Symmetry worksheet

Part A: Working out and filling in

1. 1. 3 lines

   Try every fold: upright, flat and slanting. Keep a count of each one where the halves match.

   Try every fold, upright, flat and slanting: 3 of them match exactly.

2. 2. 2 squares

   Go through the shaded squares: each needs a partner on the other side of the line. Count those partners.

   Every shaded square needs a partner on the other side of the line: 2 squares.

3. 3. 1 time

   Try a quarter, a half and three quarters of a turn: do the colours land where they were? Count the return to the start too.

   Try a quarter turn and a half turn, and count the return to the start too: 1 times.

4. 4. 1 time

   The 4 blades are the same shape, but the colours must line up too. First see how the coloured blades are spread.

   The colours must land where they were too: just 1 times in a whole turn.

5. 5. 4 holes

   How many layers does folding once make? Each hole goes through every layer. Then count the holes punched.

   Folded once, the paper has 2 layers and each hole goes through both: 2 × 2 = 4.

Part B: Choose, or true or false

1. 6. A

   Try folding each letter, first on its upright middle line, then on its flat one. Do the halves match?

   Try folding each on its upright and its flat middle line: only this one matches exactly.

2. 7. A. Only an upright one

   Fold on the upright middle first: do left and right match? Then on the flat middle: do top and bottom?

   Folded on the upright middle, left matching right means an upright line; folded on the flat middle, top matching bottom means a flat one.

3. 8. B

   For each flag, try folding on the upright and flat middle lines. Pattern and colours must both match.

   Try a flag's upright and flat middle lines: only this one matches in pattern and colour when folded.

4. 9. D. 1

   Work out what the shape is, then try upright, flat and slanting folds. If it is a circle, think about its diameters.

   Try each fold and count; a circle matches on every diameter, so it has infinitely many.

5. 10. B

   Find all the shape's lines of symmetry yourself first, then check each picture for extra or missing lines.

   Fold on each dashed line: every one must match, and every line that does match must be drawn.

6. 11. A. They match exactly

   The two sides of a line of symmetry are exactly alike. What happens when you fold?

   A line of symmetry splits a shape into two matching halves, so folded along it they match exactly.

7. 12. A

   Find the dashed creases first, then flip each hole across them, one fold at a time.

   Open it one fold at a time: each hole flips across the crease like a mirror image, just as far from it.

Part C: Word problems

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

1. 13. 2 letters

   The reflection turns things upside down. Looking the same that way means a flat line of symmetry. Check each letter.

   Looking the same upside down in the water means a flat line of symmetry: 2 letters have one.

2. 14. 3 flags

   For each flag, try the upright and flat middle lines (and a square flag's diagonals). Shapes and colours must match.

   Try each flag's upright and flat middle lines (and a square flag's diagonals): 3 flags have a line of symmetry.

3. 15. 26 folds

   First think how many lines of symmetry a square sheet has, and how many a rectangular one has.

   A square has 4 lines and a rectangle 2: 5 × 4 + 3 × 2 = 20 + 6 = 26.

4. 16. 6 squares

   First find how many squares are stitched once it is finished (squares on a slanting line need no partner), then take that from all 4 × 4.

   Finished, 10 squares are stitched (a square on a slanting line needs no partner): 16 − 10 = 6.

5. 17. 24 times

   With 4 matching blades, how many times does one whole turn look the same? It turns 6 whole turns.

   Each whole turn looks the same 4 times: 4 × 6 = 24.

6. 18. 12 holes

   Each fold doubles the layers. Work out how many layers 2 folds make first.

   Each fold doubles the layers: 2 folds make 4, so 3 × 4 = 12.