Illustrative Mathematics | v.360 Curriculum

Problem 1

Here is a rectangle.

Area diagram. A rectangle partioned vertically into 3 smaller rectangles.

Explain why the area of the large rectangle is \(2a + 3a + 4a\).
Explain why the area of the large rectangle is \((2+3+4)a\).

Problem 2

Is the area of the shaded rectangle \(6(2-m)\) or \(6(m-2)\)? Explain how you know.

Area diagram partitioned into two attached rectangles one with a shaded area.

Problem 3

Select all the expressions that represent the total area of the rectangle.

A rectangle partitioned by a vertical line segment into two smaller rectangles. the vertical side is labeled t and the top horizontal side lengths are labeled 5 and 4.

\(5t + 4t\)
\(t + 5 + 4\)
\(9t\)
\(4 \boldcdot 5 \boldcdot t\)
\(t(5+4)\)

Problem 4

ForLesson 9: The Distributive Property, Part 1

Use the distributive property to write an equivalent expression.

\(35\boldcdot 91-35\boldcdot 89\)
\(22\boldcdot 87+22\boldcdot 13\)
\(\frac{9}{11}\boldcdot \frac{7}{10}-\frac{9}{11}\boldcdot \frac{3}{10}\)

Problem 5

ForLesson 8: Equal and Equivalent

Select all the expressions that are equivalent to \(4b\).

\(b+b+b+b\)
\(b+4\)
\(2b+2b\)
\(b \boldcdot b \boldcdot b \boldcdot b\)
\(b \div \frac{1}{4}\)

Problem 6

ForLesson 4: Practice Solving Equations

Solve each equation. Show your reasoning.

\(111=14a\)

\(13.65 = b + 4.88\)

\(c+ \frac{1}{3} = 5\frac{1}{8}\)

\(\frac{2}{5} d = \frac{17}{4}\)

\(5.16 = 4e\)

Problem 7

ForLesson 5: Represent Situations with Equations

A robot did \(5\frac12\) laps around a track in 8 minutes. It took the robot \(x\) minutes to complete each lap at a constant speed. Select all the equations that represent this situation.

\(\left(5\frac{1}{2}\right)x = 8\)
\(5 \frac{1}{2} + x = 8\)
\(5 \frac{1}{2} - x = 8\)
\(5 \frac{1}{2} \div x = 8\)
\(x = 8 \div \left(5\frac{1}{2}\right)\)
\(x = \left(5\frac{1}{2}\right) \div 8\)

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