Lesson 1: Practice Problems

Problem 1

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

Four squares on a grid labeled A, B, C, D. All are tilted.

Problem 2

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

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

Problem 3

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

3 inches
7 units
100 cm
40 inches
$x$ units

Problem 4 From Unit 7 Lesson 14

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

$5.1 \times 10^{10}$
$5.1 \times 10^{24}$
$6.2 \times 10^{10}$
$6.2 \times 10^{24}$

Problem 5 From Unit 7 Lesson 15

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.

Problem 6 From Unit 7 Lesson 6

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

${(3^{2})}^{4}$
$8^{3}$
$3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3$
${(3^{4})}^{2}$
$\frac{3^{6}}{3^{- 2}}$
$3^{6} \cdot 10^{2}$