Testinar Grade 3 math

Tiling and the Distributive Property

Students will use area models and the distributive property to decompose multiplication problems.

CH06-08 Geometry and Measurement
Name
Date
Score
____ / 8
Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

  1. A rectangle is \(6\) units long and \(8\) units wide. Which shows its area broken into two smaller rectangles?

    1. \(6\times8=6\times(3+5)=(6\times3)+(6\times5)\)
    2. \(6\times8=48\)
    3. \(6+8=14\)
    4. \(6+8+6+8=28\)

  2. A rectangle has length \(5\) and width \(7\). If we split the width into \(4+3\), which equation shows the area?

    1. \(5\times7=5\times(4+3)=(5\times4)+(5\times3)\)
    2. \(5+4+3=12\)
    3. \((5+4)+(5+3)=17\)
    4. \(5\times7=35\)

  3. A rectangle is tiled by two smaller rectangles. One is \(4\times6\) and the other is \(4\times2\). What is the total area?

    1. \(48\)
    2. \(32\)
    3. \(20\)
    4. \(12\)

  4. Which of these shows tiling that proves \(3\times9=3\times(5+4)\)?

    1. Two rectangles with width \(3\): one is \(3\times5\), the other is \(3\times4\)
    2. Two rectangles with width \(2\): one is \(2\times5\), the other is \(2\times4\)
    3. A single rectangle \(3\times9\)
    4. Two rectangles with length \(9\): one is \(9\times3\), the other is \(9\times2\)

  5. A long rectangle has area \(60\) square units. It is split vertically into two parts. One part is \(4\times10\). What is the area of the other part if they share the same length?

    1. \(40\)
    2. \(20\)
    3. \(30\)
    4. \(60\)

  6. Which equation matches the tiling shown by a rectangle with one line cutting it vertically into two parts?

    1. \(7\times(3+2)=(7\times3)+(7\times2)\)
    2. \(3\times2=6\)
    3. \(7+3+2=12\)
    4. \((3\times7)+(2\times7)=35+14\)

  7. A \(8\times5\) rectangle is tiled into two smaller rectangles by a horizontal line. If one rectangle is \(8\times3\), what is the area of the other?

    1. \(16\)
    2. \(24\)
    3. \(40\)
    4. \(14\)

  8. A rectangle's area can be written as \(3\times(5+4)\). What is the total area?

    1. \(12\)
    2. \(15\)
    3. \(27\)
    4. \(20\)
Teacher and parent reference

Answer key and explanations

  1. A. \(6\times8=6\times(3+5)=(6\times3)+(6\times5)\)

    The distributive property lets us split \(8\) into \(3+5\) and add two smaller areas: \(18+30=48\). This matches tiling the rectangle in two parts.

  2. A. \(5\times7=5\times(4+3)=(5\times4)+(5\times3)\)

    \(5\times(4+3)=(5\times4)+(5\times3)=20+15=35\). Splitting the width lets us show the distributive property with area.

  3. B. \(32\)

    \((4\times6)+(4\times2)=24+8=32\). Both rectangles share width \(4\), so the total width is \(6+2=8\).

  4. A. Two rectangles with width \(3\): one is \(3\times5\), the other is \(3\times4\)

    The equation \(3\times(5+4)=(3\times5)+(3\times4)\) needs rectangles with the same width of \(3\).

  5. B. \(20\)

    One part is \(4\times10=40\). Total is \(60\). So the other part has area \(60-40=20\).

  6. A. \(7\times(3+2)=(7\times3)+(7\times2)\)

    A vertical line in a rectangle splits its width or length. Here the length is \(7\) and the other dimension splits into \(3+2\).

  7. A. \(16\)

    Total is \(8\times5=40\). One part is \(8\times3=24\). Other part is \(40-24=16\), which is \(8\times2\).

  8. C. \(27\)

    \(3\times(5+4)=3\times9=27\) or \((3\times5)+(3\times4)=15+12=27\).

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