accuracy. (graded assignment)

Step 4: Differentiate/Assessment Groups should discuss (with the class) the

procedures they used to compare positive fractions, positive decimals, a positive fraction and decimal, negative fractions, negative decimals and a negative fraction and decimal (8.14D, 8.15A).

Students will work independently to complete the Independent Practice following Unit 1 Lesson 1 (8.1A, 8.15A).

Step 4 Differentiate/Assessment Student Edition (SE) p. 5-9 Independent Practice (graded

assignment ) Student journals

Other Materials Needed: pattern blocks paper clips copies of spinners on cardstock

Day 10: Assess McDougall Little Course 3 – Assessment Book Chapter Test pp. 59-64 Choose the appropriate test for each group of students

McDougall Littell Course 3 Assessment Book – Chapter 5



Content Vocabulary: denominator equivalence fraction multiplicative inverse numerator order of operations rational number

improper fraction least common denominator like terms reciprocals simplest form mixed number

TAKS Vocabulary: compare solve

Evidence of LearningFormative Mini Assessments Interims/TAKS/Benchmarks College-Readiness

Anticipated Skills for SAT/ACT/College Board5. Mr. Hinojosa drives 382 miles round trip towork each week. Last Friday, he drove 36.4miles less than he usually drives per day.Which equation can be written to find m, theaverage number of miles Mr. Hinojosa droveto work each day last week?

(FMA 9/22/2008 TEKS 8.2A)

25. Which fraction is between 2/3 and 3/4?A ½B 3/5C* 5/7D 7/8

TEKS 8.1A - TAKS 2004, Q#2540. Carlos, Jackie, Lester, and Margie ate lunch at a restaurant. The total amount of the bill, including tax and tip, was $44.60. Carlos paid $15.00, Jackie paid 1/4 of the bill, Lester paid 20% of the bill, and Margie paid the rest of the bill. Who paid the greatest part of the bill?F* CarlosG JackieH LesterJ Margie

TEKS 8.1B - TAKS 2004, Q#40

47. To cover his bulletin board, Mr. Adams needs 1

yards of fabric and 6 yards of trim. If the fabric costs $2.79 per yard and the trim costs $1.19 per yard, which equation can be used to find c, the total cost of covering the bulletin board?A c = (2.79 + 1.5) + (1.19 + 6.25)B* c = (2.79 · 1.5) + (1.19 · 6.25)C c = (2.79 + 1.5) − (1.19 + 6.25)D c = (2.79 · 1.5) − (1.19 · 6.25)

TEKS 8.2A – TAKS 2006, Q#47

11. A recipe for 12 waffles calls for 1 cups of milk, 2

cups of flour, and 1 cups of other ingredients. How many cups of milk, flour, and other ingredients are needed

5. A box of cereal contains 18 cups of cereal. At most, how many persons can you serve from this box of

cereal if each serving must be at least cup?

A. 14B. 18C. 19D. 24E.* 25

The ACT Sample Questions, Set 3 #5

7. A circular coin has a radius of inch. When lying flat, how much area does the coin cover, in square inches?

A.

B.

C.

D.

E.*














to make 36 waffles?

A. 20 cups

B. 15 cups

C. 12 cups

D. 5 cups

TEKS 8.2B – TAKS 2006, Q#11



Mathematics – Grade 8Unit of Study: Decimals, Scientific Notation and the Pythagorean Theorem

First Grading Period – Weeks 7- 9 (10 days) CURRICULUM OVERVIEWBig Idea Unit Rationale

In real-life problem situations, students can: approximate the value of irrational numbers mentally or with a calculator express numbers in scientific notation when appropriate. Use the Pythagorean theorem

Students should understand that: the pythagoren theorem can be used to find the lengths of the sides of a right

triangle scientific notation can be used to express large numbers like the number of stars in

the galaxy as well as small numbers like the thickness of a soap bubbleEssential Questions Guiding Questions

In everyday life, where can you find examples of scientific notation?

How is the Pythagorean theorem used?

√How can the Pythagorean Theorem be used to solve real world problems?

√How do I know if an answer is reasonable?


