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8th grade · Math · Unit 7 of 17

Tessellations & Transformations

Slides, flips, turns and dilations

What your child practices

Why some shapes tessellate, naming the transformations in a tiling, and finding the image of a point after a translation, reflection, rotation or dilation on a coordinate grid.

Alaska content standards learning standard: 8.G.1; 8.G.3 · translations, reflections, rotations and dilations on the coordinate plane

How we explain it

Children can open this short lesson before they practice.

  1. A translation slides, a reflection flips, a rotation turns and a dilation resizes.
  2. A tessellation covers a surface with copies of a shape with no gaps.
  3. On a grid, a translation adds to or subtracts from x and y.

Example: Translate (1, 2) right 3 and down 4. Right 3: x = 1 + 3 = 4. Down 4: y = 2 − 4 = −2. Answer: (4, −2)

Tessellations & Transformations in Alaska

In the Alaska content standards, this is unit 7 of 17 in 8th grade Math, after Scatter Plots & Stories and before Angle Detective.

Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.

Source: Alaska Department of Education and Early Development

Sample questions

A taste of this unit. In the app, questions change every time and get easier or harder to match your child.

  1. Question 1

    A rectangle is dilated by a scale factor of 2. A side that was 5 cm long is now how long, in centimeters?

    answer boxcm

  2. Question 2

    Point A(3, 5) is translated 5 units right and 4 units down. What are the coordinates of A′?

    -9-9-8-8-7-7-6-6-5-5-4-4-3-3-2-2-1-100112233445566778899A
    • (8, 1)
    • (−1, 10)
    • (−2, 1)
    • (8, 9)

  3. Question 3

    Squares tessellate because each angle is 90°. How many squares meet at each point?

    • 8
    • 4
    • 3
    • 6

  4. Question 4

    Point A(−2, −5) is reflected in the x-axis. What are the coordinates of A′?

    -9-9-8-8-7-7-6-6-5-5-4-4-3-3-2-2-1-100112233445566778899A
    • (−5, −2)
    • (2, −5)
    • (2, 5)
    • (−2, 5)

  5. Question 5

    Point A(2, 1) is rotated 90° counterclockwise about the origin. What are the coordinates of A′?

    -9-9-8-8-7-7-6-6-5-5-4-4-3-3-2-2-1-100112233445566778899A
    • (−2, −1)
    • (−1, 2)
    • (2, −1)
    • (1, −2)

  6. Question 6

    Regular octagons alone leave square-shaped gaps. What can be added to make a tessellation?

    • squares
    • circles
    • pentagons
    • more octagons turned over

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