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8th grade · Math · Unit 3 of 15

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.

Texas Essential Knowledge and Skills (TEKS) teks student expectation: 8.3(C); 8.10(A); 8.10(C) · dilations, translations, reflections and rotations 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 Texas

In the Texas Essential Knowledge and Skills (TEKS), this is unit 3 of 15 in 8th grade Math, after Squares, Cubes & Roots and before Congruent Shapes.

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: Texas Education Agency (TEA)

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(−1, −2) 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
    • (1, −2)
    • (−1, 2)
    • (−2, −1)
    • (1, 2)

  2. Question 2

    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

  3. Question 3

    Point A(−3, −6) 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
    • (−9, −6)
    • (−3, −18)
    • (−9, −18)
    • (0, −3)

  4. Question 4

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

    • more octagons turned over
    • squares
    • circles
    • pentagons

  5. Question 5

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

  6. Question 6

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

    • dilation
    • translation
    • rotation
    • reflection

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