algebra 1 unit 1 patterns revised pacing guide … 1 – unit 1 patterns – revised pacing guide...

Algebra 1 – Unit 1 Patterns – Revised Pacing Guide

Common Core State Standards Aligned

Norwalk Public School District

NPS/CT/CCSS – DRAFT, August 2013, updated 1/6/2014 of 18

Day Goal Activity/Classwork Assessment

Suggested Homework

1 Investigation 1: Students are introduced to the value

of representing patterns using multiple

representations (tables, graphs, diagrams, equations

and verbal descriptions) by exploring the molecular

structure of hydrocarbons.

*Activity 1.1.1: Hydrocarbons on Titan *Exit Slip 1.1: Tables Together

2

3

Investigation 2: Students review

Operations on integers

Order of operations

Evaluating expressions by substituting

values in for variables

Representing algebraic expressions using

verbal descriptions, tables, and graphs

Using algebraic expressions to model real-

world situations

*Activity 1.2.1: Algebra Tiles and

Integers

(Can use integer chips)

*Exit Slip 1.2.1: Ask students to

perform operations on integers

4 *Activity 1.2.2: Patterns in Signed

Numbers

Last page of Activity 1.2.2 –

Summary table.

5 Direct Instruction: Review order of

operations (PH 1.2)

*Exit Slip 1.2.2: Ask students to

apply order of operations

HW: Prentice Hall Page 12-13 #1-

40

6 *Activity 1.2.3: Bingo with Order of

Operations

Journal Entry: Prompts students to

state rules for adding, subtracting,

multiplying and dividing integers

and to identify the error in the

simplification of an expression

(Teacher provides an incorrect

simplification of an expression on

the board)

HW: *Activity 1.2.4

7

Investigation 3: Students will write both the

recursive rule and the explicit rule for the nth term of

an arithmetic sequence

Recursive rule: What do you do to get from one term

to the next term (ie: add 6, subtract 4)

Explicit Rule: 𝑎 + (𝑛 − 1)𝑑

*Activity 1.2.7: Stack of Cups #1-7 HW: Have students complete #8

from *Activity 1.2.7

8 *Activity 1.3.1: Recursive and Explicit

Rules for Arithmetic Sequences

*Activity 1.3.2: Building Bridges

9 Direct Instruction: Recursive and

Explicit Rules for Arithmetic Sequences

(PH 5.6)

*Exit Slip 1.3: Ask students to

identify an arithmetic sequence,

create its recursive and explicit

rules, and use the pattern to solve a

problem

HW: Prentice Hall Page 270

Exercises A

10 *Activity 1.3.4: Mohegan Sun

(Extension: *Activity 1.3.3)

Journal Entry: Prompts students to

describe the characteristics of an

arithmetic sequence

11 Mid-Unit Review Review (teacher created)

12 Mid Unit Test

Algebra 1 – Unit 1 Patterns – Revised Pacing Guide




13

Investigation 4: Students examine geometric

sequences through real world applications

Recursive rule only!!!

Activity 1.4.1: Double Your Money

Journal Entry: Ask students to

describe the similarities and

differences between a geometric

and arithmetic sequence and to

provide a real-world example of

each type of sequence

14 *Activity 1.4.2: Applications of

Geometric Sequences

*Exit Slip 1.4: Ask students to find

terms in a geometric sequence,

identify the recursive rule, represent

the sequence using a table and

graph, and use the sequence to

solve a problem in the context

HW: *Activity 1.4.3: More

Geometric Sequences

15 Investigation 5: Students explore geometric patterns

of fractal designs

Introduce a SIMPLE fractal problem. As the stage

moves forward, count shaded versus unshaded

regions.

*Activity 1.5.2 #1-4

*Exit Slip 1.5: Ask students to

identify a fractal pattern and use the

pattern to make predictions

16

17 Performance Task – This performance task:

Builds on the unit theme of patterns in

nature

Assesses students’ ability to find the nth

term of an arithmetic sequence and identify

geometric and arithmetic sequences

Emphasizes the fact that not all patterns are

linear

*Unit 1 Performance Task:

Honeycombs

18

19 End-Unit Review Review (teacher created)

20 End of Unit Test

Activities with a * can be accessed on the Moodle Website

Algebra 1 – Unit : linear Equations – Revised Pacing Guide




Day Goal Activity Assessment

Suggested Homework

1 Investigation 1: Students represent expressions

using verbal descriptions and flowcharts. Students

recognize that an algebraic expression involving a

single variable term can be thought of as a sequence

of operations on the variable term

*Activity 2.1.1

Direct Instruction: Expressions vs.

