Idea Transcript
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
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