ALEX Learning Activity

  

Solving Unit Rate Problems (During)

A Learning Activity is a strategy a teacher chooses to actively engage students in learning a concept or skill using a digital tool/resource.

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  This learning activity provided by:  
Author: YVETTE AKRIDGE
System:Andalusia City
School:Andalusia City Board Of Education
  General Activity Information  
Activity ID: 2835
Title:
Solving Unit Rate Problems (During)
Digital Tool/Resource:
Solving Unit Rate Problems/PBS LearningMedia
Web Address – URL:
Overview:

In this learning activity, students will learn a strategy for solving unit rate problems from the PBS video. In the accompanying classroom activity, students watch the video and then use grocery store ads to calculate unit rates and compare prices. They share solution strategies and consider ways that unit rates can facilitate making comparisons. To get the most from the activity, students should be comfortable finding equivalent fractions and have had some exposure to the concepts of ratio and unit rate.
  Associated Standards and Objectives  
Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 7
1. Calculate unit rates of length, area, and other quantities measured in like or different units that include ratios or fractions.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Compute a unit rate for ratios that compare quantities with different units.
  • Determine the unit rate for a given ratio, including unit rates expressed as a complex fraction.

    • Example: if a runner runs 1/2 mile every 3/4 hour, a student should be able to write the ratio as a complex fraction.)
Teacher Vocabulary:
  • Unit rate
  • Ratio
  • Unit
  • Complex fractions
Knowledge:
Students know:
  • What a unit rate is and how to calculate it given a relationship between quantities.
  • Quantities compared in ratios are not always whole numbers but can be represented by fractions or decimals.
  • A fraction can be used to represent division.
Skills:
Students are able to:
Compute unit rates associated with ratios of fractional
  • lengths.
  • Areas.
  • quantities measured in like or different units.
Understanding:
Students understand that:
  • Two measurements that create a unit rate are always different (miles per gallon, dollars per hour)
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.7.1.1: Define unit rate, proportions, area, length, and ratio.
M.7.1.2: Recall how to find unit rates using ratios.
M.7.1.3: Recall the steps used to solve division of fraction problems.

Prior Knowledge Skills:
  • Recall addition and subtraction of fractions as joining and separating parts referring to the same whole.
  • Identify two fractions as equivalent (equal) if they are the same size or the same point on a number line.
  • Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model.
  • Generate equivalent fractions.
  • Define quantity, fraction, and ratio.
  • Reinterpret a fraction as a ratio.
    Example: Read 2/3 as 2 out of 3.
  • Write a ratio as a fraction.
  • Create a ratio or proportion from a given word problem, diagram, table, or equation.
  • Calculate unit rate or rate by using ratios or proportions.
Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.7.1 Calculate a unit rate (limited to whole numbers under 100).
Mathematics
MA2019 (2019)
Grade: 7
Accelerated
1. Calculate unit rates of length, area, and other quantities measured in like or different units that include ratios or fractions. [Grade 7, 1]
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Compute a unit rate for ratios that compare quantities with different units.
  • Determine the unit rate for a given ratio, including unit rates expressed as a complex fraction.
    • Example, if a runner runs mile every hour, a student should be able to write the ratio as a complex fraction.)
Teacher Vocabulary:
  • Unit rate
  • Ratio
  • Unit
  • Complex fractions
Knowledge:
Students know:
  • What and how to calculate a unit rate to represent a given relationship between quantities.
  • Quantities compared in ratios are not always whole numbers but can be represented by fractions or decimals.
  • A fraction can be used to represent division.
Skills:
Students are able to:
Compute unit rates associated with ratios of fractional:
  • Lengths.
  • Areas.
  • Quantities measured in like or different units.
Understanding:
Students understand that:
  • the two measurements that create a unit rate are always different (miles per gallon, dollars per hour).
Diverse Learning Needs:
Learning Objectives:

Students will be able to:

  • solve real-world problems involving finding and comparing unit rates.

  • define ratios and unit rates.
  Strategies, Preparations and Variations  
Phase:
During/Explore/Explain
Activity:

Procedure:

  1. Before: Review the Before Activity by watching the PBS video (10 minutes, whole group) Pause the video at 00:30 (30 seconds). Ask pairs to talk over the solution to the problem posed and jot down their solution strategies.

  2. After a few minutes, resume and finish the video. When it is over, ask students:

    • Did anyone solve the problem the same way as in the video?

    • What other ways did you find to solve the problem?

    Record students’ solution strategies or invite them to come up and do so. Emphasize the variety of possible approaches.

  3. During: Unit Rate in Ads (10 minutes, pairs)
    Distribute the ads. Ask pairs to determine which of their ads offers the best unit price, and record their calculations.

  4. As pairs finish up, pose the following question (tailored to the particular ads):

  5. If you’re going to buy [apples], which unit rate would you find more useful: price per [apple] or the number of [apples] you can buy per [$1]? Why? 

  6. Encourage students to consider which kinds of unit rate calculations might be helpful, which might be less helpful, and why.

  7. Conclusion (5 minutes, whole group)
    Ask for volunteers who worked with different ads to share their solution strategies. Highlight the variety of possible strategies. If no one volunteers, the teacher should offer different ways to work the problems.
Assessment Strategies:

The student responses during the class discussion will be used as a formative assessment.
Advanced Preparation:

  • The teacher will need to gather grocery store ads with pricing given as a ratio; for instance, 4 apples for $3. Each pair needs two or three such ads for one type of product (e.g., three ads for apples). If possible, provide a variety so that not all pairs use the same ads.

  • The teacher will need to put the students in pairs.

  • The teacher will need to sign up for a free PBS LearningMedia account.

  • To get the most from the activity, students should be comfortable finding equivalent fractions and have had some exposure to the concepts of ratio and unit rate.
Variation Tips (optional):

Activity Extension: Have students look through a wide variety of ads with pricing given as a ratio (e.g., 3 games for $49.99). They should then choose items that they would like to purchase (realistic or not) and determine what unit price they would pay.
Notes or Recommendations (optional):

This activity can stand alone or be used as a During/Explore/Explain activity for the following learning activities:

Solving for Unit Rates (Before Activity)

What Is Unit Rate and How Can We Use Unit Rate to Compare? (After Activity)
  Keywords and Search Tags  
Keywords and Search Tags: equivalent fractions, fractions, ratios, unit rates