# Lesson 2

Reasoning about Contexts with Tape Diagrams

Let’s use tape diagrams to make sense of different kinds of stories.

### Problem 1

The table shows the number of apples and the total weight of the apples.

number of apples | weight of apples (grams) |
---|---|

2 | 511 |

5 | 1200 |

8 | 2016 |

Estimate the weight of 6 apples.

### Problem 2

Select **all** stories that the tape diagram can represent.

There are 87 children and 39 adults at a show. The seating in the theater is split into 4 equal sections.

There are 87 first graders in after-care. After 39 students are picked up, the teacher put the remaining students into 4 groups for an activity.

Lin buys a pack of 87 pencils. She gives 39 to her teacher and shared the remaining pencils between herself and 3 friends.

Andre buys 4 packs of paper clips with 39 paper clips in each. Then he gives 87 paper clips to his teacher.

Diego’s family spends $87 on 4 tickets to the fair and a $39 dinner.

### Problem 3

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.

- Explain how the parts of the tape diagram represent the story.
- How much does Andre’s neighbor pay him each week to mow the lawn?

### Problem 4

Without evaluating each expression, determine which value is the greatest. Explain how you know.

- \(7\frac56 - 9\frac34\)
- \((\text-7\frac56) + (\text-9\frac34)\)
- \((\text-7\frac56) \boldcdot 9\frac34\)
- \((\text-7\frac56) \div (\text-9\frac34)\)

### Problem 5

Solve each equation.

- \((8.5) \boldcdot (\text-3) = a\)
- \((\text-7) + b = (\text-11)\)
- \(c - (\text-3) = 15\)
- \(d \boldcdot (\text-4) = 32\)