Represent and Solve Multiplication Problems

10 min

Narrative

The purpose of this Warm-up is for students to subitize or use grouping strategies to describe the images they see. When students decompose the images into groups of 10 to count efficiently, they are looking for and making use of structure (MP7). Students may need these images displayed for a longer amount of time in order to see the structure.

Launch

  • Groups of 2
  • "How many do you see? How do you see them?"
  • Flash the first image.
  • 30 seconds: quiet think time
Teacher Instructions
  • Display the first image.
  • "Discuss your thinking with your partner."
  • 1 minute: partner discussion
  • Record responses. Use multiplication expressions when students share explanations involving equal groups.
  • Repeat for the second image.

Student Task

How many do you see? How do you see them?

4 sets of arrays arranged in a square pattern. Each array has 2 rows of 5 dots.

Group of dots.

Solution Steps (4)
  1. 1
    Identify equal groups in first image
    →4 arrays, each with 2 rows of 5 dots = 4 groups of 10
  2. 2
    Skip count to find first total
    →Count by 10: 10, 20, 30, 40 dots
  3. 3
    Identify equal groups in second image
    →3 groups of 10 dots (like stairs/steps)
  4. 4
    Skip count to find second total
    →Count by 10: 10, 20, 30 dots

Sample Response

Sample responses:

  • 40: I counted by 5 (or 2 or 10) to 40.
  • 30: I saw that each step had 10, so I counted by 10 to 30.
Activity Synthesis (Teacher Notes)
  • "What pattern was helpful in finding the total number of dots?"
  • Consider asking:
    • "Who can restate the way _____ saw the dots in different words?"
    • "Did anyone see the dots the same way but would explain it differently?"
    • "Does anyone want to add an observation to the way ______ saw the dots?"
Standards
Addressing
  • 3.OA.1·Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. <em>For example, describe a context in which a total number of objects can be expressed as 5 × 7.</em>
  • 3.OA.A.1·Interpret products of whole numbers, e.g., interpret <span class="math">\(5 \times 7\)</span> as the total number of objects in 5 groups of 7 objects each. <span>For example, describe a context in which a total number of objects can be expressed as <span class="math">\(5 \times 7\)</span>.</span>

15 min

20 min