One- and Two-Step Comparison Problems

10 min

Narrative

This Warm-up prompts students to carefully analyze and compare ways to represent multiplicative comparison. In making comparisons, students have a reason to use language precisely (MP6). The activity also enables the teacher to hear the terminology students use to talk about the characteristics of multiplicative comparison representations.

Launch

  • Groups of 2
  • Display the image.
  • “Pick 3 representations that go together. Be ready to share why they go together.”
  • 1 minute: quiet think time
Teacher Instructions
  • “Discuss your thinking with your partner.”
  • 2–3 minutes: partner discussion
  • Record responses.

Student Task

Which 3 go together?

A
diagram. two rectangles.
diagram. two rectangles. bottom rectangle, quantity 2. partitioned into 6 equal parts each labeled 7. Top rectangle, quantity 1. Same size as one of 6 parts of bottom rectangle, labeled 7.

B

C
diagram. two rectangles.
diagram. two rectangles. bottom rectangle, quantity 2. partitioned into 2 parts. One part, labeled 7. Other part unknown. total length 42. Top rectangle, Quantity 1. same size as left part of bottom rectangle. Labeled 7.

D

Sample Response

Sample responses:

A, B, and C go together because:

  • They show 7.
  • They show groups of 7.

A, B, and D go together because:

  • They show how many times as many.
  • They show 6 times as many.

A, C, and D go together because:

  • They include finding the value of an unknown to show the multiplicative comparison.

B, C, and D go together because:

  • The value 42 is labeled in each of them.
Activity Synthesis (Teacher Notes)
  • “For Images A, C, and D, how does each representation show an unknown?”
  • “What is the unknown in each representation? Explain how you know.”
  • Record student responses.
  • Consider asking students to create a situation that can be described by these representations.
Standards
Addressing
  • 4.OA.1·Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.
  • 4.OA.2·Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.
  • 4.OA.A.1·Interpret a multiplication equation as a comparison, e.g., interpret <span class="math">\(35 = 5 \times 7\)</span> as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.
  • 4.OA.A.2·Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.<span>See Glossary, Table 2.</span>

20 min

15 min