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.

4 squares labeled A, B, C, D on grid.

 

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.)