Year 5 Reflection and translation: check-up and SATs-style questions

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.

1. Pick one corner of the shape. Use the same corner (A) on the start shape and on the image.
   corner A
2. Count 3 squares to the right. The matching corner of the image is 3 squares right.
   3 squares right
3. Count 2 squares down. The matching corner of the image is 2 squares down.
   2 squares down
4. Check another corner. Every corner moves the same way, so the shape only slides.
   ✓ the same move
5. Write the answer.
   3 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.

Key words. A reflection flips a shape over a mirror line. Each point and its image are the same distance from the mirror line, on opposite sides.

Method. Count from the mirror line to the image, on the other side.

1. Find the mirror line. The dashed red line is 6 squares from the left edge.
   line at 6
2. Find the image corner. A' is 8 squares from the left edge.
   A' at 8
3. Count the squares from the line. Subtract the line from the image corner.
   8 − 6 = 2
4. Write the answer.
   2 squares

Check. A is 2 squares from the line too: 6 − 4 = 2. ✓

Watch out. Count from the line, not from the 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 side up 2 squares, then count from the bottom edge.

1. Find the bottom side now. The bottom side of the house is 1 square from the bottom edge.
   1 up
2. Move it 2 squares up. Moving up adds to the height.
   1 + 2 = 3
3. Write the answer.
   3 squares

Check. The house moves up by 2, so its bottom is 3 squares up. ✓

Watch out. Count from the bottom edge of the grid.

Key words. A reflection flips a shape over a mirror line. Each point and its image are the same distance from the mirror line, on opposite sides.

Method. Count the squares from the point to the mirror line, then count the same number on the other side.

1. Find the mirror line. The dashed red line is the mirror line.
   the dashed red line
2. Count the squares from the point to the line. The point is 4 squares left the line.
   4 squares
3. Count the same number on the other side. A reflection puts the image the same distance from the line, on the other side.
   4 squares right the line
4. Write the answer.
   4 squares to the right of the mirror line

Check. The point and its image are both 4 squares from the line. ✓

Watch out. The image is on the other side of the line, not on the same side.

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. Compare the new shape with the old one.

1. Look at the size. A reflection keeps the size of the shape.
   same size
2. Look at the shape. A reflection keeps the shape. It only faces the other way.
   same shape
3. Write the answer.
   No, it has not changed size or shape

Check. A reflected shape has the same size and shape. ✓

Watch out. A reflected shape faces the other way, but it is not a new 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. Find the bottom-right corner, then move it.

1. Find the bottom-right corner. The rectangle starts 1 square across, and it is 4 squares wide, so its bottom-right corner is at 5 across.
   1 + 4 = 5 across, 0 up
2. Move it 3 squares right. Moving right adds to the across distance.
   5 + 3 = 8
3. Move it 2 squares up. Moving up adds to the height.
   0 + 2 = 2
4. Write the answer.
   8 squares across and 2 squares up

Check. The rectangle moves 3 across and 2 up, so its bottom-left corner is now at 4 across and 2 up. ✓

Watch out. Find the corner first. Then move it, one move at a time.

Key words. A reflection flips a shape over a mirror line. Each point and its image are the same distance from the mirror line, on opposite sides.

Method. Count the distance to the mirror line, then count the same distance on the other side.

1. Find the mirror line. The mirror line is 6 squares from the left edge.
   mirror line at 6
2. Count the squares from the point to the line. The point is 5 squares from the line.
   5 squares
3. Count the same number on the other side. The image is the same distance from the line, on the other side.
   6 + 5 = 11
4. Write the answer.
   11 squares from the left edge

Check. The point and its image are both 5 squares from the line. ✓

Watch out. Count from the left edge every time, so you do not mix up the two sides.

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.

1. Look at the first move. Sam moves the shape 3 squares to the right.
   +3
2. Look at the second move. Then he moves it 3 squares to the left, back the other way.
   −3
3. Decide. The two moves cancel, so the shape is back where it started.
   Yes

Check. 3 − 3 = 0, so the total move is 0. ✓

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. Move the corner across, then up or down.

1. Start at the corner. The corner is 2 squares across and 5 squares up.
   2 across, 5 up
2. Move it 4 squares right. Moving right adds to the across distance.
   2 + 4 = 6
3. Move it 3 squares down. Moving down takes away from the height.
   5 − 3 = 2
4. Write the answer.
   6 squares across and 2 squares up

Check. Go back 4 to the left and 3 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. Compare what each move does to the shape.

1. Think about a translation. A translation slides the shape. It does not turn or flip it.
   slides
2. Think about a reflection. A reflection flips the shape over a mirror line.
   flips
3. Write the answer.
   A translation slides a shape, and a reflection flips it over a mirror line.

Check. The two moves are different: one slides, the other flips. ✓

Watch out. Ask whether the shape is slid or flipped.

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 slide is a translation.

