seegongsik
Grade 4 (age 9-10)

grade 4 Plane Figure Transformations

There are three ways to move a flat shape: slides, flips and turns. A slide moves the shape to a new place without changing its direction, a flip turns it over like a mirror image so that left and right (or top and bottom) swap, and a turn rotates it around a point by a set angle. You can spot all three moves in floor tiles and wrapping-paper patterns, where one shape is repeated over and over. Slide the triangle a number of squares, then flip or turn the L-shape; however it moves, its shape and size stay the same.

Slides

➡️ Slides
①A slide keeps the shape's form, size and direction the same
②Each corner of the starting shape and the matching corner of the slid shape are the same number of squares apart
③Count how many squares the shape moved to the right and how many it moved down
3
2

Flips and Turns

90°
🔄 Flips and Turns
①A left-right flip swaps the left and right sides but keeps the top and bottom
②A top-bottom flip swaps the top and bottom but keeps the left and right
③A turn keeps the center point still and rotates the whole shape by a set angle
④Turning clockwise 90° at a time brings the shape back to the start after four turns

Summary

Slide (Translation)
Same shape and direction, new place
Describe it by how many squares it moves right, left, up or down
Flip (Reflection)
Left and right, or top and bottom, swap
Flipping twice the same way brings back the starting shape
Turn (Rotation)
Rotate a set angle around a center point
Turns of 90°, 180° and 270° are common, and a 360° turn looks the same as the start
🎯 Summary
①A shape can be moved by a slide, a flip or a turn
②However it moves, its shape and size do not change
③A slide is described by direction and distance, a flip by the way it flips, and a turn by direction and angle
④Two flips the same way or a 360° turn bring the shape back to the start
⑤Tiles and patterns repeat one shape by sliding, flipping or turning it

Examples and Unit Test

Example 1
If you slide a triangle 3 squares to the right, what happens to its shape and size?
1
A slide only changes where the shape is.
2
Its shape and size stay the same; it is now 3 squares to the right.
▸ Same shape and size, new position
Slides, flips and turns never change a shape's form or size.
Example 2
Which move swaps a shape's left and right sides, like a mirror image?
1
A mirror image has its left and right sides swapped.
2
Flipping the shape left to right swaps its left and right sides.
▸ A flip (reflection)
A left-right flip swaps the sides; a top-bottom flip swaps the top and bottom.
Unit Test
What happens if you turn a shape 360° around a point?
①It becomes twice as big
②It looks the same as at the start
③Its left and right swap
④It disappears
▸ ② It looks the same as at the start
1
360° is one complete turn.
2
After a full turn the shape is back in its starting place and direction.
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