Equations

2

*Activity 2.1.2: Representing

Expressions with Stories and

Flowcharts

Exit Slip 2.1: Requires students to

represent algebraic expressions by

verbal descriptions and flowcharts, and

convert verbal descriptions to algebraic

expressions

Activity 2.1.3: Representing

Expressions with Algebra Arrows (2

pages)

3

Investigation 2: Students solve one-step and two-

step linear equations, and construct and solve linear

equations to explore real world problems

*Activity 2.2.1: Solving Linear

Equations using Flowcharts

(Guided Practice)

4

*Activity 2.2.2: Solving Linear

Equations with Algebra Tiles

*Activity 2.2.3: Solving One-Step

Equations (Optional)

Journal Entry 1: Write your own story

of x and identify the unknown.

5

Direct Instruction (include

equations with fractions)

Practice Solving Two-Step

Equations

Teacher-Created Exit Slip

6

*Activity 2.2.4: Equations in

Education Station Problems

Exit Slip 2.2

Activity 2.2.5: New York City Cab

Fares

7

Investigation 3: Students solve multi-step equations

in a variety of real-life contexts. To solve the

equations students must combine like terms on one

side of an equation, collect variable terms on one side

and collect constants on the other side. Students also

solve equations that have no solution or an infinite

number of solutions.

*Activity 2.3.1: Combining Like

Terms with Algebra Tiles

Direct Instruction

-Combining Like Terms

8 Direct Instruction: Solving Multi-

step Equations (Combining Like

Terms only)

Exit Slip 2.3.2: asks students to identify

the steps which occurred in the process

of solving an equation

9

Direct Instruction: Solving

Equations with Variables on Both

Sides

*Activity 2.3.6: How many

Solutions?

-Discuss types of solutions (no

solution, unique solution, infinite

solutions)

*Activity 2.3.4 Practice Solving

Equations

Prentice Hall Page 98





10 Activity 2.3.3: Solving Equations

with Variables on Both Sides

Journal Entry 2: asks students to

explain how they can tell if an equation

has no solution or an infinite number of

solutions

11 Activity 2.3.7: Comparing Cab

Fares Teacher Created Exit Slip

Prentice Hall Page 99 #17-20, 38, 39

12 Mid-Unit Review (Teacher Created)

13 Mid-Unit Test (Omit Questions 8 and 9)

14

Investigation 4: Students write and solve multi-step

linear equations using the distributive property in a

number of different contexts.

Direct Instruction (Conceptual)

-Distributive Property

(Prentice Hall 1.7 Pg 46)

*Activity 2.4.2: Distributive

Property with Algebra Tiles

Additional Practice: *Activity

2.4.3 Using the Distributive

Property

*Exit Slip 2.4.1: ask students to solve

non-contextual equations using the

distributive property

Finish *Activity 2.4.2

15 *Activity 2.4.4: Walk-A-Thon

16 *Activity 2.4.5: Epic Win Epic

Fail Omit Page 3

*Exit Slip 2.4.2: ask students to solve

non-contextual equations using the

distributive property

Journal Entry 1: Ask students to

describe the graphs for a unique

solution, infinite solutions and no

solution.

17 *Activity 2.4.6: Pizza Party

(Version A has prompting

questions, Version B does not).

