Scope and Sequence: Grade 7 Mathematics Units 1-9 2012-2013 · Grade 7 Common Core State Standards Scope and Sequence…Page 5 SAMPLE DEMONSTRATIONS OF LEARNING (DOLS) Conceptual

The Newark Public Schools

Scope and Sequence: Grade 7 Mathematics Units 1-9

2012-2013

Office of Mathematics

Grade 7 Common Core State Standards Scope and Sequence…Page 1

OFFICE OF MATHEMATICS

Tina Powell – Mathematics Director Paul Oliveira – Mathematics Supervisor

WRITING COMMITTEE

Tina Powell ............................................................................................................................................................................................ Director of Mathematics

Paul Oliveira ................................................................................................................................................................................................................ Supervisor

Michele Albruzzese .......................................................................................................................................................................................................... Teacher

Tracy Blazquez ................................................................................................................................................................................................................ Teacher

Chiffon Brown ................................................................................................................................................................................................................. Teacher

Thalia Brownridge-Smith ................................................................................................................................................................................................. Teacher

John Capparelli ............................................................................................................................................................................................................... Teacher

Ivone Cardoso .................................................................................................................................................................................................................. Teacher

Darlene DeVries ............................................................................................................................................................................................................... Teacher

Whitney Farrand .............................................................................................................................................................................................................. Teacher

Correl Heron .................................................................................................................................................................................................................... Teacher

Joseph Hrdina .................................................................................................................................................................................................................. Teacher

Genell Jackson ................................................................................................................................................................................................................. Teacher

Sheyla Jannah.................................................................................................................................................................................................................. Teacher


Writing Committee continued:

Chanda Jones-Williams .................................................................................................................................................................................................... Teacher

Melissa Lisanti ................................................................................................................................................................................................................. Teacher

Susette Martins ............................................................................................................................................................................................................... Teacher

Jennifer Padilla ................................................................................................................................................................................................................ Teacher

Amy Panitch .................................................................................................................................................................................................................... Teacher

Coralie Peary ................................................................................................................................................................................................................... Teacher

Tracey Pereda.................................................................................................................................................................................................................. Teacher

Daniel Ramirez ................................................................................................................................................................................................................ Teacher

Deborah Richardson ........................................................................................................................................................................................................ Teacher

Yolanda Smith ................................................................................................................................................................................................................. Teacher

Doreen Williams-Brown ................................................................................................................................................................................................... Teacher


SEMESTER ONE

UNIT VOCABULARY

IN-DEPTH OPPORTUNITIES

7.NS.3 7.RP.2 7.EE.3 7.EE.4 7.G.6

UNIT 1:

RATIONAL NUMBERS

Addition and Subtraction of

negative and positive numbers

Horizontal Articulation

Suggested Support/Review

Standards

6.NS.5 [rational numbers]

6.NS.6a [opposites]

6.NS.7c [absolute value]

Standards Description Days Resources

7.NS.1 Apply and extend previous understandings of addition and subtraction

to add and subtract rational numbers; represent addition and

subtraction on a horizontal or vertical number line diagram.

a. Describe situations in which opposite quantities combine to

make 0. For example, a hydrogen atom has 0 charge because

its two constituents are oppositely charged.

b. Understand p + q as the number located a distance |q| from

p, in the positive or negative direction depending on

whether q is positive or negative. Show that a number and

its opposite have a sum of 0 (are additive inverses).

Interpret sums of rational numbers by describing real-world

contexts.

c. Understand subtraction of rational numbers as adding the

additive inverse, p – q = p + (–q). Show that the distance

between two rational numbers on the number line is the

absolute value of their difference, and apply this principle in

real-world contexts.

d. Apply properties of operations as strategies to add and

subtract rational numbers.

Module 7.NS.1

opposite

positive

negative

additive inverse

absolute value

rational number

Properties of Operations

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LESSON PLANNING

UNIT 1:

RATIONAL NUMBERS

Addition and Subtraction of

negative and positive

numbers

Recommended

Technologies:

Course Proficiencies Textbook Alignment Multiple

Representations

Comments

Add and subtract rational numbers. Represent addition and subtraction on a horizontal or vertical number line diagram. Understand that a number added to its “additive inverse” results in zero. Apply properties of operations as strategies to add and rational numbers. Solve real world and mathematical problems involving the four operations with rational numbers. Solve multi-stem real world and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to

calculate with numbers in any form.

CMP2: Accentuate

the Negative

Investigation 1

(Extending the

Number System)

Additional Practice

and Skills Workbook

pgs. 58-64

Investigation 2

( Adding and

Subtracting Integers)

Additional Practice

and Skills Workbook

pgs. 65-73

Concrete

Fraction Strips

Colored Chips

Algebra Tiles

Pictorial

Number Line

Bar Model

Fraction Circle

Table

Abstract

Standard

Algorithm/Equation:

(Same signs find the

sum and keep the sign.

Different signs, find

the difference and take

the sign of the

integers with the

larger absolute value)

p – q = p + (-q) p – (-q) = p + (q) -p – q = -p + (-q) -p – (-q) = -p + (q) Properties of

Operations:

Commutative

Associative

Distributive

Identity Property

Zero Property

Order of Operations:

PEMDAS

Visual representations may be helpful as students

begin this work; they become less necessary as

students become more fluent with the operations.

Examples:

Use a number line to illustrate: o p - q o p + (- q) o Is this equation true p – q = p + (-q)

-3 and 3 are shown to be opposites on the number line because they are equal distance from zero and therefore have the same absolute value and the sum of the number and it’s opposite is zero.

You have $4 and you need to pay a friend $3. What will you have after paying your friend?

4 + (-3) = 1 or (-3) + 4 = 1

NPS Common Core eBoard www.npscommoncore.newark.site.eboard.com Click the CCSS Math tab for additional materials NPS Math Modules http://www.virtualnerd.com User Id: your district email Password: teachwithvn Manipulatives Explore Learning http://www.thinkingblocks.com/ National Library of Virtual

Manipulatives

To be

determined at

the school

level

http://www.npscommoncore.newark.site.eboard.com/


http://www.virtualnerd.com/

http://www.explorelearning.com/index.cfm?method=cResource.dspBrowseCorrelations&v=s&id=USA-000

http://www.thinkingblocks.com/


http://nlvm.usu.edu/en/nav/vlibrary.html



SAMPLE DEMONSTRATIONS OF LEARNING (DOLS)

Conceptual Understanding

How do the properties of whole numbers extend to the addition and subtraction of rational numbers?

Procedural Fluency

Solve: 2/5 – 5/7 + 4/7 =

Application

Louis was doing a science experiment about temperature. He first measured the temperature of some water and found it was 17°C. Then he put the water in the freezer and recorded the temperature two hours later. It had fallen to -11°C. What was the change in temperature in two hours? What was the average rate of temperature change per hour? Show your work.

