Ratios and Proportional Relationships

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7th Math Unit 3 Information Ratios & Proportional Relationships CRCT Domain & Weight: 22% (19% RP & 3% Geometry) Flip Book for Unit 3 Unit 3 Overview Prerequisites: Unit 3 Unit Length: Approximately 28 days Checklist for Unit 3 Study Guide for Unit 3 Study Guide KEY for Unit 3 Click Here for Suggested Use of Calculators: Unit 3

Click on the links below for resources by Concept: Concept ONE: Proportional Relationships and Constant of Proportionality Concept TWO: Unit Rates Concept THREE: Scale Drawings Concept FOUR: Ratio & Percent Problems

TCSS Concept ONE: Proportional Relationships & Constant of Proportionality (Unit Rate) Standard(s) & Essential Questions

Vocabulary

Resources

Assessment

Great!!! Activator: Bad Date! MGSE7.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.



Proportional



Proportion

 E. Q. How do I recognize proportional relationships between quantities? MGSE7.RP.2b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. E. Q. How do I represent proportional relationships between quantities? CC.7.RP.2c Represent proportional relationships by equations. MGSE7.RP.2d 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.

TCSS



Eureka Math License Proportional or Not? Tables & Graphs – 6 Lessons Unit rate/Constant of Proportionality – 4 Lessons



Glencoe Textbook CCSS (2013) o Proportion Tables p. 33-40 o Proportion Graphs p. 45-52

Constant of Proportionality

CC.7.RP.2



Eureka Math Unit Rate/Constant of Proportionality



Glencoe Textbook CCSS (2013) o Constant Rate of Change p. 65-80



Short Task: Buses o Challenging task  Support: Do whole group with help  Extend: Small groups  On Target: A mix of both whole group and small group

License

Differentiation  Spotlight Task: The Fastest  Extend Proportions  Word Problems with Proportions

6/1/2016

2

TCSS Concept TWO: Unit Rates (incl. fractions) Standard(s) & Essential Questions MGSE7.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 2 miles per hour. E.Q. How do I interpret a unit rate (using words and mathematically)?

Vocabulary



Rate



Unit Rate



Ratio



Fraction



Multiplicative Inverse

Resources   

Background PowerPoint ActivInspire Rates/Ratios ActivInspire Proportions



Eureka Math Ratios & Rates Involving Fractions

These 3 resources are review from 6th grade. Only use as needed and do not spend very much time on them.

CC.7.RP.1

License

Glencoe Textbook CCSS o Basic unit rates p. 3-16 o Complex fraction unit rates p. 17-24 

Spotlight Task: Unit Rate



Unit Rate PowerPoint



Comparing Prices Video



Spotlight Task: Analyze & Apply Unit Rate



CCGPS Frameworks: Better Deal (from Ads)? o

TCSS

Assessment

6/1/2016

Glencoe Differentiation – (Unit Rate)  Extend  Word Problems

3

TCSS Concept THREE: Ratios & Scale Drawings Standard(s) & Essential Questions MGSE7.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. E.Q. How do I compute actual lengths and areas from a scale drawing?

TCSS

Vocabulary

Resources

Assessment

Activator  Brainpop – Free Scale Drawing Video



Scale Factor



Scale Drawing



Eureka Math License DO: Ratios of Scale Drawings – 4 Lessons Optional: Task: Create a Scale Drawing

CC.7.G.1 

CCGPS Glencoe Textbook p. 571-584



Graphic Organizer



Scale Drawings Power Point



CCGPS Frameworks Creating A Scale Map



Spotlight: Draw and Drive



Spotlight: Thumbs On Fire



Glencoe Differentiation (Scale Models) o Enrich o Word Problems

6/1/2016

4

TCSS Concept FOUR: Ratio & Percent Problems Standard(s) & Essential Questions MGSE7.RP.2c 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 = 𝑝𝑝 . MGSE7.RP.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, and fees. E.Q. How do I verify if two quantities are directly proportional? E.Q. How do I solve realworld problems using equivalent ratios? E.Q. How do I represent proportional relationships by equations?

TCSS

Vocabulary

Resources 

Eureka Math – DO these – Very Good! License o Solve % Proportions – 5 Lessons o Markup, Simple Interest, Tax, etc. – 3 Lessons o Real World Population & Mixtures – 2 Lessons



Ratio



Percent



Proportion



Solving Proportions Power Point



Sales Tax



Proportion: Shadow Problem



Tips





Commission



Markup



Discount

CCSS Glencoe Textbook (2013) o Solve proportions p. 55-62 o % proportions p. 103-110 &119-128 o % equation p. 129-140 o Tax, Tips, Markup p. 151-158 o Discount p. 159-166 o Simple Interest p. 167-174 o % Problem Solving p. 181



Simple Interest



CCGPS Activity: Patterns & Percents



Differentiation

Assessment

CC.7.RP.3

o Extend: CCGPS Frameworks Orange Fizz o

o

o

Tax / Tip / Markup  Extend  Word Problems Discounts  Extend  Word Problems Simple Interest  Extend  Word Problems

6/1/2016

5

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Ratios and Proportional Relationships

7th Math Unit 3 Information Ratios & Proportional Relationships CRCT Domain & Weight: 22% (19% RP & 3% Geometry) Flip Book for Unit 3 Unit 3 Overview ...

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