Line and Rotational Symmetry: a week of ready-to-teach maths
Five days of lessons for Year 4 Space. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus cut-out shapes to fold and to turn, a mini-check and every answer.
Start here: five minutes to Monday
- Skim the week at a glance on the next page.
- Print the five days. Each day is two A4 sheets: a plan and a worksheet.
- Print the fold shapes and the turning shapes, one per pair; children cut them out on Days 2 and 3.
- Open the free interactive unit on your board. Every plan tells you which picture to show and which buttons to press.
- Teach straight from the plan. Timings, talk prompts, misconceptions and answers are all on the one page.
No maths background needed
This pack is written for the busy generalist teacher. Each plan explains the idea in plain words, lists the misconceptions children bring, and gives the answers. A line of symmetry folds a shape so that its two halves match exactly. A shape has rotational symmetry when a turn of less than a full turn about its centre lands it exactly on its own outline. Some shapes have both, some one, and some neither.
One day, one lesson
The five lessons fill a week of maths, one lesson of about 50 minutes a day. Run them in order: each day stands on the one before. Every plan marks a split point if your timetable runs two shorter sessions.
Fold it, turn it
Children test symmetry with their hands: they fold a cut-out to look for matching halves, and they turn a cut-out copy on its own outline, with a pencil point at the centre, to count the turns that fit. The interactive unit is the dynamic software of the descriptor: it folds, turns and reflects on the board, and builds a symmetric pattern as children tap.
The week at a glance
One lesson a day for a week. Each day stands on the day before, so run them in order.
| Day | Lesson | Children learn and do | On screen |
|---|---|---|---|
| 1 | Lines of symmetry | Fold shapes and letters to find lines of symmetry, and test lines that look right but are not | Lines of symmetry |
| 2 | Counting the lines | Fold cut-out shapes to count every line of symmetry, from none to six | Counting lines of symmetry |
| 3 | Rotational symmetry | Turn shapes on their outlines and count how many times each fits in a full turn | Rotational symmetry |
| 4 | Completing a reflection | Complete half pictures across a mirror line on a grid, and find a mistake | Completing a reflection |
| 5 | Make it symmetric | Create a pattern with a line of symmetry and one that turns onto itself | Make it symmetric; Self-check quiz |
How the week builds
Day 1 finds lines of symmetry by folding, and Day 2 counts every line a shape has. Day 3 meets the second kind of symmetry, turning. Day 4 uses a mirror line to complete pictures, and Day 5 creates patterns with both kinds of symmetry. It builds on the shapes and their features from Year 3 (AC9M3SP01).
Materials for the week (one trip)
- From the classroom: scissors, coloured pencils, rulers, a few small mirrors if you have them, and this pack printed.
- Optional: tracing paper for turning, and pattern blocks for Day 5.
- Print one per pair: the fold shapes (Day 2) and the turning shapes (Day 3).
Words for the word wall
symmetry, line of symmetry, fold, match, half, mirror line, reflect, reflection, rotational symmetry, turn, full turn, centre, pattern
Dear families
This week in maths, Year 4 learns about symmetry: shapes that fold into two matching halves, and shapes that look the same after part of a turn.
Try this at home
- Fold a paper in half, cut a shape along the fold, and open it. Where is the line of symmetry?
- Look for symmetry in leaves, faces, butterflies, wheels and road signs.
- Which capital letters have a line of symmetry? Which look the same upside down?
- Make a symmetric pattern with buttons or coins on a table, using a ruler as the mirror line.
Symmetry I found this week
Fill one row a day. Write what you found and the kind of symmetry it has.
| Day | What I found | Line, turning or both |
|---|---|---|
| Monday | ||
| Tuesday | ||
| Wednesday | ||
| Thursday | ||
| Friday |
Printed from the free seegongsik Line and Rotational Symmetry teaching pack · seegongsik.com/au/y4/space/AC9M4SP03/pack
Lines of symmetry
A line of symmetry folds a shape so that its two halves match exactly: every point on one side has a partner the same distance away on the other. Children fold paper shapes, draw the lines of symmetry on shapes and letters (some have two, some none), and test dashed lines that look right but are not, such as the diagonal of a rectangle.
