Lesson 2

Interpret Representations of Multiplicative Comparison

Lesson Purpose

The purpose of this lesson is for students to represent situations and descriptions of multiplicative comparison using diagrams and equations.

Lesson Narrative

In this lesson, students analyze and interpret images of discrete objects (connecting cubes) and discrete tape diagrams in which each unit is visible. These diagrams are precursors for more abstract tape diagrams that are used in future lessons.

Students also make connections between the multiplicative comparison language and multiplication equations. For example, they interpret “15 is 3 times as many as 5” as \(15 = 3 \times 5\) or \(15 = 5 \times 3\)

In this unit, the convention of representing the multiplier as the first factor in equations is used. Students may write the factors in any order. In later lessons, students write division equations to represent multiplicative comparisons using their understanding of the relationship between multiplication and division.

This lesson gives students an opportunity to make sense of each equation and how it relates to a corresponding image or diagram (MP2).

  • Engagement
  • MLR8

Activity 2: Diagrams to Solve Multiplicative Comparison Problems

Learning Goals

Teacher Facing

  • Interpret different representations of multiplicative comparison (situations, diagrams, and equations).

Student Facing

  • Let’s make sense of representations of problems with “times as many.”

Required Materials

Materials to Gather

Required Preparation

CCSS Standards


Lesson Timeline

Warm-up 10 min
Activity 1 20 min
Activity 2 15 min
Lesson Synthesis 10 min
Cool-down 5 min

Teacher Reflection Questions

Students were asked to draw diagrams to represent times as many. How were students able to connect physical representations to those on paper and equations? What questions might you ask during tomorrow's lesson to support students who are still solidifying these connections?

Suggested Centers

  • How Close? (1–5), Stage 6: Multiply to 3,000 (Addressing)
  • How Close? (1–5), Stage 5: Multiply to 100 (Supporting)
  • Five in a Row: Multiplication (3–5), Stage 2: Factors 1–9 (Supporting)

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