Connected Mathematics Program 2 Correlated Assessments Additional Assessments Resources

Accentuate The Negative Partner Quiz

Accentuate The Negative Question Bank

Formative Assessments: http://njctl.org/courses/math/7th-grade/number-system/number-system-7th-grade/

Summative Assessments: http://www.state.nj.us/education/modelcurriculum/math/7u1.shtml

http://njctl.org/courses/math/7th-grade/number-system/number-system-7th-grade/


http://www.state.nj.us/education/modelcurriculum/math/7u1.shtml


UNIT VOCABULARY


7.NS.3 7.RP.2 7.EE.3 7.EE.4 7.G.6

UNIT 2:

RATIONAL NUMBERS

Multiplication and Division of negative and

positive numbers; Solving real-world

mathematical problems.


Suggested Support/Review Standards

5.NF.3 [fractions]

5.NF.4a [multiplication]

6.NS.1 [division of fractions]

UNIT 1 AND 2 ASSESSMENT

AVAILABLE


7.NS.2 Apply and extend previous understandings of multiplication and

division and of fractions to multiply and divide rational numbers.

a. Understand that multiplication is extended from fractions

to rational numbers by requiring that operations continue

to satisfy the properties of operations, particularly the

distributive property, leading to products such as (–1)(–1) =

1 and the rules for multiplying signed numbers. Interpret

products of rational numbers by describing real-world

contexts.

b. Understand that integers can be divided, provided that the

divisor is not zero, and every quotient of integers (with non-

zero divisor) is a rational number. If p and q are integers,

then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational

numbers by describing real-world contexts.

c. Apply properties of operations as strategies to multiply and

divide rational numbers.

d. Convert a rational number to a decimal using long division;

know that the decimal form of a rational number

terminates in 0s or eventually repeats.

7.NS.3

Solve real-world and mathematical problems involving the four

operations with rational numbers. (NOTE: Computations with rational

numbers extend the rules for manipulating fractions to complex

fractions.)

operations properties rational numbers

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LESSON PLANNING

UNIT 2:

RATIONAL NUMBERS

Multiplication and Division of

negative and positive numbers;

Solving real-world mathematical

problems


Representations

Comments

Multiply and divide rational numbers. Explain products of rational numbers by describing real world situations. Understand that all integers can be divided provided the divisor is not zero, and that the quotient will be a rational number. Convert a rational number to a decimal by using long division. Solve real world and mathematical problems involving the four operations with rational numbers. Solve multi-stem real world and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form. Convert between forms as

appropriate, and assess the

reasonableness of answers using

mental computations and

estimation strategies.

CMP2: Accentuate the

Negative

Investigation 3

(Multiplying and

Dividing Integers)

Additional Practice and

Skills Workbook

pgs.74-78

Investigation 4

(Properties of

Operations)

Additional Practice and

Skills Workbook

pgs.79-82

Concrete

Fraction Strips

Colored Chips

Algebra Tiles

Pictorial

Number Line

Bar Model

Fraction Circle

Tabular Representation

Abstract

Algorithm:

(Same signs will give you

a positive product or

quotient. Different signs

will give you a negative

product or quotient)

-(p/q) = (-p)/q = p/(-q)

When “p” is not equal to

zero

Properties of Operation:

Commutative

Associative

Distributive

Identity Property

Zero Property

Order of Operations:

PEMDAS

Multiplication and division of integers is an extension

of multiplication and division of whole numbers.

Equation Number

Line

Model

Context

2 x 3 = 6

Selling

two

posters at

$3.00 per

poster

2 x -3 = -6

Spending

3 dollars

each on 2

posters

Examples: Examine the family of equations. What

patterns do you see? Create a model and context for

each of the products.

Recommended Technologies: NPS Common Core eBoard www.npscommoncore.newark.site.eboard.com Click the CCSS Math tab for additional materials NPS Math Modules http://www.virtualnerd.com User Id: your district email Password: teachwithvn Manipulatives Explore Learning http://www.thinkingblocks.com/ National Library of Virtual

Manipulatives

To be

determined at

the school

level











Using only one cut, how would you divide 7 pieces of licorice among 5 people so that each person gets the exact same amount of licorice without bending the licorice without bending the licorice?

Show your work using drawings, numbers and words.

Explain your strategy for solving the problem.

Verify your answer another way.

Procedural Fluency

Solve:

a. 161.18 7.8 = b. 2 ½ x 7 ½ =

Application

The Herms family takes their sailboat to an island in a nearby lake for a picnic. The island is 6 miles from shore. It takes the family 3/4 hour to sail to the island and only 2/5 of an hour to sail back to shore with a stronger wind. What was the family’s average rate of sailing speed (miles per hour) for the entire trip?

Connected Mathematics Program 2 Correlated Assessments Additional Assessments Resources

Accentuate The Negative Partner Quiz

Accentuate The Negative Multiple Choice Items

Accentuate The Negative Question Bank

Accentuate The Negative Unit Test

Formative Assessments: http://njctl.org/courses/math/7th-grade/number-system/number-system-7th-grade/






UNIT VOCABULARY


7.NS.3 7.RP.2 7.EE.3 7.EE.4 7.G.6

UNIT 3: UNIT RATES Understanding and Applying Unit Rates. Horizontal Articulation Suggested Support/Review Standards Standards6.RP.2 [ratios]


7.RP.1

Compute unit rates associated with ratios of fractions, including ratios

of lengths, areas and other quantities measured in like or different

units. For example, if a person walks 1/2 mile in each 1/4 hour, compute

the unit rate as the complex fraction (1/2)/(1/4) miles per hour,

equivalently 2miles per hour.

common denominator

equation

equivalent

equivalent ratios

proportion

ratio

unit rate

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LESSON PLANNING

UNIT 3 UNIT RATES Understanding and Applying Unit Rates Horizontal Articulation Suggested Support/Review Standards Standards6.RP.2 [ratios] Recommended Technologies: NPS Common Core eBoard www.npscommoncore.newark.site.eboard.com Click the CCSS Math tab for additional materials NPS Math Modules http://www.virtualnerd.com User Id: your district email Password: teachwithvn Manipulatives Explore Learning http://www.thinkingblocks.com/ National Library of Virtual Manipulatives

Course Proficiencies Textbook

Alignment

Multiple

Representations

Comments

Use ratios of lengths, areas and other quantities to compute unit rates associated with ratios of fractions. Convert between forms as appropriate, and assess the reasonableness of answers using mental computations and estimation strategies. Compute actual

lengths and areas of a

geometric figure from

scale drawings and

reproductions of the

figure.

