Solve Multiplicative Comparison Problems with Large Numbers
10 min
Narrative
The purpose of this Warm-up is to elicit the idea that discrete diagrams can be inefficient for representing greater numbers, which will be useful when students interpret and use more abstract tape diagrams later in the lesson. While students may notice and wonder many things about the diagram, ideas and questions for how the student could better represent the comparison are the important discussion points.
Launch
- Groups of 2
- Display the image.
- “What do you notice? What do you wonder?”
- 1 minute: quiet think time
Teacher Instructions
- “Discuss your thinking with your partner.”
- 1 minute: partner discussion
- Share and record responses.
Student Task
What do you notice? What do you wonder?
photograph of student work. Noah's 9 pages. connecting cube tower, 9. Clare's 8 times as many pages. connecting cubes tower, 9, repeated 5 times. connecting cube towers, 5. repeated 3 times. run off page. crossed out. Text at the bottom, quote not finished, sad face drawn.
Sample Response
Students may notice:
- It looks like a diagram showing the number of pages.
- Noah read 9 pages.
- Part of the diagram representing Clare’s pages is scribbled out.
- There wasn’t enough space to draw the number of pages Clare has, with 2 columns.
Students may wonder:
- Why are parts of the diagram scribbled out?
- Why didn’t the student draw a smaller diagram?
Activity Synthesis (Teacher Notes)
- “Does this diagram show that Clare read 8 times as many pages as Noah?”
- “Why do you think the student who drew this diagram scribbled parts out?” (Maybe they ran out of space. There wasn’t enough room to draw all the pages the same size and keep them together in groups.)
- “What might be challenging about drawing each page when there are a lot of objects?” (It takes a lot of time and space. You might lose count.)
- “What other ways could you make a diagram to show greater amounts?” (Use numbers instead of drawing each part.)
- “Today we are going to look at diagrams that show comparisons with greater numbers, and think about when we might use them to represent and solve our own problems.”
Standards
Addressing
- 4.OA.2·Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.
- 4.OA.A.2·Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.<span>See Glossary, Table 2.</span>
15 min
20 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Solve Multiplicative Comparison Problems with Large Numbers
10 min
Narrative
The purpose of this Warm-up is to elicit the idea that discrete diagrams can be inefficient for representing greater numbers, which will be useful when students interpret and use more abstract tape diagrams later in the lesson. While students may notice and wonder many things about the diagram, ideas and questions for how the student could better represent the comparison are the important discussion points.
Launch
- Groups of 2
- Display the image.
- “What do you notice? What do you wonder?”
- 1 minute: quiet think time
Teacher Instructions
- “Discuss your thinking with your partner.”
- 1 minute: partner discussion
- Share and record responses.
Student Task
What do you notice? What do you wonder?
photograph of student work. Noah's 9 pages. connecting cube tower, 9. Clare's 8 times as many pages. connecting cubes tower, 9, repeated 5 times. connecting cube towers, 5. repeated 3 times. run off page. crossed out. Text at the bottom, quote not finished, sad face drawn.
Sample Response
Students may notice:
- It looks like a diagram showing the number of pages.
- Noah read 9 pages.
- Part of the diagram representing Clare’s pages is scribbled out.
- There wasn’t enough space to draw the number of pages Clare has, with 2 columns.
Students may wonder:
- Why are parts of the diagram scribbled out?
- Why didn’t the student draw a smaller diagram?
Activity Synthesis (Teacher Notes)
- “Does this diagram show that Clare read 8 times as many pages as Noah?”
- “Why do you think the student who drew this diagram scribbled parts out?” (Maybe they ran out of space. There wasn’t enough room to draw all the pages the same size and keep them together in groups.)
- “What might be challenging about drawing each page when there are a lot of objects?” (It takes a lot of time and space. You might lose count.)
- “What other ways could you make a diagram to show greater amounts?” (Use numbers instead of drawing each part.)
- “Today we are going to look at diagrams that show comparisons with greater numbers, and think about when we might use them to represent and solve our own problems.”
Standards
Addressing
- 4.OA.2·Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.
- 4.OA.A.2·Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.<span>See Glossary, Table 2.</span>