Year 5: Sliding shapes: translations
Part of the Year 5 reflection and translation chapter. Chapter overview · whole chapter on one page
Sliding shapes: translations
A translation slides a shape from one place to another. Every point of the shape moves the same distance, in the same direction. The shape does not turn, flip or change size. The new shape is called the image. We name the corners of the image with a dash, so the image of corner A is A'.
To describe a translation, count the squares across (to the right or to the left), then count the squares up or down. Always say the across move first.
| Word | What it means | Example |
|---|---|---|
| right | across, to the right: the shape moves on the right-hand side | 3 squares right |
| left | across, to the left: the shape moves on the left-hand side | 2 squares left |
| up | the shape moves higher up the grid | 4 squares up |
| down | the shape moves lower down the grid | 1 square down |
Key ideas
- A translation slides a shape. It keeps its size, its shape and the way it faces.
- Every point moves the same distance, in the same direction.
- Describe a move as the squares across (right or left), then the squares up or down.
Key words. A translation slides a shape. Every point moves the same distance, in the same direction. The shape does not turn, flip or change size.
Method. Count the squares across, then up or down, from one corner. Every corner moves the same way.
- Pick one corner of the shape. Use the same corner (A) on the start shape and on the image.corner A
- Count 3 squares to the right. The matching corner of the image is 3 squares right.3 squares right
- Count 1 square down. The matching corner of the image is 1 squares down.1 squares down
- Check another corner. Every corner moves the same way, so the shape only slides.✓ the same move
- Write the answer. 3 squares to the right and 1 square down
Check. Count from another corner and you get the same move. ✓
Watch out. Count the squares on the grid. Do not count the sides of the shape.
Key words. A translation slides a shape. Every point moves the same distance, in the same direction. The shape does not turn, flip or change size.
Method. Start at the first number, then add or take away the move.
- Start at the first number. The counter starts 2 squares from the edge.2
- Move 5 squares right. Moving right or up adds. Moving left or down takes away.2 + 5 = 7
- Write the answer. 7
Check. Move 5 squares the other way to get back to 2. ✓
Watch out. Moving left takes away. Count carefully across the squares.
Key words. A translation slides a shape. Every point moves the same distance, in the same direction. The shape does not turn, flip or change size.
Method. Count the squares across, then up or down, from one corner. Every corner moves the same way.
- Pick one corner of the shape. Use the same corner (A) on the start shape and on the image.corner A
- Count 2 squares to the left. The matching corner of the image is 2 squares left.2 squares left
- Count 2 squares down. The matching corner of the image is 2 squares down.2 squares down
- Check another corner. Every corner moves the same way, so the shape only slides.✓ the same move
- Write the answer. 2 squares to the left and 2 squares down
Check. Count from another corner and you get the same move. ✓
Watch out. Count the squares on the grid. Do not count the sides of the shape.
Watch out
A common mistake is to count the sides of the shape instead of the squares on the grid. Count the squares between the start and the image. Also, a move with no up or down part is just a move across, so do not invent an up or down move.
Exercise 10A Describing translations
Non-calculatorKey words. A translation slides a shape. Every point moves the same distance, in the same direction. The shape does not turn, flip or change size.
Method. Count the squares across, then up or down, from one corner. Every corner moves the same way.
- Pick one corner of the shape. Use the same corner (A) on the start shape and on the image.corner A
- Count 3 squares to the right. The matching corner of the image is 3 squares right.3 squares right
- Check up and down. There is no move up or down, so the corner stays at the same height.0 squares up or down
- Check another corner. Every corner moves the same way, so the shape only slides.✓ the same move
- Write the answer. 3 squares to the right
Check. Count from another corner and you get the same move. ✓
Watch out. Count the squares on the grid. Do not count the sides of the shape.
Key words. A translation slides a shape. Every point moves the same distance, in the same direction. The shape does not turn, flip or change size.
Method. Count the squares across, then up or down, from one corner. Every corner moves the same way.