CMP2: Comparing

and Scaling

Investigation 1

(Strategies for

Representing

Quantitative

Comparisons)

Additional Practice

and Skills

Workbook pgs. 39-

43

Investigation 2

(Comparing Ratios,

Percents, and

Fraction)

Additional Practice

and Skills

Workbook pgs. 44-

47

Investigation 3

(Comparing and

Scaling Rates)

Additional Practice

and Skills

Workbook pgs. 48-

53

Concrete

Partitioning with

manipulatives

Pictorial

Fraction Strips

(Tape Diagrams)

Double Line

Diagrams

Tabular

Representation

Graphing

Abstract

Scale Factor

(within and

between)

Iteration

Algorithm

Part/Whole

Relationship

Part/Part

Relationship

Connected Mathematics Programs 2 does not address unit rates in the 6

th grade CMP2 books.

Therefore, visit the sites below for horizontal articulation tasks. http://illustrativemathematics.org/standards/k8 http://insidemathematics.org/common-core-math-tasks/6thgrade/6-2007%20Candies.pdf http://insidemathematics.org/commmon-core-math-tasks/6th-grade/6-2009%20Truffles.pdf Ratios arise in situations in which two (or more) quantities are related. Sometimes the quantities have the same units (e.g., 3 cups of apple juice and 2 cups of grape juice), other times they do not (e.g., 3 meters and 2 seconds). To distinguish ratios and rates, using the term “ratio” when units are the same and “rate” when units are different. Rates arise in situations in which two (or more) different quantities are related. Examples: “3 cups of flour for every 2 eggs” or “3 meters in 2 seconds”

To be

determined at

the school

level






http://illustrativemathematics.org/standards/k8

http://insidemathematics.org/common-core-math-tasks/6thgrade/6-2007%20Candies.pdf

http://insidemathematics.org/common-core-math-tasks/6thgrade/6-2007%20Candies.pdf

http://insidemathematics.org/commmon-core-math-tasks/6th-grade/6-2009%20Truffles.pdf

http://insidemathematics.org/commmon-core-math-tasks/6th-grade/6-2009%20Truffles.pdf



Conceptual Understanding Create a table of values for the following scenarios. Ryan is making a fruit drink. The directions say to mix 5 cups of water with 2 scoops of powdered fruit mix. How many cups of water should he use with 9 scoops of fruit mix?

Teaching Tips:

Procedural Fluency

Solve: a. A 2.6 kg bag of carrots for $7.05= ____ per kg b. $17.40 for 12 hours = _____ per hour c. 70 chairs in 5 rows = _____ in each row

Teaching Tips:

Application

Kell works at an after-school program at an elementary school. The table below shows how much money he earned every day last week.

Monday Wednesday Friday

Time Worked

1.5 hours 2.5 hours 4 hours

Money Earned

$12.60 $21.00 $33.60

Mariko has a job mowing lawns that pays $7 per hour.

a. Create a similar table of values for Mariko. Who would make more money for working 10 hours? Explain or show work.

b. Graph of the proportional relationship between the two quantities.

c. Generate the equation that represents the two quantities.

d. How does the constant of proportionality (-ies) help you understand who has the better paying job?

Connected Mathematics Program 2 Assessments Additional Assessment Resources

Comparing and Scaling Check Up

Comparing and Scaling Partner Quiz

Comparing and Scaling Multiple Choice Items

Comparing and Scaling Question Bank

Comparing and Scaling Unit Test

Formative Assessments: http://njctl.org/courses/math/7th-grade/ratios-proportions/ratios-proportions-7th-grade-2/

http://njctl.org/courses/math/7th-grade/ratios-proportions/ratios-proportions-7th-grade-2/



UNIT VOCABULARY


7.NS.3 7.RP.2 7.EE.3 7.EE.4 7.G.6

UNIT 4:

PROPORTIONAL REASONING AND

RELATIONSHIPS

Rates, Ratios, and Percents, and

Estimating



6.RP.2 [ratios]

6.RP.3 [application of rates]

7.NS.1 [+/- rational numbers]

7.NS.2 [x/ rational numbers]

7.NS.3 [application of rational #s]

UNIT 3 AND 4 ASSESSMENT

AVAILABLE


7.RP.2 Recognize and represent proportional relationships between quantities. a. Decide whether two quantities are in a proportional

relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

c. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

Module

7.RP.1-2

7.RP.3 Use proportional relationships to solve multistep ratio and percent

problems. Examples: simple interest, tax, markups and

markdowns, gratuities and commissions, fees, percent increase and

decrease, percent error.

Module

7.NS.2-3;

RP.3

7.EE.3

Solve multi-step real-life and mathematical problems posed with

positive and negative rational numbers in any form (whole numbers,

fractions, and decimals), using tools strategically. Apply properties of

operations to calculate with numbers in any form; convert between

forms as appropriate; and assess the reasonableness of answers using

mental computation and estimation strategies.

equivalent ratio

proportion

ratio commission

fee

gratuity (tax)

percent of change

percent of decrease

percent of increase

principal

sales tax

scale drawing

simple interest

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LESSON PLANNING

UNIT 4:

PROPORTIONAL REASONING AND

RELATIONSHIPS

Rates, Ratios, and Percents, and Estimating

Horizontal Alignment


6.RP.2 [ratios]

6.RP.3 [application of rates]

7.NS.1 [+/- rational numbers]

7.NS.2 [x/ rational numbers]

7.NS.3 [application of rational #s]

Vertical Alignment

8.EE.5 [graphing relationships]

8.EE.7 [Linear Equations]

8.EE.8 [Simultaneous Linear Equations]

Recommended Technologies: NPS Common Core eBoard www.npscommoncore.newark.site.eboard.com Click the CCSS Math tab for additional materials NPS Math Modules http://www.virtualnerd.com User Id: your district email Password: teachwithvn Manipulatives Explore Learning http://www.thinkingblocks.com/ National Library of Virtual Manipulatives

Course Proficiencies Use ratios of lengths, areas and other quantities to compute unit rates associated with ratios of fractions. Recognize and represent proportional relationships between quantities. Identify a constant of proportionality. Represent proportional relationships by equations. Solve multi-step ratio and percent problems.

Textbook

Alignment

Comparing and Scaling Investigation 1 Making Comparison Investigation 2 Comparing Ratios, Percent, and Fractions Investigation 3 Comparing and Scaling Rates Investigation 4 Making Sense of Proportions Moving Straight Ahead Investigation 1 Walking rates Investigation 2 Exploring Linear Functions with graphs and Tables Investigation 3

Solving Equation

Investigation 4

Exploring Slope

Variables and Patterns Investigation 1

Variables, Tables,

and Coordinate

Graphs

Investigation 2 Analyzing Graphs and Tables

Multiple

Representations

Concrete

Bar Models

Paper Strips

Number Lines

Pictorial

Table

representation

Graphical

representation

Abstract

Finding the

Unit

Rate/Constant

of

Proportionality

Simplifying

Rates

Setting up a

Proportion

Creating an

Equation

Comments

The constant of proportionality is

shown in the first column of the table

and by the slope of the line on the

graph.

