Partial Products in Diagrams
10 min
Narrative
This Warm-up prompts students to compare and contrast different diagrams that can be used to represent and calculate products of two-digit numbers. 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 these partial-products diagrams, which they worked with in grade 4. They will extend the diagrams to represent the product of a three-digit number and a two-digit number later in the lesson.
Students use their knowledge of the properties of area to support their understanding of multiplication, with these rectangular diagrams. A genuine area diagram would be difficult to read, so the individual pieces are not drawn to scale.
Launch
- Groups of 2
- Display the image.
- “Pick 3 diagrams 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 partitioned horizontally.
A, B, and D go together because:
- They show only the outside has numbers and the inside is blank.
A, C, and D go together because:
- The top width has the value 42.
- The side length has the value 33.
B, C, and D go together because:
- They are partitioned vertically.
Activity Synthesis (Teacher Notes)
- “How might Diagram C be helpful for calculating the product 42×33?” (I can add those numbers to get the value of 42× 33.)
- Highlight that this is the type of Diagram C that will be used throughout the next several lessons. The purpose of the diagram is to help us see different ways to calculate the products of numbers.
Standards
- 5.NBT.5·Fluently multiply multi-digit whole numbers using the standard algorithm.
- 5.NBT.B.5·Fluently multiply multi-digit whole numbers using the standard algorithm.
15 min
20 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Partial Products in Diagrams
10 min
Narrative
This Warm-up prompts students to compare and contrast different diagrams that can be used to represent and calculate products of two-digit numbers. 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 these partial-products diagrams, which they worked with in grade 4. They will extend the diagrams to represent the product of a three-digit number and a two-digit number later in the lesson.
Students use their knowledge of the properties of area to support their understanding of multiplication, with these rectangular diagrams. A genuine area diagram would be difficult to read, so the individual pieces are not drawn to scale.
Launch
- Groups of 2
- Display the image.
- “Pick 3 diagrams 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 partitioned horizontally.
A, B, and D go together because:
- They show only the outside has numbers and the inside is blank.
A, C, and D go together because:
- The top width has the value 42.
- The side length has the value 33.
B, C, and D go together because:
- They are partitioned vertically.
Activity Synthesis (Teacher Notes)
- “How might Diagram C be helpful for calculating the product 42×33?” (I can add those numbers to get the value of 42× 33.)
- Highlight that this is the type of Diagram C that will be used throughout the next several lessons. The purpose of the diagram is to help us see different ways to calculate the products of numbers.
Standards
- 5.NBT.5·Fluently multiply multi-digit whole numbers using the standard algorithm.
- 5.NBT.B.5·Fluently multiply multi-digit whole numbers using the standard algorithm.