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Activity 1

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

None

Materials

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Activity Narrative

The purpose of this activity is for students to interpret and solve multiplicative comparison problems. Students interpret tape diagrams that label each box with a value, which is different from the discrete diagrams from previous lessons. They also write equations to represent the situations and explain how the equations connect to the tape diagrams (MP2). The problems in this activity have unknown lesser quantities, greater quantities, or multipliers. Questions are provided to support students in representing the unknown in tape diagrams and in identifying the unknown in given situations.

Action and Expression: Develop Expression and Communication. Provide alternative options for expression. Encourage students to examine each diagram first and write down or talk about what they know with a partner before answering each set of questions.
Supports accessibility for: Visual-Spatial Processing, Language

Launch

Groups of 2
Display and read the first problem.
30 seconds: quiet think time
1 minute: partner discussion
“Is 15 pages too high or too low of an estimate for Andre?” (Too low, because the diagram shows he should have read more than Mai.)
“If Andre read 9 times as many pages as Mai, what number should replace the question mark in the diagram? Why?” (135, because the 9 rectangles represent 9 times as many as 15. There should be 9 fifteens.)
30 seconds: quiet think time
1 minute: partner discussion

Activity

3 minutes: independent work time
8 minutes: partner work time
Monitor for students who:
- Explain the connection between their equations and the diagram.
- Show understanding that each rectangle represents the same amount.

Mai and Andre compare the numbers of pages they read on the first day of the reading competition.

diagram. two rectangles. bottom rectangle, Andre's pages. partitioned into 9 equal parts, total length question mark. Top rectangle, Mai's pages. Same size as one of 9 parts of bottom rectangle, labeled 15.

What would be a good estimate for the number of pages Andre read?
The diagram shows the pages Lin and Kiran each read on 1 day of the reading competition.

diagram. two rectangles. bottom rectangle, Kiran's pages. partitioned into 6 equal parts each labeled 9, total length question mark. Top rectangle, Lin's pages. Same size as one of 6 parts of bottom rectangle, labeled 9.
1. Complete the statement and explain how you know.
  
  Kiran read _____ times as many pages as Lin.
2. Write a multiplication equation that compares the pages read by Lin and by Kiran.
3. How many total pages did Kiran read?
Jada read some pages. Han read 60 pages altogether.

diagram. two rectangles. bottom rectangle, Han's pages. partitioned into 3 equal parts each labeled question mark, total length 60. Top rectangle, Jada's pages. Same size as one of the 3 parts of bottom rectangle, labeled question mark.
1. How many times as many pages as Jada did Han read? Explain how you know.
2. Write a multiplication equation to compare the pages Han read with the number of pages Jada read. Use a symbol to represent the unknown.
3. How many pages did Jada read? Explain how you know.
Elena reads 72 pages. Clare reads 9 pages.

diagram. two rectangles. bottom rectangle, Elena's pages. partitioned into 2 parts. One part labeled 9. Other part unknown. total length, 42. Top rectangle, Clare's pages, same length as left part of bottom rectangle, also labeled 9.
1. How is this diagram different from the earlier diagrams?
2. Write a multiplication equation to compare the pages read by Elena and by Clare. Use a symbol to represent the unknown.
3. How many times the number of pages as Clare does Elena read?

Student Response

to access Student Response.

Advancing Student Thinking

If students write equations without unknowns, consider asking:

“What information do you know from looking at the diagram? What information is unknown?
"What equation could you write to represent this situation? Use a symbol to represent the unknown value.”

Activity Synthesis

Select 2–3 students to share their responses and their reasoning.
“How do the diagrams help us figure out what we know about the situation and what we need to find out?” (Each diagram shows two quantities being compared, and the ‘times as many’ amount that compares them. The quantity that is missing is the part we need to find out.)
“How do the diagrams show ‘times as many’?” (‘Times as many’ is represented by the number of times each rectangle in the diagram is repeated.)
Display:
“How does this equation help us find the number of pages Jada read?” (We know that Han read 60 pages, which is 3 times as many as Jada, because the diagram shows 3 equal-size rectangles for Han and one rectangle for Jada. We just need to know the amount that each rectangle represents, which will be the amount of pages that Jada read.)

Activity 2

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

None

Materials

None

Activity Narrative

The purpose of this activity is for students to represent multiplicative comparison situations and solve for an unknown factor or unknown product.

In the Activity Synthesis, students make connections between the description, their diagram, and multiplication equations that represent the situation (MP2).

MLR8 Discussion Supports. Synthesis: At the appropriate time, give students 2–3 minutes to make sure everyone in their group can explain “strategy,” “equation,” and “diagram.” Invite groups to rehearse what they will say when they share with the whole class.
Advances: Speaking, Conversing, Representing

Launch

Groups of 2
Read directions for the activity aloud.
“What will we do with each problem in this task?” (Write an equation, with the unknown represented by a symbol, draw a diagram to show comparison, and answer the question.)

Activity

4 minutes: independent work time
2 minutes: partner discussion about the first problem
“Share with your partner how you represented the unknown value in your diagram and in your equation.”
“Work with your partner on the rest of the problems.”
8 minutes: partner work time
Monitor for students who:
- Draw and label each comparison.
- Identify and represent the unknown in their equation and in their diagram.
- Use “times as many” language to describe each comparison.
If students finish early, they can create their own situation and question, and then trade with their partner. The partner will write the equation, draw a diagram, and answer the question.

For each situation:

Write an equation to represent the situation. Use a symbol to represent the unknown.
Draw a diagram to show the comparison.
Answer the question about the situation.

Lin read 7 books. Diego read 8 times as many books as Lin.
1. Equation:
2. Diagram:
3. How many books did Diego read?
Tyler has some books. Clare has 72 books, which is 12 times as many books as Tyler.
1. Equation:
2. Diagram:
3. How many books does Tyler have?
Noah read 13 books. Elena read 130 books.
1. Equation:
2. Diagram:
3. Complete the statement:
  
  _______________ read _____ times as many books as _______________.

Student Response

to access Student Response.

Advancing Student Thinking

Activity Synthesis

“What information did you use in each situation to know how to draw each diagram?”
- The number of repeating rectangles in the greater quantity represents “times as many.”
- The row with one rectangle is the amount being multiplied.
- The row with multiple rectangles represents the greater quantity in the comparison.
“How is the last problem different from the first two?” (The unknown value is how many “times as many.”)

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Lesson 4

Solve Multiplicative Comparison Problems with Large Numbers

Warm-up

Instructional Routines

Materials

Activity Narrative

Launch

Activity

Student Response

Advancing Student Thinking

Activity Synthesis

Activity 1

Standards Alignment

Building On

Addressing

4.OA.1

4.OA.2

Building Toward

Instructional Routines

Materials

Activity Narrative

Launch

Activity

Student Response

Advancing Student Thinking

Activity Synthesis

Activity 2

Standards Alignment

Building On

Addressing

4.OA.2

Building Toward

Instructional Routines

Materials

Activity Narrative

Launch

Activity

Student Response

Advancing Student Thinking

Activity Synthesis

Lesson Synthesis

Standards Alignment

Building On

Addressing

4.OA.2

Building Toward