Reasoning about Contexts with Tape Diagrams

Warmup

Activity #1

 Explain a Tape Diagram.

Here is a story with a diagram that represents it.

• Answer the questions that follow.

(1.) Mai made 50 flyers for five volunteers in her club to hang up around school. She gave 5 flyers to the first volunteer, 18 flyers to the second volunteer, and divided the remaining flyers equally among the three remaining volunteers.

Explain why the diagram above represents the story, and work to find any unknown amounts in the story.

(2.) To thank her five volunteers, Mai gave each of them the same number of stickers. Then she gave them each two more stickers. Altogether, she gave them a total of 30 stickers.

Explain why the diagram above represents the story, and work to find any unknown amounts in the story.

(3). Mai distributed another group of flyers equally among the five volunteers. Then she remembered that she needed some flyers to give to teachers, so she took 2 flyers from each volunteer. Then, the volunteers had a total of 40 flyers to hang up.

Explain why the diagram above represents the story, and work to find any unknown amounts in the story.

Activity #2

 Draw a Tape Diagram.

• Read the story below carefully.
• Answer the questions that follow.

(1.) Noah and his sister are making gift bags for a birthday party. Noah puts 3 pencil erasers in each bag. His sister puts x stickers in each bag. After filling 4 bags, they have used a total of 44 items.

(a.) Draw a tape diagram to represent the story.

(b.) Describe how you would find any unknown amounts in the story/tape diagram above.

(2.) Noah’s family also wants to blow up a total of 60 balloons for the party. Yesterday they blew up 24 balloons. Today they want to split the remaining balloons equally between four family members.

(a.) Draw a tape diagram to represent the story above.

(b.) Describe how you would find any unknown amounts in the story/tape diagram above.

(3.) Noah’s family bought some fruit bars to put in the gift bags. They bought one box each of four flavors: apple, strawberry, blueberry, and peach. The boxes all had the same number of bars. Noah wanted to taste the flavors and ate one bar from each box. There were 28 bars left for the gift bags.

(1.) Draw a tape diagram to represent the story.

(2.) Describe how you would find any unknown amounts in the story/tape diagram above.

Activity #3

 Design a shape with a Repeating Pattern.

• Interact with the applet below.
• Answer the questions that follow.

Design a tiling that uses a repeating pattern consisting of 2 kinds of shapes (e.g., 1 hexagon with 3 triangles forming a triangle).

(a.) How many times did you repeat the pattern in your picture?

(b.) How many individual shapes did you use?

Challenge #1

Andre wants to save $40 to buy a gift for his dad. Andre’s neighbor will pay him weekly to mow the lawn, but Andre always gives a$2 donation to the food bank in weeks when he earns money. Andre calculates that it will take him 5 weeks to earn the money for his dad’s gift. He draws a tape diagram to represent the situation.

(1.) Explain how the parts of the tape diagram represent the story.

(2.) How much does Andre’s neighbor pay him each week to mow the lawn?

Challenge #2

Select all stories that the tape diagram can represent.

Challenge #3

Quiz Time