Year 5: The shape has not changed
Part of the Year 5 reflection and translation chapter. Chapter overview · whole chapter on one page
The shape has not changed
When a shape is translated or reflected, its size and its shape stay the same. We say that the shape has not changed. A translation slides the shape. A reflection flips it over a mirror line. Neither one makes the shape bigger, smaller, longer or shorter.
A shape that is made bigger, or stretched so that one side is longer, has changed. It is not a translation or a reflection of the first shape.
Key ideas
- A translation or a reflection keeps the size and shape of a shape.
- Only the position changes, and for a reflection the way the shape faces also changes.
- A shape that is bigger, or stretched, has changed.
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 sizes and the shapes of the blue and the orange house.
- Compare the width. The blue house is 4 squares wide, and the orange house is 4 squares wide.4 = 4
- Compare the height. The blue house is 4 squares high, and the orange house is 4 squares high.4 = 4
- Compare the shape. The two houses have the same corners in the same order, just in different places.same shape
- Decide. The house has only moved, so its size and shape have not changed.No, it has not changed
Check. Only the place of the house has changed. ✓
Watch out. Check the size and the shape, not only where the shape is.
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 two triangles side by side.
- Compare the bottom sides. The blue bottom side is 3 squares long, and the orange bottom side is 3 squares long.3 = 3
- Compare the other sides. The other sides match too, because the orange triangle is a mirror image.the same
- Decide. A reflection keeps the size and shape, although it faces the other way round.No, the shape has not changed
Check. The two triangles are exactly the same size and shape. ✓
Watch out. A reflection can change the way a shape faces, but not its size.
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 lengths of the sides of the two triangles.
- Measure the blue bottom side. The blue bottom side is 3 squares long.3 squares
- Measure the orange bottom side. The orange bottom side is 6 squares long, which is twice as long.6 squares
- Decide. The sides are not the same length, so the shape has changed.Yes, the shape has changed
Check. 6 is twice 3, so the orange shape is twice as big. ✓
Watch out. Compare the same side of each shape.
Watch out
A common mistake is to think a shape has changed because it is in a different place or faces a different way. For a translation or a reflection, the size and shape stay the same. Only a shape that is made bigger or stretched has changed.
Exercise 10E Has the shape changed?
Non-calculatorKey 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. A translation only moves a shape, so check the size and the shape.
- Look at the size. The house is the same size after it has moved.same size
- Look at the shape. The corners are in the same order, so the shape is the same.same shape
- Write the answer. It has only moved, so it has not changed.No
Check. The house has only slid to a new place. ✓
Watch out. A new place does not mean a new shape.
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 a reflection does to the size and shape.
- Look at the two triangles. The orange triangle is the blue triangle flipped over the mirror line.flipped
- Check the size. Flipping does not stretch or shrink the shape.same size
- Decide. The shape has not changed size or shape. It faces the other way round.No
Check. A flipped shape has the same size and shape. ✓
Watch out. A flipped shape faces the other way, but it is still the same shape.
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 lengths of the sides.
- Measure the blue side. The bottom side of the blue triangle is 3 squares long.3 squares
- Measure the orange side. The bottom side of the orange triangle is 6 squares long.6 squares
- Decide. Each side is twice as long, so the orange triangle is a bigger shape.Yes
Check. The orange triangle is twice as big, so it has changed. ✓
Watch out. A shape made bigger has changed, so it is not a reflection or a translation.
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. Look at each choice and ask if the size and shape are kept.
- Check A. A slide keeps the size and the shape.A: has not changed
- Check B. A stretch makes the shape wider, so its shape has changed.B: has changed
- Check C. Making a shape twice as big changes its size.C: has changed
- Write the answer. A
Check. Only A keeps the same size and shape. ✓
Watch out. Only a slide or a flip keeps the shape the same.
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. A translation keeps the lengths of the sides the same.
- Look at the blue rectangle. The blue rectangle is 5 squares long and 3 squares high.5 long, 3 high
- Look at the orange rectangle. Sliding it does not change its sides.the same sides
- Write the answer. 5 squares long and 3 squares high
Check. The orange rectangle has the same sides, so 5 and 3 are right. ✓
Watch out. A slide keeps every side the same length.
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 a reflection does to the size.
- Look at Sam. Sam says a reflection changes the size of a shape.Sam: size changes
- Look at Dana. Dana says a reflection does not change the size.Dana: size stays
- Decide. A reflection only flips the shape, so its size stays the same. Dana is right.Dana
Check. A reflection keeps the size and shape, so Dana is right. ✓
Watch out. Flipping does not make a shape bigger or smaller.
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. Add the four sides of the rectangle.
- Write the sides. A rectangle 5 squares by 3 squares has two sides of 5 and two sides of 3.5 + 3 + 5 + 3
- Add them up. The perimeter is all four sides added together.5 + 3 + 5 + 3 = 16
- Write the answer. The translated rectangle has the same sides, so its perimeter is the same.16 squares
Check. 2 × (5 + 3) = 16. ✓
Watch out. A translation keeps the perimeter the same.
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. A reflection keeps every side the same length.
- Write the perimeter of the shape. The shape has a perimeter of 14 squares.14 squares
- Think about the image. Each side of the image is the same length as the side it came from.same sides
- Write the answer. 14 squares
Check. The image has the same sides, so the perimeter is still 14. ✓
Watch out. The perimeter of a reflection is the same as the original.
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. Translating and reflecting both keep the size of the shape.
- Write the area of the shape. The shape covers 9 squares of the grid.9 squares
- Move and flip the shape. A translation and a reflection keep the size of the shape.same size
- Write the answer. 9 squares
Check. The image still covers 9 squares. ✓
Watch out. Moving and flipping a shape does not change how many squares it covers.
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 it means to be the same shape.
- Check Tom. A reflection makes an image with the same size and shape as the original.same size and shape
- Check the difference. The image only faces the other way round.faces the other way
- Decide. So Tom is right: the two shapes are the same, but one is the mirror image of the other.Yes
Check. A shape and its mirror image are the same size and shape. ✓
Watch out. The same shape can face a different way.
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 a translation changes.
- Check the place. The new shape is in a different place on the grid.position changes
- Check the size and shape. The size and shape are the same, because the shape has only slid.size and shape stay
- Decide. Ruby is not right. The shape looks the same, only in a new place.No
Check. Only the position changed. ✓
Watch out. A new place does not change the shape.
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. Count the corners of the original, then the corners of the image.
- Count the corners of the original. The original shape has 6 corners.6 corners
- Count the corners of the image. Each corner of the original has one image, so the image also has 6 corners.6 corners
- Write the answer. 6 corners
Check. A reflection keeps the same number of corners. ✓
Watch out. Every corner has a matching corner in the image.
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. Find the shape that is not like the other two.
- Look at the slide. A slide keeps the size and shape.same size
- Look at the flip. A flip keeps the size and shape.same size
- Look at the bigger shape. A shape made twice as big has a different size.different size
- Write the answer. The bigger shape is the odd one out, because the other two keep the same size and shape.the shape made twice as big
Check. The other two keep the same size and shape. ✓
Watch out. Look at what each move does to the size.