# Lesson 1

The Areas of Squares and Their Side Lengths

Let’s investigate the squares and their side lengths.

### Problem 1

Find the area of each square. Each grid square represents 1 square unit.

### Problem 2

Find the length of a side of a square if its area is:

1. 81 square inches
2. $$\frac{4}{25}$$ cm2
3. 0.49 square units
4. $$m^2$$ square units

### Problem 3

Find the area of a square if its side length is:

1. 3 inches
2. 7 units
3. 100 cm
4. 40 inches
5. $$x$$ units

### Problem 4

Evaluate $$(3.1 \times 10^4) \boldcdot (2 \times 10^6)$$. Choose the correct answer:

A:

$$5.1 \times 10^{10}$$

B:

$$5.1 \times 10^{24}$$

C:

$$6.2 \times 10^{10}$$

D:

$$6.2 \times 10^{24}$$

(From Unit 7, Lesson 14.)

### Problem 5

Noah reads the problem, “Evaluate each expression, giving the answer in scientific notation.” The first problem part is: $$5.4 \times 10^5 + 2.3 \times 10^4$$.

Noah says, “I can rewrite $$5.4 \times 10^5$$ as $$54 \times 10^4$$. Now I can add the numbers: $$54 \times 10^4 + 2.3 \times 10^4 = 56.3 \times 10^4$$.”

Do you agree with Noah’s solution to the problem? Explain your reasoning.

(From Unit 7, Lesson 15.)

### Problem 6

Select all the expressions that are equivalent to $$3^8$$.

A:

$$(3^2)^4$$

B:

$$8^3$$

C:

$$3 \boldcdot 3 \boldcdot 3 \boldcdot 3 \boldcdot 3 \boldcdot 3 \boldcdot 3 \boldcdot 3$$

D:

$$(3^4)^2$$

E:

$$\frac{3^6}{3^{\text-2}}$$

F:

$$3^6 \boldcdot 10^2$$

(From Unit 7, Lesson 6.)