A common error is to reverse the position of the variables when writing equations. Students may find it useful to use variables specifically related to the quantities rather than using x and y. Constructing verbal models can also be helpful. A student might describe the situation as “the number of packs of gum times the cost for each pack is the total cost in dollars”. They can use this verbal model to construct the equation. Students can check their equation by substituting values and comparing their results to the table. The checking process helps student revise and recheck their model as necessary. X axis is the independent variable Y axis is the dependent variable

Students should be able to explain or

show their work using a

representation (numbers, words,

pictures, physical objects, or

equations)

To be

determined

at the school

level







LESSON PLANNING (CONTINUED)

Recommended Technologies: NPS Common Core eBoard www.npscommoncore.newark.site.eboard.com Click the CCSS Math tab for additional materials NPS Math Modules http://www.virtualnerd.com User Id: your district email Password: teachwithvn Manipulatives Explore Learning http://www.thinkingblocks.com/ National Library of Virtual Manipulatives

Investigation 3: Rules and Equations Investigation 4:

Calculator Tables

and Graphs

Stretching and Shrinking Investigation 4: Similarity and Ratios Investigation 5 Using Similar Triangles and Rectangles Accentuate the

Negative

Investigation 1

Extending the

Number System

Investigation 2

Adding and

Subtracting

Integers

Investigation 3

Multiplying and

Dividing Integers

Investigation 4

Properties of

Operations

and verify that their answer is

reasonable.

Models help students to identify the

parts of the problem and how the

values are related.

For percent increase and decrease,

students identify the starting value,

determine the difference, and

compare the difference in the two

values to the starting value.









If a glider has a glide ratio of 1/10 , it goes down 1 foot for

every 10 fee it travels horizontally.

a) Suppose two gliders start at the same height, one with a

glide ration 2/7 and one with a glide ratio of 0.3. If they glide

until they hit the ground, which one will have glided the

farther horizontal distance? For this problem, try using a

diagram of the two planes in action to help explain your

response.

b) If both planes are dropped from a height of 70 feel, how

far will each have to travel before they hit the ground?

Procedural Fluency

Find the unit rate for each situation:

a) driving 180 km in 3 hours

b) 54 hot dogs for 18 people

c) 160 words typed in 4 minutes

d) $27.40 for 4 hours of work

e) $12.64 for 8 pack of juice boxes

Application

At Whole Foods Market, the gourmet coffee costs $18.96 for

3 pounds.

a) What is the cost per pound of coffee?

b) Represent the relationship between the cost of the coffee

and the number of pounds in a table of values.

c) Let x be the number of pounds of coffee and y be the total

cost of x pounds. Draw a graph o the proportional

relationship between the number of pound of coffee and the

total cost.

d) How can you see the cost per pound of coffee in the

graph?

e) Write an equation that relates y, the cost of the coffee,

and x, the number of pounds.


Stretching and Shrinking Check Up 1 (Inv 2)

Variables and Patterns Check Up 1, Check Up 2, Partner Quiz, Multiple Choice Items, Question Bank, and Unit Test

Moving Straight Ahead Check Up 1, Check Up 2,

Comparing and Scaling Check Up, Partner Quiz, Multiple Choice Items, Question Bank, and Unit Test

Formative Assessments: http://njctl.org/courses/math/7th-grade/ratios-proportions/ratios-

proportions-7th-grade-2/






UNIT VOCABULARY


7.NS.3 7.RP.2 7.EE.3 7.EE.4 7.G.6

UNIT 5:

PROPORTIONAL REASONING

Scale Drawing



6.G.1 [area]

7.RP.2 [proportions]

UNIT 5 ASSESSMENT

AVAILABLE (2 items)


7.G.1 Solve problems involving scale drawings of geometric figures, including

computing actual lengths and areas from a scale drawing and

reproducing a scale drawing at a different scale.

proportion

ratio

scale

scale drawing

scale factor

scale model

similar figures

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LESSON PLANNING

UNIT 5:

PROPORTIONAL REASONING

Scale Drawing



6.G.1 [area]

7.RP.2 [proportions]

Vertical Alignment

8.G.4 [Sequences that exhibit similarity]

Recommended Technologies:

NPS Common Core eBoard www.npscommoncore.newark.site.eboard.com Click the CCSS Math tab for additional materials NPS Math Modules http://www.virtualnerd.com User Id: your district email Password: teachwithvn Manipulatives Explore Learning http://www.thinkingblocks.com/ National Library of Virtual Manipulatives

Course Proficiencies Textbook

Alignment

Multiple

Representations

Comments

Compute actual lengths and areas of a geometric figure from scale drawings and reproductions of the figure.

Stretching and Shrinking

Investigation 2

Similar Figures

Investigation 3

Similar Polygons

Investigation 4

Similarity and Ratios

Investigation 5

Using Similar

Triangles and

Rectangles

Comparing and Scaling

Investigation 4

Making Sense of

Proportions

Concrete

Bar model

Paper strips

Number line

Pictorial

Table representation

Graphs

Equivalent ratios

Abstract

Finding the constant of

proportionality

Algorithm for scale factor:

Image/actual figure

or

Actual figure/image

EX: a/b = c/d

Students should build a good working definition of similar in mathematical terms. Students will begin to see connections between geometry and algebra. Using the coordinate system, they draw several geometric figures. Some of the figures are similar to one another and others are not.

Students explore algebraic rules that cause images to change size and to move about the coordinate plane. Compare angle measures and lengths of corresponding sides informally as they investigate transformations. Find that for two figures to be similar corresponding angles must be congruent and corresponding sides must grow or shrink by the same factor.

To be

determined

at the school

level










While shopping for sneakers, Juan finds two pairs he

likes. One pair costs $55 and the other costs $165. He

makes the following statements about the prices.

“The expensive sneakers cost $110 more than the

cheaper sneakers.” “The expensive sneakers cost

three times as much as the cheaper sneakers.”

a. Are both of his statements accurate?

b. How are the comparison methods Juan uses similar

to the methods you use to compare the sizes and

shapes of similar figures?

c. Which method is more appropriate for comparing

the size and shape of an enlarged or reduced figure to

the original? Explain.

Procedural Fluency

1. The scale on a map suggests that 1 centimeter represents an actual distance of 5 kilometers. The map distance between two towns is 8 centimeters. What is the actual distance? 2. Find the missing value in the pair of similar

polygons. Round to the nearest tenth if necessary.

