Students discover how to use equations and inequalities to model relationships between quantities, and investigate the meaning of having a solution to an equation or an inequality.
In Unit 6, sixth graders move from expressions to equations and inequalities. They revisit familiar diagrams such as tape diagrams to model equations, and they discover new models such as balances and hanging mobiles. Students investigate what it means to be a solution to an equation or an inequality and how use equations and inequalities to model relationships between quantities. When using an equation or inequality to represent realworld situations, students must decontextualize the situation to represent it using variables and symbols and then recontextualize in order to interpret what their answer means in regard to the situation at hand (MP.2). In this unit, students bring concepts from three domains together: Ratios and Proportions, Number Sense, and Expressions and Equations. They revisit percentages from Unit 2 and solve percent problems using equations. They study relationships between different quantities and draw on their ratio reasoning where relevant. A note on fluency: solving equations provides a good opportunity for students to continue development of and to demonstrate fluency with decimal operations and fraction division. Several problems involve computing with decimals and dividing by fractions; include additional problems in practice for students as needed.
Several prior skills support students in this unit. In fifth grade, students analyzed patterns and relationships when they studied standard 5.OA.3. They also observed what happened when these relationships were plotted on the coordinate plane. In previous sixthgrade units, students studied algebraic and numerical expressions and collections of equivalent ratios. Students draw on all of these concepts and skills in this unit.
There are many future connections to the standards in this unit. In seventh grade, students will deeply investigate proportional relationships in the form $$y=rx$$, understanding the value of $$r$$ as the constant of proportionality. They’ll further investigate the graphs of these equations, and in eighth grade, students will compare across multiple representations of proportional relationships. Students will also become exposed to increasingly more complex equations and inequalities to solve.
Pacing: 17 instructional days (14 lessons, 2 flex days, 1 assessment day)
This assessment accompanies Unit 6 and should be given on the suggested assessment day or after completing the unit.
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inequality
equation
solution
substitution
percent equation
independent variable
dependent variable
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Tape diagram 
Example:

Balance/mobile 
Example:

6.EE.B.6
6.EE.B.7
Represent equations in the form $${ x+p=q }$$ and $${px=q}$$ using tape diagrams and balances.
6.EE.B.5
Define and identify solutions to equations.
6.EE.B.6
6.EE.B.7
Write equations for realworld situations.
6.EE.B.6
6.EE.B.7
Solve onestep equations with addition and subtraction.
6.EE.B.6
6.EE.B.7
Solve onestep equations with multiplication and division.
6.RP.A.3.C
6.EE.B.7
Solve percent problems using equations.
6.EE.B.6
6.EE.B.7
Solve multipart equations leading to the form $${x+p=q }$$ and $${px=q}$$.
6.EE.B.5
6.EE.B.8
Define and identify solutions to inequalities.
6.EE.B.8
Write and graph inequalities for realworld conditions. (Part 1)
6.EE.B.8
Write and graph inequalities for realworld conditions. (Part 2)
6.EE.B.6
6.EE.B.8
Solve onestep inequalities.
6.RP.A.3.A
6.EE.C.9
Write equations for and graph ratio situations. Define independent and dependent variables.
6.RP.A.3.A
6.EE.C.9
Represent the relationship between two quantities in graphs, equations, and tables. (Part 1)
6.RP.A.3.A
6.EE.C.9
Represent the relationship between two quantities in graphs, equations, and tables. (Part 2)
Key: Major Cluster Supporting Cluster Additional Cluster
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