Con

cept

s

8.1 Numbers, operation, and quantitative reasoning. The student understands that different forms of numbers are appropriate for different situations. The student is expected to:

8.1(A) compare and order rational numbers in various forms including integers, percents, and positive and negative fractions and decimals;

8.1(D) express numbers in scientific notation, including negative exponents, in appropriate problem situations. 8.2 Numbers, operation, and quantitative reasoning. The selects and uses appropriate operations to solve problems and justify solutions. The student is expected to:

8.2(B) use appropriate operations to solve problems involving rational numbers and justify selections;

8.2(C) evaluate a solution for reasonableness.

8.7(B) use geometric concepts and properties to solve problems in fields such as art and architecture

8.7 (C) use pictures or models to demonstrate the Pythagorean Theorem

8.9 Measurement. The student uses indirect measurement to solve problems. The student is expected to:

8.9(A) use the Pythagorean Theorem to solve real-life problems


I can: arrange positive and negative fractions, decimals, percents and integers in order

from least to greatest or greatest to least (TEKS 8.1A). use the Pythagorean Theorem to solve real-life problems (8.9A). write very large and very small numbers using scientific notation (TEKS 8.1D). choose the correct operation to solve problems (TEKS 8.2B). evaluate a solution to make sure it makes sense (TEKS 8.2C).


8.14(A) identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics;

I can: identify mathematics in everyday experiences, activities in and outside of school,

with other subjects and with other math topics (8.14A). apply mathematics in everyday experiences, activities in and outside of school, with

other subjects and with other math topics (8.14A). use a problem-solving model to solve problems (8.14B). select and use different strategies to solve problems (8.14C).



Skill

s8.14(B) use a problem-solving model that incorporates understanding the problem,

making a plan, carrying out the plan, and evaluating the solution for reasonableness;

8.14(C) select or develop an appropriate problem-solving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem; and

8.14(D) select tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation, and number sense to solve problems.8.15 Underlying processes and mathematical tools. The student communicates about Grade 8 mathematics through informal and mathematical language, representations, and models. The student is expected to:

8.15(A) communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models; and

choose the right tool or method to solve problems (8.14D). use the systematic list strategy to solve problems (8.14C). use the make a drawing or model strategy to solve problems (8.14C). explain mathematical ideas using words, pictures, objects, and symbols (8.15A).


Evidence of LearningAt least 80% of the time, students will demonstrate on paper that they are able to: add, subtract, multiply and divide decimals in problem situations solve problems that involve identifying the square root of a number estimate the value of an irrational number. write numbers in scientific notation



Mathematics – Grade 8Unit of Study: Decimals, Scientific Notation and the Pythagorean Theorem

First Grading Period – Weeks 7- 9 (10 days) CURRICULUM GUIDEEssential Pre-requisite Skills

Grade 6 Compare and order non-negative rational numbers (TEKS 6.1A). Generate equivalent forms of rational numbers to include whole numbers,

fractions and decimals (TEKS 6.1B). Use integers to represent real-life situations (TEKS 6.1C). Write prime factorization using exponents (TEKS 6.1D). Use addition and subtraction to solve problems with fractions and decimals

(TEKS 6.2B).

Grade 7 Compare and order integers and positive rational numbers (TEKS 7.1A). Convert between fractions, decimals, whole numbers, and percents (TEKS 7.1B). Represent squares and square roots using geometric models (TEKS 7.1C) Use addition, subtraction, multiplication and division to solve problems with fractions and

decimals (TEKS 7.2B). Simplify numerical expressions involving order of operations and exponents (TEKS 7.2E). Select and use appropriate operations to solve problems and justify the selection

(TEKS 7.2F).

The Teaching and Learning PlanInstructional Model & Teacher Directions

The teacher will…Assessment for Learning

so students can…. Resources

Days 1 – 9:Step 1: Problem Solving: Begin each day with problem solving for 10 minutes.Use the following experiences from McDougal Littell Teachers Edition, pp. 786 - 794. You may want to prepare transparencies of the problems so they can easily be displayed to the class (or you can prepare a class set of copies). These pages are also located in the Easy Planner CD, so they can be displayed to the class using a projector. The identified problems will be teacher directed for the purposes of building a background in problem solving strategies. *Some of these problems may require the use of graph paper. The problems are suggestions, please feel free to choose any question you’d like from pp. 796-800 as a substitution.