Application

On grid paper, draw a rectangle with an area of 14

square centimeters. Label it ABCD.

a. Write and use a coordinate rule that will make a

rectangle similar

to rectangle ABCD that is three times as long and

three times as wide. Label it EFGH

b..How does the perimeter of rectangle EFGH

compare to the perimeter of rectangle ABCD?

c. How does the area of rectangle EFGH compare to

the area of rectangle ABCD?

d. How do your answers to parts (b) and (c) relate to

the scale factor from rectangle ABCD to rectangle

EFGH?


Stretching and Shrinking Check Up 2, Partner Quiz, Multiple Choice Items, Question Bank, and Unit Test

Formative Assessments: http://njctl.org/courses/math/7th-grade/ratios-proportions/ratios-proportions-7th-

grade-2/

Summative Assessments: http://njctl.org/courses/math/7th-grade/ratios-proportions/ratios-proportions-7th-

grade-2/

(registration is required to access assessments-registration is free of charge)






UNIT VOCABULARY


7.NS.3 7.RP.2 7.EE.3 7.EE.4 7.G.6

UNIT 6:

LINEAR EXPRESSIONS

Adding, Subtracting, Factoring,

Expanding, and Rewriting



6.EE.3 [mathematical expressions]

6.EE.4 [equivalent expressions]

UNIT 6 ASSESSMENT AVAILABLE


7.EE.1 Apply properties of operations as strategies to add, subtract, factor, and

expand linear expressions with rational coefficients.

7.EE.2 Understand that rewriting an expression in different forms in a problem

context can shed light on the problem and how the quantities in it are

related. For example, a + 0.05a = 1.05a means that “increase by5%” is the

same as “multiply by 1.05.”

Module

7.EE.1-2

properties of operations

coefficient

factor

expand

equivalent expression

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LESSON PLANNING

UNIT 6:

LINEAR EXPRESSIONS

Adding, Subtracting, Factoring, Expanding, and

Rewriting



6.EE.3 [mathematical expressions]

6.EE.4 [equivalent expressions]

Vertical Alignment

8.NS.1 [Decimal Expansion]

8.EE.7b [Expanding Expressions]

8.EE.8a [Parts of Intersection]

8.EE.8b [Estimating Solutions by Graphing]


NPS Common Core eBoard www.npscommoncore.newark.site.eboard.com Click the CCSS Math tab for additional materials NPS Math Modules http://www.virtualnerd.com User Id: your district email Password: teachwithvn Manipulatives Explore Learning http://www.thinkingblocks.com/ National Library of Virtual Manipulatives

Course

Proficiencies

Textbook

Alignment

Multiple

Representations

Comments

Add, subtract, factor, and expand liner expressions with rational coefficients.

Apply properties of operations to calculate with numbers in any form.

Moving

straight

Ahead

Investigation

3

Solving

Equations

Investigation

4

Exploring

Slope

Common

Core

Transition

Kit

Investigation

2 Equivalent

Expressions

Concrete

Bar Models

Algebra Tiles

Pictorial

Tabular

Representation

Graphing

Abstract

Simplifying

Expressions/Combining

Like Terms

Generating an

equation

a+.05a=1.05a

Properties of

Operations:

Commutative

Associative

Distributive

Additive and

Multiplicative Identity

Like terms: terms in an expression that have the same variable raised to the same power

If two or more like terms are being added or subtracted, they can be combined.

To combine like terms add/subtract the coefficient but leave the variable alone.

When we factor an expression, we find all numbers or variables that divide into all of the parts of an expression.

We can check our work by using the distributive property to see that the two expressions are equal.

When using the distributive property, be careful with your signs.

To be

determined

at the school

level









1) Sean is buying a new DVD player and speakers for

$315.The store offers him an interest-free payment

plan that allows him to pay in monthly installments

of $25.

a. How much will Sean still owe after one payment?

After two payments? After three payments?

b. Use n to stand for the number of payments and a

for the amount still owed. Write an equation for

calculating a for any value of n.

c. Use your equation to make a table and a graph

showing the relationship between n and a.

d. As n increases by 1, how does a change? How is

this change shown in the table? How is it shown on

the graph?

e. How many payments will Sean have to make in all?

How is this shown in the table? How is this shown on

the graph?

2) Describe the relationship between the variables

in words and with an equation.

x 1 2 5 10 20

y 4 8 20 40 80

x 1 2 3 4 5

y 6 11 16 21 26

Procedural Fluency

Use the equation to complete the table:

1. y = 4x + 3

x 1 2 5 10 20

y

2. m = 100 – k

k 1 2 5 10 20

m

3. d = 3.5t

t 1 2 5 10 20

d

Application

Bicycles that were popular in the 1890s were called

“penny farthing” bicycles. These bikes had front

wheels with diameters as great as

5 feet! Suppose the front wheel of these bicycles

have a diameter of 5 feet.

a. What is the radius of the front wheel?

b. How far will one bike travel in 100 turns of the

front wheel?

c. How many times will the front wheel turn in a 3-

mile trip?

d. Compare the number of times the wheels of

Masako’s bike turn in a 1-mile trip [see part (f) of

Exercise 28] with the number of times the

front wheel of this penny-farthing bike turns in a 3-

mile trip. Why are the numbers related this way?



Variables and Patterns Check Up 1, Check Up 2, Partner Quiz, Multiple Choice Items, Question Bank, and Unit Test

Moving Straight Ahead Check Up 1, Check Up 2, Partner Quiz, Multiple Choice Items, Question Bank, and Unit Test

Formative Assessments: http://njctl.org/courses/math/7th-grade/expressions-equations/

Summative Assessments: http://njctl.org/courses/math/7th-grade/expressions-equations/


http://njctl.org/courses/math/7th-grade/expressions-equations/

http://njctl.org/courses/math/7th-grade/expressions-equations/


SEMESTER TWO

UNIT VOCABULARY


7.NS.3 7.RP.2 7.EE.3 7.EE.4 7.G.6

UNIT 7:

LINEAR EQUATIONS AND INEQUALITIES



6.EE.6 [variables]

6.EE.7 [practical]

6.EE.8 [inequalities]

7.NS.3 [division]



7.EE.4

Use variables to represent quantities in a real-world or mathematical

problem, and construct simple equations and inequalities to solve

problems by reasoning about the quantities.

a. Solve word problems leading to equations of the form px + q

= r and p(x + q) = r, where p, q, and r are specific rational

numbers. Solve equations of these forms fluently. Compare

an algebraic solution to an arithmetic solution, identifying

the sequence of the operations used in each approach. For

example, the perimeter of a rectangle is 54 cm. Its length is

6 cm. What is its width?

b. Solve word problems leading to inequalities of the form px +

q > r or px + q < r, where p, q, and r are specific rational

numbers. Graph the solution set of the inequality and

interpret it in the context of the problem. For example: As a

salesperson, you are paid $50 per week plus $3 per sale. This

week you want your pay to be at least $100. Write an

inequality for the number of sales you need to make, and

describe the solutions.

