Math 7 Sampler - Home - Standards Plus

Sampler

Grade 7Mathematics

Program Overviewand Sample Lessons

National Award Winning

Program

Standards Plus’ Lost Learning Packages Will Help Your Students Catch Up and Move Forward.

How it Works:

• Teach the lost essential standards from the previous grade-level

• Transition to teaching the current high-impact grade-level standards

• Provide scaffolded intervention for students that need more help

Standards Plus targeted, teacher-directed lessons are concise and easy to teach. Every lesson includes a print and an online version.

In-Class And

Works in All School Configurations:

Teachers are the most important factor in student learning. That’s why every Standards Plus Lesson is directly taught by a teacher.

• Teachers directly teach lessons to the students in-class or over a video/phone conference.

• Students complete the lessons in their printed student edition or respond in the Standards Plus Digital Platform.

PRINT & DIGITAL

Distance Learning

Contact us to customize a lost learning package for your school.Call 1-877-505-9152 or email [email protected].

Grants of up to $3,500 are available.

Catch Up with

Standards Plus 6th Grade High Impact Standards Materials

Teach in 7 weeks 40 minutes per day

Move Forward with

Standards Plus 7th Grade High Impact Standards Materials

Teach in 14 weeks 20 minutes per day

Lessons

that teach

prerequisite

skills are

included

in every

grade level.

6th Grade

High ImpactStandards Materials

Sample 7th Grade Lost Learning Package

7th Grade

High ImpactStandards Materials

+

+

+

PROVIDEINTERVENTION

Catch upin

FALL

Move Forward in WINTER

& SPRING

“The average student could begin the next school year having lost as much as a third of the expected progress in reading and half the expected progress in math.”

- Study published by the NWEA and Brown University

Lessons Included in Standards Plus

Grade Level Lessons and Assessments136 Lessons and 34 Assessments (DOK 1-2)

Students learn essential grade level skills with targeted 15-20 minute lessons.Brief formative assessments are provided to monitor student progress.

Tier 2 & Tier 3 Intervention Lessons100+ Lessons (DOK 1-2)

Students learn prerequiste skillls that scaffold below grade-level. These lessons are for students that need more support and are available to print in the Standards Plus Digital Platform. Printed student editions can be purchased separately.

Performance Lessons12+ Lessons (DOK 3)

Performance lessons require students to apply the skills they learned in previous Standards Plus lessons. These lessons provide students the opportunity to incorporate

technology, text analysis, reflection and research.

Integrated Projects3 Projects (DOK 4)

Integrated projects incorporate standards from multiple topics and is a long-term project that will be completed during multiple class sessions.

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3

Here’s what’s included with Standards Plus

Your Standards Plus purchase includesPrint, Digital, and Downloadable Intervention PDFs

• Scaffold the instruction of skills necessary for mastery of grade level standards as indicated by the formative assessments.

• If students are assessed online, our digital platform automatically groups students for intervention.

• The entire Standards Plus Intervention Program is included as downloadable PDFs in the digital platform.

PRINT

DIGITAL

DOWNLOADABLE INTERVENTION PDFs

Teacher Edition

Digital Platform

Student Edition

• Online versions of the printed lessons and assessments.

• Students apply their content knowledge to a digital environment that matches high-stakes online assessments.

• Online assessments help you create targeted intervention groups

LanguageArtsLanguageArtsGrade 3Grade 3

Teacher Edition

Standards PLUS

Written directly to the CA Standards by CA Educators

A ?&f“

gISBN: 978-1-61032-273-7

9 7 8 1 6 1 0 3 2 2 7 3 7

CCL3-TE

Language ArtsGrade 3

www.standardsplus.orgPhone: 877.505.9152 • Fax:909.484.6004

10604 Trademark Pkwy. N., Suite 302Rancho Cucamonga, CA 91730

• Explicit direct instruction Teacher Lesson Plans

• Every student lesson, assessment, performance lesson, and integrated project

• Student response pages for every lesson, assessment, performance lesson, and integrated project

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Ready-To-Teach Direct Instruction Lessons

Standards Plus lessons are written in the Direct Instruction format because it is the most effective research-based instructional delivery model and it is proven to increase student achievement.

Common Core Standards Plus® – Mathematics – Grade 4 Domain: Measurement and Data Focus: Relative Size of Measurement Units Lesson: #4 Standard: 4.MD.1 Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...

Lesson Objective: Students will place customary units for length, volume, mass, and time in order from largest to smallest.

Introduction: “Today we will compare customary units of measurement and place units in order from largest to smallest for length, volume, mass, and time. In the United States, we use a system made up of standard or customary units of measure such as feet, inches, quarts, pounds, minutes, and hours to determine units of length, volume, mass, and time.” Instruction: “The customary system of measurement is commonly used in our everyday life. Look at the top of your page. There is a customary measurement chart displaying units of length, volume, mass, and time. (Review the units for each and stress their relationships. E.g., 1 yd = 3 ft = 36 in, 1 gal = 4 qts, etc. Read chart aloud with students.) Look at the units of length listed below the customary measurement chart. The units are listed from longest to shortest: mile, yard, foot, and inch. In the customary units, mile is the longest unit. Since smaller units make up the largest unit, yard is the next longest unit. The unit after that is foot. One foot is shorter than a yard, but longer than an inch. Therefore, it is listed third in the order. Since an inch is the shortest unit of measurement for length, it is listed last.” Guided Practice: “Look at the example on this page. We are asked to put the units of volume in order from most to least (pint, ounce, cup, quart). Think. Which unit is more? Use the customary measurement chart to help you decide. (Pause.) If you think that quart is the most, you are correct. Write the unit quart on the first blank. Remember, it always takes more of a smaller unit to equal a larger unit. Look at the remaining units. Place them on the blanks from most to least.” Allow students to share their answer with a partner, and then provide the correct order. Elicit volunteers to share why they placed the units in a particular order. Require students to use academic language. Stress the relationships between the units (quart, pint, cup, and ounce). Independent Practice: “Complete problems 1-5 on your own. Use the customary measurement chart to help you list the units in order from largest to smallest.” Review: Review problems 1-5 with students. If time permits, require students to explain their answers. Closure: “Today we reviewed measurement equivalents and relative size within customary units of length, volume, and mass, as well as units of time, and placed units in order from largest to smallest. Can you think of items that you use each day that are measured in length, volume, mass, or time?” Answers: 1. year, day, hour, minute

2. ton, pound, ounce 3. 1 yard, 2 feet, 12 inches 4. 1 year, 1 month, 7 days, 24 hours 5. Answers may vary. A possible answer is 16 ounces, which is equal to 2

cups because it is the most.

Standards Plus Lesson Timeline

Introduction

Instruction

Guided Practice

Independent Practice

Review &Closure

1 min.

2 min.

5 min.

6 min.

7 min.

8 min.

9 min.

10 min.

11 min.

12 min.

13 min.

14 min.

15 min.

16 min.

17 min.

Introduction

Instruction

Guided Practice

Independent Practice

Review &Closure

3 min.

4 min.

Standards Plus works becauseteachers teach every lesson to every student

Quality InstructionLeads to Improved Achievement

Master All Grade-Level Standards


5

TEACH TEST PROVIDEINTERVENTION

How it works:

1. Teach a grade level standard with four 15-20 minute lessons

2. Assess the standard with a formative assessment in print or online

3. If the standard is not mastered, print the downloadable Intervention lessons that scaffold instruction below grade level.

15-20 min. Print and Online

Daily Lessons

Assess using Print

or Digital

to practice state assessment-like technology

Intervention Lessonsare downloadable

to print in Standards Plus

Digital

Implementation Options

Implementation Options: Print + Digital (Online)

Teach the lessons using print materials and have the students take the weekly assessment online to match requirements of state test.

