The idea in brief. Count to the line, then count the same again past it. Do it one corner at a time, or one square at a time, and never by eye. And when the line runs corner to corner, counting along a row is not the same as counting down a column: the diagonal swaps them over, so a square three along and one down from the line comes back one along and three down.
Lesson video, with the working
Completing a symmetric figure on a grid
4 min 35 s
The film teaches 2 questions in turn. Each question shows first; its working is written as the film explains it.
The grid below shows some shaded squares and a dashed line. The dashed line is a line of symmetry of the finished figure. Shade the least number of squares so that the figure is symmetric about the dashed line.
Shade only squares with no partner.
First pair: already shaded.
Second row: 1 left, 1 down. Shade.
Third row, left: 2 up, 2 right. Shade.
Third row, right: 1 left, 1 down. Shade.
least number of squares to shade = 1 + 1 + 1 = 3
Ans: 3 unit squares
Example 2
The grid below shows half of a symmetric figure. The dashed line is its line of symmetry. Shade 6 more squares so that the figure is symmetric about the dashed line.
3 squares above. 3 squares below.
2 squares above. 2 squares below.
1 square above. 1 square below.
squares to shade = 1 + 1 + 1 + 1 + 1 + 1 = 6
Ans: 6 unit squares
How to solve it
Take the shaded squares one at a time. Shade only for squares that have no partner yet.
Count to the line, then the same distance beyond it. A partner is on the other side of the line.
For the diagonal, the path turns: 1 square left, then 1 down; or 2 up, then 2 right.
One pair is already shaded. The other three squares need partners, so 1 plus 1 plus 1 is 3.
For a line across the grid, stay in the same column: 3 squares above matches 3 below; 2 above matches 2 below.
Shade the 6 partners. Check by folding along the line to see whether the squares fit exactly.
Count to the line, then match on the other side. A fold checks that the squares fit exactly.
Practice questions with worked solutions
Question 1 is free to try. The other 9 open in the free trial, each with its full working.
Question 1 of 10 · Basic · free to tryThe grid below shows half of a symmetric figure. The dashed line is its line…The grid below shows half of a…
The grid below shows half of a symmetric figure. The dashed line is its line of symmetry. Shade 5 more squares so that the figure is symmetric about the dashed line.
Work it out on paper, then open the working and check your answer against it.
First row: the shaded square touches the line, so it is 1 square from the line. Count 1 square past the line in the same row and shade that square.
Second row: the shaded square is 1 square from the line, so shade the square 1 past the line in that row.
Third row: the shaded square touching the line is 1 square from it, so shade the square 1 past the line in that row.
Third row: the shaded square beside it is 2 squares from the line, so shade the square 2 past the line in that row.
Fourth row: the shaded square is 1 square from the line, so shade the square 1 past the line in that row.
squares to shade = 1 + 1 + 1 + 1 + 1 = 5
Answer: 5 unit squares
For parents
How can I support my child with completing symmetric figures?
The given part of a figure tells your child what must appear across the line of symmetry.
What your child learns here
The given part of a figure tells your child what must appear across the line of symmetry. The Primary 4 syllabus asks children to complete a symmetric figure on a square grid, which means preserving shape and distance while reversing its position across the line. Working from corresponding corners or cells makes the task precise, including when the line is horizontal or sloping.
Locate the specified line of symmetry before completing any outline or shading, and keep the original given part fixed.
Place each matching point on the opposite side at the same perpendicular distance from the line, using the grid to locate it.
For a vertical or horizontal line, count the matching row or column intervals carefully and join corresponding vertices in order.
Check reflected shaded cells and any points lying on the symmetry line, which keep their position when the figure is completed.
Does the answer make sense?
With a vertical symmetry line, a corner three grid intervals to its left must have a partner three intervals to its right on the same row. Your child can check every corner pair that way, then compare the joining edges; one correctly placed corner does not guarantee the rest of the completion.
How to practise these questions
The current completion set uses shaded cells on square grids. Basic questions complete patterns across a vertical or diagonal line. Intermediate work includes a differently sloping line and finding the least extra shading needed across a horizontal line. Challenge questions restrict how many additional cells may be shaded, so your child must account for matching cells already present. Work through the existing shaded cells systematically and locate each partner before adding anything. A partner that is already shaded needs no extra action. Compare the completed pattern with the solution and check the number of newly shaded cells separately from the total shaded area; those are different counts, and the question may ask specifically for the additions.
Questions parents ask
Should my child copy the shape in the same direction? The completed part is a mirror match across the specified line, so its orientation changes. Simply moving the original shape sideways usually does not produce that match. Ask your child to locate individual corresponding corners first, then join them in the same sequence. This helps preserve the figure's relationships without relying on an overall visual guess.
What happens to a point on the line of symmetry? It stays where it is, because its distance from the line is zero. Your child does not need to create another point beside it. In an outline completion, that point can connect the original part to its reflected part. Checking fixed points first can make the structure of the unfinished figure easier to understand.
How does my child handle a sloping symmetry line? The same equal-distance and fold-match rule applies, but measuring sideways across rows may no longer locate the matching point. Your child should follow the orientation of the given line and use the square-grid relationships shown in the solution. After completing the figure, imagining the fold provides a useful check that the added part lies in the correct direction.
