Illustrative Mathematics | v.360 Curriculum

Problem 1

Select all the expressions that represent the area of the large, outer rectangle.

\(5(2+4)\)
\(5 \boldcdot 2 + 4\)
\(5 \boldcdot 2 + 5 \boldcdot 4\)
\(5 \boldcdot 2 \boldcdot 4\)
\(5 + 2+ 4\)
\(5 \boldcdot 6\)

Explain how each expression is equivalent to \(50 \boldcdot 19\).
Use the diagram if needed.

Complete each calculation using the distributive property.

\(\displaystyle 98 \boldcdot 24\) \(\displaystyle (100-2) \boldcdot 24\)

\(\displaystyle 21 \boldcdot 15\) \(\displaystyle (20 + 1) \boldcdot 15\)

\(\displaystyle 0.51 \boldcdot 40\) \(\displaystyle (0.5 + 0.01) \boldcdot 40\)

Select all the expressions that represent the area of the shaded rectangle on the left side of the figure.

\(12(20+4.5)\)
\(20 \boldcdot 12 \boldcdot 15.5\)
\(15.5 \boldcdot 12\)
\(15.5 \boldcdot 12 + 4.5 \boldcdot 12\)
\(20 \boldcdot 12 - 4.5\boldcdot12\)
\(12(20-4.5)\)

On graph paper, draw diagrams that represent \(a+a+a+a\) and \(4a\) when \(a\) is 1, 2, and 3. What do you notice?
Do \(a+a+a+a\) and \(4a\) have the same value for any value of \(a\)? Explain how you know.

120% of \(x\) is equal to 78.

Kiran’s aunt is 17 years older than Kiran.