Students are introduced to the concept of ratios, learning ratio language to describe the association between two or more quantities and different strategies to solve ratio problems.
In unit 1, sixthgrade students have the opportunity to study a concept that is brand new to them: ratios. They learn how to use ratio language to describe the association between two or more quantities, expanding their abilities to analyze relationships and see multiplicative patterns. Students learn many ways to represent ratios, starting with discrete drawings and working their way to abstract tables. These representations become important tools in their ratios toolkit, enabling students to be strategic about which tools to use for different problems (MP.5). When students work with tables and double number lines, they discover how structure can shine light on a relationship, especially when comparing multiple ratio situations (MP.7).
Throughout the unit, students see similar problems posed to them in different lessons. This is to support students learning new strategies to solve ratio problems and to compare and contrast different approaches. By the end of the unit, students should be able to select a strategy they think is best for a problem and to explain their choice.
In fourth and fifth grade, students learned the difference between multiplicative and additive comparisons and they interpreted multiplication as a way to scale. Students will access these prior concepts in this unit as they investigate patterns and structures in ratio tables and use multiplication to create equivalent ratios.
The work students do in this unit connects directly to Unit 2: Rates & Percent and reappears in Unit 6: Equations and Inequalities when students analyze and graph relationships between independent and dependent variables. Beyond sixth grade, students extend their understanding of ratios and rates to investigate proportional relationships in seventh grade. This sets the groundwork for the study of functions, linear equations, and systems of equations, which students will study in eighth grade and high school.
This unit includes the MAspecific standard 6.RP.3e, which refers to a specific type of ratio problem about an object’s mass and volume. While this context is specific to this MA standard, it poses a realworld example of ratio problems that is worthwhile to solve.
Pacing: 21 instructional days (18 lessons, 2 flex days, 1 assessment day).
This assessment accompanies Unit 1 and should be given on the suggested assessment day or after completing the unit.
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Guide to Assessments
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ratio
double number line
part to part ratio
part to whole ratio
multiplicative relationship
equivalent ratio
ratio table
tape diagram
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Discrete drawing 
Example: The ratio of teaspoons of cinnamon to cups of raisins is 4:8. 

Double number line 
Example: For every 2 cups of milk, there are 3 cups of flour. 

Ratio table 
Example: A turtle travels 3 feet every 9 seconds.


Tape diagram 
Example: The ratio of girls to boys in a 6th grade class is 4 to 5. 
6.RP.A.1
Define ratio and use ratio language to describe associations between two or more quantities.
6.RP.A.1
Represent ratios using discrete drawings. Understand that the order of numbers in a ratio matters.
6.RP.A.1
Define and find equivalent ratios.
6.RP.A.1
Reason with equivalent ratios and determine if two ratios are equivalent.
6.RP.A.3
Represent ratios using double number lines and identify equivalent ratios.
6.RP.A.3
Solve ratio problems using strategies including double number lines.
6.RP.A.3
6.RP.A.3.B
Find equivalent ratios using ratios with “per 1” unit.
6.RP.A.3
Compare situations using equivalent ratios and double number lines.
6.RP.A.3
Use ratio reasoning to solve a threeact task.
6.RP.A.3
6.RP.A.3.A
Represent ratios in tables.
6.RP.A.3
6.RP.A.3.A
Understand the structure of ratio tables. Solve ratio problems using tables.
6.RP.A.3
6.RP.A.3.A
Solve ratio problems using tables, including those involving total amounts.
6.RP.A.3.A
Compare ratios using tables.
6.RP.A.1
6.RP.A.3
6.RP.A.3.A
Solve ratio problems using different strategies.
6.RP.A.1
6.RP.A.3
Solve part:part ratio problems using tape diagrams.
6.RP.A.1
6.RP.A.3
Solve part:whole ratio problems using tape diagrams.
6.RP.A.3
Solve more complex ratio problems using tape diagrams.
6.RP.A.3
Solve ratio problems using a variety of strategies, including reasoning about diagrams, double number lines, tables, and tape diagrams. Summarize strategies for solving ratio problems.
Key: Major Cluster Supporting Cluster Additional Cluster
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