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8th grade · Math · Unit 7 of 19

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.

New York State Learning Standards learning standard: NY-8.G.1; NY-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 New York

In the New York State Learning Standards, this is unit 7 of 19 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: New York State Education Department (NYSED)

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

    Point A(−6, −5) is translated 4 units right and 3 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
    • (−2, −2)
    • (−9, −1)
    • (−2, −8)
    • (−10, −8)

  2. Question 2

    Which rule describes a dilation by a scale factor of 3 about the origin?

    • (x, y) → (3x, y)
    • (x, y) → (3x, 3y)
    • (x, y) → (x/3, y/3)
    • (x, y) → (x + 3, y + 3)

  3. Question 3

    Point A(−4, 5) 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
    • (5, 4)
    • (−5, −4)
    • (4, 5)
    • (−4, −5)

  4. Question 4

    Point A(6, −5) is dilated by a scale factor of 3 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
    • (6, −15)
    • (18, −15)
    • (18, −5)
    • (9, −2)

  5. Question 5

    A rectangle is dilated by a scale factor of 5. A side that was 6 cm long is now how long, in centimeters?

    answer boxcm

  6. Question 6

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

    • squares
    • pentagons
    • circles
    • more octagons turned over

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