# Lesson 1

Mystery Bags

### Problem 1

Lin is interested in how many of her classmates watch her favorite TV show, so she starts asking around at lunch. She gets the following responses:

- yes
- yes
- yes
- no
- no
- no
- no
- no
- no
- no
- yes
- no
- no
- no

If she asks one more person randomly in the cafeteria, do you think they will say “yes” or “no”? Explain your reasoning.

### Solution

For access, consult one of our IM Certified Partners.

### Problem 2

An engineer tests the strength of a new material by seeing how much weight it can hold before breaking. Previous tests have held these weights in pounds:

- 1,200
- 1,400
- 1,300
- 1,500
- 950
- 1,600
- 1,100

Do you think that this material will be able to hold more than 1,000 pounds in the next test? Explain your reasoning.

### Solution

For access, consult one of our IM Certified Partners.

### Problem 3

A company tests two new products to make sure they last for more than a year.

- Product 1 had 950 out of 1,000 test items last for more than a year.
- Product 2 had 150 out of 200 last for more than a year.

If you had to choose one of these two products to use for more than a year, which one is more likely to last? Explain your reasoning.

### Solution

For access, consult one of our IM Certified Partners.

### Problem 4

Put these numbers in order from least to greatest.

- \(\frac{1}{2}\)
- \(\frac{1}{3}\)
- \(\frac{2}{5}\)
- 0.6
- 0.3

### Solution

For access, consult one of our IM Certified Partners.

### Problem 5

A small staircase is made so that the horizontal piece of each step is 10 inches long and 25 inches wide. Each step is 5 inches above the previous one. What is the surface area of this staircase?

### Solution

For access, consult one of our IM Certified Partners.

(From Unit 7, Lesson 15.)