We are learning to
- find a line of symmetry by folding,
- draw the lines of symmetry on shapes and letters,
- explain why a line is or is not a line of symmetry.
Success criteria
- I can draw the lines of symmetry on a shape, or say that it has none.
- I can explain why the diagonal of a rectangle is not a line of symmetry.
You need
Scrap paper and scissors, a small mirror if you have one, and a paper rectangle to fold. The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Fold and cut Fold a sheet in half, cut a shape along the fold and open it: the fold is a line of symmetry. Then show the board (see the box). Ask: “Fold a rectangle corner to corner. Do the two halves match?” |
| 30 min | Find the lines Children do Parts A and B, folding a copy or holding a mirror on a line to check. Ask: “The letter H has two lines of symmetry. Which other letters have more than one?” |
| 10 min | My own Children do Part C and swap with a partner, who checks the line. Ask: “How could you check your partner’s line with a mirror?” |
Two half-sessions instead? Split after Part A; start Session B with the dashed lines.
Watch for these ideas
- Thinking any line through the middle is a line of symmetry, such as the diagonal of a rectangle.
- Looking only for lines that go down, and missing lines across.
- Thinking every shape has exactly one line.
Answers
- Part A: 1 1 (down), 2 1 (across), 3 1 (across), 4 none, 5 1 (down), 6 1 (down), 7 none, 8 2 (down and across).
- Part B: 1 no, 2 yes, 3 yes, 4 no, 5 yes, 6 no. The no lines fold one half onto a different shape. Part C: answers vary.
Lines of symmetry
A. Draw every line of symmetry. Write how many lines.
B. Is the dashed line a line of symmetry? Ring yes or no.
C. Draw a picture or a letter with one line of symmetry. Draw the line.
Counting the lines
Some shapes have more than one line of symmetry: a square has four, a rectangle two, an equilateral triangle three and a regular hexagon six. Some have none: a scalene triangle and a parallelogram cannot be folded into matching halves at all. Children cut out the fold shapes, fold each one every way they can, and record its lines.
We are learning to
- count all the lines of symmetry of a shape,
- know the lines of symmetry of common shapes,
- recognise shapes that have no line of symmetry.
Success criteria
- I can fold a shape every way and count its lines of symmetry.
- I can name a shape with no line of symmetry.
You need
The fold shapes (cut-out sheet 1), one per pair, scissors and rulers. The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Count on the board Show the board (see the box). Children hold up fingers for the number of lines. Ask: “A square has 4 lines and a rectangle only 2. What makes the difference?” |
| 30 min | Fold and record Pairs cut out the fold shapes and fold each one every way; children draw the lines in Part A. Ask: “Fold the parallelogram corner to corner. Why do the halves not match?” |
| 10 min | Most and none Children do Parts B and C. Ask: “Which shape had the most lines? Could a shape have even more?” |
Two half-sessions instead? Split after cutting out; start Session B with the folding.
Watch for these ideas
- Counting only the lines through corners, or only the lines through the middles of sides.
- Thinking a parallelogram has two lines because its sides come in pairs.
- Counting the same line twice, once from each end.
Answers
- Part A: 1 square 4, 2 rectangle 2, 3 equilateral triangle 3, 4 isosceles triangle 1, 5 scalene triangle 0, 6 regular hexagon 6, 7 rhombus 2, 8 parallelogram 0.
- Part B: the most is the regular hexagon (6); none: the scalene triangle and the parallelogram. Part C: for one line an isosceles triangle or a kite, for none a scalene triangle; any correct drawing.
Counting the lines
A. Fold your cut-out shapes. Draw every line of symmetry. Write how many.
B. Which shape has the most lines of symmetry? Which have none?
C. Draw a shape with exactly one line of symmetry, and a shape with none.
Rotational symmetry
A shape has rotational symmetry when a turn of less than a full turn about its centre lands it exactly on its own outline. Children turn a cut-out copy on its outline, a pencil point at the centre: a square fits 4 times in a full turn, a parallelogram 2 times, and an arrow only once, which means no rotational symmetry. A parallelogram has turning symmetry but no line of symmetry, so the two kinds are different.
We are learning to
- recognise rotational symmetry by turning a shape,
- count how many times a shape fits onto its outline in a full turn,
- tell line symmetry from rotational symmetry.
