Year 5: Drawing a translation
Part of the Year 5 reflection and translation chapter. Chapter overview · whole chapter on one page
Drawing a translation
To draw a translation, move every corner the same number of squares. Start with one corner. Count the squares across, then count the squares up or down, and put a dot. Then do the same for every other corner, and join the dots in the same order.
Check your drawing: the new shape must be the same size and shape as the old one.
Key ideas
- To draw a translation, move every corner the same number of squares.
- Count across first, then up or down.
- Check that the new shape is the same size and shape as the old one.
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 bottom-left corner, one move at a time.
- Start at the corner. The bottom-left corner is 1 square from the left edge and 0 squares from the bottom.1 across, 0 up
- Move 2 squares to the right. Moving right adds to the across distance.1 + 2 = 3
- Move 3 squares up. Moving up adds to the height.0 + 3 = 3
- Write the answer. 3 squares from the left edge and 3 squares from the bottom
Check. The new corner is 2 squares right and 3 squares up from the old one. ✓
Watch out. Add the moves to the numbers. Do not write the moves on their own.
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 bottom-left corner, one move at a time.
- Start at the corner. The bottom-left corner of the house is 4 squares from the left edge and 4 squares from the bottom.4 across, 4 up
- Move 3 squares to the left. Moving left takes away from the across distance.4 − 3 = 1
- Move 2 squares down. Moving down takes away from the height.4 − 2 = 2
- Write the answer. 1 square from the left edge and 2 squares from the bottom
Check. Go back 3 squares to the right and 2 squares up to reach the start. ✓
Watch out. Left and down take away. Right and up add.
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 right. The matching corner of the image is 2 squares right.2 squares right
- 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 right 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 move some corners and not others. Every corner must move the same number of squares, in the same way. When you have finished, check that the new shape is still the same size.
Exercise 10B Drawing a shape after a translation
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. Move each corner 3 squares to the right. Start with the left side.
- Find the left side now. The left side is 1 square from the left edge.1 square
- Move it 3 squares to the right. Moving right adds to the across distance.1 + 3 = 4
- Write the answer. The new left side is 4 squares from the left edge.4 squares
Check. The new house is still 4 squares wide. ✓
Watch out. Count from the left edge of the grid, not from 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. Move the top corner up 2 squares, then count from the bottom edge.
- Find the top corner now. The top corner is 3 squares above the bottom edge.3 up
- Move it 2 squares up. Moving up adds to the height.3 + 2 = 5
- Write the answer. 5 squares
Check. The triangle is 3 squares tall, so the new bottom is 2 squares up. ✓
Watch out. Count the squares from the bottom edge of the grid.
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. Move the bottom-left corner 2 squares right and 1 square down.
- Find the across distance. The corner starts 1 square from the left edge.1 + 2 = 3
- Find the height. The corner starts 3 squares from the bottom.3 − 1 = 2
- Write the answer. The corner is 3 squares from the left edge and 2 squares from the bottom.3 squares from the left edge and 2 squares from the bottom
Check. Go back 2 squares left and 1 square up to reach the start. ✓
Watch out. Down takes away from the height. Right adds to the across distance.
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 where the tip is, then move it 4 squares to the left.
- Find the tip now. The tip of the arrow is 9 squares from the left edge.9 across
- Move it 4 squares to the left. Moving left takes away from the across distance.9 − 4 = 5
- Write the answer. 5 squares
Check. Move 4 squares right from 5 and you are back at the tip. ✓
Watch out. The tip is the point on the right, so start there.
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. The bottom side of the house is 1 square from the bottom edge. Only the up move changes its height.
- Find the bottom side now. The bottom side is 1 square from the bottom edge.1 square
- Look at the move up. A move to the right does not change the height. A move up adds to the height.up 0
- Find the new height. Add the up move to the height.1 + 0 = 1
- Write the answer. 1 square
Check. The house is still the same height, so its bottom side only moves up by 0. ✓
Watch out. A move to the right does not change how high a shape 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. The bottom side of the house is 1 square from the bottom edge. Only the up move changes its height.