Exit Slip (Teacher Created)

(Prentice Hall Page 100-101)

18

Direct Instruction: Prentice Hall

Page 90 Example 4 (Clearing

Fractions)

*Activity 2.4.8 Fraction Busters

Prentice Hall Page 91 #21-29

19

Investigation 5: Students apply the principles of

solving equations to literal equations in order to

change the subject of an equation or formula


Prentice Hall 2.6

*Activity 2.5.3: Literal Equations

with Flowcharts

Journal Entry 1: have students explain

what it means to solve for a particular

variable

*Activity 2.5.2

20 *Activity 2.5.1: Literal Equations

Journal Entry 2: have students show

that they understand the meaning of

“literal equation”





21

Performance Task – Students make consumer

decisions about the purchase of iPods and downloads

The task requires students to model situations with

linear equations and use the equations to solve

problems

Performance Task: iPods

22

23

Investigation 6: Students will write linear

inequalities that model real world scenarios and solve

multi-step linear inequalities


*Activity 2.6.2: Equations and

Inequalities

Procedural Questions

*Activity 2.6.1: Representing

Inequalities

24 *Activity 2.6.4: Working with

Inequalities (Both pages)

25 *Activity 2.6.3: When do we flip

it

Journal Entry: asks students to explain

when and why they reverse an

inequality symbol when solving an

inequality

*Activity 2.6.5: Practice with

Inequalities

26 *Activity 2.6.6: Putting it all

Together

Exit Slip 2.6.1: asks students to solve

multi-step linear equalities

27 *Activity 2.6.8: Inequalities in the

Real World

Exit Slip 2.6.2: asks students to write a

linear inequality to model a situation

and then solve an inequality and

interpret the solution

28 End-Unit Review (Teacher Created)

29 End of Unit Test (Omit 5f, 6 and 7)

Algebra 1 – Unit 3: Functions – Revised Pacing Guide




Day Goal Activity Assessment Suggested Homework

1 Investigation 1: Students explore and define

relations, functions, domain, and range


*Activity 3.1.1b

Journal Entry: Ask students to define

function in their own words and to give

an example

*Activity 3.1.1a

2 Investigation 1: Activities are designed for whole-

class, small group, and paired discussions Activity 3.1.2: Is it a function?

Exit Slip 3.1: Ask students to determine

if a mapping diagram represents a

function and to identify range and

domain

3

Investigation 2: Students examine relations and

functions presented by tables, graphs and verbal

descriptions, identify the input and output variables,

dependent and independent variables, classify

relations as functions or non-functions, and examine

the domains of selected real world functions


*Activity 3.2.2: Hartford

Precipitation (A or B)

Journal Entry: Ask students how to use

a table or a graph to determine whether

a relation is a function

*Activity 3.2.3: Functions

Everywhere

4

Investigation 2: Students perform experiments

(Celsius and Fahrenheit, The Raven and the Jug) and

collect data that can be modeled by a function

Choose between the two:

*Activity 3.2.4: Celsius and

Fahrenheit

*Activity 3.2.5: The Raven and

the Jug

5

Investigation 3: Students are introduced to function

notation, learn to evaluate functions written in

function notation, and explore piecewise functions to

solve real world problems


(Prentice Hall 5.2)

OR

*Activity 3.3.1: Function

Machines

Exit Slip 3.3: Ask students to represent

a function using function notation and

use function notation to explore the

situation

6

Direct Instruction: Function

Notation (Prentice Hall 5.2-5.3)

“What is Function Notation” youtube

video by Maria Andersen

Additional *Activity 3.3.5:

Piecewise Functions

Journal Entry: Ask students to describe

the meaning of f(x)

Activity 3.3.4: Hot Air Balloons

7

Investigation 4: Students are introduced to linear

and non-linear functions and applications of linear

and non-linear functions

Discuss *Parent Function

Reference Sheet.

Choose between Activities 3.4.1-

3.4.9

Optional: Explore graphs in graphing

calculator (Lab on Pg 253 in Prentice

Hall)

Exit Slip 3.4: Ask students to explore

the graph of a non-linear function and

identify its domain and range

8

9 Writing Function Rules

Direct Instruction: Writing Function

Rules from tables, graphs and real

world context

(Prentice Hall 5.4)

Algebra 1 – Unit 3: Functions – Revised Pacing Guide




10

Functions Performance Task

Unit 3 Performance Task

(See NB Performance Task in

Binder)

11

12 End-Unit Review Review

13 End of Unit Test Note: Pay Attention to Question 3d.

Algebra 1 – Unit 4: Linear Functions – Revised Pacing Guide





1

Investigation 1: Distinguish between linear and non-linear functions in

context.


(Prentice Hall 5.1)

Use *Activity 4.1.1 Page 1 as an

exit slip.