15-20 min. Daily Lessonsusing Standards Plus

Print Materials

Online Assessmentsusing Standards Plus Digital to practice

state assessment-like technology

Intervention Lessons

provided in Standards Plus

Digital

TEACH TESTPROVIDE

INTERVENTION

11





Print Materials





Digital

TEACH TESTPROVIDE

INTERVENTION

11





Print Materials





Digital

TEACH TESTPROVIDE

INTERVENTION

11

USING STANDARDS PLUS

Lesson sets 4 lessons + 1 assessment

1 2 3 4 1 +

How it works:

1.  Teach a grade level standard with four 15-20 minute lessons

2.  Assess the standard with a formative assessment

3.  If the standard is not mastered, Standards Plus Intervention lessons that scaffold instruction below grade level are embedded and easy to download and printusing Standards Plus Digital

8

Quality InstructionLeads to Improved Achievement

Master All Grade-Level Standards


Mathematics Grade 7Lesson Index

WHY STANDARDS PLUS INCREASES STUDENT ACHIEVEMENT

WHY STANDARDS PLUS INCREASES STUDENT ACHIEVEMENT

Students master grade level standards using the proven effective Standards Plus process

Teachers:Teachers are the most important factor in student learning. That’s why every Standards Plus lesson is directly taught by a teacher.

Direct Instruction format:“Direct Instruction is a proven method of instruction that fosters the most significant gains in student achievement and results in deep and enduring understanding of the concept.” (Peladeau, Forget & Gagne, 2003).

Discrete learning targets:Each lesson has a clear learning objective, providing easily understood instruction which allows students to learn and retain the information in their long term memory.

Multiple exposures to each standard/skill: Each standard/skill is broken down and presented in at least 4 lessons (sometimes more) providing multiple opportunities to practice and develop a deep understanding of a specific skill allowing for long term retention.

Immediate feedback:“The most powerful single modification that enhances achievement is feedback.” (John Hattie, 1992)Every lesson provides immediate feedback to the students.

Immediate intervention:For students who need further instruction to master a standard/skill, immediate intervention lessons are available that scaffold below grade level and provide the necessary instruction that allows students to master the standard.

www.standardsplus.org • 1-877-505-9152

Students master grade level standards using the proven effective Standards Plus process

The lesson index lists every Standards Plus Mathematics Grade 7 lesson.

The highlighted lessons indicate the High Impact Tested Standards.

Mathematics Grade 7Lesson Index

Common Core Standards Plus – Mathematics – Grade 2

Domain Lesson Focus Standard(s) TE Page

St. Ed. Page

DOK Level

Additio

n & Sub

tractio

n – NBT Part 2

(N

umbe

r and

Ope

ratio

ns in

Bas

e Te

n St

anda

rds:

2.N

BT.5

-‐2.N

BT.9

)

1 Add Within 100 2.NBT.5: Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

156 68

1-‐2 2 Add Within 100 158 69

3 Subtract Within 100 160 70


E1 Evaluation – Add and Subtract Within 100 164 72

5 Commutative Property of Addition

2.NBT.5

166 73

1-‐2 6 Associative Property of Addition 168 74

7 Associative Property of Addition 170 75

8 Additive Identity Property 172 76

E2 Evaluation – Properties of Operations 174 77

9 Relating Addition and Subtraction

2.NBT.5

176 79

1-‐2

10 Relating Addition and Subtraction 178 80

11 Relating Addition and Subtraction 180 81

12 Missing Addends 182 82

E3 Evaluation – Relating Addition and Subtraction 184 83

13 Add Using Place Values 2.NBT.5 186 85

1-‐2

14 Add Using the Commutative Property 2.NBT.6 Add up to four two-‐digit numbers using strategies based on place value and properties of operations.

188 86

15 Add Using the Associative Property 190 87

16 Add Using the Associative Property 192 88

E4 Evaluation – Add Using Place Values and Properties

2.NBT.5, 2.NBT.6 194 89

P4 Performance Lesson #4 – How Do You Compute? (2.NBT.5, 2.NBT.6) 196 91-‐94 3 17 Add Within 1000 2.NBT.7: Add and subtract within 1000,

using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-‐digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.

202 95

1-‐2

18 Composing Numbers in Addition 204 96

19 Subtract Three-‐Digit Numbers 206 97

20 Decomposing in Subtraction 208 98


21 Add Within 1000

2.NBT.7

212 101

1-‐2 22 Add Within 1000 214 102




25 Relating Addition and Subtraction

2.NBT.7

222 107

1-‐2 26 Relating Addition and Subtraction 224 108

27 Missing Addend 226 109

28 Missing Addend 228 110

E7 Evaluation – Relate Addition and Subtraction 230 111

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Common Core Standards Plus® ‐ Mathematics – Grade 7 – Lesson Index

Domain Lesson Focus Standard(s) Student Page

DOK Level

Ratio

s & Propo

rtiona

l Relationships

(Ratios &

Propo

rtiona

l Relationships Stand

ards: 7.RP

.1 – 7.RP.3)

1 Unit Rate

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.

.

3

1‐2

2 Unit Rate 4

3 Unit Rate 5

4 Unit Rate 6

E1 Evaluation – Unit Rate 7

P1 Performance Lesson #1 – Using Unit Rates (7.RP.1) 9‐10 3

5 Proportional Relationships 7.RP.2a: 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.

11

1‐26 Proportional Relationships

7.RP.2a, 7.RP.2b: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

12 7 Proportional Relationships 13‐148 Proportional Relationships 15‐16

E2 Evaluation – Proportional Relationships 17

9 Proportional Relationships 7.RP.2a, 7.RP.2b

19

1‐2

10 Proportional Relationships 20‐21

11 Multistep Ratio Problems 7.RP.3: Use proportional relationships to solve multi‐step ratio and percent problems. Examples: simple interest, tax, markups & markdowns, gratuities & commissions, fees, percent increase & decrease, percent error.

22

12 Multistep Ratio Problems 23

E3 Evaluation – Proportional Relationships

7.RP.2a, 7.RP.2b, 7.RP.3 24

13 Multistep Ratio Problems

7.RP.3

25

1‐2


15 Simple Interest 27


E4 Evaluation – Simple Interest 29

17 Sales Tax & Gratuities

7.RP.3

31

1‐2

18 Sales Tax & Gratuities 32

19 Discount 33

20 Discount 34

E5 Tax, Gratuity, & Discount 35

21 Markup

7.RP.3

37

1‐2

22 Markup 38

23 Commission & Fees 39

24 Commission & Fees 40

E6 Commission & Fees 41

Standards Plus - Math Grade 7 Lesson Index

Hig

h Im

pact

St

anda

rds




DOK Level

Ratio

s & Propo

rtiona

l Re

latio

nships

25 Percent Increase/Decrease

7.RP.3

43

1‐2

26 Percent Increase/Decrease 44 27 Percent Error 45 28 Percent Increase, Decrease, & Error 46

E7 Markdown, Markup, Commission & Percent of Change 47

P2 Performance Lesson #2 – Exploring Proportionality (7.RP.2a, 7.RP.2b, 7.RP.3) 49‐52 3

The Num

ber S

ystem

(The

Num

ber S

ystem Stand

ards: 7.NS.1a

‐c, 7

.NS.2b

‐d, 7

.NS.3)

1 Opposite Quantities on the Number Line 7.NS.1a: 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.

53

1‐2

2 Opposite Quantities on the Number Line 54

3 Adding Rational Numbers on the Number Line

7.NS1.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.