Problem Solving Strategy: Day 1: Make a Model, p. 786 Day 2: Draw a Diagram, p. 787 Day 3: Guess, Check, and Revise, p. 788 Day 4: Work Backward, p. 789 Day 5: Make a List or Table, p. 790 Day 6: Look for a Pattern, p. 791 Day 7: Break Into Parts, p. 792 Day 8: Solve a Simpler Problem, p. 793 Day 9: Use a Venn Diagram, p. 794

Step 1: Problem Solving use the strategies of making a

model, drawing a diagram, guessing, checking and revising, working backward, making a systematic list, looking for a pattern and solving a simpler problem in order to solve problems (8.14C) (Days 1 – 9)

Step 1: Problem Solving McDougal Littell Course 3 –

problem Solving Strategy Review, pp. 786 - 800

Day 1: McDougal Littell, 5.6 Adding and Subtracting Decimals, pp. 260-264. Refer to the page numbers below for a detailed script of the lesson.Step 1: Problem Solving (see beginning of Unit)Step 2: Interactive Learning Prepare the computer and LCD projector Begin by asking the students to silently read paragraph above Example 1 Read Example 1, the Dancing problem to the class as they follow along. Ask students to rewrite the numbers in the table as whole numbers. Then have them answer

the questions in the opening paragraph.

Step 2: Interactive Learning Students have an opportunity to

practice adding and subtracting decimals by working through the example problems as a class (8.2B)

Students use estimation to justify their answers (8.2A)


Presentations Course 3 Chapter 4 Lesson 6 Examples 1 – 4





www.classzone.com – Lesson 5.6: The teacher will display the PP for lesson 5.6 to students. Students should have their books open to page 260. Ask students to work problems on their own paper. Work through examples 1-4 as a class, using the Guided Practice as skill practice.

Step 3: Visual Learning and Practice p. 263-264 #45 & 47: As students work in pairs to solve #45 & 47, pp. 263-264, the teacher

should actively monitor student work to ensure that the students are solving the problem properly. Have groups share their explanations with the class.


Step 3: Visual Learning and Practice Now students will actively explore

mathematical concepts by working on problem solving questions in pairs. Students should be prepared to share their explanations with the class either by discussion or with a visual representation on chart paper (8.14A, 8.14B, 8.15A)

Step 3: Visual Learning and Practice McDougal Littell Course 3,

Lesson 5.6, p. 263-264

Step 4: Differentiate/AssessmentStruggling Learners: See Best Practices Toolkit (BPT) p. 138 for suggestions on teaching this lesson to students

of different ability levels. Teacher will monitor students and/or work with small groups to provide interventions for

struggling students. Advanced Learners: Assign problem 49, p. 264, to those students who finish quickly and understand the previous

problems.

Journal Writing: Have students summarize the major points of the lesson and answer this question: How is adding decimals different from adding whole numbers? (Marzano – Similarities and Differences)

Suggested Homework: pp. 262-263 #11-15 odd, 18, 19-23 odd, 37. (graded assignment )

Step 4: Differentiate/Assessment Students who are struggling can use

place value to help adding/subtracting decimals


Step 4: Differentiate/Assessment McDougal Littell Course 3, pp.



Day 2: McDougal Littell, 5.7 Multiplying and Dividing Decimals, pp. 265-269, using the Activity Generator Course 3. Refer to the page numbers below for a detailed script of the lesson.

Step 1: Problem Solving (see beginning of Unit)Step 2: Interactive Learning Prepare computer and LCD projector Discuss with students what they already know about multiplying and diving whole numbers.

Add that multiplying and dividing with decimals is almost the same, the only extra thing to worry about is where to place the decimal point. (Marzano – Similarities and Differences)

www.classzone.com – Lesson 5.7: The teacher will display the PP for lesson 5.7 to students. Students should have their books open to page 265. Ask students to work problems on their own paper. Work through examples 1-2 as a class.

Step 2: Interactive Learning Students will be discussing

properties of multiplication and division as a class (8.2B).

Students have an opportunity to multiplying and dividing decimals by working through the example problems as a class (8.1A, 8.2B)

Step 2: Interactive Learning McDougal Littell Course 3,

Lesson 5.7, pp. 265-266 www.classzone.com – PowerPoint

Presentations Chapter 5 Lesson 7 Examples 1 – 2.






Step 3: Visual Learning and Practice Using the Activity Generator – Course 3 – 5.7 Exploring Decimal Multiplication and

Division make copies of the steps and tables for small groups of 2-3 students. **See the Teacher Note’s located at the bottom of this activity for preparation and materials.