*Activity 4.1.4 Stories and Graphs

2

Investigation 2:

Represent linear functions in verbal, tabular and

graphical forms for real world contexts and situations.

*Activity 4.2.1: Pizza Problem

3

Investigation 2:

Learn to recognize constant additive change – and,

thereby, linear functions – in verbal, tabular and

graphical forms of a function

*Activity 4.2.2: Recognizing

Linear Functions *Exit Slip 4.2.2

*Activity 4.2.3: Using Tables to

Determine if a Function is Linear

4 Investigation 2:

Connect real world contexts connect the mathematics

Choose between the two:

*Activity 4.2.4: Draining a

Swimming Pool

*Activity 4.2.7: Teddy Bear Sale

*Activity 4.2.5: Ordering DVDs

5

Quiz on Investigations 1 and 2:

This quiz assesses whether students can:

Determine if a function is linear given a table of values

Sketch a graph of a linear function from verbal

descriptions of real world situations, including

distance-time functions, and vice versa

State the meaning of the intercepts and other ordered

pairs in context

Identify the intercepts and whether a function is

increasing or decreasing from a verbal description,

graph or table of values

(Teacher Created)

6

Investigation 3:

Determine run, rise and slope given two points, and

thus develop the slope formula

Identify slope from a table or graph

Identify increasing functions as having positive slope

and decreasing functions as having negative slope

Graph a line given a point and the slope

*Activity 4.3.1: What is Slope?

(Last page optional)

*Activity 4.3.2 #1-2 in class

*Activity 4.3.2 #3a-h

7

Investigation 3:

Identify larger absolute value of slope with steeper

lines

Graph a line by creating a table of values when given

an equation

*Activity 4.3.4: Magnitude of

Slope Exit Slip 4.3.2

*Activity 4.3.3: Positive and

Negative Slope (Pages 1-2 only)





8 Investigation 3

Identify and graph horizontal and vertical lines

*Activity 4.3.5: Horizontal and

Vertical Lines

*Activity 4.3.6: Additional Practice

with Horizontal and Vertical Lines

9

Investigation 3

Recognize and interpret rates in the form of units of the

y per units of the x

Identify slope from a verbal description, table or graph

of a real world situation

Real-Life Applications of

Slope/Unit Rate

*Activity 4.3.1 Last Page Only

*Exit Slip 4.3.1

10

Investigation 4: Using technology, students examine the

effects of changing the parameters m and b in the slope-

intercept form of a line

*Activity 4.4.1: Effects of

Changing Parameters *Exit Slip 4.4.1

11

Investigation 4: Students write the equation of a line in

slope intercept form given a verbal description of a

situation, a table of values or a graph of a linear function

*Activity 4.4.2: Slope Intercept

Form

Activity 4.4.3: Practice with Slope

Intercept Form

12

Investigation 4: Students write the equation of a line in

slope intercept form given a verbal description of a

situation, a table of values or a graph of a linear function

Additional Practice Graphing and

Writing Equations in Slope

Intercept Form

Prentice Hall 6.2/Teacher Created

Kuta Workshop

13 Investigation 4: Students interpret the meaning of slope and

y-intercept in context *Activity 4.4.5: Applications of

Slope Intercept Form *Exit Slip 4.4.2

14 Investigation 4: Students will learn to identify pairs that are

parallel or perpendicular from their slopes


*Activity 4.4.6

Activity 4.4.7 Pages 1 and 2 only

15 Mid-Unit Review (Teacher Created)

16 Mid Unit Test

17

Investigation 5:

Solve direct variation problems and recognize that

direct variation is a linear function that has y-intercept

= 0 and slope y/x = constant of proportionality

Direct Instruction: Direct

Variation (Prentice Hall 5.5)

18

Investigation 5:

Solve direct variation problems and recognize that

direct variation is a linear function that has y-intercept

= 0 and slope y/x = constant of proportionality

*Activity 4.5.2: More Direct

Variation

19

Investigation 5:

Recognize the standard and slope intercept forms of a

linear equation

Direct Instruction: Standard Form

(Prentice Hall 6.3)

*Activity 4.5.4: More Standard Form

#1-5

20 Investigation 5:

Find the x- and y- intercepts of an equation, interpret *Activity 4.5.4 #6-8

*Exit Slip 4.5 Prentice Hall Pg 301-302





them in context, use them to graph an equation

21 Investigation 5:

Transform standard form to slope intercept form

Teacher Created Practice

transforming from standard form

to slope intercept form.

