Multiplication and Division
10 min
Narrative
This Warm-up prompts students to compare four representations. The reasoning here prepares students to connect the previous multiplication work to the division work of this lesson. It gives students an opportunity to use precise terms such as “factors,” “product,” and “quotient” in making comparisons (MP6). During the discussion, ask students to explain the meaning of any terms they use.
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
- Share and record responses.
Student Task
Which 3 go together?
Sample Response
Sample responses:
A, B, and C go together because:- They are diagrams.
- They show the number 4 (number of circles in a column, side length, value of the expression).
- They are related to a multiplication equation with a factor of 4.
- They represent a total of 24.
- They have numbers as labels or part of an expression.
Activity Synthesis (Teacher Notes)
- “What equation can each diagram represent?” (The array represents 4×6=24 because there are 4 rows of 6 dots, and there are 24 dots in the array. The area diagram could represent 4×7=28 or 28÷4=7 since the sides are 4 and 7, and the area is 28. The tape diagram could represent 24÷3=? or 3×?=24 because we know the total is 24 and there are 3 groups, but we don’t know how many are in each group.)
Standards
- 3.OA.6·Understand division as an unknown-factor problem. <em>For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.</em>
- 3.OA.B.6·Understand division as an unknown-factor problem. <span>For example, find <span class="math">\(32 \div 8\)</span> by finding the number that makes <span class="math">\(32\)</span> when multiplied by <span class="math">\(8\)</span>.</span>
25 min
10 min
Knowledge Components
All skills for this lesson
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Multiplication and Division
10 min
Narrative
This Warm-up prompts students to compare four representations. The reasoning here prepares students to connect the previous multiplication work to the division work of this lesson. It gives students an opportunity to use precise terms such as “factors,” “product,” and “quotient” in making comparisons (MP6). During the discussion, ask students to explain the meaning of any terms they use.
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
- Share and record responses.
Student Task
Which 3 go together?
Sample Response
Sample responses:
A, B, and C go together because:- They are diagrams.
- They show the number 4 (number of circles in a column, side length, value of the expression).
- They are related to a multiplication equation with a factor of 4.
- They represent a total of 24.
- They have numbers as labels or part of an expression.
Activity Synthesis (Teacher Notes)
- “What equation can each diagram represent?” (The array represents 4×6=24 because there are 4 rows of 6 dots, and there are 24 dots in the array. The area diagram could represent 4×7=28 or 28÷4=7 since the sides are 4 and 7, and the area is 28. The tape diagram could represent 24÷3=? or 3×?=24 because we know the total is 24 and there are 3 groups, but we don’t know how many are in each group.)
Standards
- 3.OA.6·Understand division as an unknown-factor problem. <em>For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.</em>
- 3.OA.B.6·Understand division as an unknown-factor problem. <span>For example, find <span class="math">\(32 \div 8\)</span> by finding the number that makes <span class="math">\(32\)</span> when multiplied by <span class="math">\(8\)</span>.</span>