# ALEX Lesson Plan

## How Far Can You Leap?

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This lesson provided by:
 Author: Tim McKenzie Organization: UAB/UABTeach The event this resource created for: CCRS General Lesson Information
 Lesson Plan ID: 33080 Title: How Far Can You Leap? Overview/Annotation: This lesson will allow students to become familiar with the concept of unit rate. Through an open investigation students will develop methods to find unit rate with a table, equivalent ratios, or an equation. This is a lesson to be used as part of a unit with "Painter Problems" and "How Big Should It Be?"This is a College- and Career-Ready Standards showcase lesson plan.
Associated Standards and Objectives
Content Standard(s):
 Mathematics MA2015 (2016) Grade: 6 1 ) Understand the concept of a ratio, and use ratio language to describe a ratio relationship between two quantities. [6-RP1] Examples: "The ratio of wings to beaks in the bird house at the zoo was 2:1 because for every 2 wings there was 1 beak." "For every vote candidate A received, candidate C received nearly three votes." NAEP Framework NAEP Statement:: 4NPO4a: Use simple ratios to describe problem situations. NAEP Statement:: 8NPO3a: Perform computations with rational numbers. NAEP Statement:: 8NPO4a: Use ratios to describe problem situations. NAEP Statement:: 8NPO4b: Use fractions to represent and express ratios and proportions. NAEP Statement:: 8NPO4d: Solve problems involving percentages (including percent increase and decrease, interest rates, tax, discount, tips, or part/whole relationships). Alabama Alternate Achievement Standards AAS Standard: M.AAS.6.1- Select a ratio to match a given statement and representation. Mathematics MA2015 (2016) Grade: 6 2 ) Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. [6-RP2] Examples: "This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar." "We paid \$75 for 15 hamburgers, which is a rate of \$5 per hamburger." (Expectations for unit rates in this grade are limited to non-complex fractions.) NAEP Framework NAEP Statement:: 8NPO3a: Perform computations with rational numbers. NAEP Statement:: 8NPO4a: Use ratios to describe problem situations. NAEP Statement:: 8NPO4b: Use fractions to represent and express ratios and proportions. NAEP Statement:: 8NPO4d: Solve problems involving percentages (including percent increase and decrease, interest rates, tax, discount, tips, or part/whole relationships). Alabama Alternate Achievement Standards AAS Standard: M.AAS.6.2- Recognize rate vocabulary in a real-world situation (e.g., miles per hour, dollars per pound). Mathematics MA2015 (2016) Grade: 6 3 ) Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. [6-RP3] a. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. [6-RP3a] b. Solve unit rate problems including those involving unit pricing and constant speed. [6-RP3b] Example: If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours' At what rate were lawns being mowed' c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. [6-RP3c] d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. [6-RP3d] NAEP Framework NAEP Statement:: 8M2b: Solve problems involving conversions within the same measurement system such as conversions involving square inches and square feet. NAEP Statement:: 8M2c: Estimate the measure of an object in one system given the measure of that object in another system and the approximate conversion factor. For example: Distance conversion: 1 kilometer is approximately 5/8 of a mile. Money conversion: U.S. dollars to Canadian dollars. Temperature conversion: Fahrenheit to Celsius. NAEP Statement:: 8NPO3a: Perform computations with rational numbers. NAEP Statement:: 8NPO4a: Use ratios to describe problem situations. NAEP Statement:: 8NPO4b: Use fractions to represent and express ratios and proportions. NAEP Statement:: 8NPO4d: Solve problems involving percentages (including percent increase and decrease, interest rates, tax, discount, tips, or part/whole relationships). Alabama Alternate Achievement Standards AAS Standard: M.AAS.6.3- Solve simple real-world problems using ratio/rate reasoning. M.AAS.6.3a- Answer simple questions about a table of equivalent ratios with whole-number measurements. M.AAS.6.3b- Calculate unit-rate problems, including those involving unit pricing. M.AAS.6.3c- Identify a percentage equivalent to a fraction (e.g., 1/2, 1/4, 1). M.AAS.6.3d- Identify the decimal equivalent of a percentage (limited to 10%, 20%, 25%, 40%, and 50%). Mathematics MA2015 (2016) Grade: 7 1 ) Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. [7-RP1] NAEP Framework NAEP Statement:: 8NPO1b: Model or describe rational numbers or numerical relationships using number lines and diagrams. NAEP Statement:: 8NPO1d: Write or rename rational numbers. NAEP Statement:: 8NPO1e: Recognize, translate or apply multiple representations of rational numbers (fractions, decimals, and percents) in meaningful contexts. NAEP Statement:: 8NPO3a: Perform computations with rational numbers. NAEP Statement:: 8NPO3f: Solve application problems involving rational numbers and operations using exact answers or estimates as appropriate. NAEP Statement:: 8NPO4a: Use ratios to describe problem situations. NAEP Statement:: 8NPO4b: Use fractions to represent and express ratios and proportions. NAEP Statement:: 8NPO4c: Use proportional reasoning to model and solve problems (including rates and scaling). Alabama Alternate Achievement Standards AAS Standard: M.AAS.7.1- Calculate a unit rate (numbers limited to whole numbers under 100).

Local/National Standards:

Math Practice Standards:

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.

Primary Learning Objective(s):

I CAN identify and develop ratios in real world situations.

I CAN identify equivalent ratios.

I CAN compare ratios in real world situations.

I CAN use equivalent ratios to find the unit rate.