22

Investigation 6:

Students will write the equation of a line in slope intercept

form, point-slope form, or standard form given:

The slope and y-intercept

The slope and one ordered pair on the line

Two ordered pairs

An ordered pair and an equation of a parallel or

perpendicular line

Activity 4.6.2: Point Slope Form

of an Equation

Prentice Hall 6.4

Exit Slip 4.6.1

23

Activity 4.6.3 Pages 1 and 2

24 Investigation 6:

Students will be able to apply point slope form in real world

situations

Activity 4.6.3: Pages 3 and 4

Teacher Created Practice

Exit Slip 4.6.2

25

Investigation 6:

Students will identify the advantages of each of

the 3 different forms of the line and choose among

them

Transform an equation from slope-intercept or

point-slope to standard form

Transform an equation from point-slope or

standard form to slope-intercept form

Activity 4.6.4 (a or b): Can We

Both Be Right?

Activity 4.6.6: Finding and Using

Linear Equations

Activity 4.6.5

26

Performance Task: State of the States

This performance task:

o Requires students to work with data for the

populations of Connecticut, Kansas, Louisiana, and

Nevada between the years of 2000 and 2008

o Assesses students’ ability to distinguish linear from

non-linear function, and increasing from decreasing

functions

o Find a linear equation to model nearly linear data

o Compare two different linear models

o Use the linear model to predict population

o Evaluate the accuracy of the model

(Teachers may choose to do

Performance Task after End of Unit

Test as a lead in to Scatterplots)

27

28 End-Unit Review

Students will be able to answer the

following questions:

1. Given the graph of a linear

function, including a horizontal

line, identify the corresponding

equation, create a table of values,

identify the y-intercept and slope,

and write the equation of a line

parallel and a line perpendicular

(See Chapter 4 Review in NB Files

under file name

AlgNB 4.R – HW – Unit 4 Review)





to the given line.

2. Find the point-slope form of an

equation between two points and

transform the equation into slope-

intercept form.

3. Choose which of the 3 forms of a

linear equation to use to model

contextual situations, identify and

explain the meaning of the slope

and the y-intercept in context.

4. Choose a linear model, graph or

table to predict or analyze

something in a contextual

situation.

28 End of Unit Test

Algebra 1 – Unit 5: Scatter Plots and Trend Lines – Revised Pacing Guide





1

Investigation 1: Students will explore and define measures

of center.

*Activity 5.1.1: Hurricanes *Exit Slip 5.1.1

*Activity 5.1.2 Pages 1 and 2 only

2

Investigation 1: Students will explore measures of spread

and display data in dot plots, histograms and box-and-

whisker plots

*Activity 5.1.2 Page 3

*Activity 5.1.4: The Five-Number

Summary

*Exit Slip 5.1.2

*Activity 5.1.3: More histograms

3 Investigation 1: Students will analyze real world data by

hand and using a graphing calculator

*Activity 5.1.6: Box and Whisker

Plots (Choose between Version A or

Version B)

*Activity 5.1.5: Outliers and the

1.5xIQR Rule

4 *Activity 5.1.7: Test Grades

(Possible Group Activity)

5

Investigation 2: Students are introduced to scatter plots and

trend lines and use the equation of trend lines to make

predictions.

*Activity 5.2.1: Sea-Level Rise

(Use Powerpoint 5.2.1 on Moodle site) *Exit Slip 5.2.1

*Activity 5.2.2: Scatter Plots and

Trend Lines (May do Pages 1 and 2

only).

6

Investigation 2: Students will continue to use the equation

of trend lines to make predictions and learn the meaning of

interpolation and extrapolation.

*Activity 5.2.3: Television,

Homework and Test Scores

*Activity 5.2.4: Height and Shoe Size

#1-3 (collect data)

Journal Entry: Describe the

difference between interpolation

and extrapolation. Give an

example of each. Which is more

useful and why?