Module

7.EE.3-4

equation inequality variable(s)

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LESSON PLANNING

UNIT 7:

LINEAR EQUATIONS AND INEQUALITIES



6.EE.6 [variables]

6.EE.7 [practical]

6.EE.8 [inequalities]

7.NS.3 [division]

Vertical Alignment

8.EE.5 [graphing proportional relationships]

8.EE.6 [similar triangle to explain slope]

8.EE.7 [solve linear equations in one

variable]

8.EE.8 [system of equations]

8.F.4 [function model between two

quantities]

8.F.5 [describe functions qualitatively by

analyzing graphs]

Course

Proficiencies

Textbook Alignment Multiple Representations Comments

Use variables to represent quantities and construct equations and inequalities to solve problems about quantities.

Variables and Patterns

Investigation 1:

Variables Tables and Coordinate

Graphs

(Additional Practice Pg. 58-64)

Investigation 2:

Analyzing Graphs and Tables

(Additional Practice Pg. 65-73)

Investigation 3:

Rules and Equations (Additional

Practice Pg. 74-78)

Moving

Straight Ahead

Investigation 1: Walking rates (Additional Practice and Skills

Workbook pgs. 83- 86)

Investigation 2: Exploring Linear Functions with graphs and Tables (Additional Practice and Skills

Workbook pgs. 87- 92)

Investigation 3

Solving Equations

(Additional Practice and Skills

Workbook pages 93-98)

Investigation 4

Exploring Slope

(Additional Practice and Skills

Workbook pages103-112)

Concrete

Bar Models

Algebra Tiles

Pictorial

Tabular Representation

Graphing

Abstract

Simplifying

Expressions/Combining

Like Terms

Create an Equation:

Y=mx + b

Create an Equivalent

Equation:

a+.05a=1.05a

Properties of Operations:

Commutative

Associative

Distributive

Identity

Zero

A relationship is linear if there is

a constant rate of change

between the two variables

(Slope of a Line).

Students should be comfortable

representing linear relationships

using graphs, tables, equations,

and stories.

Develop the concept of constant

rate or slope

y (Change in y) (y2-y1)

x , (Change in x), (x2-x1),

rise

run

(graphs)

Connect ratio and rate concepts

in linear functions

Attend to precision when

graphing

Be sure to use the linear

function, y=mx+b, and ensure

that the students understand

the meaning of each variable

Often problems call for the form

c≤ mx+b or c≥mx+b. Inequalities

have infinitely many solutions.

The algebraic, numerical and

To be

determined

at the school

level


Common Core Transition Kit

Investigation 3

(Inequalities)

graphic strategies that lead to

solutions of linear inequalities

are related to those of

equations. The key difference is

that when you multiply or divide

both sides of an inequality by a

negative number, the directions

of the inequality is reversed.


UNIT 8:

POPULATIONS

Sampling, Inferences, and Comparing



6.SP.1 [stats]

6.SP.2 [data]


NPS Common Core eBoard http://www.npscommoncore.newark.site.eboard.com Click the CCSS Math Tab for additional materials NPS Math Modules http://www.virtualnerd.com – click Log In; password protected User Id: your district email Password: teachwithvn

Progressive Math Initiative:

http://njctl.org/courses/math/7th-grade-

math/

Manipulatives: http://nlvm.usu.edu/en/nav/vlibrary.html http://www.explorelearning.com/index.cfm?method=cResource.dspBrowseCorrelations&v=s&id=USA-000 http://www.thinkingblocks.com/



7.SP.1, 2

Understand that statistics can be used to gain information about a

population by examining a sample of the population; generalizations

about a population from a sample are valid only if the sample is

representative of that population. Understand that random sampling

tends to produce representative samples and support valid inferences.

Use data from a random sample to draw inferences about a population

with an unknown characteristic of interest. Generate multiple samples

(or simulated samples) of the same size to gauge the variation in

estimates or predictions. For example, estimate the mean word length in

a book by randomly sampling words from the book; predict the winner

of a school election based on randomly sampled survey data. Gauge how

far-off the estimate or prediction might be.

7.SP.3 Informally assess the degree of visual overlap of two numerical data

distributions with similar variability, measuring the difference between

the centers by expressing it as a multiple of a measure of variability. For

example, the mean height of players on the basketball team is 10 cm

greater than the mean height of players on the soccer team, about twice

the variability (mean absolute deviation) on either team; on a dot plot,

the separation between the two distributions of heights is noticeable.

7.SP.4 Use measures of center and measures of variability for numerical data

from random samples to draw informal comparative inferences about

two populations. For example, decide whether the words in a chapter of

a seventh-grade science book are generally longer than the words in a

chapter of a fourth-grade science book.

7.SP.5 Understand that the probability of a chance event is a number between

0 and 1 that expresses the likelihood of the event occurring. Larger

numbers indicate greater likelihood. A probability near 0 indicates an

unlikely event, a probability around 1/2 indicates an event that is

neither unlikely nor likely, and a probability near 1 indicates a likely

event.

7.SP.6 Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly200 times.

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http://njctl.org/courses/math/7th-grade-math/








UNIT VOCABULARY


7.NS.3 7.RP.2 7.EE.3 7.EE.4 7.G.6


SAMPLING, INFERENCES, AND

COMPARING POPULATIONS

Understanding and Applying



7.SP.7 Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

a. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.

b. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?

7.SP.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

a. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

b. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.

c. Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4donors to find one with type A blood?

probability model

frequencies

random

chance outcome

compound event

organized list

simulation

likely/unlikely

variability/measure of variability

measure of center

comparative inference

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The two data sets below depict random samples of

the housing prices sold in the King River and Toby

Ranch areas of Arizona. Based on the prices below,

which measure of center will provide the most

accurate estimation of housing prices in Arizona?

Explain your reasoning.

o King River area {1.2 million, 242000, 265500, 140000, 281000, 265000, 211000}

Toby Ranch homes {5million, 154000, 250000, 250000, 200000, 160000, 190000}

Procedural Fluency

If you choose a point in the square, what is the

probability that it is not in the circle?

Application

Show all possible arrangements of the letters in the

word FRED using a tree diagram. If each of the letters

is on a tile and drawn at random, what is the

probability that you will draw the letters F-R-E-D in

that order? What is the probability that your “word”

will have an F as the first letter?


