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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.

Maine Learning Results 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 Maine

In the Maine Learning Results, 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: Maine 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

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

  2. Question 2

    Point A(−4, 1) 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
    • (4, 1)
    • (1, −4)
    • (−4, −1)
    • (4, −1)

  3. Question 3

    Which rule describes a reflection in the x-axis?

    • (x, y) → (−x, y)
    • (x, y) → (x, −y)
    • (x, y) → (y, x)
    • (x, y) → (−x, −y)

  4. Question 4

    Why can't regular pentagons tessellate on their own?

    • Their angles of 108° do not add to exactly 360° at a point.
    • Their sides are too long.
    • Pentagons have too few sides.
    • Their angles are too small to meet.

  5. Question 5

    Rows of identical bricks in a wall are each slid along without turning. Which transformation is that?

    • reflection
    • rotation
    • translation
    • dilation

  6. Question 6

    A shape with an area of 2 cm² is dilated by a scale factor of 5. What is the area of the image, in square centimeters?

    answer boxcm²

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