55

4 Adding Rational Numbers on the Number Line 56

E1 Adding Rational Numbers 7.NS.1a, 7.NS.1b 57

5 Adding Quantities on the Number Line 7.NS.1b 59

1‐2

6 Subtraction and Additive Inverses 7.NS1c: 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.

60 7 Absolute Value on a Number Line 61 8 Absolute Value in Real‐World Contexts 62

E2 Evaluation – Adding and Subtracting Rational Numbers 7.NS.1b, 7.NS.1b 63

9 Adding and Subtracting Integers

7.NS.1d: Apply properties of operations as strategies to add and subtract rational numbers.

65

1‐2

10 Adding and Subtracting Integers 66 11 Adding and Subtracting Integers 67 12 Adding and Subtracting Decimals 68 E3 Adding and Subtracting Decimals 69

13 Adding and Subtracting Decimals

7.NS.1d

71

1‐2

14 Adding and Subtracting Decimals 72 15 Adding and Subtracting Decimals 73 16 Adding and Subtracting Decimals 74

E4 Evaluation – Adding and Subtracting Decimals 75

P3 Performance Lesson #3 – Adding and Subtracting Rational Numbers (7.NS.1a, 7.NS.1b, 7.NS.1c, 7.NS.1d) 77‐78 3

17 Multiplying Integers with Tiles 7.NS.2a: 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.

79

1‐2

18 Multiplying Integers on a Number Line 80 19 Integers and the Distributive Property 81 20 Products in Real‐World Contexts 82 E5 Evaluation – Multiplying Integers 83


Hig

h Im

pact

St

anda

rds

Hig

h Im

pact

St

anda

rds




DOK Level

The Num

ber S

ystem

(The

Num

ber S

ystem Stand

ards: 7.NS.1a

‐c, 7

.NS.2b

‐d, 7

.NS.3)

21 Decimals and the Distributive Property 7.NS.2a 85

1‐2

22 Multiplying Fractions

7.NS.2a, 7.NS.2b: 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.

86

23 Dividing Rational Numbers 7.NS.2b

87

24 Dividing Rational Numbers 88

E6 Evaluation – Multiplying and Dividing Rational Numbers 7.NS.2a, 7.NS.2b 89

25 Multiplying Rational Numbers 7.NS.2c: Apply properties of operations as strategies to multiply and divide rational numbers.

91

1‐2

26 Dividing Rational Numbers 92

27 Converting Rational Numbers to Decimals

7.NS.2d: 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.

93

28 Converting Rational Numbers to Decimals 94

E7 Evaluation – Multiplying, Dividing and Converting Rational Numbers 7.NS2c, 7.NS2d 95

P4 Performance Lesson #4 – Multiplying and Dividing Rational Numbers (7.NS.2a, 7.NS.2b, 7.NS.2c, 7.NS.2d) 97‐99 3

29 Solving Problems Involving the Four Operations with Rational Numbers

7.NS3: Solve real‐world and mathematical problems involving the four operations with rational numbers.

100

1‐230 Solving Problems Involving the Four

Operations 101

31 Solving Real‐World Problems 102

32 Solving Real‐World Problems 103

E8 Solving Real‐World Problems 104 Integrated Project #1 – Launching Your Business (7.RP.1, 7.RP.2a, 7.RP.2b, 7.RP.2c, 7.RP.2d, 7.RP.3, 7.NS.1, 7.NS.1a, 7.NS.1b, 7.NS.1c, 7.NS.1d, 7.NS.2, 7.NS.2a, 7.NS.2b, 7.NS.2c, 7.NS.2d, 7.NS.3)

105‐108 4

Prerequisite Standards Plus Domains: Ratios and Proportional Relationships and The Number System

Project Objective: The students will create a plan to launch a new business. They will present their plans to the class.

Overview: In this project, the students will create a business plan. They will determine a business that they would like to have, research and determine prices for their goods or services, and determine the percent of profit they would expect to make. They will create a spreadsheet that shows their expected activity in the first year of operation. Since this is a learning activity, all components will be completed in class.


Hig

h Im

pact

St

anda

rds




DOK Level

Expression

s and

Equ

ations

(Exp

ressions and

Equ

ations Stand

ards: 7.EE

.1‐3, 7

.EE.4a

‐b)

1 Simplify Algebraic Expressions

7.EE.1: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

109

1‐2

2 Generate Equivalent Expressions 110



E1 Evaluation – Generating Equivalent Expressions 113

5 Factor Generate Equivalent Expressions 7.EE.1

115

1‐2

6 Factor Generate Equivalent Expressions 116

7 Expressions in Problem Situations 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 by 5%” is the same as “multiply by 1.05.”

117

8 Expressions in Problem Situations 118

E2 Evaluation – Use Properties of Operations to Generate Equivalent Expressions

7.EE.1 & 7.EE.2 119

P5 Performance Lesson #5 – Working with Expressions (7.EE.1, 7.EE.2) 121‐122 3

9 Solve Multi‐Step Real‐Life Problems 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.

123

1‐2

10 Solve Multi‐Step Real‐Life Problems 124



E3 Evaluation – Solving Multi‐Step Real‐Life Problems 127

13 Solving Multi‐Step Real‐Life Problems

7.EE.3

129

1‐2

14 Solving Multi‐Step Real‐Life Problems 130



E4 Evaluation – Solve Multi‐Step Real‐Life Problems 133

17 Solve Equations in the Form of px +q = r

7.EE.4a: 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.

135

1‐2

18 Solve Equations in the Form of p (x +q) = r 136

19 Solve Word Problems 137

20 Solve Word Problems 138

E5 Evaluation – Solve Linear Equations and Word Problems 139

P6 Performance Lesson #6 – Equations ‐ (7.EE.3, 7.EE.4a) 141‐142 3


Hig

h Im

pact

St

anda

rds

Hig

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pact

St

anda

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Lesson Focus Standard(s) Student Page

DOK Level

21 Solve Word Problems 7.EE.4a

143

1‐2

22 Solve Linear Equations and Word Problems 144

23 Solve and Graph Solutions to Inequalities

7.EE.4b: 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.

145

24 Solve and Graph Solutions to Inequalities 146

E6 Evaluation – Solve Equations and Inequalities 7.EE.4a and 7.EE.4b 147

25 Solve Word Problems Leading to Inequalities

7.EE.4b

149

1‐2

26 Solve Word Problems Leading to Inequalities 150



E7 Evaluation – Solve Word Problems Leading to Inequalities 153

P7 Performance Lesson #7 – Inequalities (7.EE.4a, 7.EE.4b) 155‐156 3 Integrated Project #2 – In the Real World… (7.EE.1, 7.EE.2, 7.EE.3, 7.EE.4, 7.EE.4a, 7.EE.4b, 7.RP.1, 7.RP.3) 157‐158 4

Prerequisite Standards Plus Domain: Expressions and Equations

Project Objective: The students will analyze a scenario of income over a year and write expressions, equations, and inequalities to interpret fluctuations. The students will analyze the information to estimate future income under given circumstances.

Overview: In this project, the students will analyze a report of income over a year for a painter. They will write expressions, equations, and inequalities to interpret the fluctuations and provide a written explanation of the fluctuations. They will analyze the information to determine how to influence future earnings and estimate those earnings. The students will share their findings in peer groups. Since this is a learning activity, all components will be completed in class.


