Unit 6, Lesson 2
Reasoning about Contexts with Tape Diagrams
Grade 7
2.1
Warm-up
What do you notice? What do you wonder?
2.2
Activity
For each story, work with your group to:
- Identify any unknown amounts in the story.
- Explain how the diagram represents the story.
- Find the value of the variable in the diagram.
- 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.
- 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.
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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. That meant the volunteers had a total of 40 flyers to hang up.
Student Lesson Summary
Tape diagrams are useful for representing how quantities are related and can help us answer questions about a situation.
Example: A school receives 46 copies of a popular book. The library takes 26 copies and the remainder are split evenly among 4 teachers. How many books does each teacher receive?
This situation involves a total formed by 4 equal parts and one other part. We can represent the situation with a diagram labeled 46 for the total number of books. That total length is divided into parts—one long part labeled 26 for the books given to the library and 4 equal-sized parts for the books split among 4 teachers. We label each of those parts with a variable, , because we don’t know how many books each teacher got. Using the same variable, , in each part means that the same number is represented four times.
Some situations have parts that are all equal, but each part has been increased from an original amount:
Example: A company manufactures a special type of sensor, and packs them in boxes of 4 for shipment. Then a new design increases the weight of each sensor by 9 grams. The new package of 4 sensors weighs 76 grams. How much did each sensor weigh originally?
We can represent this situation with a rectangle representing a total of 76 split into 4 equal parts. Each part shows that the new weight, , is 9 more than the original weight, .
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