Translation on a coordinate grid

What it does on screen

The board is a coordinate grid with a blue shape on it, the same grid as the Coordinates Grid tool. Along the top you pick one quadrant, two or four. Beside the grid is a small table of every corner's coordinates, before and after, and a Notice card. The line under the grid says the move in words, like "Translated 7 right, 2 up".

There are two boards, picked from the top row.

• Move it. You set the move and the shape goes there.
• Describe the move. Two shapes are already on the grid, and the class works out how one became the other.

Move it

• Pick a shape. A triangle, a rectangle or an L-shape. Plot my own lets you tap grid points to make any shape, and tapping the first point again closes it.
• Drag it to a new start. Grab the shape by its middle and it snaps from point to point.
• Set the move. The arrows in the black bar at the bottom set how far left or right and how far up or down. They read in words, "7 right" and "2 up", not as plus and minus numbers.
• Move. The shape slides to where it lands, drawn in red with a dashed edge, and its corners are labelled A′, B′ and C′.
• Step by step. Corner A hops one square at a time. It goes across first, then up or down, and each hop gets a yellow number as it lands. The first hop is 1, so the start square is never counted. When it arrives the red shape appears.
• Trail and Arrow. Trail keeps the numbered hops on the board. Arrow draws one straight line from A to A′.
• Hide image. The move is set but the answer stays hidden, so the class can point to where they think it lands, or come up and draw it with the pen. Show image brings it back.
• Undo and Clear. Undo steps back one move. Clear takes the red shape away and leaves the blue one where it is (on Plot my own it clears your points too).

It never lets a move take the shape off the grid. If you press an arrow once too often the move stays as it is, and a small note says that is as far as it goes.

Describe the move

This is the reverse question, and the one that turns up in tests. A blue shape and a black shape are on the grid, and the class has to say how the blue one moved to make the black one.

• New pair gives a new shape and a new move. Easy only moves one way, left, right, up or down. Harder moves both ways. Across the axis lands the black shape on the other side of an axis, so the coordinates go from negative to positive or back.
• A star sits on the same corner of both shapes, so everyone counts from the same point. Star a corner moves it to the next corner, which is a good way to show that any corner gives the same answer.
• Count for me hops from star to star, across first and then up or down, the same way as Step by step.
• Reveal fills in the two lilac answer boxes, like "5 right" and "3 down", and draws the arrow. With Answer as Coordinates on, it shows the star's coordinates before and after as well.

How to use it in a lesson

1. Start with Step by step. Set a move, press it, and count the hops out loud together. Then point at the table and ask what happened to the numbers.
2. Let them find the rule. Do two or three more. Cover the Notice card with a sticky note until someone says "the x goes up by 7 every time".
3. Hide the image. Set a new move, press Hide image, then Move. Children come up and put a finger, or the pen, where they think A′ is. Then Show image.
4. Swap to Describe the move. Put a pair up and give them a minute on mini whiteboards. Count for me checks it.
5. Use the pen. Write over the board to ring a corner, mark a count, or have a child draw the image before you show it.

Ideas by year group

• Year 4. One quadrant and Easy pairs. Describe each move as "3 squares right" and keep the counting slow with Step by step.
• Year 4. Plot my own. One child plots a shape, another sets the move, and a third says where corner A will land before anyone presses Move.
• Year 5. Two quadrants and Harder pairs. Ask for the coordinates of every corner after the move before you show the table.
• Year 6. Four quadrants and Across the axis. Moves that cross zero, like (−3, 2) to (4, −1), are where the counting goes wrong, so stop on the axis and count it together.
• Year 6. Hide image, then ask how they could find A′ without counting at all. Someone will get to "add 7 to the x".

The misconceptions it helps with

Counting the starting square. This is the big one. A child puts a finger on the corner, says "1", and ends up a square short. Here the corner has to hop before it gets a number, so 1 is always the first square it lands on.

Counting from one corner and to another. A star on both shapes gives everyone the same corner to count from and to.

Moving one corner and drawing the rest by eye. The image is the same shape, the same way up and the same size. Every corner moves by exactly the same amount, and the table shows it row by row.

Mixing up the order or the direction. It always goes across first, then up or down, the same habit as reading coordinates. Words like "4 left" sit where a minus sign would be, so the direction is never a guess.

Crossing the axis. From −2 to 3 is 5 squares, not 1. Counting the hops across the y-axis one at a time makes that plain to see.

Frequently asked questions