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.
Math
Unit 6
6th Grade
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 to use equations and inequalities to model relationships between quantities. When using an equation or inequality to represent real-world 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 re-visit 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 sixth-grade 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)
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The following assessments accompany Unit 6.
Have students complete the Pre-Unit Assessment and Pre-Unit Student Self-Assessment before starting the unit. Use the Pre-Unit Assessment Analysis Guide to identify gaps in foundational understanding and map out a plan for learning acceleration throughout the unit.
Have students complete the Mid-Unit Assessment after lesson 6.
Use the resources below to assess student mastery of the unit content and action plan for future units.
Use student data to drive your planning with an expanded suite of unit assessments to help gauge studentsâ€™ facility with foundational skills and concepts, as well as their progress with unit content.
Unit Launch
Prepare to teach this unit by immersing yourself in the standards, big ideas, and connections to prior and future content. Unit Launches include a series of short videos, targeted readings, and opportunities for action planning.
Model | Example |
Tape diagram | |
Balance/mobile |
dependent variable
equation
inequality
independent variable
percent equation
solution
substitution
To see all the vocabulary for Unit 6, view our 6th Grade Vocabulary Glossary.
To see all the materials needed for this course, view our 6th Grade Course Material Overview.
Topic A: Reasoning About and Solving Equations
Topic B: Reasoning About and Solving Inequalities
Topic C: Representing and Analyzing Quantitative Relationships
Key
Major Cluster
Supporting Cluster
Additional Cluster
CCSS.MATH.PRACTICE.MP1 — Make sense of problems and persevere in solving them.
CCSS.MATH.PRACTICE.MP2 — Reason abstractly and quantitatively.
CCSS.MATH.PRACTICE.MP3 — Construct viable arguments and critique the reasoning of others.
CCSS.MATH.PRACTICE.MP4 — Model with mathematics.
CCSS.MATH.PRACTICE.MP5 — Use appropriate tools strategically.
CCSS.MATH.PRACTICE.MP6 — Attend to precision.
CCSS.MATH.PRACTICE.MP7 — Look for and make use of structure.
CCSS.MATH.PRACTICE.MP8 — Look for and express regularity in repeated reasoning.
Unit 5
Numerical and Algebraic Expressions
Unit 7
Geometry