How to teach transformations for math

Written by taylor divico
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How to teach transformations for math
Create a coordinate plane on grid paper to demonstrate transformations within quadrants. (Jupiterimages/ Images)

Teaching transformations requires providing students with the necessary vocabulary to explain the movement of shapes on a grid. Clues can help kids identify the type of movement and to distinguish between rotations, reflections and translations. Educators should equip students with geometry lessons on the number of degrees in a full rotation or circle and within each grid quadrant before introducing transformations. You can implement bodily-kinesthetic movements to reinforce these concepts.

Skill level:
Moderately Easy

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Things you need

  • Overhead projector
  • Grid transparency
  • Grid paper
  • Transparency markers
  • Plastic geometric shapes
  • Masking tape

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  1. 1

    Provide students with grid paper. Ask them to draw and label the x and y axes. Model the placement and labelling of each quadrant, if not pre-taught. Tell the students to label the upper right quadrant as I, the upper left quadrant as II, the lower left quadrant as III and the lower right quadrant as IV.

  2. 2

    Explain to students that a circle has 360 degrees, and each quadrant is worth one fourth of 360 degrees. Divide 360 by 4 on the board to show that each quadrant represents 90 degrees.

  3. 3

    Supply each student with an isosceles triangle. Place a labelled grid on your overhead projector. Turn a plastic see-through polygon counterclockwise from quadrant I to quadrant 4. Ask the students to add 90 degrees each time the shape moves into a new quadrant. Allow students to chant "90, 180, 270, 360" to help them memorise the number of degrees per quadrant.

  4. 4

    Explain that a rotation occurs when shapes turn around a point. Demonstrate to students how the triangle turns around a centre point. Draw arrows on the grid to exemplify the turning of the triangle and how different angles face different areas when moving from one quadrant to the next.

  5. 5

    Explain that a reflection or flip occurs when a 180 degree movement happens. Place a shape such as a trapezoid on your grid. Provide students with two trapezoid shapes. Explain to students that the axes provide a mirror image effect when a shape flips over the line. Position a second trapezoid to show a mirror image of the first. Demonstrate this on the y and x axes.

  6. 6

    Explain that a translation occurs when a slide happens. Place a scalene triangle on your grid. Give scalene triangles to students for placement on their grids. Slide the triangle from one quadrant to another. Show students the movement of a slide while pointing out that the angles of the shape are pointing in the same directions before moving.

  7. 7

    Create grids on your floor using masking tape. Split students up into small groups to practice transformation movements on these grids.

  8. 8

    Ask the students to slide side-to-side and front-to-back from one quadrant into another without changing the direction they are facing to show you a translation.

  9. 9

    Ask the students to rotate a certain number of degrees by turning one foot and placing the other foot into a different quadrant on the grid. Remind students that each time they turn, they are facing a different direction and that this is called a rotation.

  10. 10

    Place students into pairs and ask them to stand next to each other. Direct one partner to become the mirror image of the other by standing across from and facing the other child. Explain that this movement is a flip and is called a reflection.

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