Explore Multiplication Strategies with Rectangles
10 min
Narrative
The purpose of this How Many Do You See? is for students to use grouping strategies to describe the quantities they see.
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.
- Repeat for each image.
- Keep the images displayed for the Launch of the next activity.
Student Task
How many do you see? How do you see them?
Solution Steps (3)
- 1Image 1: count squares→16 squares (4 groups of 4, or 2×4 + 2×4)
- 2Image 2: count squares→24 squares (2 groups of 12, or 4 rows × 6)
- 3Image 3: count squares→18 squares (6 groups of 3, or 5×3 + 1×3)
Sample Response
- 16: I see 4 groups of 4. I see 4 columns and 2 groups of 2 in each column. I see 2×4 or 8 blue squares and 2×4 or 8 white squares.
- 24: I see 2 groups of 12. I see 4 rows with 6 in each row.
- 18: I see 5 columns of 3 and then 1 more column of 3. I see 6 groups of 3.
Activity Synthesis (Teacher Notes)
- “How can we use amounts that we can see quickly to find the total number of squares?” (We can look for repetition of the number of squares that we can easily see. We can add to or multiply the number of squares we can easily see.)
- Consider asking:
- “Who can restate the way _____ saw the squares in different words?”
- “Did anyone see the squares the same way but would explain it differently?”
- “Does anyone want to add an observation to the way _____ saw the squares?”
Standards
Addressing
- 3.MD.7.c·Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning.
- 3.MD.C.7.c·Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths <span class="math">\(a\)</span> and <span class="math">\(b + c\)</span> is the sum of <span class="math">\(a \times b\)</span> and <span class="math">\(a \times c\)</span>. Use area models to represent the distributive property in mathematical reasoning.
- 3.OA.7·Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
- 3.OA.C.7·Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that <span class="math">\(8 \times 5 = 40\)</span>, one knows <span class="math">\(40 \div 5 = 8\)</span>) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
20 min
15 min
Knowledge Components
All skills for this lesson
Role Legend
Target
Essential
Supporting
Foundational
All lesson KCs
3 skills
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Explore Multiplication Strategies with Rectangles
10 min
Narrative
The purpose of this How Many Do You See? is for students to use grouping strategies to describe the quantities they see.
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.
- Repeat for each image.
- Keep the images displayed for the Launch of the next activity.
Student Task
How many do you see? How do you see them?
Solution Steps (3)
- 1Image 1: count squares→16 squares (4 groups of 4, or 2×4 + 2×4)
- 2Image 2: count squares→24 squares (2 groups of 12, or 4 rows × 6)
- 3Image 3: count squares→18 squares (6 groups of 3, or 5×3 + 1×3)
Sample Response
- 16: I see 4 groups of 4. I see 4 columns and 2 groups of 2 in each column. I see 2×4 or 8 blue squares and 2×4 or 8 white squares.
- 24: I see 2 groups of 12. I see 4 rows with 6 in each row.
- 18: I see 5 columns of 3 and then 1 more column of 3. I see 6 groups of 3.
Activity Synthesis (Teacher Notes)
- “How can we use amounts that we can see quickly to find the total number of squares?” (We can look for repetition of the number of squares that we can easily see. We can add to or multiply the number of squares we can easily see.)
- Consider asking:
- “Who can restate the way _____ saw the squares in different words?”
- “Did anyone see the squares the same way but would explain it differently?”
- “Does anyone want to add an observation to the way _____ saw the squares?”
Standards
Addressing
- 3.MD.7.c·Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning.
- 3.MD.C.7.c·Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths <span class="math">\(a\)</span> and <span class="math">\(b + c\)</span> is the sum of <span class="math">\(a \times b\)</span> and <span class="math">\(a \times c\)</span>. Use area models to represent the distributive property in mathematical reasoning.
- 3.OA.7·Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
- 3.OA.C.7·Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that <span class="math">\(8 \times 5 = 40\)</span>, one knows <span class="math">\(40 \div 5 = 8\)</span>) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.