Describing Movements

Translation is a slide: every point of a shape moves the same amount left/right and up/down, with size, shape and orientation unchanged. On a first-quadrant coordinate grid, learners describe a move from one position to another ('3 units right'), carry out a two-part translation ('4 right and 2 up') and state new coordinates, and predict an image before plotting. The core procedural insight: a horizontal move changes only the x-coordinate (right adds to x), a vertical move only the y-coordinate (up adds to y). The main errors mirror coordinate errors — reversing the right/up amounts, changing the wrong coordinate, direction/sign slips, off-by-one line counting, and confusing the description of the move with the destination coordinates.

• Reversal — swapping the right and up amounts (applying the horizontal shift to y and the vertical to x).
• Changing the wrong coordinate — altering y for a move described as 'right', or changing both coordinates for a single-direction move.
• Getting the direction sign wrong — moving left when 'right' is stated, or subtracting instead of adding.
• Counting squares rather than numbered lines, giving an off-by-one image position.
• Confusing the description of the MOVE with the destination coordinates (stating where it ends when asked how it moved, or vice versa).

• Coordinate grid showing a start point and its translated image with the slide arrow
• Component decomposition: horizontal move (Δx) then vertical move (Δy)
• Rule form: (x, y) → (x + right, y + up)
• A shape and its translated copy, same size and orientation, every vertex shifted equally
• Number-line counting of the move along each axis from the start position

• Separate the two components explicitly: a rightward move changes only x (add to the first number), an upward move only y (add to the second) — do the horizontal and vertical parts one at a time.
• Describe moves precisely and consistently: 'units right/left and up/down', matching the along-then-up order of coordinates.
• Have children PREDICT the new coordinates by adjusting x and y before plotting, then check by plotting — so the rule is used, not just the picture.
• Stress translation invariance: the shape does not turn, flip, or resize — every vertex shifts by the same amounts; check two vertices moved identically.
• Count moves against numbered lines from the start point, not squares, to avoid off-by-one slips.
• Contrast a horizontal-only move (y unchanged) with a two-part move, so children see when a coordinate should and shouldn't change.