Slides & flips of shapes
Theory
Slides and flips are two ways to move a shape. A slide (translation) moves a shape along without turning it over, and a flip (reflection) turns it over a line to make a mirror image. This Year 3 maths page shows how to tell them apart, how to describe a slide on a grid by counting squares, how to flip a shape across a line, and how a shape and its flip make a symmetrical picture. In the Australian Curriculum and the Victorian Curriculum slides and flips are Year 5 content; in Western Australia they are taught in Year 3. Curriculum: VC2M5SP03 / AC9M5SP03.
A slide moves a shape to a new place. Every part moves the same distance in the same direction, and the shape still faces the same way. The maths word for a slide is a translation.
A flip turns a shape over a line, like a page turning over. The new shape is a mirror image: it faces the other way. The maths word for a flip is a reflection, and the line is the mirror line or fold line.
Slides and flips never change the size or the shape. Only the position changes (and, for a flip, the way it faces). A third move, a turn (rotation), spins a shape about a point.
On a square grid, a slide is described by counting squares: how many left or right, and how many up or down. In a flip, every point ends up the same distance from the mirror line on the other side.
| Move | Maths word | Faces the same way? | Same size and shape? |
|---|---|---|---|
| Slide | Translation | Yes | Yes |
| Flip | Reflection | No, it is a mirror image | Yes |
| Turn | Rotation | It is turned | Yes |
How to describe a slide on a grid
- Pick one corner. Choose a corner of the shape that is easy to see.
- Count across. Count the squares left or right to the same corner of the moved shape.
- Count up or down. Then count the squares up or down. Say both, for example 2 left and 3 up.
- Going back. To undo a slide, move the same number of squares the opposite way (left instead of right, down instead of up).
How to flip a shape across a line
- Measure from the line. For each square or corner, count how far it is from the mirror line.
- Go the same distance across. Mark the matching place the same distance on the other side, in the same row (or column).
- Check the facing. The flipped shape should be a mirror image, facing the other way. Folding along the line would put one shape exactly on the other.
(i) It moves up 2 squares and looks exactly the same.
(ii) It appears on the other side of a dashed line, written back to front.
(i) It moved without turning over, so it is a slide.
(ii) Back to front means it is a mirror image, so it is a flip.
Use the square corner of each triangle.
From \(A\) to \(B\) it moves \(5\) squares to the right and \(1\) square down.
The triangle is still the same way up, so this is a slide: \(5\) right and \(1\) down.
The two squares in the far-left column are in the 3rd column from the line, so they go to the 3rd column on the right of the line, in the same rows.
The other square is in the 2nd column from the line, so it goes to the 2nd column on the right, in the same row.
The flipped L has \(3\) squares and faces the other way.
(i) A glass door opening along its track.
(ii) Your hand seen in a mirror.
(i) The door moves along and keeps facing the same way: a slide.
(ii) A mirror shows a mirror image: a flip.
A flip makes a mirror image, so the new flag points left.
The two flags together make a symmetrical picture. The dashed line is its line of symmetry: folding along it puts one flag exactly on the other.
Common pitfalls
Frequently asked questions
What is the difference between a slide and a flip?
A slide moves a shape along and it still faces the same way. A flip turns the shape over a line, so it becomes a mirror image facing the other way.
Does a flip change the size of a shape?
No. A flip keeps the same size and the same shape. Only the position and the way it faces change.
How do I describe a slide on a grid?
Pick one corner, then count how many squares it moves left or right and how many it moves up or down.
Is a flip the same as a turn?
No. A turn (rotation) spins a shape about a point. A flip turns it over a line and makes a mirror image.
What is a mirror line?
The mirror line is the line a shape is flipped over. The shape and its flip are the same distance from it, on opposite sides, like a fold line.
Where do I see slides and flips?
A sliding door or a train moving along a straight track shows a slide. A reflection in a mirror or in still water shows a flip. Folding a wet paint picture in half makes a flip too.