Data Distributions Check Up 1, Check Up 2, Partner Quiz, Multiple Choice Items, Question Bank, and Unit Test

What Do You Expect Partner Quiz, Multiple Choice Items, Question Bank, and Unit Test

Formative Assessments: http://njctl.org/courses/math/7th-grade/2d-geometry/

http://njctl.org/courses/math/7th-grade/geometry/

Summative Assessments: http://njctl.org/courses/math/7th-grade/2d-geometry/



http://njctl.org/courses/math/7th-grade/2d-geometry/





LESSON PLANNING

Unit 8:

POPULATIONS

Sampling, Inferences, and Comparing



6.SP.1 [stats]

6.SP.2 [data]

Vertical Alignment

8.SP.1 [bivariate measurement]

8.SP.2 [line of best fit]



Progressive Math Initiative


Manipulatives http://nlvm.usu.edu/en/nav/vlibrary.html http://www.explorelearning.com/index.cfm?method=cResource.dspBrowseCorrelations&v=s&id=USA-000 http://www.thinkingblocks.com/


Representations

Comments

Use random sampling results to make generalizations about a population. Determine if generalizations about a population are valid based on random samplings. Determine informal comparative inferences about two populations based on the differences between the centers. Understand that all probability is a number between zero and one.

Predict the probability of

an event based on the

relative frequency of that

event.

Develop a probability

model.

Use an organized list, a

table, a tree diagram or a

simulation to find the

probability of a

compound event.

Common Core

Transitional Kit

Investigation 5

Variability

Data Distributions

Investigation 2

Making Sense of

Measure of Center

(Addition Practice Pg.

164- 166)

Investigation 3

Comparing Distributions:

Equal Numbers of Data

Values (Additional

Practice Pg. 167-170)

Investigation 4

Comparing Distributions:

Unequal Numbers of

Data Values (Additional

Practice Pg. 171 – 173)

What Do You Expect?

Investigation 1

Evaluating Games of

Chance (Additional

Practice Pg. 139-144)

Investigation 2

Analyzing Situations

Using an Area Model

(Additional Practice Pg.

145-149)

Investigation 3

Expected Value

Concrete

Population Simulation

(Manipulatives)

Survey Questions

Data Collections

Spinners

Number Cubes

Random

SamplingActivities

Area Models

Pictorial

Tables

Graphs:

Scatter Plot

Bar Graphs

Histogram

Stem and Leaf

Line Graph/Plot

Pie Graphs/Charts

Abstract

Experimental

Probability

Theoretical Probability

Algorithm:

# of Favorable

Outcomes

# of Total Outcomes

Measures of Central

Tendencies and

Variability

The Process of Statistical Investigation (Doing Meaningful Statistics) involves four parts: pose a question, collect the data, analyze the data, and interpret the analysis in light of the question. When completed, students need to communicate the results.

Questions such as these are helpful: • What question was asked that resulted in these data being collected? • How do you think the data were collected? • Why are these data represented using this kind of presentation? • What are ways to describe the

data distribution?

Students can collect data using

physical objects or graphing

calculator or web-based

simulations. Students can also

develop models for geometric

probability (i.e. a target).

Measures of center include mean,

median, and mode.

The measures of variability

include range, mean absolute

deviation, and interquartile range.

Graph comprehension should

including reading the data (lifting

information), reading between









(Additional Practice 150-

152)

Investigation 4

Binomial Outcomes

(Additional Practice Pg.

153-155)

the data (interpretation and

integration of the data), reading

beyond the data (extending,

predicting, and inferring the data)

Students need multiple

opportunities to perform

probability experiments and

compare these results to

theoretical probabilities.

Critical components of the

experiment process are making

predictions about the outcomes

by applying the principles of

theoretical probability, comparing

the predictions to the outcomes

of the experiments, and

replicating the experiment to

compare results.

Experiments can be replicated by

the same group or by compiling

class data.

Experiments can be conducted

using various random generation

devices including, but not limited

to, bag pulls, spinners, number

cubes, coin toss, and colored

chips.


UNIT VOCABULARY


7.NS.3 7.RP.2 7.EE.3 7.EE.4 7.G.6

UNIT 9:

2-D and 3-D FIGURES

Angles, Planes, (Surface) Area,

Circumference, Volume



6.G.1 [area]

6.G.3 [polygons]

6.G.4 [3 dimensions]


7.G.2 Draw (freehand, with ruler and protractor, and with technology)

geometric shapes with given conditions. Focus on constructing triangles

from three measures of angles or sides, noticing when the conditions

determine a unique triangle, more than one triangle, or no triangle.

7.G.3 Describe the two-dimensional figures that result from slicing three-

dimensional figures, as in plane sections of right rectangular prisms and

right rectangular pyramids.

7.G.4 Know the formulas for the area and circumference of a circle and use

them to solve problems; give an informal derivation of the relationship

between the circumference and area of a circle.

7.G.5 Use facts about supplementary, complementary, vertical, and adjacent

angles in a multi-step problem to write and solve simple equations for

an unknown angle in a figure.

7.G.6 Solve real-world and mathematical problems involving area, volume and

surface area of two- and three-dimensional objects composed of

triangles, quadrilaterals, polygons, cubes, and right prisms.

proportion

ratio

scale

scale drawing

scale factor

scale model

similar figures

construction

included angle

non-included angle

unique triangle

cross section

cylinder

edge

face

net

prism

pyramid

rectangular prism

rectangular pyramid

solid

surface area

vertex

adjacent angles

angle pairs

complementary angles

congruent angles

corresponding angles

supplementary angles

transversal

vertical angles

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UNIT 9:

2-D and 3-D FIGURES

Angles, Planes, (Surface) Area,

Circumference, Volume



6.G.1 [area]

6.G.3 [polygons]

6.G.4 [3 dimensions]

Vertical Alignment

8.G.1-5 [congruency and similarity]

8.G.6 -8 [Pythagorean theorem]

8.G.9 [volume of cylinders, cones, spheres]


Course Proficiencies Textbook Alignment Multiple Representations Comments

Draw geometric shapes with specific given conditions. Describe the two-dimensional figures that result from slicking three-dimensional figures, as in a plane section of the three-dimensional figure. Solve problems using the formulas for area and circumference of a circle. Use knowledge of supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. Solve real world problems involving area, volume and surface area.

CC Transitional Kits

Investigation 4

Geometry Topics

Filling and Wrapping

Investigation 1

Building Boxes

(Additional Practice

Pg. 114-117)

Investigation 2

Designing

Rectangular Boxes

Additional Practice

Pg. 118-124)

Investigation 3

Prisms and Cylinders


Pg. 125-131)

Investigation 4

Cones, Spheres and

Pyramids


Pg.132-135)

Stretching and

Shrinking

Investigation 2

Similar Figures


Pg. 24-26)

Investigation 3

Similar Polygons


Pg. 27-30)

Concrete

Solids

Boxes

Wedges

Real life representations

(eg: doors, windows, steps,

corners)

Angle ruler

Nets

Projections and views

Pictorial

3-Dimensional scale

drawings of polygons

Angles drawn to

Measure

Coordinate graphs

Abstract

Refer to the 7th grade

reference sheet for

formulas for surface area

and volume

Supplementary angles:

pairs of angles that add up

to 180 degrees.

