# 9. Playing In Common: Multiplicative comparisons involving fractions (FP)

teaches Common Core State Standards 111.7.3.I http://ritter.tea.state.tx.us/rules/tac/chapter111/index.html
teaches Common Core State Standards 111.26.3.E http://ritter.tea.state.tx.us/rules/tac/chapter111/index.html
teaches Common Core State Standards 111.5.5.B http://ritter.tea.state.tx.us/rules/tac/chapter111/index.html
teaches Common Core State Standards 111.5.5.C http://ritter.tea.state.tx.us/rules/tac/chapter111/index.html
teaches Common Core State Standards 4.AT.3 http://www.doe.in.gov/standards/mathematics
teaches Common Core State Standards 5.C.5 http://www.doe.in.gov/standards/mathematics
teaches Common Core State Standards MAFS.4.OA.1.1 http://www.cpalms.org/Public/search/Standard
teaches Common Core State Standards CCSS.Math.Content.4.OA.A.1 http://corestandards.org/Math/Content/4/OA/A/1
teaches Common Core State Standards CCSS.Math.Content.4.NF.B.4b http://corestandards.org/Math/Content/4/NF/B/4/b
teaches Common Core State Standards CCSS.Math.Practice.MP6 http://corestandards.org/Math/Practice/MP6
teaches Common Core State Standards CCSS.Math.Practice.MP1 http://corestandards.org/Math/Practice/MP1

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Lesson objective: Interpret and solve equations when one quantity is some number of times as much as another quantity.

This lesson helps to build procedural skill with using multiplication to compare amounts that include a fraction.  An equation stating "Amount $$\times$$ How many times greater $$=$$Greater amount" is used here because it supports students' understanding that, while any part of this equation may be missing in a comparison problem, the problem can still be solved using multiplication. This work develops students' understanding that because fractions are numbers, the meaning of multiplicative comparison does not change when fractions are involved.

Students engage in Mathematical Practice 1 (make sense of problems and persevere in solving them) as they evaluate what information comparison problems ask them to find and then determine the best way to find the missing information.

Key vocabulary:

• compare
• comparison factor
• product
• value

Special materials needed:

• game cards for "In Common" (see "Additional materials")
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