The focus of this lesson is situations that lead to equations of the form \(px+q=r.\) Tape diagrams are used to help students understand why these situations can be represented with equations of this form, and to help them reason about solving equations of this form. Students also attend to the meaning of the equation’s solution in the context (MP2). Note that we are not generalizing solution methods yet; just using diagrams as a tool to reason about solving equations.
Lesson overview
 4.1 Warmup: Algebra Talk: Seeing Structure (10 minutes)

4.2 Activity: Situations and Diagrams (15 minutes)
 There is a digital applet in this activity.

4.3 Activity: Situations, Diagrams, and Equations (10 minutes)
 Includes "Are you Ready for More?" extension problem
 Lesson Synthesis
 4.4 Cooldown: Finding Solutions (5 minutes)
Learning goals:
 Coordinate tape diagrams, equations of the form \(px+q=r\), and verbal descriptions of the situations.
 Explain (orally and in writing) how to use a tape diagram to determine the value of an unknown quantity in an equation of the form \(px+q=r\).
 Interpret (in writing) the solution to an equation in the context of the situation it represents.
Learning goals (student facing):
 Let’s see how tape diagrams can help us answer questions about unknown amounts in stories.
Learning targets (student facing):
 I can draw a tape diagram to represent a situation where there is a known amount and several copies of an unknown amount and explain what the parts of the diagram represent.
 I can find a solution to an equation by reasoning about a tape diagram or about what value would make the equation true.
Glossary:
 Access the complete Grade 7 glossary.
Standards:
 This lesson builds on the standard: CCSS.6.EE.B.5MS.6.EE.5MO.6.EEI.B.4
 This lesson builds towards the standard: CCSS.7.EE.B.4.aMS.7.EE.4aMO.7.EEI.B.4b
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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