*Activity 5.2.4 #4-11 for HW

7

Investigation 3: Students will use the graphing calculator to

find the linear regression equation, find the correlation

coefficient and interpret the meaning of the correlation

coefficient.

*Activity 5.3.1: Fitting Lines with

Technology

*Activity 5.3.2: Evolution of

Telephone (Optional – if time allows)

8 Investigation 3: Students will be able to explain the

difference between correlation and causation.

*Activity 5.3.3: Correlation and

Causation

Journal Entry: Describe the

difference between correlation

and causation.

*Activity 5.3.4: Shark Attack

Worksheet

9

Investigation 4: Students will be collecting and analyzing

in interdisciplinary activities. They will apply all of their

knowledge from the previous two investigations.

*Activity 5.4.1: Forensic

Anthropology – teacher directed

(Use Powerpoint 5.4.1 on Moodle site)

10

11 Choose 1 Activity Between:

*Activity 5.4.2 and *Activity 5.4.7

Mid-Unit Quiz

Quiz provided in NB Files

12

Algebra 1 – Unit 5: Scatter Plots and Trend Lines – Revised Pacing Guide




13

Investigation 5: Students will work with data sets that

contain outliers to identify the influence that outliers have

on the calculation and interpretation of the slope, y-

intercept, linear regression equation and correlation

coefficient.

*Activity 5.5.1: Outliers *Exit Slip 5.5: Cooling Off

*Activity 5.5.3: Home Prices

14 *Activity 5.5.4: Chicago Bulls

*Activity 5.5.6: Sea Glass

*Activity 5.5.5 Crickets

Chirping (Change/Omit # 3)

15

Investigation 6: Students will explore situations in which

the data are best represented by a piecewise linear function,

will fit a line to each section of the data and will use the

lines to make predictions.

*Activity 5.6.1: Swimming Records

-teacher directed

16

*Activity 5.6.2: Paychecks and

Triathlons

17 *Activity 5.6.3: Dog Food

*Exit Slip 5.6

18 *Activity 5.6.5: Bike Tours

*Activity 5.6.6: Creating Stories

19 End of Unit Review (Teacher Created)

20 End of Unit Test/Performance Task

Algebra 1 – Unit 6: Systems of Equations – Revised Pacing Guide





1

Investigation 1: Students will solve systems of linear

equations by making tables, solving linear equations in one

variable and graphing lines.

Direct Instruction: Solving Systems by

Graphing

(Prentice Hall 7.1)

*Activity 6.1.3: Solving Systems of

Equations by Graphing.

2

Investigation 1: Students will find and interpret solutions of

systems of linear equations and use systems of linear

equation to solve real world problems.

*Activity 6.1.2: Choosing a Gym Exit Slip 6.1

*Activity 6.1.4

3

Investigation 2: Students will use the substitution method

to solve systems of linear equations.


Substituion

(Prentice Hall 7.2)

*Activity 6.2.2 Page 1 only

4

*Activity 6.2.2 Page 2-3

Supplement with more Applications

from PH

*Activity 6.2.3: More Practice with

Substitution

5 *Activity 6.2.4: Drag Racing

-Teacher directed

6

*Activity 6.2.6: Solutions to Systems

of Equations (Possible Group activity)

*Activity 6.2.7: One for All and All

for One

Prentice Hall 7.2 Application

Problems

7

Investigation 3: Student will use the elimination method to

solve systems of equations and interpret the solution of a

system of linear equations within the context of the problem.


Elimination (include mult problems)

(Prentice Hall 7.3)

(Optional: *Activity 6.3.4: Mechanics

of Elimination Method)

*Exit Slip 6.3.1

Prentice Hall 7.3 Practice Problems

8 *Activity 6.3.2: Exploring the Number

of Solutions *Exit Slip 6.3.2

9 *Activity 6.3.3: Applications of the

Elimination Method

Prentice Hall 7.3 Application

Problems

10 Suggested: Explore Systems of Linear Inequalities

11

12

*Performance Task

13

14 End of Unit Review

15 End of Unit Test

Algebra 1 – Unit 7: Introduction to Exponential Functions – Revised Pacing Guide




Day Goal Activity/Classwork Assessment Suggested Homework

1

Investigation 1: Students will be introduced to exponential

growth patterns and illustrate how exponential growth

compares to linear growth

*Activity 7.1.2: Is it a Good Deal?