Hig

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pact

St

anda

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Expr

essi

ons &

Equ

ation

sDomain




DOK Level

Statistic

s and

Proba

bility

(Statis

tics &

Proba

bility Stan

dards: 7.SP.1‐6, 7.SP.7a

‐b, 7

.SP.8a

‐c)

1 Understanding Probabilities 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.

159

1‐22 Understanding Probabilities 160

3 Experimental Probabilities 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.

161

4 Experimental Probabilities 162

E1 Evaluation – Theoretical and Experimental Probability 163

5 Determine Probabilities 7.SP.7a: Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events.

165

1‐2

6 Determine Probabilities 166

7 Understanding Probabilities 7.SP.7b: Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.

167‐168

8 Understanding Probabilities 169

E2 Evaluation – Determining Probability 7.SP.7a‐b 170

9 Finding Probabilities of Compound Events

7.SP.8a: 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.

171

1‐2

10 Finding Compound Probabilities 7.SP.8a‐b: Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. 172

11 Finding Compound Probabilities 7.SP.8b 173

12 Using a Simulation

7.SP.8c: 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 4 donors to find one with type A blood?

174

E3 Finding Compound Probabilities 7.SP.8a, 7.SP.8b, and 7.SP.8c 175

P8 Performance Lesson #8 – Exploring Probability(7.SP.5, 7.SP.6, 7.SP.7a, 7.SP.7b, 7.SP.8a, 7.SP.8b, 7.SP.8c)

177‐178 3

13 Sample Population

7.SP.1: 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.

179

1‐214 Making Inferences of a Population 7.SP.2: 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.

180 15 Making Inferences of a Population 181 16 Evaluate Multiple Samples 182

E4 Evaluation – Random Sampling and Drawing Inferences

7.SP.1, 7.SP.2 183

17 Assess Overlap Between Data Distributions

7.SP.3: Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability.

185‐186

1‐2

18 Assess Overlap of Data Distributions 187‐188

19 Inferences about Two Populations 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.

189‐190

20 Inferences about Two Populations 191

E5 Evaluation – Inferences about Two Populations 192

P9 Performance Lesson #9 – Exploring Statistics (7.SP.1, 7.SP.2, 7.SP.3, 7.SP.4) 193‐195 3





DOK Level

Integrated Project #3 – Powerful Words (7.SP.1, 7.SP.2, 7.SP.3, 7.SP.4, 7.SP.5, 7.SP.6,7.SP.7, 7.SP.7a, 7.SP.7b, 7.SP.8, 7.SP.8a, 7.SP.8b, 7.SP.8c) 196‐197 4

Prerequisite Standards Plus Domain: Statistics and Probability

Project Objective: The students will analyze four different sources of print to determine the average word length in each. They will determine the probability of finding a similar average word length in similar materials. They will test their theories and report the results.

Overview: In this project the students will select four different sources of print (e.g., magazines, newspapers, comic books, novels, graphic novels, math textbooks, history books, etc.). They will sample three different sets of 100 words within each source to find the average word length. They will analyze and display their findings. Then they will predict the average word length in materials similar to those they have sampled. They will determine the probability of similar word lengths and test their theories. They will select the results of one print source and the similar source to which it was compared to share with the class. Since this is a learning activity, all components will be completed in class.

Geom

etry

(Geo

metry Stand

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.G.1‐6)

1 Scale Factors

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.

199

1‐2

2 Similar Figures 200

3 Computing Lengths and Area of Scale Drawings 201

4 Reproduction of Scale Drawings 202‐203

E1 Evaluation – Similarity and Scale Drawings 204

P10 Performance Lesson #10 – Draw It to Scale (7.G.1) 205‐207 3 5 Classification of Triangles

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.

208

1‐2

6 Constructing Triangles Using Angles 209

7 Constructing Triangles Using Side Lengths 210

8 Determining Unique Triangles 211

E2 Evaluation – Constructions 212

9 Planes and Three‐Dimensional Figures 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.

213

1‐2

10 Relationship of Pi 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.

214

11 Circumference of a Circle 215

12 Circumference of Circles in Real‐Life 216

E3 Slicing 3‐Dimensional Figures and Circumference of a Circle

7.G.3 and 7.G.4 217

P11 Performance Lesson #11 – Two‐ and Three‐Dimensional Figures (7.G.2, 7.G.3, 7.G.4) 219‐221 3

13 Area of a Circle 7.G.4

222

1‐2

14 Areas of Circles in Real‐Life 223

15 Complimentary and Supplementary Angles

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.

224

16 Vertical Adjacent Angles 225

E4 Evaluation – Circular Area and Angles 7.G.4 and 7.G.5 226





DOK Level

Geom

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.G.1‐6)

17 Finding Unknown Angles 7.G.5

227

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18 Unknown Angles in Real‐World 228

19 Area of Parallelograms 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.

229

20 Area of Triangles 230

E5 Evaluation – Finding Unknown Angles and Area 7.G.5, 7.G.6 231

P12 Performance Lesson #12 – All About Angles (7.G.4, 7.G.5, 7.G.6) 233 3

21 Area of Trapezoids

7.G.6

234

1‐2

22 Area of Composite Figures 235

23 Area in Real‐World Contexts 236

24 Surface Area of Prisms and Pyramids 237

E6 Evaluation – Area in Real‐World Contexts 238

25 Surface Area of Cubic Figures

7.G.6

239

1‐2

26 Surface Area in Real‐World Context 240

27 Volume 241

28 Volume in Real‐World Contexts 242

E7 Surface Area and Volume 243




15-20 Minute Lessons and Formative Assessments

Students Learn the essential tested standards

14 Lesson Sets (4Lessons+1Assessment)DOK 1-256 Lessons and 14 Assessments

5+ Performance Lessons DOK 3-4

Frequent Performance LessonsStudents deepen and Apply their knowledge

50+ Intervention Lessons DOK 1-2-3

Scaffolded Intervention LessonsStudents who need more support, learn the prerequisite skills necessary for the mastery of grade-level standards

Target the High Impact Standards with our14-Week Intensive SBAC Review Program

The 14-Week Intensive SBAC Review program includes:

Contact Us for more information about this program.


17

Sample Lessons Included in this Booklet



DOK Level

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Common Core Standards Plus® – Mathematics – Grade 7Domain: Statistics and Probability Focus: Understanding Probabilities Lesson: #1Standard: 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.

Lesson Objective: Students will understand that a probability of a chance event is between 0 and 1.

Introduction: “Today we will begin learning about probability. We will understand that a probability of a chance event can be 0, 1, or any number between 0 and 1.”

Instruction: “Probability is the likelihood that an event will happen. We can find the theoretical probability of an event by using the ratio: number of favorable outcomes

total possible outcomes. For example, if we take a

coin, there is heads on one side and tails on the other. If we flip the coin, the theoretical probability of obtaining a heads is 1/2 since the number of favorable outcomes is 1 (one heads) and the total possible outcomes is 2 (heads or tails). Another example, if we have 4 green marbles and 7 blue marbles in a bag, the probability of randomly selecting a blue marble is 7/11. There are 7 blue marbles and 11 total marbles to choose from. Today we will also determine the likelihood of an event. Events that are unlikely have probabilities closer to 0. Events that are likely have probabilities closer to 1. Events that are neither unlikely nor likely have probabilities closer to 1/2. Probabilities cannot be less than 0 or greater than 1. Probabilities can be written as fractions, decimals, or percents.”

Guided Practice: “Let’s complete the examples together. In Example A, circle the numbers that can represent a probability. (Pause) Remember that probabilities cannot be less than zero, so cross out the negative numbers. Probabilities cannot be greater than 1, so cross out 5/2, 5, and 16. You should have circled 12%, 2/7, 0, 0.89, 99/100. A probability can be zero. That means the probability an event will happen is impossible. A probability of 1 means the event is certain. Now let’s do Example B. A bag contains 1 red marble, 12 yellow marbles, and 2 green marbles. A marble is randomly selected from the bag. What is the likelihood of choosing each color? (unlikely, neither unlikely nor likely, or likely) Let’s first write out the theoretical probability of selecting each color. The total number of marbles will be the denominator. That number represents the total favorable outcomes. We have a total of 15 marbles. The numerator of our ratio is represented by the number of favorable outcomes. For red, the probability is 1/15. For yellow, the probability is 12/15. For green, the probability is 2/15. Now we can decide the likelihood of drawing each color. For red, it is unlikely. For yellow, it is likely. For green, it is unlikely. Converting the fractions to decimals makes comparison easier.”