Complementary angles:

angles whose measures

sum to 90°

Conditions may involve points,

line segments, angles,

parallelism, congruence, angles,

and perpendicularity.

Angle relationships that can be

explored include but are not

limited to:

***Same-side (consecutive) interior and same-side (consecutive) exterior angles are supplementary.

Using a clay model of a rectangular prism, describe the shapes that are created when planar cuts are made diagonally, perpendicularly, and parallel to the base. Students understanding of

volume can be supported by

focusing on the area of base

times the height to calculate

volume.

Students understanding of

surface area can be supported

by focusing on the sum of the

area of the faces.

Nets can be used to evaluate

surface area calculations.


Progressive Math Initiative

http://njctl.org/courses/math/7th-grade-

math/

Manipulatives http://nlvm.usu.edu/en/nav/vlibrary.html http://www.explorelearning.com/index.cfm?method=cResource.dspBrowseCorrelations&v=s&id=USA-000 http://www.thinkingblocks.com/

To be

determined

at the school

level

http://en.wikipedia.org/wiki/Angle

http://en.wikipedia.org/wiki/Degree_(angle)

http://en.wikipedia.org/wiki/Angle














Mr.Turner’s classroom is 20 feet wide, 30 feet long,

and 10 feet high.

a. Label the dimensions of the classroom on your

sketch.

b. Find the volume of the classroom. Why might this

information be useful?

c. Find the total area of the walls, the floor, and the

ceiling. Why might this information be useful?

Procedural Fluency

Find the Area:

Application

The city of Centerville plans to dig a rectangular

landfill. The landfill will have a base with dimensions

700 ft by 200 ft and a depth of 85 ft.

a. How many cubic feet of garbage will the landfill

hold?

b. What information do you need to determine how

long the landfill can be used until it is full?

c. Centerville hires an excavator to dig the hole for

the landfill. How many cubic yards of dirt will he have

to haul away?


Filling and Wrapping Check Up 1, Check Up 2, Partner Quiz, Multiple Choice Items, Question Bank, and Unit Test

Stretching and Shrinking Partner Quiz, Multiple Choice Items, Question Bank, and Unit Test

Formative Assessments: http://njctl.org/courses/math/7th-grade/2d-geometry/ http://njctl.org/courses/math/7th-grade/geometry/

Summative Assessments: http://njctl.org/courses/math/7th-grade/2d-geometry/ http://njctl.org/courses/math/7th-grade/geometry/ (registration is required to access assessments-registration is free of charge)






APPENDIX NPS Common Core eBoard http://www.npscommoncore.newark.site.eboard.com Click the CCSS Math tab for additional materials NPS Math Modules http://www.virtualnerd.com – click Log In; password protected User Id: your district email Password: teachwithvn Manipulatives http://nlvm.usu.edu/en/nav/vlibrary.html http://www.explorelearning.com/index.cfm?method=cResource.dspBrowseCorrelations&v=s&id=USA-000 http://www.thinkingblocks.com/

UNIT 1

http://www.explorelearning.com/index.cfm?method=cResource.dspBrowseCorrelations&v=s&id=USA-000 http://www.thinkingblocks.com/

http://illustrativemathematics.org/illustrations/314



UNIT 2 http://www.explorelearning.com/index.cfm?method=cResource.dspBrowseCorrelations&v=s&id=USA-000 http://www.thinkingblocks.com/


http://map.mathshell.org.uk/materials/tasks.php?taskid=387#task387

UNIT 3 Direct link to Problems http://illustrativemathematics.org/illustrations/828 http://illustrativemathematics.org/illustrations/470 http://illustrativemathematics.org/illustrations/82



















http://map.mathshell.org.uk/materials/tasks.php?taskid=271#task271 Exemplars: http://www.nps.k12.nj.us/newarkpublicschools/lib/newarkpublicschools/MathDepartment/DIFF%20MATH%20I/html/task124.html http://www.nps.k12.nj.us/newarkpublicschools/lib/newarkpublicschools/MathDepartment/DIFF%20MATH%20II/html/task400.html

UNIT 4 NPS Common Core eBoard http://www.npscommoncore.newark.site.eboard.com Click the CCSS Math Tab for additional materials NPS Math Modules

http://www.virtualnerd.com – click Log In; password protected

User Id: your district email

Password: teachwithvn

Manipulatives




Direct link to Problems

7.RP2



http://map.mathshell.org.uk/materials/tasks.php?taskid=389&subpage=expert

http://map.mathshell.org.uk/materials/tasks.php?subpage=apprentice&taskid=358

7.RP3




7.EE3


http://www.nps.k12.nj.us/newarkpublicschools/lib/newarkpublicschools/MathDepartment/DIFF%20MATH%20I/html/task124.html

http://www.nps.k12.nj.us/newarkpublicschools/lib/newarkpublicschools/MathDepartment/DIFF%20MATH%20II/html/task400.html
















UNIT 5

NPS Common Core eBoard

http://www.npscommoncore.newark.site.eboard.com

Click the CCSS Math Tab for additional materials

NPS Math Modules


User Id: your district email

Password: teachwithvn

Manipulatives





7.RP2





7.RP3




7.EE3



















UNIT 6

NPS Common Core eBoard

http://www.npscommoncore.newark.site.eboard.com

Click the CCSS Math Tab for additional materials

NPS Math Modules


User Id:your district email

Password:teachwithvn

Manipulatives





http://www.illustrativemathematics.org/illustrations/542




https://njctl.org/courses/math/7th-grade/expressions-equations/

Exemplars:

http://www.nps.k12.nj.us/newarkpublicschools/lib/newarkpublicschools/MathDepartment/DIFF%20MATH%20III/html/task498.html











https://njctl.org/courses/math/7th-grade/expressions-equations/



UNIT 7


UNIT 8







Exemplars:

http://www.nps.k12.nj.us/newarkpublicschools/lib/newarkpublicschools/MathDepartment/DIFF%20MATH%20III/html/nctm3_9.html

UNIT 9




Direct link to Problems:



Exemplars:







http://www.nps.k12.nj.us/newarkpublicschools/lib/newarkpublicschools/MathDepartment/DIFF%20MATH%20III/html/nctm3_9.html








Exemplars:











Documents

Scope and Sequence: Grade 7 Mathematics Units 1-9 2012-2013 · Grade 7 Common Core State Standards Scope and Sequence…Page 5 SAMPLE DEMONSTRATIONS OF LEARNING (DOLS) Conceptual