(Graphing calculator needed)

*Exit Slip 7.1.1

*Activity 7.1.3: A Closer Look at

Population Data

(Students need calculator – does not

need to be graphing)

2

Investigation 2: By extending patterns based on properties

of positive integer exponents, students learn the meaning of

zero, negative, and rational exponents

*Activity 7.2.1: Exploring Growth

Patterns

(Guided Practice)

3

*Activity 7.2.2: The Meaning of

Integer Exponents Pages 1-3

(Properties with Positive Numeric

Exponents)

Kuta Practice Worksheet

4

*Activity 7.2.2: The Meaning of

Integer Exponents Pages 4-5

(Properties with negative exponents)

*Exit Slip 7.2.1

Kuta Practice Worksheet

5 *Activity 7.2.3: Exploring the

Meaning of Rational Exponents

6

Direct Instruction: Relationship

between Roots and Exponents

*Activity 7.2.4: Roots and Exponents

*Exit Slip 7.2.2

7

Investigation 2: Students will begin to understand that the

exponential function will always overtake the linear

function.

*Activity 7.2.6a: How Much Rice

*Activity 7.3.1: Building Walls Page

1 Only! (In preparation for

tomorrow’s lesson)

8

Investigation 3: Students will explore the effects of

changing the parameters a and b in the general exponential

function f(x) = abx.

*Activity 7.3.1: Building Walls-

Finish *Exit Slip 7.3

*Activity 7.3.3: Effects of Parameter

Pages 1-3 Only (In preparation for

tomorrow’s lesson).

9

*Activity 7.3.3: Effects of Parameters

- Finish

(Graphs of Exponential Functions by

hand)

10

*Activity 7.3.2: Exploring the Graph

𝑦 = 𝑎𝑏𝑥

(Graphing Calculators needed)

Algebra 1 – Unit 7: Introduction to Exponential Functions – Revised Pacing Guide




11

Investigation 4: They will understand that when b > 1 the

function models exponential growth and that when 0 < b < 1

the function models exponential decay. They will identify a

as the initial value or y- intercept. They will identify

exponential functions and distinguish exponential functions

from other types of functions, especially linear functions,

from tables of values and real- world contexts

*Activity 7.3.5: Growth and Decay

Situations

Finish Activity 7.3.5 for Homework

12 *Activity 7.3.6: Identifying

Exponential Functions Exit Slip 7.4

13

Investigation 5: Students explore the relationship between

rates of change and the growth or decay factor they have

learned to associate with the parameter b in the general form

of the exponential function 𝑓(𝑥) = 𝑎 ∙ 𝑏𝑥

*Activity 7.5.1: Percent’s and Percent

Change

14

*Activity 7.5.2: Percent Change and

Exponential Functions

*Activity 7.5.3: Percent Change

Situations

*Activity 7.5.3: Percent Change

Situations (Finish)

15

*Activity 7.5.4: Modeling Exponential

Functions: What is the Percent

Change?

16

Investigation 5: Students will explore and discuss

compound interest and the concepts of doubling time and

half-life.

*Activity 7.5.5: Compound Interest

*Activity 7.5.6: Doubling Time and

Half-Life

17

Investigation 6: Students model the increasing

concentration of carbon dioxide in the earth’s atmosphere

with an exponential equation of the form 𝑓(𝑥) = 𝑎 ∙ 𝑏𝑥

Students analyze global temperature data and model the

increasing trend with a linear model of the form y = mx + b.

*Activity 7.6.1: OPTIONAL


19 End of Unit Test (Quiz?)

(Teacher Modify for 2014)

Required Investigations

Required Activities

Algebra 1 – Unit 8: Quadratic Functions – Revised Pacing Guide


Norwalk Public Schools



1

Foundational Skills: Students will perform

operations on polynomials.

Adding and Subtracting Polynomials

Multiplying and Factoring (GCF) a Monomial and a

Polynomial (Activity 8.5.1)

Multiplying Binomials

Multiplying Special Cases

Prentice Hall 9.1-9.4 2

3

4

Investigation 1: Students will compare

another non-linear pattern of growth with

linear and exponential patterns

by looking at data.