Success criteria
- I can say whether a shape has rotational symmetry and how many times it fits in a full turn.
- I can name a shape with one kind of symmetry and not the other.
You need
The turning shapes (cut-out sheet 2), one per pair, scissors and a sharp pencil. The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Turn the pinwheel Show the board (see the box). Children say whether it will look the same before each turn. Ask: “After a quarter turn the pinwheel looks the same. Does every shape?” |
| 30 min | Turn and count Pairs cut out the copies, lay each on its base, hold the centre with a pencil point and turn it all the way round, counting the fits. Then Part A. Ask: “The arrow fits back only after a full turn. Does it have rotational symmetry?” |
| 10 min | Both, one or neither Children do Part B. Ask: “The letter S has no line of symmetry. What symmetry does it have?” |
Two half-sessions instead? Split after turning the cut-outs; start Session B with Part A.
Watch for these ideas
- Counting the full turn as rotational symmetry: every shape fits again after a full turn.
- Turning about a corner instead of the centre.
- Thinking a shape with no line of symmetry has no symmetry at all.
Answers
- Part A: 1 square 4, yes; 2 parallelogram 2, yes; 3 letter S 2, yes; 4 equilateral triangle 3, yes; 5 arrow only 1, no rotational symmetry; 6 pinwheel 4, yes; 7 letter T only 1, no rotational symmetry; 8 regular hexagon 6, yes.
- Part B: letter H both, letter S turning only, letter T line only, letter F neither, kite line only, rectangle both.
Rotational symmetry
A. Turn each shape about its centre dot. How many times does it fit in a full turn?
B. Tick the kinds of symmetry each shape has.
| Shape | Line symmetry | Rotational symmetry |
|---|---|---|
letter H | □ | □ |
letter S | □ | □ |
letter T | □ | □ |
letter F | □ | □ |
kite | □ | □ |
rectangle | □ | □ |
Completing a reflection
Reflecting copies each square to the same distance on the other side of the mirror line, so half a picture can be completed into a symmetric one. A square touching the line has its partner touching the line on the other side; a square two away has its partner two away. Children complete pictures across a mirror line that goes down and one that goes across, then find the square that breaks the symmetry of a finished picture.
We are learning to
- reflect squares across a mirror line on a grid,
- complete a picture so that it is symmetric,
- check a picture for symmetry.
Success criteria
- I can complete a picture so that it is symmetric about the mirror line.
- I can find a square that breaks the symmetry.
You need
Coloured pencils, and a small mirror if you have one. The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Reflect on the board Show the board (see the box). Children point to where each partner goes first. Ask: “This square is two squares from the line. Where does its partner go?” |
| 30 min | Complete the pictures Children do Part A, counting from the line for every square. Ask: “Count the squares from the mirror line, not from the edge of the grid.” |
| 10 min | Spot the mistake Children do Parts B and C, then check one picture with a mirror on the line. Ask: “How did you find the square in the wrong place?” |
Two half-sessions instead? Split after the first two pictures; start Session B with the third.
Watch for these ideas
- Copying the half across instead of reflecting it, so both halves face the same way.
- Counting from the edge of the grid instead of from the mirror line.
- Leaving a gap at the line when a square touches it.
Answers
- Part B: in row 5 from the top, the square on the right is 2 squares from the line but its partner on the left is 3 squares away, so it belongs 1 square further out (column 7 from the left). Part C: answers vary.
Completing a reflection
A. Colour the squares on the other side of the mirror line to complete each picture.
B. One square in this picture is in the wrong place. Circle it.
C. Hold a mirror on the line of one of your pictures. What do you see?
Make it symmetric
Today children use symmetry to create. A pattern with a line of symmetry is made by colouring one side and reflecting it. A pattern with rotational symmetry is made by colouring one quarter and turning it a quarter turn into each of the other quarters. On the board the unit’s tapping grid does the first kind by software: every tap and its reflection appear together.
We are learning to
- create a pattern with a line of symmetry,
- create a pattern that looks the same after a quarter turn,
- describe the symmetry of a pattern.
Success criteria
- I can make a pattern that is symmetric about a mirror line.