Students will work in small groups of 3 students to model the course and complete the table. Prepare index cards with math vocabulary words. There will be 3 cards for each word, one card will have the word, card 2 will have a definition, and card three will have a picture. Depending on the number of students in your class, 10 words (30 cards) will be enough. After handing out the cards, students should find their partners by matching words, pictures, and definitions. Monitor students to ensure they are using the correct decimal places. Each student may be

responsible for a different runner. Ask students to provide their answers to the Draw Conclusion section and discuss with the

group.


mathematical concepts by modeling a running course with tape and yardsticks and completing a table for runners.

Students should be prepared to share their explanations with the class from their completed table (8.14A, 8.14B, 8.15A).

Resources for Steps 3-4 can be found in the McDougal Littell Middle School Activity Generator Course 3 - Lesson 5.7 Exploring Decimal Multiplication and Division

Step 4: Differentiate/Assessment Students often make mistakes when working with decimals. Ensure that students are

carefully placing the decimal point in the numbers they are working. Remind students that the number of decimal places in the product is equal to the total

number of decimal places in the factors. Teacher will monitor students and/or work with small groups to provide interventions for

struggling students.

Journal Writing: Have students describe the similarities and differences of multiplying and dividing with decimals and without decimals. Collect journals and respond to students writing.

Suggested Homework: pp. 267-268 #5-13 odd, 36-37, 46. (graded assignment )

Step 4: Differentiate/Assessment Students can use prior knowledge of

multiplying and dividing whole numbers to support multiplying and dividing with decimals.





Other Materials Needed: yard sticks masking tape

Days 3-4 : Accelerated Curriculum for Mathematics Grade 8 TAKS Unit 1 Lesson 2 Scientific Notation TE pp. 18 - . Refer to the page numbers below for the Launch and Explore/Summarize sections for a detailed script of the lesson. This lesson should take approximately 3 days to complete.

Day 3

Step 1: Problem Solving (see beginning of Unit)Step 2: Interactive Learning pp. 4-6: The teacher will distribute copies of the Spin Cycle worksheet SE p. 10 to each

student (to save paper, copy the Place Value and Scientific worksheet SE p. 11 on the back).

Students will complete Part 1 individually, then students will share their solutions with their group. Do the same for Parts 2 and 3.

Use the facilitation questions on pp. 19 – 20 to have a class discussion about values of numbers.

Step 2: Interactive Learning Students will work as a whole group

to create the largest and smallest values from given numbers on a spinner (8.1D).

Students have an opportunity to discuss results with their group and use that information to continue with parts 2 and 3 (8.1D)

Steps 2-4: Accelerated Curriculum for

Mathematics Grade 8 TAKS (Region IV) TE pp. 18-30 and SE pp. 10-15

Accompanying CD for Accelerated Curriculum for Mathematics Grade 8 TAKS – Lesson 2 Scientific Notation

Step 2: Interactive Learning Teacher Edition (TE) pp. 19-21 Student Edition (SE) pp. 10



Step 3: Visual Learning and Practice Explore: Distribute copies of Place Value and Scientific worksheet SE p. 11 to each

student. Display a transparency of the Place Value and Scientific worksheet on the overhead. Discuss the Facilitation Questions from the TE pp. 24 – 25 with the class as you work

together as a whole group to complete the table. (Continue this portion on Day 4 if you run out of time.)


mathematical concepts by working on problem solving questions in a whole group. Students should be prepared to share their explanations with the class. (8.14A, 8.14B, 8.15A)

Step 3: Visual Learning and Practice Teacher Edition (TE) pp. 22-26 Student Edition (SE) pp. 11-13

Day 4(see beginning of Unit for problem solving activity) Review previous day’s activity and answer any questions students may still have before

moving on. Continue discussing the Facilitation Questions with the students and clarify as necessary.

Step 4: Differentiate/Assessment Teacher will distribute copies of Scientifically Speaking worksheet and accompanying TAKS

problems, SE pp. 14 - 15, as an assessment. Students may work in pairs or individually. Teacher will monitor students and/or work with small groups to provide interventions for

struggling students.

Write the following prompt on the boar/overhead and ask students to respond in their math journals. Collect the journals and respond to the students’ writing.


