7th Grade Unit 2: Ratio and Proportional Relationship

Prerequisite Skills: • Ratio concepts • Unit rates associated with non-complex fractions • Equivalent ratio tables • Plotting Points on a Coordinate Plane • Simplifying fractions • Units of Measures • Greatest Common Factor

Welcome our second math unit!!!

UNIT OVERVIEW: In this unit students will learn how to analyze, recognize and compute proportional relationships to solve real-world and mathematical problems. In this unit, students build on their 6th grade experiences with ratios, unit rates, and fraction division to analyze proportional relationships. They decide whether two quantities are in a proportional relationship, identify constants of proportionality, and represent the relationship by equations. In 7th grade students will find unit rates in ratios involving fractional quantities. Students will set up an equation with equivalent fractions and use reasoning about equivalent fractions to solve them. Also, in this section students will determine if two quantities are proportional by using tables, equations, and graphs. The shortcut of “cross products” should be examined later as students begin to recognize patterns and why the shortcut works. Students should not be using “cross products” first. They need to identify the unit rate given a table, graph, equation, diagrams, and a verbal description. Knowing the constant of proportionality (unit rate) students will be able to write equations in the form y=kx

Learning Target 1: I can compute unit rates with ratios of lengths and areas and other quantities measured in like and unlike units. 7.RP.1 Example

A) Determine ratio

Ratio is an ordered pair of two non-negative integers. It shows the relative sizes of two or more like values.

B)Differentiate between

ratios and rate Rate is a ratio that compares two quantities with different kinds of units.

Example:

7th Grade Unit 2: Ratio and Proportional Relationship

C) Compute unit rate Unit Rate is a rate that is simplified so that it has a

denominator of 1 unit. Example: Lexi painted 2 faces in 8 minutes at the Crafts Fair. At this rate, how many faces can she paint in 40 minutes?

RATE UNIT RATE NAME

A rate of speed

Gas Mileage

Unit price

D) unit cost/ unit price Examples:

7th Grade Unit 2: Ratio and Proportional Relationship

Learning Target 2: I can compute unit rate involving complex fractions 7.RP.2b, 7.RP.2c

A) Complex Fractions A complex fraction is simply a fraction whose numerator or denominator (or both) are fractions.

7th Grade Unit 2: Ratio and Proportional Relationship

B) Word Problems Word Problem Samples:

1. A lawn company advertises that they can spread 7,500 square feet of grass seed in . Find the number of square feet of grass seed that can be spread in 4 hours.

2. Debra can run in How many miles per hour can she run?

3. Monica is painting her house. She paints square feet in At this rate how many square feet can she paint each hour?

Learning Target 3: I can decide whether two quantities are in 7.RP.A.2 a proportional relationship

A) proportional relationship (table)

Two variables are proportional if they maintain a constant ratio

Which table(s) shows a proportional relationship between x and y?

7th Grade Unit 2: Ratio and Proportional Relationship

B) proportional relationship (graph)

Parts of a coordinate plane

Example:

Dependent and Independent Variable

Ø Scaleofthegraphisexactlythesameasthescaleinthetable.

Ø Theratiosinthetablearetheorderedpairsofthepointsinthegraph.

Ø Non-plottedpoint(10,110),doesnotaffectthegraph.

7th Grade Unit 2: Ratio and Proportional Relationship

C.) Non-Proportional

Relationship Characteristics of Non-Proportional Graphs.

D.) Interpret points of a

graph

Ø ThegraphdoesNOTstartorpassthroughtheorigin.

Ø Thegraphisastraightlinegoinginanupwarddirection.

Ø TheorderedpairsdoNOThaveaconstantrateofchange.

, , areNOT

equal.

Ø ThegraphdoesNOTstartorpass

throughtheorigin.Ø Thegraphisastraightlinegoinginan

downwarddirection.Ø TheorderedpairsdoNOThavea

constantrateofchange.

, , areNOT

equal.

7th Grade Unit 2: Ratio and Proportional Relationship

E.) Constant of

proportionality in equation

Constantofproportionality:Thenumberrepresentingtheratioofanytwocorrespondingsidesintwosimilargeometricfigures.

Which point shows the unit rate? What does the ratio of the y-coordinate to the x-coordinate for each pair of points on the graph represent? What does point C represent?

1. Laila claims that point C shows that 16 tickets cost $2. Is she correct? Explain your reasoning.

2. Which point on the graph shows the unit rate? Explain your answer.

7th Grade Unit 2: Ratio and Proportional Relationship

Mastery Quizzes: 50 pts. each Mastery quizzes are short quizzes that assess 2 – 3 learning objectives. Your child will be given this quiz once the learning objectives have been taught in class. The best way to prepare for these quizzes is by completing classwork and homework. If your child is struggling with homework assignments please contact us, or have your child attend an extra help session.

Ø Mastery Quiz 1: will assess the following learning objectives under the learning target: Learning Target: I can compute unit rate with ratios of lengths and areas and other quantities measured in like and unlike units.

o I can determine a ratio of two quantities. o I can differentiate between ratios and rates o I can compute unit ratios, unit rates / unit cost / unit price

Ø Mastery Quiz 2: will assess the following learning objectives under the learning target:

Learning Target: I can compute unit rate involving complex fractions. o I can compute unit rate (review). o I can simplify complex fractions to find unit rate. o I can use unit rate to solve problems involving complex fractions.

Ø Mastery Quiz 3: will assess the following learning objectives under the learning target:

Learning Target: I can decide whether two quantities are in a proportional relationship. o I can set up and use a ratio table to show equivalent ratios. o I can use ratio tables to represent and analyze proportional relationships.

Ø Mastery Quiz 4: will assess the following learning objectives under the learning target:

Learning Target: I can decide whether two quantities are in a proportional relationship. o I can graph linear relationships of two quantities in a given situation. o I can interpret (describe) the characteristic of a proportional and non-proportional graph of two

quantities.

Ø Mastery Test 5: will assess the following learning objectives under the learning target: Learning Target: I can decide whether two quantities are in a proportional relationship.

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

o I can represent proportional relationships as an equation (y=kx), where k is the proportionality constant using a graph and ratio tables.

7th Grade Unit 2: Ratio and Proportional Relationship

Unit Test: 100 pts. Approximate date:_________________________ Review your notes of the daily lesson for the whole unit 2 to prepare for this test. Performance Task: 100 pts.: Approximate date:_________________________ This is an in class assessment. It is a multi-step word problem, similar to the kind of questions you will see on Day 3 of the NYS test. Culminating Project: 100 pts. The culminating project will be assigned in the middle of the unit. It will not be due until the end of the unit. It will assess all learning targets. You will be able to access this on weebly. Learning Activities You will be completing a variety of learning activities in class that reflect the learning targets for Unit 2. These will be graded, and you will be able to track your own progress online.

Good luck!

Math Teachers