- I can make a pattern that looks the same after a quarter turn.
You need
Coloured pencils, and pattern blocks if you have them. The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Tap and reflect Show the board (see the box). Children predict where the second square will appear. Ask: “If I tap this square, where will its partner light up?” |
| 30 min | Make two patterns Children do Parts A and B, then swap and check a partner’s patterns. Ask: “Turn your page a quarter turn. Does your turning pattern still look the same?” |
| 10 min | Class game Run the self-check quiz as a class game. Children do Part C at home. Ask: “Which question was hardest, and why?” |
Two half-sessions instead? Split after Part A; start Session B with the turning pattern.
Watch for these ideas
- Reflecting a square to the same side of the line.
- Turning one quarter the wrong way: check by turning the page a quarter turn.
- Thinking a pattern must fill every square to be symmetric.
Answers
- Part A: patterns vary; every coloured square has a partner the same distance from the line on the other side.
- Part B: patterns vary; turned a quarter turn, the whole pattern looks the same, so it fits 4 times in a full turn. Part C: answers vary.
Make it symmetric
A. A pattern with a line of symmetry
Colour at least six squares on the left of the line. Then colour their reflections on the right.
B. A pattern that turns onto itself
Colour a design in the top-left quarter. Turn it a quarter turn clockwise into the next quarter, and again, and again.
C. Symmetry hunt
Fold shapes
One sheet per pair, for Day 2. Cut out each shape on its dashed line, then fold it every way you can. Every fold that makes the two halves match is a line of symmetry.
Teacher note: square 4, rectangle 2, equilateral triangle 3, isosceles triangle 1, scalene triangle 0, regular hexagon 6, rhombus 2, parallelogram 0.
Turning shapes
One sheet per pair, for Day 3. Keep each base shape on the sheet. Cut out its copy, lay it on the base, push a pencil point through both centre dots, and turn the copy slowly all the way round. Count the times it fits the outline exactly.
Teacher note: equilateral triangle fits 3 times, parallelogram fits 2 times, plus sign fits 4 times, arrow fits 1 time in a full turn; the arrow, fitting only once, has no rotational symmetry.
What we know: Symmetry
- Draw every line of symmetry on this letter.
- How many lines of symmetry does this rectangle have? ____
- Is the dashed line a line of symmetry? Ring yes or no. Why? ________________
- Tick the shapes that have rotational symmetry.A □B □C □
- How many times does an equilateral triangle fit onto its outline in one full turn? ____
- Complete the picture so that it is symmetric about the mirror line.
- Write a capital letter that has no line of symmetry. ____
- Draw a shape with exactly 2 lines of symmetry.
Answers and marking guide
Answers
- 1 line, down the middle of the U.
- 2.
- No: folded on the diagonal, the two halves do not land on each other.
- A (parallelogram) and C (square).
- 3.
- Each square lands as far from the line on the other side.
- Any of F, G, J, L, N, P, Q, R, S and Z (in plain capitals).
- A rectangle, a rhombus or an oval, for example.
A quick three-level guide
| Idea | Working towards | At standard | Beyond |
|---|---|---|---|
| Line symmetry (Q1, Q2, Q3, Q7) | draws a line through the middle whether or not the halves match | finds every line of symmetry, or none, and tests a line by folding | explains why a diagonal is or is not a line of symmetry |
| Rotational symmetry (Q4, Q5) | counts the full turn, or turns about a corner | says whether a shape fits onto itself in part of a turn, and how many times | names shapes with one kind of symmetry and not the other |
| Creating (Q6, Q8) | copies a half across instead of reflecting it | completes a reflection and draws a shape with given symmetry | creates a pattern with both kinds of symmetry |
Eight questions, three ideas. A child at standard finds lines of symmetry and tests them, recognises rotational symmetry by turning, and uses a mirror line to create symmetric pictures.
Weekly class record
Jot a tick as you move around the room; the mini-check fills any gaps. A tick a day is plenty.
| Name | Lines of symmetry | Counts the lines | Rotational symmetry | Completes a reflection | Makes patterns |
|---|---|---|---|---|---|
The five columns are the five days: lines of symmetry, counting the lines, rotational symmetry, reflections, and making patterns.