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:
 81 square inches
 \(\frac{4}{25}\) cm^{2}
 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
Evaluate \((3.1 \times 10^4) \boldcdot (2 \times 10^6)\). 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
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
Select all the expressions that are equivalent to \(3^8\).
\((3^2)^4\)
\(8^3\)
\(3 \boldcdot 3 \boldcdot 3 \boldcdot 3 \boldcdot 3 \boldcdot 3 \boldcdot 3 \boldcdot 3\)
\((3^4)^2\)
\(\frac{3^6}{3^{\text2}}\)
\(3^6 \boldcdot 10^2\)