Grade 4 (age 9-10)

Plane Figure Transformations

Transformations

There are three ways to move a shape: sliding, flipping, and turning. Sliding keeps the shape and just changes its position, flipping mirrors it left-right, and turning spins it around a center point. You can spot these moves in paper folding and floor tile patterns. Here you can slide a triangle and turn it by an angle, and see that its shape and size never change.

Let's slide a shape!

➡️ Slide = Translation

①Shape and size don't change

②Only position changes (translation)

③Count how far horizontally and vertically

Right by3

Down by2

Flip and Rotate

Angle90°

🔄 Features of Transformations

①Slide: only position changes, shape stays

②Flip: mirror image, left-right (or up-down) reversed

③Rotate: spin around a center point

Summary

Slide (Translation)

Shape stays, position moves

Slide consistently horizontally and vertically

Flip (Reflection)

Reverse left-right or up-down across an axis

Same as a mirror image

Rotate (Rotation)

Rotate by a fixed angle around a center

90°, 180°, 270°, 360° are common

🎯 Key Points

①Three transformations: slide, flip, rotate

②Shape and size never change

③Slide = direction+distance, flip = axis, rotate = center+angle

④These appear in patterns and tilings

⑤You can combine several transformations

Examples and Unit Test

Example 1

If a triangle is slid 3 cells to the right (translation), what happens to its shape and size?

Sliding (translation) is a transformation that changes only the position.

The shape and size stay the same; only the position moves 3 cells to the right.

▸ Shape and size unchanged; only position moves

For any transformation (slide, flip, or turn), the shape and size do not change.

Example 2

Which transformation makes a figure left-right reversed, like a mirror image?

A mirror image is reversed left-right (or up-down) across an axis of symmetry.

Reversing a figure across an axis of symmetry is called a flip (reflection).

▸ Flip (reflection)

A flip reverses left-right or up-down across an axis, like a mirror.

Unit Test

What happens if you rotate a figure 360° about a point?

①it doubles in size

②it returns to the start

③it flips left-right

④it disappears

▸ ② it returns to the start

360° is one complete full turn.

After a full turn, the figure comes back to its original position, exactly as it started.

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