Lesson 2

Reasoning about Contexts with Tape Diagrams

Lesson Narrative

In this lesson, students represent and reason about contexts using tape diagrams. Students may have had experience with tape diagrams in earlier grades, and have seen some examples of their use in prior units. For example, tape diagrams were used to represent percent increase and decrease situations. First, they interpret some given tape diagrams. Then, they interpret a story and create tape diagrams. While the contexts lead to equations of the forms $$p(x+q) =r$$ and $$px+q = r$$, this lesson is not about writing equations. Likewise, students are asked to find an unknown value in several story problems, but the intention is for them to use any reasoning that makes sense to them. It is not expected that they write and solve equations, or that any particular method is stressed.

Learning Goals

Teacher Facing

• Draw and label a tape diagram to represent relationships between quantities in a situation.
• Explain (orally and in writing) how to use a tape diagram to determine the value of an unknown quantity in a situation.
• Interpret a tape diagram that represents a relationship of the form $px+q=r$ or $p(x+q)=r$.

Student Facing

Let’s use tape diagrams to make sense of different kinds of stories.

Student Facing

• I can explain how a tape diagram represents parts of a situation and relationships between them.
• I can use a tape diagram to find an unknown amount in a situation.