Base-Ten Diagrams to Represent Division
10 min
Narrative
This Warm-up prompts students to carefully analyze and compare features of base-ten diagrams, looking not only at the number and types of shapes in each diagram, but also the value each diagram represents. Students have a reason to use language precisely (MP6) as they recall what they know about representations of numbers in base-ten. The activity also enables the teacher to hear how students talk about these representations.
The analysis prepares students for the activities in the lesson, in which they use base-ten diagrams to find whole-number quotients.
Launch
- Groups of 2
- Display image.
- “Pick 3 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?
Sample Response
Sample responses:
- A, B, and C go together because they have a column with just a single square.
- A, B, and D go together because they have tens.
- A, C, and D go together because they show 111.
- B, C, and D go together because they have 10 blocks.
Activity Synthesis (Teacher Notes)
- “How is it that A and C both show 111?” (If a small square represents 1, then a rectangle is 10 and a large square is 100. In A: 100+10+1=111. In C: 100+11=111.)
- “How do we know that D also shows 111?” (Each group in D represents (3×10) + 7 or 37. Three groups of 37 makes 111.)
- “Suppose we don’t know what a small square represents except that it represents the same value in all diagrams. Can we tell if C and D represent the same value? How?” (Yes. We know that 10 small squares make 1 rectangle and 10 rectangles make 1 large square. In D, we’d have 21 small squares and 9 rectangles. Trading 10 small squares for a rectangle gives 10 rectangles and 11 small squares, which is equal to 1 large square and 11 small squares.)
Standards
- 4.NBT.6·Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
- 4.NBT.B.6·Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
15 min
20 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Base-Ten Diagrams to Represent Division
10 min
Narrative
This Warm-up prompts students to carefully analyze and compare features of base-ten diagrams, looking not only at the number and types of shapes in each diagram, but also the value each diagram represents. Students have a reason to use language precisely (MP6) as they recall what they know about representations of numbers in base-ten. The activity also enables the teacher to hear how students talk about these representations.
The analysis prepares students for the activities in the lesson, in which they use base-ten diagrams to find whole-number quotients.
Launch
- Groups of 2
- Display image.
- “Pick 3 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?
Sample Response
Sample responses:
- A, B, and C go together because they have a column with just a single square.
- A, B, and D go together because they have tens.
- A, C, and D go together because they show 111.
- B, C, and D go together because they have 10 blocks.
Activity Synthesis (Teacher Notes)
- “How is it that A and C both show 111?” (If a small square represents 1, then a rectangle is 10 and a large square is 100. In A: 100+10+1=111. In C: 100+11=111.)
- “How do we know that D also shows 111?” (Each group in D represents (3×10) + 7 or 37. Three groups of 37 makes 111.)
- “Suppose we don’t know what a small square represents except that it represents the same value in all diagrams. Can we tell if C and D represent the same value? How?” (Yes. We know that 10 small squares make 1 rectangle and 10 rectangles make 1 large square. In D, we’d have 21 small squares and 9 rectangles. Trading 10 small squares for a rectangle gives 10 rectangles and 11 small squares, which is equal to 1 large square and 11 small squares.)
Standards
- 4.NBT.6·Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
- 4.NBT.B.6·Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.