1. Look at the words. Turning and flipping are not slides.
   turn, flip
2. Write the answer.
   slide

Check. A translation slides the shape. ✓

Watch out. A translation slides the shape without turning 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. Count the squares from the left-hand corner.

1. Find the left-hand corner. The left-hand corner of the blue triangle is 1 square from the left edge.
   1 across
2. Find the image corner. The image corner is 5 squares from the left edge.
   5 across
3. Write the answer. The shape has moved 4 squares to the right and no squares up or down.
   4 squares to the right

Check. 5 − 1 = 4. ✓

Watch out. There is no up or down move, so do not write 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. Start at the first number, then add or take away the move.

1. Start at the first number. The counter starts 2 squares from the edge.
   2
2. Move 5 squares right. Moving right or up adds. Moving left or down takes away.
   2 + 5 = 7
3. 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 reflection flips a shape over a mirror line. Each point and its image are the same distance from the mirror line, on opposite sides.

Method. Count the squares from the point to the mirror line, then count the same number on the other side.

1. Find the mirror line. The dashed red line is the mirror line.
   the dashed red line
2. Count the squares from the point to the line. The point is 3 squares left the line.
   3 squares
3. Count the same number on the other side. A reflection puts the image the same distance from the line, on the other side.
   3 squares right the line
4. Write the answer.
   3 squares to the right of the mirror line

Check. The point and its image are both 3 squares from the line. ✓

Watch out. The image is on the other side of the line, not on the same side.

Key words. A reflection flips a shape over a mirror line. Each point and its image are the same distance from the mirror line, on opposite sides.

Method. The image is the same distance from the line, on the other side.

1. Write the distance to the line. The point is 4 squares from the mirror line.
   4 squares
2. Find the image. The image is on the other side, the same distance from the line.
   4 squares
3. Write the answer.
   4 squares

Check. The point and its image are both 4 squares from the line. ✓

Watch out. The image is the same distance on the other side.

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. Reverse each part of the move.

1. Write the move. Ruby moved the shape 3 squares to the left and 2 squares up.
   3 left, 2 up
2. Reverse the across move. To go back, move 3 squares to the right.
   3 right
3. Reverse the up move. To go back, move 2 squares down.
   2 down
4. Write the answer.
   3 squares to the right and 2 squares down

Check. 3 right and 2 down brings the shape back to the start. ✓

Watch out. Reverse each part of the move: left becomes right, up becomes down.

Key words. A reflection flips a shape over a mirror line. Each point and its image are the same distance from the mirror line, on opposite sides.

Method. Count the distance to the mirror line, then count the same distance on the other side.

1. Find the mirror line. The mirror line is 5 squares from the bottom edge.
   mirror line at 5
2. Count the squares from the point to the line. The point is 3 squares from the line.
   3 squares
3. Count the same number on the other side. The image is the same distance from the line, on the other side.
   5 − 3 = 2
4. Write the answer.
   2 squares from the bottom edge

Check. The point and its image are both 3 squares from the line. ✓

Watch out. Count from the bottom edge every time, so you do not mix up the two sides.

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 top-right corner first, then move it.

1. Find the top-right corner now. The rectangle starts 2 squares from the left edge and is 6 squares wide, so its right side is 8 squares from the edge.
   2 + 6 = 8
2. Find its height. It starts 1 square from the bottom and is 2 squares high, so its top is 3 squares from the bottom.
   1 + 2 = 3
3. Move it 3 squares to the right. Moving right adds to the across distance.
   8 + 3 = 11
4. Move it 4 squares up. Moving up adds to the height.
   3 + 4 = 7
5. Write the answer.
   11 squares from the left edge and 7 squares from the bottom

Check. The rectangle is still 6 squares wide: 11 − 3 − 2 = 6. ✓

Watch out. Find the corner before the move, then add the moves to it.

Key words. A reflection flips a shape over a mirror line. Each point and its image are the same distance from the mirror line, on opposite sides.

Method. The mirror line is halfway between a point and its image.

1. Look at the point and its image. The image is 2 squares to the right of the line.
   image: 2 right
2. Find the point. The point must be the same distance on the other side of the line.
   point: 2 left
3. Decide. So Ali is right: the point is 2 squares to the left of the line.
   Yes

Check. Each point and its image are the same distance from the line, on opposite sides. ✓

Watch out. Check the distance on both sides, and the side of the line.

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 the size and shape of each move.

1. Look at Ruby. A translation and a reflection both keep the size and shape of the shape.
   Ruby: size stays
2. Look at Dana. A reflection only flips the shape. It cannot make it larger.
   Dana: wrong
3. Give an example. A rectangle 3 squares by 2 squares, reflected in a line, is still 3 squares by 2 squares.
   3 by 2 stays 3 by 2
4. Decide. So Ruby is right, and Dana is wrong.
   Ruby is right

Check. A flipped rectangle is still 3 squares by 2 squares. ✓

Watch out. A reflection flips a shape. It does not stretch it.