Lesson 2 Interpret Representations of Multiplicative Comparison

    • Let’s make sense of representations of problems with “times as many.”

Warm-up How Many Do You See: Times as Many

How many do you see? How do you see them?

diagram. Rectangle partitioned into 3 equal parts.
diagram. rectangle partitioned into 6 equal parts. Blue, 3. Yellow, 3.
diagram. 12 equal parts. blue, 3. orange, 3. blue, 3. orange, 3.

Activity 1 Represent “Times as Many”

2 Connecting cube towers. Mai's cubes, 6. Kiran's cubes, 2.

  1. Jada has 4 times as many cubes as Kiran. Draw a diagram to represent the situation.

  2. Diego has 5 times as many cubes as Kiran. Draw a diagram to represent the situation.

  3. Lin has 6 times as many cubes as Kiran. How many cubes does Lin have? Explain or show your reasoning.

Activity 2 Diagrams to Solve Multiplicative Comparison Problems

Here are four sets of descriptions, diagrams, and equations that compare pairs of quantities.
Match each description to a diagram and an equation that represent the same situation. Be prepared to explain your reasoning.

  1. A.

    Lin has 3 cubes.
    Jada has 2 times as many.

    B.

    Han has 3 cubes.
    Elena has 3 times as many.

    C.

    D.

    Priya had 5 cubes.
    Noah had 3 times as many.

    E.

    F.

    G.

    diagram of 2 towers of linking cubes. The first one with 5 blue, 5 orange, 5 blue. The second with 5 blue.

    H.

    2 diagrams. Quanitity 1 with 3 blue cubes. Quantity 2 with 3 blue and 3 orange linking cubes.

    I.

    J.

    Mai has 4 cubes.
    Diego has 4 times as many.

    K.

    2 diagrams. Quantity 1 with 3 blue cubes. Quanitity 2 with 3 blue, 3 orange, and 3 blue cubes.

    L.

    2 diagrams. Quantity 1 with 4 blue cubes. Quanitity 2 with 4 blue, 4 orange, 4 blue, and 4 orange cubes.

    Record your matches here:

    Set 1:

    Set 2:

    Set 3:

    Set 4:

Practice Problem

Problem 1

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.