- Pick one corner of the shape. Use the same corner (A) on the start shape and on the image.corner A
- Check across. There is no move across, so the corner stays in the same column.0 squares across
- Count 2 squares up. The matching corner of the image is 2 squares up.2 squares up
- Check another corner. Every corner moves the same way, so the shape only slides.✓ the same move
- Write the answer. 2 squares up
Check. Count from another corner and you get the same move. ✓
Watch out. Count the squares on the grid. Do not count the sides of the shape.
Key words. A translation slides a shape. Every point moves the same distance, in the same direction. The shape does not turn, flip or change size.
Method. Count the squares across, then up or down, from one corner. Every corner moves the same way.
- Pick one corner of the shape. Use the same corner (A) on the start shape and on the image.corner A
- Count 4 squares to the left. The matching corner of the image is 4 squares left.4 squares left
- Count 1 square down. The matching corner of the image is 1 squares down.1 squares down
- Check another corner. Every corner moves the same way, so the shape only slides.✓ the same move
- Write the answer. 4 squares to the left and 1 square down
Check. Count from another corner and you get the same move. ✓
Watch out. Count the squares on the grid. Do not count the sides of the shape.
Key words. A translation slides a shape. Every point moves the same distance, in the same direction. The shape does not turn, flip or change size.
Method. Count the squares across, then up or down, from one corner. Every corner moves the same way.
- Pick one corner of the shape. Use the same corner (A) on the start shape and on the image.corner A
- Check across. There is no move across, so the corner stays in the same column.0 squares across
- Count 3 squares up. The matching corner of the image is 3 squares up.3 squares up
- Check another corner. Every corner moves the same way, so the shape only slides.✓ the same move
- Write the answer. 3 squares up
Check. Count from another corner and you get the same move. ✓
Watch out. Count the squares on the grid. Do not count the sides of the shape.
Key words. A translation slides a shape. Every point moves the same distance, in the same direction. The shape does not turn, flip or change size.
Method. Start at the first number, then add or take away the move.
- Start at the first number. The counter starts 4 squares from the edge.4
- Move 3 squares right. Moving right or up adds. Moving left or down takes away.4 + 3 = 7
- Write the answer. 7
Check. Move 3 squares the other way to get back to 4. ✓
Watch out. Moving left takes away. Count carefully across the squares.
Key words. A translation slides a shape. Every point moves the same distance, in the same direction. The shape does not turn, flip or change size.
Method. Start at the first number, then add or take away the move.
- Start at the first number. The counter starts 4 squares from the edge.4
- Move 2 squares left. Moving right or up adds. Moving left or down takes away.4 − 2 = 2
- Write the answer. 2
Check. Move 2 squares the other way to get back to 4. ✓
Watch out. Moving left takes away. Count carefully across the squares.
Key words. A translation slides a shape. Every point moves the same distance, in the same direction. The shape does not turn, flip or change size.
Method. Start at the first number, then add or take away the move.
- Start at the first number. The counter starts 4 squares from the edge.4
- Move 6 squares right. Moving right or up adds. Moving left or down takes away.4 + 6 = 10
- Write the answer. 10
Check. Move 6 squares the other way to get back to 4. ✓
Watch out. Moving left takes away. Count carefully across the squares.
Key words. A translation slides a shape. Every point moves the same distance, in the same direction. The shape does not turn, flip or change size.
Method. Find the new distance across and the new distance up, one at a time.
- Find the new distance from the left edge. The square starts 1 square from the left edge and moves 4 squares to the right.1 + 4 = 5
- Find the new distance from the bottom. It starts 1 square from the bottom and moves 3 squares up.1 + 3 = 4
- Write the answer. 5 squares from the left edge and 4 squares from the bottom
Check. Move back 4 to the left and 3 down, and you reach the start again. ✓
Watch out. Moving right or up adds. Do not add the 4 and the 3 together.
Key words. A translation slides a shape. Every point moves the same distance, in the same direction. The shape does not turn, flip or change size.