Independent Practice: “It is your turn to apply the same analysis to the practice problems.”

Review: When the students are finished, go over the correct answers.

Closure: “Today we reviewed theoretical probability. We reviewed that a probability of a chance event can be 0, 1, or any number between 0 and 1. We determined if an event was likely, unlikely, or neither.”

Answers: 1. Unlikely: 99 2 0.1 7%999 19

; Neither unlikely nor likely: 38 648% 75 13 Likely: 77 90.97 81 102. It is likely a customer would receive a flashlight since the probability is close to

1. It is unlikely a customer would receive a sun visor since the probability is closer to 0.

3. 3. Red probability is 1 .15 Blue probability is 0.

Statistics & Probability - Teacher Lesson Plan - Sample


19


Examples:A. Circle the numbers below that can represent a probability.

12% 2 5 990.34 5 16 0 0.89 17 2 100

B. A bag contains 1 red marble, 12 yellow marbles, and 2 green marbles. A marble is randomly selected from the bag. What is the likelihood of choosing each color? (unlikely, neither unlikely nor likely, or likely)

Red:________________ Yellow: _________________ Green: _________________

Directions: Complete the following problems.

1. The numbers shown below are probabilities of different chance events. Determine if each event is unlikely, neither unlikely or likely, or likely by writing the probability on the appropriate line.

99 2 38 77 6 948% 0.97 0.1 7%999 19 75 81 13 10

Unlikely: __________________________________________________

Neither unlikely or likely: ______________________________________

Likely: ___________________________________________________

2. A local store was celebrating a grand opening. The store manager decided to give away small gifts to the customers on opening day. Each customer who entered the store received either a flashlight or a sun visor. The probability of a customer receiving each gift is shown in the chart below.

Gift Probability

Flashlight 0.8

Sun Visor 15

Explain the likeliness of a customer receiving either gift and give your reasoning.

3. In Example B, what is the probability of randomly selecting a red marble? A blue marble?

Statistics & Probability - Student Page - Sample


Common Core Standards Plus® – Mathematics – Grade 7Domain: Statistics and Probability Focus: Understanding Probabilities Lesson: #2Standard: 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. Lesson Objective: Students will understand that a probability of a chance event is between 0 and 1.

Introduction: “Today we will continue learning about theoretical probability. We will understand that a probability of a chance event can be 0, 1, or any number between 0 and 1.”

Instruction: “Probability is the likelihood that an event will happen. We can find the theoretical probability of an event by using the ratio:

number of favorable outcomestotal possible outcomes

For example, the probability of rolling a 4 on a number cube is 1 .6 There is one 4 and six

possible numbers on the cube that can be rolled. Today we will also determine the likelihood of an event. Events that are unlikely have probabilities closer to 0. Events that are likely have probabilities closer to 1. Events that are neither unlikely nor likely have probabilities

closer to 1 .2 Probabilities cannot be less than 0 or greater than 1. Probabilities can be

written as fractions, decimals, or percents.”

Guided Practice: “Let’s complete the example problem together. Circle the numbers that can represent a probability. Take a minute to circle the numbers now. (Pause) Since

probabilities cannot be negative or greater than one, we are only left with 2 ,0.2, 3.4%.3 ”

Independent Practice: “It’s your turn to apply the same analysis to the practice problems.”


Closure: “Today we reviewed theoretical probability and determined a theoretical probability from given information. We reviewed that a probability of a chance event can be 0, 1, or any number between 0 and 1. We determined if an event was likely, unlikely, or neither.” Answers: 1. Answers will vary. For unlikely, the numbers should be 0 to about 0.4.

For neither, the numbers should be 0.45 to 0.55. For likely, the numbers should be 0.75 to 1. Check for a decimal, fraction, and percent.

2.number of favorable outcomes

total possible outcomes3. Probabilities cannot be less than zero because both the numerator and

denominator of the ratio in problem 2 are always positive. Probabilities cannot be more than one because the number of favorable outcomes will always be a subset of the total. It can equal the total but can never be more than the total.

4. B

5.20 544 11

Common Core Standards Plus® – Mathematics – Grade 7Domain: Statistics and Probability Focus: Experimental Probabilities Lesson: #3 Standard: 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.

Lesson Objective: Students will approximate the probability of a chance event by collecting data on the chance event and then by observing its long-run relative frequency. They will also predict the approximate relative frequency.

Introduction: “Today you will approximate the probability of a chance event by collecting data on the event and then by observing its long-run relative frequency, and predict the approximate relative frequency.”

Instruction: “Today and tomorrow, we will run experiments, and from the data, determine the probability of an event. We call the probability based on experiments or simulations experimental probability. We will run enough trials of the chance event to be able to approximate theoretical probabilities. The more trials run, the closer the experimental probability approaches the theoretical probability. We will use the experimental probabilities to predict the frequency of a specific outcome.”

Guided Practice: “We will start today’s lesson by gathering the data from many trials. We will be rolling two dice 20 times in small groups and record the sum of the dice after each roll. We will then pull the frequencies of the sums together as a total for the class. Before we begin the experiment, let’s answer the example question. If you roll two identical dice 1,000 times, do you think it is unlikely, likely, or neither to roll a sum of 7? What do you think and why? To help, think of all the possible outcomes you could roll. How many are there? Let’s write them down.

1,1 2,1 3,1 4,1 5,1 6,1 1,2 2,2 3,2 4,2 5,2 6,2 1,3 2,3 3,3 4,3 5,3 6,3 1,4 2,4 3,4 4,4 5,4 6,4 1,5 2,5 3,5 4,5 5,5 6,5 1,6 2,6 3,6 4,6 5,6 6,6

That’s 36 different outcomes. There are only a few combinations that result in a sum of 7. Therefore it is unlikely you will roll a sum of 7. Now it’s time to roll your two dice together 20 times. Write the sum by placing a tally mark in the appropriate box of your chart. We will combine the results of all the groups to fill in the frequencies in the last column in a few minutes. Work quickly.” After a few minutes, collect the class’ data in the chart.

Independent Practice: “Use the data in our class chart to answer the remaining questions.”


Closure: “Today you approximated the probability of a chance event by collecting data and observing its long-run relative frequency and predicted the approximate relative frequency.”

Answers: 1. Answers will vary; if dice are unavailable, use these data for students. Sum of 2 Dice Total Class Frequency Sum of 2 Dice Total Class Frequency

2 9 8 43 3 18 9 32 4 26 10 22 5 31 11 16 6 41 12 8 7 54

2. 54 18%300

3. Yes, it is unlikely to roll a sum of 7. 4. It is more likely to roll a sum of 7 than any other sum based on the data. 5. If each group rolls 100 times, then there will be 1,500 events. 1500 × 0.18 = 270. 6. Answers will vary. The student could base their answer from the data the class collected, or they could find the theoretical probability of 1/6 and use that to find the answer. They should provide their explanation of their method. Based on data: 1000000 × 0.18 = 180000; using theoretical probability: 11000000 166,6676

Common Core Standards Plus® – Mathematics – Grade 7Domain: Statistics and Probability Focus: Experimental Probabilities Lesson: #4Standard: 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. Lesson Objective: Students will approximate the probability of a chance event by evaluating the collected data. By observing its long-run relative frequency, they will predict the approximate relative frequency.

