Primary 4 Symmetry Study Guide

Primary 4 symmetry in five short steps: what a line of symmetry is, then symmetric figures, testing folds, shaded grids, and completing figures across a straight or diagonal line. Each step has something to fold or shade, and worked examples follow.

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What is a line of symmetry?

A line of symmetry is a fold line where the two halves fit exactly.

Fold a figure along a straight line. If every part of one half lands exactly on the other half, that fold line is a line of symmetry, and the figure is a symmetric figure.

In this chapter your child learns to:

  • tell whether a figure is symmetric by picturing the fold;
  • test a line, and try every fold, diagonals included;
  • check that shaded squares on a grid land on shaded squares;
  • complete a symmetric figure by counting to the line, then the same again past it.
1

Step 1

Identifying symmetric figures

Symmetric means one fold makes the halves fit exactly. A symmetric figure has at least one line of symmetry. Two halves of the same size are not enough: they must be mirror images, so that every corner and edge lands on another when the figure is folded.

Decide, then watch the fold

A
B
C
D
Decide for each figure: symmetric or not? Then watch the fold check your answer.
Try it

Figure B was cut into two halves of the same size. Why is it not a symmetric figure?

▶ Watch the lesson: Lines of symmetryPractise 17 questions →
2

Step 2

Testing lines of symmetry

Try all four folds, then count the ones that fit. Fold left to right, top to bottom, and along both diagonals. Count only the folds where the halves fit exactly. A rectangle fits from left to right and from top to bottom. Its diagonals cut it into halves of the same size, but the long and short sides do not match.

Pick a fold to test it

Choose a figure

Test a fold

Lines of symmetry: 0

Choose a fold. The left or top half flips over the line. Count the folds that fit.
Try it

A plus sign has four arms of the same length. How many lines of symmetry does it have?

▶ Watch the lesson: Lines of symmetryPractise 17 questions →
3

Step 3

Lines of symmetry on a square grid

The shaded squares must land on shaded squares. On a square grid, the figure is the shaded squares. Fold along each line and check them one at a time. If a single shaded square lands on an unshaded one, that fold is not a line of symmetry.

Tap squares to shade them

Figures

Fold to check

2 of 4 folds fit: diagonal and other diagonal.
Try it

On a 5 by 5 grid, only the middle row is shaded: 5 squares across. How many lines of symmetry does the shaded figure have?

▶ Watch the lesson: Lines of symmetryPractise 17 questions →
4

Step 4

Completing a symmetric figure on a square grid

Count to the line, then the same again past it. Take the shaded squares one at a time. A square that touches the line is 1 square from it, so its partner touches the other side. Stay in the same row when the line runs up and down, and in the same column when it runs across. Shade only squares that have no partner yet.

Shade the partners

Choose a line

Do it

6 shaded squares have no partner yet. Tap a square on the other side of the dashed line to shade it, or press Show me a partner.
Try it

The grid shows half of a symmetric figure, with 7 shaded squares on one side of the dashed line. How many more squares must be shaded to complete the figure?

▶ Watch the lesson: Complete the figurePractise 10 questions →
5

Step 5

Completing a figure across a diagonal line

Across a diagonal, the path turns at the line. When the line runs corner to corner, go along the row to the line, then turn and go the same number of squares down the column. One square left means one square down; two squares up means two squares right. A square the line passes through is its own partner.

Shade the partners

1 pair is already shaded, and the square on the line is its own partner. 3 squares have no partner yet. Tap to shade, or press Show me a partner.
Try it

The dashed line runs from the top left corner of the grid to the bottom right corner. A shaded square is in row 1, column 4. Which square is its partner?

▶ Watch the lesson: Complete the figurePractise 10 questions →

Primary 4 symmetry questions, worked step by stepHave a go at each one first. Then open a hint, or reveal the working line by line.

Lines of symmetryBasic

Some squares on the grid are shaded. Is the dashed line a line of symmetry of the shaded figure?

Fold along the dashed line in your head. Check where each shaded square lands.
  1. Fold along the dashed line. Check the shaded squares row by row.
  2. Row 2: the squares in columns 2 and 3 land on each other.
  3. Row 1: the square in column 2 lands on column 3, which is not shaded.
  4. So not every shaded square lands on a shaded square.
Answer: No. The shaded square in row 1 lands on an unshaded square.
Lines of symmetryBasic

The figure is a rectangle with a square cut out of the middle of its top side. How many lines of symmetry does it have?