Method. Look at the way each shape faces, not only where it is.
- Look at the blue shape. Its corner, where the two arms meet, is at the bottom left.corner at the bottom left
- Look at the orange shape. Its corner is at the bottom right, so the shape has turned.corner at the bottom right
- Check the rule for a translation. A translation only slides a shape. It never turns it.turned, so not a slide
- Decide. Ruby is wrong, because a shape that has been turned is not a translation.No
Check. A translated shape faces the same way as the original. ✓
Watch out. Check the way a shape faces, not only where it is.
Key words. A translation slides a shape. Every point moves the same distance, in the same direction. The shape does not turn, flip or change size.
Method. Add the two moves: one across to the right and then back to the left.
- Write the first move. The shape moves 3 squares to the right.+3
- Write the second move. Then it moves 3 squares to the left, back the way it came.−3
- Add the moves together. Moves in opposite directions cancel each other out.3 − 3 = 0
- Write the answer. The total move is 0 squares, so the shape ends where it started.back where it started
Check. The total move is 0 squares. ✓
Watch out. Two equal moves in opposite directions cancel out.
Key words. A translation slides a shape. Every point moves the same distance, in the same direction. The shape does not turn, flip or change size.
Method. Add the across moves and add the up and down moves separately.
- Add the across moves. Two squares to the right and then one square to the right.2 + 1 = 3 squares to the right
- Add the up and down moves. One square up and then three squares down.1 − 3 = −2, so 2 squares down
- Write the single move. One move with 3 across and 2 down does the same job.3 squares to the right and 2 squares down
Check. 3 squares right and 2 squares down is the same as the two moves. ✓
Watch out. Add the across moves, then the up and down moves. Do not mix them up.
Key words. A translation slides a shape. Every point moves the same distance, in the same direction. The shape does not turn, flip or change size.
Method. A translation only slides a shape.
- Look at A. Turning changes the way a shape faces, so it is not a translation.turn: not a slide
- Look at B. Sliding the shape 3 squares to the right is a translation.slide: yes
- Look at C. Flipping over a line is a reflection, not a translation.flip: not a slide
- Write the answer. B
Check. Only B slides the shape without turning or flipping it. ✓
Watch out. A translation keeps the shape facing the same way.
Key words. A translation slides a shape. Every point moves the same distance, in the same direction. The shape does not turn, flip or change size.
Method. Find the new position of the left side and the right side, then measure from the left edge.
- Find the left side. The left side starts on the left edge, at 0 squares. It moves 3 squares to the right.0 + 3 = 3
- Find the right side. The house is 4 squares wide, so its right side starts 4 squares from the edge.4 + 3 = 7
- Write the answer. 7 squares
Check. The house is still 4 squares wide: 7 − 3 = 4. ✓
Watch out. The width of a shape does not change when it is translated.
Key words. A translation slides a shape. Every point moves the same distance, in the same direction. The shape does not turn, flip or change size.
Method. Find the gap between the two triangles.
- Write the first move. Tom moves the triangle 4 squares down.4 squares down
- Write the second move. Sam moves the same triangle 4 squares up.4 squares up
- Find the gap. The two places are on opposite sides of the start, so the gap is the two moves added together.4 + 4 = 8
- Write the answer. No, they are 8 squares apart
Check. The two triangles are 8 squares apart. ✓
Watch out. Moving up and moving down can be added to find the gap between two places.
Key words. A translation slides a shape. Every point moves the same distance, in the same direction. The shape does not turn, flip or change size.
Method. Think about what a translation does to every point.
- Check Ali. In a translation every point moves the same distance and in the same direction.the same for every point
- Check Dana. The top corner and the bottom corner move the same amount, so the top corner does not move further.top and bottom move the same
- Decide. Ali is right, and Dana is wrong.Ali
Check. Every corner of a slid shape moves the same way. ✓
Watch out. In a slide, the whole shape moves together.