Introduction: “Today you will approximate the probability of a chance event by evaluating collected data on the event and then by observing its long-run relative frequency, you will predict the approximate relative frequency.”

Instruction: “Today we will evaluate experimental results and from the data, determine the approximate probability of an event. We call the probability based on experiments or simulations experimental probability. We will run enough trials of the chance event to be able to approximate theoretical probabilities. The more trials run, the closer the experimental probability approaches the theoretical probability. We will use the experimental probabilities to predict the frequency of a specific outcome. In the last lesson we took the time to run our own experiment and collect data. Today we will be given data from experiments.”

Guided Practice: “Let’s complete the examples together. A bag contains 25 marbles of 5 different colors. A marble is randomly drawn from the bag and the color of the marble is recorded. The marble is put back in the bag. This process is repeated 400 times. The chart shows the results. Using the data from the marble experiment, what is the best estimate for the number of red marbles in the bag? Let’s set up a proportion and solve.

43 (# times red was drawn) (# red marbles) 1075; 400 = or 2.6875 3400 (# of draws in all) 25 (# total marbles) 400r r r

From the data, we estimate there are 3 red marbles in the bag. Now how many purple? Set

up a proportion and solve. 158 ; 9.875 10400 25p p . From the data, we estimate there

are 10 purple marbles in the bag. If the process is repeated 1200 times, what will be the approximate frequency of green marbles drawn? Since 1200 is 3 times the 400 trials, we can simply multiply the result of the 400 trials by three. We get 155 3 345. ”

Independent Practice: “Now you will apply the same evaluation and process on your own.”

Review: When the students are done, go over the problems. If the students do not have enough time to finish, then they can write down the answers as you go over the problems.

Closure: “Today you approximated the probability of a chance event by evaluating data on the event and then by observing its long-run relative frequency, you predicted the approximate relative frequency.”

Answers: 1. True:

221 1855 4

2. False: The probability is approximately 12

since 404 1855 2

3. False: This is the approximate probability of the chance event based on the experiment and is not the theoretical probability.

4. 404 ; 945855 2000x x


Lesson Objective: Students will understand that a probability of a chance event is between 0 and 1.

Introduction: “Today we will begin learning about probability. We will understand that a probability of a chance event can be 0, 1, or any number between 0 and 1.”

Instruction: “Probability is the likelihood that an event will happen. We can find the theoretical probability of an event by using the ratio: number of favorable outcomes

total possible outcomes. For example, if we take a

coin, there is heads on one side and tails on the other. If we flip the coin, the theoretical probability of obtaining a heads is 1/2 since the number of favorable outcomes is 1 (one heads) and the total possible outcomes is 2 (heads or tails). Another example, if we have 4 green marbles and 7 blue marbles in a bag, the probability of randomly selecting a blue marble is 7/11. There are 7 blue marbles and 11 total marbles to choose from. Today we will also determine the likelihood of an event. Events that are unlikely have probabilities closer to 0. Events that are likely have probabilities closer to 1. Events that are neither unlikely nor likely have probabilities closer to 1/2. Probabilities cannot be less than 0 or greater than 1. Probabilities can be written as fractions, decimals, or percents.”

Guided Practice: “Let’s complete the examples together. In Example A, circle the numbers that can represent a probability. (Pause) Remember that probabilities cannot be less than zero, so cross out the negative numbers. Probabilities cannot be greater than 1, so cross out 5/2, 5, and 16. You should have circled 12%, 2/7, 0, 0.89, 99/100. A probability can be zero. That means the probability an event will happen is impossible. A probability of 1 means the event is certain. Now let’s do Example B. A bag contains 1 red marble, 12 yellow marbles, and 2 green marbles. A marble is randomly selected from the bag. What is the likelihood of choosing each color? (unlikely, neither unlikely nor likely, or likely) Let’s first write out the theoretical probability of selecting each color. The total number of marbles will be the denominator. That number represents the total favorable outcomes. We have a total of 15 marbles. The numerator of our ratio is represented by the number of favorable outcomes. For red, the probability is 1/15. For yellow, the probability is 12/15. For green, the probability is 2/15. Now we can decide the likelihood of drawing each color. For red, it is unlikely. For yellow, it is likely. For green, it is unlikely. Converting the fractions to decimals makes comparison easier.”

Independent Practice: “It is your turn to apply the same analysis to the practice problems.”


Closure: “Today we reviewed theoretical probability. We reviewed that a probability of a chance event can be 0, 1, or any number between 0 and 1. We determined if an event was likely, unlikely, or neither.”

Answers: 1. Unlikely: 99 2 0.1 7%999 19

; Neither unlikely nor likely: 38 648% 75 13 Likely: 77 90.97 81 102. It is likely a customer would receive a flashlight since the probability is close to

1. It is unlikely a customer would receive a sun visor since the probability is closer to 0.

3. 3. Red probability is 1 .15 Blue probability is 0.

Lesson Set at a Glance

Lesson Sets build student competence



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Common Core Standards Plus® – Mathematics – Grade 7 Domain: Statistics and Probability Focus: Theoretical and Experimental Probability

Evaluation: #1

Directions: Complete the following problems independently.

1. Circle the numbers that represent a probability.

1 90.5 0 2.2 5.6% 99.9%2 8

2. Is it unlikely, neither unlikely nor likely, or likely for the following events to occur?

Flip a coin and get tails Roll a 5 on a number cube Chose a white sock from a drawer of 10 pairs of white socks and 2 pairs of black

socks

3. What is the theoretical probability of randomly choosing a black marble from a bag of 29 black marbles, 134 white marbles, and 15 red marbles? Write your answer as a percent.

4. Doris used a computer simulation of a spinner with 8 equal sized colored sections. She conducted a total of 700 spins. The computer displayed the frequencies that the spinner landed as shown in the chart below.

Spinner Simulation

Color Frequency Red 87 Blue 85

Brown 89 Orange 95 Yellow 88 Green 85 Black 79 Pink 92

Based on the data Doris collected, predict the frequency of landing on brown if the spinner is spun 70 times and 1400 times.

Statistics & Probability Assessment Sample



1 2 3 4 1 +

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Performance Lesson - Teacher Lesson Plan - Sample

Common Core Standards Plus® – Mathematics – Grade 7Performance Lesson #8 – Domain: Statistics and Probability

St. Ed. Pgs. 177-178

Lesson Objective: The students will represent probabilities using fractions, decimals, and percent. They will conduct a probability experiment and predict frequency.

Overview: Students will use their knowledge of probability as addressed in the first three weeks of the Common Core Standards Plus Statistics and Probability Daily Lessons 1-12, E1-E3.

Students will:• Represent probabilities using fractions, decimals, and percent.• Conduct a probability experiment using six number cards to generate and predict frequencies.

Guided Practice: (Required Student Materials: St. Ed. Pg. 177)• Review vocabulary.• Review fractions, decimals, and percent as methods to demonstrate likely, unlikely, and neutral

situations.

Standard Reference: 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 exactly 200 times. 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. 7.SP.7a: 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. 7.SP.7b: 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. 7.SP.8a: 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. 7.SP.8b: 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. 7.SP.8c: 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 4 donors to find one with type A blood?

Required Student Materials: • Student Pages: St. Ed. Pgs. 177-178 (Student Worksheet)• *** (You may choose to have students recreate the number cards on a separate sheet of paper or on card stock.)