Activity 8.1.1 – Quadratics in the Kitchen

o Teacher Note: Provide the data for the table given in

the overview for this investigation

Exit Slip 8.1.1

5 Activity 8.1.4 – Recognizing Quadratic Functions by Table

6 Activity 8.1.6 – Exploring the Graph of

cbxaxy 2

o Teacher Note: Identify the Axis of Symmetry and

Vertex, but we will go more in depth with those

concepts in Investigation 2

7 Exit Slip 8.1.2 Prentice Hall 10.1

8 Investigation 2: Students will discover the

line of symmetry of a parabola whose

equation is given in standard form. Given an

equation in vertex form, students will

investigate the effects of the parameters a, h

and k on the graph of a parabola, identify

the vertex and whether the parabola opens

up or down. Students will reverse the

process and write an equation in vertex

form for a parabola given its vertex and one

other point. Students will learn to transform

a quadratic function from standard form to

vertex form

Activity 8.2.1a – Design a Solar Cooker

9 Activity 8.2.2 – Graphing in Vertex Form

10

Activity 8.2.3 – Exploring Parameters with Geometer

Sketchpad

o Teacher Note: This activity can be done without the

software or you can get a free copy for your

SMARTboard (must get permission)

Exit Slip 8.2 – Investigating

Parameters

11 Activity 8.2.6 – Transforming Functions in Standard Form

to Vertex Form

Activity 8.3.1 –

Fenway Park

12 Investigation 3: Students will learn to

apply the Square Root property and the

principle of “undoing” to solve equations of

the form khxay 2)( . They will

then apply this skill to finding the y-

intercepts of parabolas with functions in

vertex form and applications of functions

given in vertex form.

Activity 8.3.2 – The Square Root Property

13

Activity 8.3.3 & 8.3.4 (Combination of the two) – Solving

Two-Step & Multi-Step Equations using the Square Root

Property

Exit Slip 8.3.1 – Solving

Two-Step Equations with

Square Roots

Finish the Combination

of 8.3.3 & 8.3.4

14 Activity 8.3.5 – Finding x-intercepts of Parabolas Exit Slip 8.3.2 – Finding the

x-intercepts

Algebra 1 – Unit 8: Quadratic Functions – Revised Pacing Guide


Norwalk Public Schools


**Teacher Note: You may switch the order of the investigations depending on your situation; i.e. investigation 5 may come before investigation 4.**

15

Continue work from Days 12-14 Activity 8.3.6 – Solving Quadratic Equations in Standard

Form

16 Investigation 4: Students will discover that

quadratic functions can be expressed in

factored form and will model real world

situations using quadratic functions in

factored form. Using the graph of a

quadratic function in factored form, students

will find the vertex of the parabola to solve

a variety of problems. They will learn how

to multiplying polynomials and apply this

skill to convert quadratic functions in

factored form to quadratic functions in

standard form.

Activity 8.4. – TEACHER CHOICE (see Moodle site) Teacher choice

17 Activity 8.4. - TEACHER CHOICE (see Moodle site) Teacher choice

18 Activity 8.4.5 – Multiplying Polynomials Teacher choice

19 Activity 8.4.- TEACHER CHOICE (see Moodle site) Teacher choice

20

Investigation 5: Students will factor

quadratic trinomials of various forms and

convert quadratic functions in standard form

to quadratic functions in factored form.

They will learn that factoring polynomials is

the inverse operation of multiplying

polynomials.

Activity 8.5.2 – Factoring Trinomials

Prentice Hall – Investigation: Using Models to Factor (Page

480)

o Teacher Note: Use the Area Models from Prentice Hall

to demonstrate while teaching because these models

WILL be incorporated in SBAC assessment items

Prentice Hall 9.5

21 Prentice Hall 9.5

22 Activity 8.5.3 – Find Your Match Prentice Hall 9.6

23 Activity 8.5.4 – Solving Quadratic Equations by Factoring Prentice Hall 10.4

24 Investigation 6: Students will learn how to

solve quadratic equations by completing the

square and using the quadratic formula.

25 TEACHER CHOICE (see Moodle site) Teacher choice


27 End of Unit Test

algebra 1 unit 1 patterns revised pacing guide … 1 – unit 1 patterns – revised pacing guide...

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