Lesson 12 Story Problems and Diagrams

    • Let’s make sense of diagrams and solve story problems.

Warm-up Notice and Wonder: Mancala

What do you notice? What do you wonder?

Mancala game board. Some holes have seeds. Some holes are empty. Seeds outside of the game board.

Activity 1 Interpret the Diagram

Circle the diagrams that match each story. Then explain your match to your partner.

  1. Clare captured 54 seeds. Han captured 16 fewer seeds than Clare. How many seeds did Han capture?

    1. Diagram. Two rectangles of equal length. Rectangle on top shaded, labeled Clare, total length, 54.  Rectangle on bottom, labeled Han, partitioned into two parts. First part, shaded, total length, question mark. Second part has dashed outline, total length, 16.
    2. Diagram. One Rectangle partitioned into 2 parts. First part, labeled Clare, total length, 54. Second part labeled Han, total length, 16. Total length of rectangle, question mark.
    3. Diagram. Two rectangles of equal length. Rectangle on top labeled Clare, total length, 54. Rectangle on bottom, labeled Han. Partitioned into two parts. First part, shaded, total length, 16. Second part has dashed outline, total length, question mark.

  2. Clare has 54 seeds on her side of the board. Han has 16 seeds on his side. How many seeds are on the board in all?

    1. Diagram. Two rectangles of equal length. Top rectangle, shaded, labeled Clare, total length, 54. Bottom rectangle labeled Han, partitioned into two parts. First part, shaded, total length 16. Second part has a dashed outline, total length question mark.
    2. Diagram. One rectangle partitioned into two parts. First part, labeled Clare, total length, 54. Second part, labeled Han, total length, 16. Total length of rectangle, question mark.

  3. Clare has 54 seeds. 16 seeds are in her hand. The rest of her seeds are on the game board. How many of her seeds are on the game board?

    1. Diagram. One rectangle partitioned into 2 parts. 1 part, labeled board, total length, 54. Other part, labeled hands, total length, 16. Total length of rectangle, question mark.
    2. Diagram. Two rectangles of equal length. Top rectangle labeled hand, partitioned into two parts. First part, shaded, total length 16. Second part has a dashed outline, total length question mark. Bottom rectangle, shaded, labeled board, total length, 54.
    3. Diagram. One rectangle partitioned into 2 parts. 1 part, labeled hands, total length 16. Other part, labeled board, total length question mark. Total length of rectangle, 54.

  4. There are 54 seeds on the game board. Some seeds are on Han’s side. 16 seeds are on Clare’s side. How many seeds are on Han’s side of the board?

    Choose the 2 diagrams that match.

    1. Diagram. One rectangle partitioned into two parts. First part labeled Clare, total length, 54. Second part labeled Han, total length, 16. Total length of rectangle, question mark.
    2. Diagram. One rectangle partitioned into two parts. First part, labeled Han, total length, question mark. Second part, labeled Clare, total length, 16. Total length of rectangle, 54.
    3. Diagram. Two rectangles of equal length. Top rectangle, shaded, labeled Han, total length 54. Bottom rectangle labeled Clare, partitioned into two parts. First part, shaded, total length 16. Second part has a dashed outline, total length question mark.
    4. Diagram. One rectangle partitioned into two parts. First part, labeled Clare, total length, 16. Second part, labeled Han, total length, question mark. Total length of rectangle, 54.

Activity 2 Card Sort: Story Problems and Diagrams

  1. Match each story problem with a diagram. Explain why the cards match.

  2. Choose 2 story problems and solve them. Show your thinking.

Practice Problem

Problem 1

There are 83 people on the stairs. 47 of them are going up and some of them are coming down.

  1. Explain why the tape diagram shows the story.

    Diagram. One rectangle partitioned into 2 parts. 1 part, labeled going up, total length, 47. Other part, labeled going down, total length, question mark. Total length, 83.

  2. How many people are coming down the stairs? Explain or show your reasoning.