Common Core Standards Plus® is not licensed for duplication. Copying is illegal. © 2013 Learning Plus Associates

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Performance Lesson - Teacher Lesson Plan - SampleSt. Ed. Pgs. 177-178

Independent Practice: (Required Student Materials: St. Ed. Pgs. 177-178)Have the students:

• Analyze the meanings of likely, unlikely, and neutral to represent each using fractions, decimals, and percentages.

• Conduct a probability experiment using six number cards (1, 1, 1, 2, 2, 3).• Predict the frequency for larger numbers of counts.

Review & Evaluation:• Class discussion topic: Why did students have different results? Were the predicted frequencies

closer than the actual across the class?



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Performance Lesson - Student Page - Sample


Vocabulary: Probability: The likelihood that an event will happen; can be 0, 1, or any number between 0 and 1.

Likely: Probabilities that are close to 1 are likely to happen.

Unlikely: Probabilities that are close to 0 are unlikely to happen.

Neutral: Neither likely or unlikely; probabilities close to ½.

Theoretical probability: The number of favorable outcomes divided by the total possible outcomes.

Experimental probability: Probability based on experiments or simulations.

Frequency: How often an outcome occurs.

Fair: There are equal chances of an outcome.

Compound event: Two or more simple events; tossing a die is a simple event and tossing two dice is a compound event.

Compound probability: The probability of the first event multiplied by the probability of the second event multiplied by the probability of the third event and so on.

Simulation: A procedure in which you set up a model of a real situation.

Statistics: A discipline that studies the collection, analysis, interpretation, and presentation of data.

Statistical question: A question where you expect answers to vary.

Random sampling: A collection of data from the population that is random or collected without a method or pattern.

Sampling variation: The sample mean varies across different possible samples of the same population.

Variability or Variance: The spread of distances between values in a data set.

Directions: Use a fraction, a decimal, and percent to write numbers that represent the following probabilities. 1. Likely event: 2. Unlikely event: 3. Neither likely nor unlikely event:


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Performance Lesson - Student Page - Sample

Directions: Cut out the numbers below. Place them in a bag. Draw out one number. Record the draw and return the number to the bag. Repeat until you have drawn 50 times. Determine the theoretical probability of drawing each number. Determine the likelihood of drawing each number. Predict the frequency of drawing a 2 if you were to draw 100 times. Predict the frequency of drawing a 3 if you were to draw 500 times.

1 1 1

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Common Core Standards Plus® – Mathematics – Grade 7 Domain: Geometry Focus: Scale Factors Lesson: #1Standard: 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.

Lesson Objective: Students will use proportional reasoning to determine if figures are similar and state their scale factor.

Introduction: “Today you will use proportional reasoning to determine whether two figures are similar. You will compare a new figure to an original figure and describe the relationship between the two figures using a scale factor.”

Instruction: “Today we will be working with two figures that look alike, but are different in size. When figures have the same shape but are reduced or enlarged we call them similar. Two figures are similar if their corresponding angles are congruent and their corresponding sides are proportional. We can compare corresponding sides using a ratio. If you want to compare a side of an original figure that has a measure of 5 with a new figure that has a corresponding side with a measure of 10, you can set up a ratio to compare the two as new 10 1= =

original 5 2. When

corresponding sides are proportional, we call their ratio (in simplest form) a scale factor. When we are comparing two figures we often use the same letters. The original figure may have vertices that are labeled A, B, C, and our new figure that has been either reduced or enlarged may be labeled A ,B ,C .”

Guided Practice: “Let’s complete the examples together. We are given two figures and asked to determine whether they are similar. In Example A the original figure is on the left with vertices A, B, C, D, and the enlarged figure is on the right with vertices A ,B ,C ,D . We can determine whether the two figures are similar using proportional reasoning. First we need to determine which measures of the figures represent corresponding sides and compare them using a ratio. We always consider the new figure to the original by placing the measure of the new figure in the numerator and the measure of the original figure in the denominator. This technique produces a scale factor that is consistent with the size differences that we are given. If a scale factor is greater than one, our new figure is an enlargement of the original. If a scale factor is less than one, then we know our new figure will be a reduction of the original. Let’s compare segments

AB with A B and DE with D E giving us 9 3=6 2 and

12 3=8 2 . Since both ratios are equivalent we can

say9 12=6 8 are proportional and our scale factor is 3

2 . Now let’s look at Example B and compare

the same segments as the previous example 8 4 12 3= and =6 3 8 2

. The two ratios are not congruent

and therefore not proportional to each other. Even though the two figures look like they are the same shape, we cannot say that they are similar figures.”

Independent Practice: “Complete the exercises by determining whether the figures are similar using proportional reasoning and state the scale factor, in the same manner we did in the example.”


Closure: “Today you compared new figures to original figures and determined whether they were similar using proportional reasoning.”

Answers: 1. 5 1 4 2= and =15 3 14 7

; not similar figures

3. 7 1 2 1= and =21 3 6 3

; scale factor is 13

2. 9 3 15 3= and =3 1 5 1


4. 8 2 9= and4 1 5


Geometry - Teacher Lesson Plan - Sample


27


Directions: Determine whether the figures are similar using proportional reasoning. If similar, state the scale factor.

Example A: Example B:

1. 2.

3. 4.

Geometry - Student Page - Sample


Common Core Standards Plus® – Mathematics – Grade 7 Domain: Geometry Focus: Similar Figures Lesson: #2Standard: 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.

Lesson Objective: Students will use proportions to find the missing side given two figures that are similar.

Introduction: “Today you will set up a proportion given two similar figures in order to find a missing dimension.”

Instruction: “Today we will continue to work with similar figures. You have learned that if two figures are similar, then their corresponding angles are congruent and their corresponding sides are proportional. We can compare corresponding sides using a ratio.

Ratios are set up systematically neworiginal

. We consider the side of the new figure first and

place it in the numerator and then compare it to the corresponding side of the original figure and place it in the denominator. Each ratio represents the scale factor of the two figures. If we know that two figures are similar and we are missing the dimension of one side, we can use a proportion to solve for the missing dimension.”

Guided Practice: “Let’s complete the example together. We are to find the missing side given the two similar figures. Since we know that the two figures are similar, we can conclude that their corresponding sides are proportional. We compare the new figure on the right to the original figure on the left, 10 corresponds to 5 and 4.5 corresponds to the missing

dimension. Our two ratios are proportional 10 4.5=5 x

. To solve we must first simplify

2 5 4.5=1 5 x

which gives us 2 4.5=1 x

. If we cross multiply our equation we are left with 2x = 4.5

. After dividing both sides by 2 we can conclude that our missing side is 2.25.”

Independent Practice: “Complete the exercises by finding the missing side given the two similar figures, in the same manner we did in the example.”


Closure: “Today you set up a proportion given two similar figures in order to find a missing dimension.”

Answers: 1. 15 20= ,x = 24x 32

2. x 15= ,x = 96 10

3. x 13= ,x = 6.513 26

4. 30 18= ,x = 2440 x

Common Core Standards Plus® – Mathematics – Grade 7 Domain: Geometry Focus: Computing Lengths and Area of Scale Drawings Lesson: #3Standard: 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.

Lesson Objective: Students will use a scale drawing to compute actual lengths and area.

Introduction: “Today you will use proportional reasoning to convert dimensions of a scale drawing to actual length. You will use actual lengths to find the square footage of a given area.”

Instruction: “Today we will be working with scale drawings which are two-dimensional representations of an actual object. A scale drawing is mathematically similar to the original object. For two objects to be mathematically similar, their dimensions are proportional. A scale factor is a ratio that represents the relationship between the actual object and the scale drawing. When a scale factor is applied to an object it either reduces or enlarges it. For example, a scale factor of 1 to 4, also written 1

4 or 0.25, reduces the object. The scale drawing is a fraction or

partial piece of the original object. An example of a scale factor that enlarges an object would be 4 to 1, also written 4

1 or just 4. The scale drawing is 4 times the size of the original object.”

