Translating and reflecting shapes

Year 6 pupils learn to translate shapes on a four-quadrant coordinate grid (adding/subtracting signed amounts to matching coordinates) and to reflect shapes in the x- or y-axis by negating exactly one coordinate. The goal is to DERIVE the sign rules from geometry — points move perpendicular to the mirror axis, so the coordinate measuring distance from that axis flips sign while the other stays — rather than memorise a swap. Core errors: changing the wrong coordinate (reflecting in the wrong axis), sliding instead of reflecting (no reversal), wrong translation signs for left/down moves, and reversing the ordered pair.

• Reflecting in the x-axis but changing the sign of the WRONG coordinate (negating x instead of y), effectively reflecting in the other axis.
• Reflecting by sliding/translating the shape rather than reflecting it, so the image is not reversed.
• Getting the translation sign wrong — adding when the move is left or down instead of subtracting.
• Reversing the coordinate pair (writing the y-value before the x-value) when stating image vertices.

• Four-quadrant coordinate grid with the x- and y-axes as mirror lines
• Coordinate mapping notation: translation (x, y) → (x+a, y+b); reflection in x-axis (x, y) → (x, −y); in y-axis (x, y) → (−x, y)
• Real mirror / Mira placed on an axis to check the image, as a scaffold
• Paired worked example showing the same vertex reflected in each axis to contrast which coordinate changes

• Derive the sign rules from the geometry, not memorised swaps: reflecting in the x-axis flips the shape VERTICALLY, so the vertical (y) coordinate changes sign and x stays; reflecting in the y-axis flips it HORIZONTALLY, so x changes sign and y stays.
• Tie the rule to equal distance: the image is the same distance from the axis as the original, on the opposite side — (x, y) and (x, −y) are both |y| from the x-axis (Oak National Academy).
• Explicitly separate the two axis rules with worked pairs — e.g. (−4, 1) reflects to (4, 1) in the y-axis but to (−4, −1) in the x-axis — so pupils feel which single coordinate changes each time (Oak).
• Confront reflection-as-translation head-on with examples and non-examples: a slid shape keeps its orientation, a reflected shape is reversed; use real mirrors as a scaffold, then move to reasoning with coordinates (Oak).
• For translation, treat each direction as a signed change to the matching coordinate — '2 down' subtracts 2 from y — and have pupils PREDICT image coordinates before plotting.
• Avoid 'straight across/down' language; say points move perpendicular to the mirror line, so the correct coordinate change is understood rather than transposed (NCETM KS3 6.3).