- Find the bottom side now. The bottom side is 1 square from the bottom edge.1 square
- Look at the move up. A move to the right does not change the height. A move up adds to the height.up 2
- Find the new height. Add the up move to the height.1 + 2 = 3
- Write the answer. 3 squares
Check. The house is still the same height, so its bottom side only moves up by 2. ✓
Watch out. A move to the right does not change how high a shape 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. The bottom side of the house is 1 square from the bottom edge. Only the up move changes its height.
- Find the bottom side now. The bottom side is 1 square from the bottom edge.1 square
- Look at the move up. A move to the right does not change the height. A move up adds to the height.up 2
- Find the new height. Add the up move to the height.1 + 2 = 3
- Write the answer. 3 squares
Check. The house is still the same height, so its bottom side only moves up by 2. ✓
Watch out. A move to the right does not change how high a shape 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. Look at the direction of the move.
- Check the move Sam was given. Three squares to the right is a move across only.across 3, up 0
- Check what Sam did. Sam moved the triangle up, so it is in the wrong place.up instead of across
- Write the answer. He moved it up instead of across.
Check. Three squares to the right has no up or down part. ✓
Watch out. Read the direction of the move before you draw.
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 bottom-right corner now, then move it.
- Find the bottom-right corner now. The rectangle is 4 squares wide, so the bottom-right corner is 4 squares from the left edge.4 across, 0 up
- Move it 3 squares to the right. Moving right adds to the across distance.4 + 3 = 7
- Move it 1 square up. Moving up adds to the height.0 + 1 = 1
- Write the answer. 7 squares from the left edge and 1 square from the bottom
Check. The new rectangle is still 4 squares wide and 2 squares high. ✓
Watch out. Find the corner first, then move it.
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. Move the corner across, then down.
- Find the across distance. The top-right corner is 5 squares from the left edge. It moves 2 squares to the left.5 − 2 = 3
- Find the height. The corner is 6 squares from the bottom. It moves 4 squares down.6 − 4 = 2
- Write the answer. 3 squares from the left edge and 2 squares from the bottom
Check. Move 2 squares right and 4 squares up from the new corner to reach the old one. ✓
Watch out. Left and down both take away from the numbers.
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. Try both orders and compare the place each one ends in.
- Try the first order. Move 2 squares right, then 3 squares up.2 right, then 3 up: ends at 2 across and 3 up
- Try the second order. Move 3 squares up, then 2 squares right.3 up, then 2 right: ends at 2 across and 3 up
- Decide. Both orders end at the same place, so the order does not change the answer.Yes
Check. Adding the across moves and the up moves in any order gives the same total. ✓
Watch out. Each move is a shift, so the shift can be done in either order.
Key words. A translation or a reflection keeps the size and shape of a shape. Only its position (and, for a reflection, the way it faces) can change.
Method. Think about what changes and what stays the same in a slide.
- Look at the three choices. The position changes when the shape moves.position: changes
- Look at the size. A slide keeps the same size.size: stays the same
- Look at the direction. A slide keeps the way the shape faces.direction: stays the same
- Write the answer. position
Check. Only the position changes in a translation. ✓
Watch out. A translation changes where the shape is, not what it is like.
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 left-hand corner of the old triangle, then add the across move.
- Find the old corner. The left-hand corner of the blue triangle is 1 square from the left edge.1 across
- Add the across move. The new triangle is 3 squares to the right.1 + 3 = 4
- Write the answer. 4 squares
Check. The up move of 2 does not change the across distance. ✓
Watch out. Use only the across part of the move for this question.
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 and up moves to the numbers from the edges.
- Start with the counter. The counter is 4 squares from the left edge and 5 squares from the bottom.4 across, 5 up
- Move it 3 squares to the right. Moving right adds to the across distance.4 + 3 = 7
- Move it 1 square down. Moving down takes away from the height.5 − 1 = 4
- Write the answer. 7 squares from the left edge and 4 squares from the bottom
Check. Go back 3 squares to the left and 1 square up to reach the start. ✓
Watch out. Left and down take away, right and up add.
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 move that undoes the first move.
- Write the first move. The shape moved 4 squares to the right.+4
- Write the move that undoes it. To go back, move the same number of squares the other way.4 squares to the left
- Write the answer. 4 squares to the left
Check. 4 squares right then 4 squares left is a total move of 0. ✓
Watch out. Undo a move by moving the same number of squares the other way.