Try all four folds: left to right, top to bottom and both diagonals.
  1. Fold left to right. The halves fit exactly, and the cut-out folds onto itself.
  2. Fold top to bottom. The cut-out at the top lands where there is no cut-out, so the halves do not fit.
  3. Neither diagonal fold makes the halves fit exactly.
  4. Lines of symmetry = 1
Answer: 1
Lines of symmetryIntermediate

Some of the squares on the grid are shaded. How many lines of symmetry does the shaded figure have?

Test the corner square in row 1, column 1 first. Where does each fold send it?
  1. Fold left to right. Row 1, column 1 lands on row 1, column 4, which is not shaded.
  2. Fold top to bottom. Row 1, column 1 lands on row 4, column 1, which is not shaded.
  3. Fold along the diagonal from top left to bottom right. Every shaded square lands on a shaded square.
  4. Fold along the other diagonal. Every shaded square lands on a shaded square.
  5. Lines of symmetry = 1 + 1 = 2
Answer: 2
Complete the figureIntermediate

The grid shows part of a symmetric figure. The dashed line is its line of symmetry. Shade the least number of squares to complete the figure. How many squares do you shade?

Go row by row. A square that touches the line has its partner touching the other side.
  1. Row 1: the square touches the line, so shade its partner in row 1, column 4.
  2. Row 2: columns 3 and 4 are already a pair. Column 2 is 2 squares from the line, so shade row 2, column 5.
  3. Row 3: column 1 is 3 squares from the line, so shade row 3, column 6.
  4. Row 4: column 2 is 2 squares from the line, so shade row 4, column 5.
  5. Least number of squares to shade = 1 + 1 + 1 + 1 = 4
Answer: 4 squares: row 1, column 4; row 2, column 5; row 3, column 6; row 4, column 5.
Complete the figureChallenge

The dashed line is a line of symmetry of the completed figure. Shade 3 more squares to complete the figure. Then state how many lines of symmetry the completed figure has.

Across a diagonal, go along the row to the line, then the same number of squares down. Then test all four folds on the finished figure.
  1. Row 1, column 2 and row 2, column 1 are already a pair.
  2. Row 1, column 3: 2 squares left to the line, then 2 squares down. Shade row 3, column 1.
  3. Row 2, column 4: 2 left, then 2 down. Shade row 4, column 2. Row 3, column 4: 1 left, then 1 down. Shade row 4, column 3.
  4. The completed figure is a ring of 8 squares. It fits when folded left to right, top to bottom and along both diagonals.
  5. Lines of symmetry = 1 + 1 + 1 + 1 = 4
Answer: Shade row 3, column 1; row 4, column 2; and row 4, column 3. The completed figure has 4 lines of symmetry.
6

Step 6

Check yourself

Five quick questions on folds and partners. Nothing is saved; your answers point to the practice that helps next.

1. How many lines of symmetry does a square have?

2. A figure is cut into two halves of the same size. Does that make it a symmetric figure?

3. Which capital letter has exactly 2 lines of symmetry?

4. A shaded square is 3 squares to the left of an up-and-down line of symmetry. Where is its partner?

5. The dashed line runs from top left to bottom right. A shaded square's path to the line is 2 squares left. How does the path go on to its partner?

0/5
Answer all five to see where to practise next.
For parents

How to use this guide. Symmetry is about picturing a fold before making it. In each step, ask your child to say which fold will fit, or which square is the partner, before they press the button. Saying the guess first and then watching the fold is what builds the picture in their head. Each step takes two or three minutes.

Paper helps too. Fold a sheet in half, cut a shape along the fold, and open it out: the crease is a line of symmetry. For grid questions, a pencil and squared paper work well. Count to the line out loud, then count the same again on the other side. Then try the worked examples, revealing the working one line at a time.

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Lessons and practice

P4 Symmetry lessons and practice

2 lesson videos and 30 questions across two subtopics, from Basic to Challenge, each with a worked solution.

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