Suggested Homework/Independent Practice: The teacher will distribute copies of the Independent Practice, SE pp. 12 - 13, and assess for 80% accuracy.(graded assignment)

Step 4: Differentiate/Assessment Students can work individually or in

pairs to justify their answer to the Scientifically Speaking problem (8.14A, 8.15A).

Students will work independently to complete the suggested homework for additional skill practice (8.1C).

Step 4: Differentiate/Assessment Teacher Edition (TE) pp. 28-30 Student Edition (SE) pp. 12-15

(graded assignment)

Days 5, 6 & 7: Pythagorean TheoremStep 1: Problem Solving (see p. 21 Curriculum Guide)Step 2: Interactive Learning This activity is meant to be a teacher-led whole class activity and does not lend itself to 4

different steps. Use the activity Discovering the Pythagorean Theorem. You can use the Tangram Template in the activity to cut out tangrams, or use commercial

sets of tangrams. Follow the procedures outlined under Game Procedures. Use the Facilitation Questions to guide the discussion of the Model of the Pythagorean

Theorem.Make the connection between the model and a2 + b2 = c2

Step 2: Interactive LearningStudents will create a model of the Pythagorean Theorem (8.7C)

Step 2: Interactive Learning Discovering the Pythagorean

Theorem activity

Additional materialstangrams – either commercial or made from the templa

Step 3: Visual Learning and Practice Use the teacher notes and the student activity pages from Pythagorean Theorem Models

activity. The teacher notes and answer key precede the student activity pages. The students may choose not to use the cut out squares as directed in the first instruction

and may quickly move to using the formula for right triangles. Some students will definitely need use the squares in order to fill out the chart.

Students should work in groups of 3 or 4 for this activity.

Step 3: Visual Learning and Practice Students will create a model of the

Pythagorean Theorem (8.7C)Students will communicate mathematical ideas (8.15A)

Step 3: Visual Learning and Practice Pythagorean Theorem Models

activity Parts 1, 2, 3

Additional Materials:graph paper used to make various sized squares



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Discuss part 1 as a class prior to working on parts 2 and 3. Assign parts 2 & 3 Circulate and ask students to justify their answers as they are working.Step 4: Differentiate/Assessment Use the activities Pythagorean Theorem Application on Triangles and Pythagorean Theorem

Applications.(Graded Assignment) Students will apply what they have learned in the previous activities to solving problems

involving the Pythagorean Theorem.Struggling Learners: Reduce the amount of problems assigned Work in a small group with the students to reinforce the process Provide calculators for students as needed

Any unfinished work should be completed as homework. Additional homework could be assigned from McDougal Littell Course 3 p. 485.

√How can the Pythagorean Theorem be used to solve real world problems? How can geometric properties be used in real world situations and/or careers?

Step 4: Differentiate/Assessment Students will use geometric concepts

and properties to solve problems (8.7B)

Students will create a model of the Pythagorean Theorem (8.7C)

Students will use the Pythagorean Theorem to solve real-life problems (8.9A).

Students will communicate mathematical ideas (8.15A)

Step 4: Differentiate/AssessmentPythagorean Theorem Application on Triangles and Pythagorean Theorem Applications.(Graded Activity(

Day 8: Pythagorean Theorem Scavenger HuntStep 1: Problem Solving (see p. 32 Curriculum Guide) The nature of this activity does not lend itself to a 4 step process. The problems for the Pythagorean Theorem Scavenger Hunt can be found by following this

link – use pages 4 – 13 only. The problems are also available in the Appendix for Accelerated Curriculum for Mathematics

Grade 8 TAKS (Region 4). Appendix is the CD in back of book.

Students should work together in groups of 3. Ask students to line up according to height. Starting at one end of the line, make groups of 3 students. Post the Scavenger Hunt pages (4-13 from the link) randomly around the room or in an area

where there is space enough to spread out the pages. Each group of students will be assigned to begin on a different problem page.

Students should have calculators available for working the problems. The students work the problem that is displayed on the bottom half of their page and record

their work on the Scavenger Hunt Recording Page (Student Edition p. 136). Once the group has completed the problem and agrees on the answer, and each student

has recorded work on their own Recording page, they should find the Scavenger Hunt page around the room that has their answer on the top half of the page. This page now has the students’ next problem on it.

The teacher should be actively monitoring and asking the Facilitation Questions from Teacher’s Edition p. 275.

