Section A: Practice Problems Multiplicative Comparison

Section Summary

Details

In this section, we learned to use multiplication and the phrase “ times as many” or “ times as much” for comparing two quantities.

At first, we used cubes and drawings to represent the quantities. For example: Andre has 3 cubes and Han has 12. We compared the number of cubes by:

  • saying “Han has 4 times as many cubes as Andre”

  • drawing diagrams that shows 3 pieces for Andre and 4 times as many pieces for Han
    2 Connecting cube towers. Andre, blue, 3. Han, blue, 3. yellow, 3. red, 3. white, 3.
    2 Connecting cube towers. Andre, blue, 3. Han, blue, 3. yellow, 3. blue, 3. yellow, 3.

  • writing an equation such as

As the numbers got larger, drawing every unit of each quantity became less convenient, so we used simpler diagrams with numbers to represent the size of the quantities.

If Andre has 30 cubes and Han has 4 times as many, we can represent the comparison with a diagram like this:

diagram. two rectangles.

We ended by comparing quantities in which one quantity is ten times as much as another. We also recalled some patterns in the numbers when we multiplied a number by 10.

Problem 1 (Pre-Unit)

Write a multiplication expression represented by each diagram.

Problem 2 (Pre-Unit)

Each bottle contains 2 liters of water. How many liters of water are there in 6 bottles?

Problem 3 (Pre-Unit)

Find the value of each product. Explain or show your reasoning.

Problem 4 (Pre-Unit)

Find the value of each expression.

Problem 5 (Lesson 1)

connecting cube tower, 2.

Here are some connecting cubes.
Select all pictures that show 4 times as many connecting cubes.

  1. Connecting Cube Tower. Blue, 2. Orange, 4.
  2. Connecting Cube Tower. 8, blue.
  3. Connecting Cube Tower. Blue, 2. Orange, 2. Yellow, 2. Green, 2
  4. Connecting Cube Tower, 4, blue.
  5. Connecting Cube Tower. Orange, 4. Blue, 2.

Problem 6 (Lesson 2)

Han read 4 books during the summer. Priya read 3 times as many books as Han.

  1. Draw a diagram that represents the situation.

  2. Write an equation that represents the situation.

Problem 7 (Lesson 3)

Mai exercised 3 times as many hours as Tyler last week. Mai exercised for 15 hours.

  1. Write an equation to represent the situation.

  2. How many hours did Tyler exercise last week?

Problem 8 (Lesson 4)

Diego has 8 songs on his playlist. Mai has 3 times as many songs as Diego.

  1. Write an equation that represents the situation.

  2. Draw a diagram that represents the situation.

  3. Explain how the diagram and equation are related.

  4. How many songs are on Mai’s playlist?

Problem 9 (Lesson 5)

Lin scored 6 points in her basketball game on Saturday. She scored 3 times as many points in her basketball game on Sunday. How many points did Lin score altogether in the two games? Explain or show your reasoning.

Problem 10 (Lesson 6)

  1. If diagram A represents 15, what does diagram B represent? Explain your reasoning.

    diagram. two rectangles. Bottom rectangle, B. partitioned into 5 equal parts. Top rectangle, A. Same size as one of the 5 parts of bottom rectangle.

  2. If diagram B represents 100, what does diagram A represent? Explain your reasoning.

Problem 11 (Exploration)

The diagram represents the books that Diego and Lin brought to the book fair.

diagram. two rectangles.

For each question, explain or show your reasoning.

  1. If Lin brought 10 books, how many books did Diego bring?

  2. If Diego brought 21 books to the fair, how many books did Lin bring?

  3. If Lin and Diego brought 60 books altogether, how many did they each bring?

Problem 12 (Exploration)

Write a comparison story problem.
Trade problems with a partner.

  1. Draw a diagram and write an equation to represent the situation.

  2. Solve the story problem.