Before this unit, students worked with ratios of whole numbers and with whole number percentages. Now they start to work with ratios of fractions and fractional percentages. In this lesson they encounter situations where a ratio of fractions arises naturally. They compute scale factors and unit rates associated with ratios of fractions. They consider a situation involving a ratio where the second number is 100, in order to prepare for thinking about a percentage as a particular type of rate, and they compare rates associated with different ratios. The representations they use—tape diagrams and double number lines—are the same as they have used previously, but in the context of more complicated ratios.
The Mona Lisa task has more than one reasonable answer, and students must make sense of the situation in order to choose one (MP1).
Lesson overview
 2.1 Warmup: Number Talk: Division (5 minutes)
 2.2 Activity: A Train is Traveling at . . . (10 minutes)

2.3 Activity: Comparing Running Speed (10 minutes)
 Includes "Are you Ready for More?" extension problem

2.4 Optional Activity: Scaling the Mona Lisa (10 minutes)
 There is a digital applet in this activity.
 Lesson Synthesis
 2.5 Cooldown: Comparing Orange Juice Recipes (5 minutes)
Learning goals:
 Compare and contrast (orally and in writing) different strategies for solving a problem involving equivalent ratios with fractional quantities.
 Explain (orally and in writing) how to find and use a unit rate to solve a problem involving fractional quantities.
Learning goals (student facing):

Let's calculate some rates with fractions.
Learning targets (student facing):
 I can solve problems about ratios of fractions and decimals.
Glossary:
 unit rate  A unit rate is a rate per 1. For example, 12 people share 2 pies equally. One unit rate is 6 people per pie, because \(12 \div 2 = 6\). The other unit rate is \(\frac16\) of a pie per person, because \(2 \div 12 = \frac16\).
 Access the complete Grade 7 glossary.
Standards
 This lesson builds on the standards:CCSS.7.G.A.1MS.7.G.1MO.7.GM.A.1CCSS.6.RP.A.3MO.6.RP.A.3b MS.6.RP.3CCSS.6.NS.A.1MS.6.NS.1MO.6.NS.A.1a
 This lesson builds towards the standards:CCSS.7.RP.A.1MS.7.RP.1MO.7.RP.A.1CCSS.7.RP.A
IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 20172019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/mathcurriculum/.
Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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