The directions for this activity are also outlined in Teacher’s Edition pp. 274-276

Journal Writing: Ask students to write a paragraph explaining the Pythagorean Theorem so that a younger student would understand how it could be used to solve problems like the ones they just completed.

Pythagorean Theorem Scavenger Hunt Students will use geometric concepts

and properties to solve problems in fields such as art and architecture as they calculate the area and perimeter of the bases of the floats for the parade (8.7B).


Students will identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics (8.14A).

Students will communicate mathematical ideas using language, appropriate units, and numerical models by writing in their journals about the Pythagorean Theorem (8.15A).

Pythagorean Theorem Scavenger Hunt Accelerated Curriculum for

Mathematics Grade 8 TAKS (Region 4)

Teacher Edition pp. 274-476 Student Edition p. 136 Pythagorean Theorem Scavenger

Hunt (pp. 4-13 only) Pages 4 – 13 can also be found in

the Appendix (CD in back of Accelerated Curriculum Book)



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√Why is it important to understand all the variables of the Pythagorean Theorem?

How is the Pythagorean Theorem used in everyday situations?

Suggested Homework: Indirect Measurement – application problems using the Pythagorean Theorem. (Graded Assignment)Day 9 Assessment:Step 1: Problem Solving (see p. 22 Curriculum Guide)On Level Learners: Administer the Quiz for Pythagorean Theorem.(Graded Assignment)Struggling Learners: For students who need additional assistance, use the quiz more as a teaching tool than as a

quiz grade. Advanced Learners: For students who have completed and mastered all the activities, assign problem #37,

McDougal Littell Course 3, p. 486. This will challenge them to find a relationship between the lengths of the sides of obtuse triangles.

Writing Prompt: Give at least 3 examples of using the Pythagorean Theorem in a real world situation.

Be certain to include in your assessment reference these questions for students to respond to:

How is the Pythagorean Theorem used in everyday situations?


Assessment Students will use pictures or models

to demonstrate the Pythagorean Theorem (8.7C)


Students will make connections between the Pythagorean Theorem and real world situations.

Assessment Quiz for Pythagorean Theorem .

(Graded Assignment)

Day 10: Real World Project (Students will need meter sticks or yard sticks) Have students measure and calculate the perimeter and area of their desks and the walls in

the classroom. Extension: If a bucket of paint contains 1 gallon and covers 125 square feet and the tax rate

is 8.125%. How much will it cost to paint the walls? Your desk?

The students will describe how they solve this problem in their journals.

Students will need meter sticks or yard sticks

Content Vocabulary: decimal exponent real numbers number Pythagorean Theorem

TAKS Vocabulary: compare arrange estimate justifyevaluate



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Evidence of LearningFormative Mini Assessments TAKS/Benchmarks College-Readiness

Anticipated Skills for SAT/ACT/College Board

2005 Interim Assessment

(FMA 10/13/2008 TEKS 8.1A)

42. A librarian arranged some books on the shelf using the Dewey decimal system. Choose the group of book numbers that is listed in order from least to greatest.

F 549.010, 549.101, 549.02, 549.3G 392.4, 397.46, 399.53, 399.062H 101.2, 101.04, 104.21, 110.0J* 834, 834.19, 834.2, 834.29

TEKS 8.1A – TAKS 2003, Q#42

46. A certain bacterium measures approximately 0.000015 millimeter in length. How is this length expressed in scientific notation?F* 1.5 × 10 –5 mmG 1.5 × 10 –4 mmH 0.15 × 10 5 mmJ 15 × 10 4 mm

TEKS 8.1D – TAKS 2003, Q#46

16. Cody's parents bought a big-screen television for $1,099.99 and a DVD player for $99.99, including tax. Cody's parents plan to pay the total amount in 18 equal monthly payments. What is a reasonable amount for each monthly payment?F $50.00G $150.00H $113.00J* $67.00

TEKS 8.2C – TAKS 2004, Q#16

2. A particle travels 1 10 8 centimeters per second in a straight line for 4 10 –6 seconds. How many centimeters has it traveled?

F. 2.5 10 2

G. 2.5 10 13

H. 4 10 2

J. 4 10 –14

K. 4 10 –48





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how many persons can you serve from this box of cereal if each serving must be at least ¾ cup?

A. 14 B. 18

C. 19 D. 24

E. 25

(ACT Practice Test)






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