Guided Practice: “Let’s complete the example together. The scale drawing represents a floor plan with a scale factor of 1 to 4.75. This would mean that there is an original object that was reduced by 1

4.75 to fit on a grid where one unit represents one foot. We want to find the

dimensions of the original object. If 1

4.75was applied to the original object to get the scale drawing,

then we must apply the inverse 4.75

1 or multiply by 4.75 to find the dimensions of the original

object. We will determine how many square feet are in the original master bedroom. Rounding units on the grid to ½ a unit and multiplying by the inverse scale factor, we can say that the left side of the bedroom is 3.5 units or 16.625 feet, the left base is 5.5 units or 26.125 feet, the right side is 2.5 units or 11.875 feet, and the right base is 3 units or 14.25 feet. Now that we have our dimensions, we can decompose or break apart our figure into two rectangles. If we multiply length times width or base times height, we can find the area or square feet of our two rectangles. The left rectangle is 226.125 16.625 = 434.33ft , and the right rectangle is 211.875 14.25 = 169.22ft .If we combine the two rectangles and round to the nearest foot, we get a total of 604 square feet.”

Independent Practice: “It’s your turn to apply the same process to the given task. You will be using information from the example problem, but with additional square footage. Continue to round units on the grid to ½ a unit and square feet to the nearest foot.”

Review: When the students are finished, go over the answer grid.

Closure: “Today you used proportional reasoning to convert dimensions of a scale drawing to actual length. You also used the actual lengths to find the total square footage of the given area.”

Answers: 1.

3 feet = 14.25 ft.

Area of the top rectangle 564.06 feet squared plus the area of the bottom rectangle 169.22 feet squared equals a total of 733 square feet.

The square footage of the new master bedroom increased by 129 square feet.

2.5 feet = 11.875 feet

5 feet = 23.75feet

masterbedroom

5 feet = 23.75

Common Core Standards Plus® – Mathematics – Grade 7 Domain: Geometry Focus: Reproduction of Scale Drawings Lesson: #4Standard: 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.

Lesson Objective: Students will reproduce a sketch with given dimensions at a different scale factor.

Introduction: “Today you will continue using proportional reasoning to reproduce a scale drawing on a grid. You will use dimensions and a scale factor, which will assist you in translating the information into an accurate representation of the actual object.”

Instruction: “Today we will continue working with scale drawings. Remember, scale drawings are two-dimensional representations of an actual object. A scale drawing is mathematically similar to the original object. For two objects to be mathematically similar, their dimensions are proportional. Each dimension on the scale drawing uses the same scale factor, but can use the same or different units of measure. For example, 4 feet 2 inches represents two different units of measure. Before applying a scale factor, you must convert the dimension into a single unit measure. When a scale factor is applied to an object it either reduces or enlarges it. We will use the notation of the colon in today’s lesson. For example, a scale factor of 4 to 1 can be written 4:1, which enlarges the object. The scale drawing is 4 times as large as the original object.”

Guided Practice: “Let’s complete the example together. Using a scale factor of 1:1.5, accurately draw a scale drawing of the rectangle on the grid below. One unit on the grid represents one foot. First we must consider that the dimensions given are in feet and inches. We need to convert them to the same unit of measure. Let’s convert to inches. There are 12 inches in a foot. Nine feet is 108 inches. Adding in 10 inches, we get the horizontal dimension as 118 inches. Doing the same for the vertical dimension, we get 41 inches.Since our scale is in feet, we must calculate the number of feet for each dimension. We divide both dimensions by 12. We get 9.8 feet horizontally and 3.42 feet vertically. Next we apply the scale factor. The scale factor is 1.5:1 which means we are enlarging the sketch by taking 1 foot of the object and representing it by 1.5 feet on our scale drawing. Since one unit box on the grid represents one foot, we must multiply our dimensions by 1.5. We get 14.7 for the horizontal dimension and 5.13 for the vertical dimension. We do our best to estimate on the grid where 0.7 of a box is and 0.13 of a box is.” Model for students the drawing below.

Independent Practice: “You will see the word sketch used in the problem. A sketch is a drawing done by hand that is not exactly to scale. You will also need to find the missing dimension before you can complete the scale drawing.”

Review: When the students are finished, go over the answer grid.

Closure: “Today you continued to use proportional reasoning to reproduce a scale drawing on a grid. You used dimensions and a scale factor, which assisted you in translating the information into an accurate representation of the actual object.”

Answers: 1. The missing dimension is 35 inches or 2 feet 11 inches. The student reproduces the floor plan using a 1 : 3 scale factor with each unit equaling 1 foot.


Lesson Objective: Students will use proportional reasoning to determine if figures are similar and state their scale factor.

Introduction: “Today you will use proportional reasoning to determine whether two figures are similar. You will compare a new figure to an original figure and describe the relationship between the two figures using a scale factor.”

Instruction: “Today we will be working with two figures that look alike, but are different in size. When figures have the same shape but are reduced or enlarged we call them similar. Two figures are similar if their corresponding angles are congruent and their corresponding sides are proportional. We can compare corresponding sides using a ratio. If you want to compare a side of an original figure that has a measure of 5 with a new figure that has a corresponding side with a measure of 10, you can set up a ratio to compare the two as new 10 1= =

original 5 2. When

corresponding sides are proportional, we call their ratio (in simplest form) a scale factor. When we are comparing two figures we often use the same letters. The original figure may have vertices that are labeled A, B, C, and our new figure that has been either reduced or enlarged may be labeled A ,B ,C .”

Guided Practice: “Let’s complete the examples together. We are given two figures and asked to determine whether they are similar. In Example A the original figure is on the left with vertices A, B, C, D, and the enlarged figure is on the right with vertices A ,B ,C ,D . We can determine whether the two figures are similar using proportional reasoning. First we need to determine which measures of the figures represent corresponding sides and compare them using a ratio. We always consider the new figure to the original by placing the measure of the new figure in the numerator and the measure of the original figure in the denominator. This technique produces a scale factor that is consistent with the size differences that we are given. If a scale factor is greater than one, our new figure is an enlargement of the original. If a scale factor is less than one, then we know our new figure will be a reduction of the original. Let’s compare segments

AB with A B and DE with D E giving us 9 3=6 2 and

12 3=8 2 . Since both ratios are equivalent we can

say9 12=6 8 are proportional and our scale factor is 3

2 . Now let’s look at Example B and compare

the same segments as the previous example 8 4 12 3= and =6 3 8 2

. The two ratios are not congruent

and therefore not proportional to each other. Even though the two figures look like they are the same shape, we cannot say that they are similar figures.”

Independent Practice: “Complete the exercises by determining whether the figures are similar using proportional reasoning and state the scale factor, in the same manner we did in the example.”


Closure: “Today you compared new figures to original figures and determined whether they were similar using proportional reasoning.”

Answers: 1. 5 1 4 2= and =15 3 14 7


3. 7 1 2 1= and =21 3 6 3


2. 9 3 15 3= and =3 1 5 1


4. 8 2 9= and4 1 5


Lesson Set at a Glance

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Common Core Standards Plus® – Mathematics – Grade 7Domain: Geometry Focus: Similarity and Scale Drawings

Evaluation: #1

1. Determine whether the figures are similar using proportions. If similar, state the scale factor.

2. Find the missing side given the two similar figures.

3. Using a scale factor of 4:1, accurately draw a scale drawing of the rectangle on the gridbelow. One unit on the grid represents one foot.

1 foot 3 inches

3 feet 9 inches

Geometry Assessment Sample



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