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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.

Arizona Academic Standards learning standard: 8.G.A.1; 8.G.A.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 Arizona

In the Arizona Academic 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: Arizona Department of Education

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

    What do the angles that meet at one point in a tessellation add to?

    • 180°
    • 720°
    • 90°
    • 360°

  2. Question 2

    A shape with an area of 10 cm² is dilated by a scale factor of 2. What is the area of the image, in square centimeters?

    answer boxcm²

  3. Question 3

    Point A(5, −3) is translated 5 units left and 5 units up. What are the coordinates of A′?

    -9-9-8-8-7-7-6-6-5-5-4-4-3-3-2-2-1-100112233445566778899A
    • (10, 2)
    • (0, 2)
    • (10, −8)
    • (0, −8)

  4. Question 4

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

    • pentagons
    • more octagons turned over
    • circles
    • squares

  5. Question 5

    Point A(−2, 3) is reflected in the y-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
    • (3, −2)
    • (2, −3)
    • (2, 3)
    • (−2, −3)

  6. Question 6

    Point A(−4, 2) 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, −4)
    • (−4, −2)
    • (4, −2)
    • (2, 4)

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