Reflect and translate on the coordinate grid: what children learn
Year 6 pupils draw and translate simple shapes on the coordinate plane and reflect them in the axes.
In this game children match points to where they land after a reflection in the x-axis or y-axis, or a translation. Reflecting in an axis changes the sign of one coordinate, so it is quick once children see the pattern.
This topic covers the Year 6 statutory requirement in the National Curriculum in England (Geometry – position and direction): pupils should be taught to “draw and translate simple shapes on the coordinate plane, and reflect them in the axes”. Year 6 pupils are usually aged 10–11.
For families following US standards, the closest Common Core standard is 6.NS.C.6.b, which is taught in Grade 6.
How to play
Pick a card on the left, then the card on the right that matches it. Each game has 6 pairs. Wrong matches are counted as mistakes, and you get three stars for a game with no mistakes.
Step by step
- Reflect in the y-axis. The point flips left to right. Change the sign of the x-coordinate: (3, −2) becomes (−3, −2).
- Reflect in the x-axis. The point flips top to bottom. Change the sign of the y-coordinate: (−4, 1) becomes (−4, −1).
- Translate. Add or subtract from each coordinate: 5 up adds 5 to the y-coordinate.
- Check on a grid. Sketch the axes and plot the point to check.
Worked examples
Example 1: (3, −2) reflected in the y-axis
Working: Change the sign of x.
Answer: (−3, −2)
Example 2: (−4, 1) reflected in the x-axis
Working: Change the sign of y.
Answer: (−4, −1)
Example 3: (−1, −2) translated 5 up
Working: −2 + 5 = 3.
Answer: (−1, 3)
Common mistakes and how to fix them
- Changing the wrong coordinate. Reflecting in the y-axis flips across the y-axis, which changes x.
- Changing both signs. That is a half turn round the origin, not a reflection.
- Errors adding across zero. Use a number line for translations that cross the axes.
Activities to try at home
- Draw a shape on a four-quadrant grid and reflect it in each axis.
- Fold a grid along an axis and pierce through a point to find its reflection.
- Make a symmetrical pattern in all four quadrants.
Ideas for the classroom
- Pupils reflect a shape in the x-axis and then the y-axis and compare.
- Give a point and its image and ask pupils which axis it was reflected in.
- Combine a translation and a reflection and ask for the final coordinates.
Free printable game and worksheet
The free printable starts with a game sheet, such as a colour-by-answer picture, an answer maze or a secret-code joke, followed by a worksheet. Both use the same checked questions as the online game, and the answers are on the last page. Print it, or save it as a PDF from your browser’s print menu.
Open the free printable game and worksheet
Frequently asked questions
Is reflecting in an axis different from other mirror lines?
No, but the axes make it neat: only the sign of one coordinate changes.
What comes next?
At secondary school, pupils reflect in lines such as y = x and learn rotations and enlargements.
Can it be played with a keyboard?
Yes. Tab to a card, press Enter to pick it, then pick its partner.