Teaching pack: Transformations and Symmetry (Year 5)

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Teaching pack · Year 5 Spaceseegongsik /au

Transformations and Symmetry: a week of ready-to-teach maths

Five days of lessons for Year 5 Space. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus nine before-and-after cards to sort by the move and twelve shape cards to fold and turn, a mini-check and every answer.

AC9M5SP03

describe and perform translations, reflections and rotations of shapes, using dynamic geometric software where appropriate; recognise what changes and what remains the same, and identify any symmetries

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 move cards once per pair and the shape cards once per child, and find tracing paper (baking paper works).
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. The big idea of the week: a shape can be moved three ways, by a slide (translation), a flip (reflection) or a turn (rotation), and none of them changes its size or shape. A slide changes only where it is; a flip and a turn also change the way it faces. A shape has symmetry when a flip or a turn puts it back exactly on itself.

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.

On the board

This pack is the printable half of a free interactive unit, which is the dynamic geometry tool for the week: its five pictures slide, flip and turn a triangle on a grid at the press of a button, and test shapes for lines of symmetry and turning symmetry. A self-check quiz runs as a class game on Day 5.

seegongsik.com/au/y5/space/AC9M5SP03

Aligned to the Australian Curriculum V9 (AC9M5SP03). This pack is original material from seegongsik, independently produced and not endorsed by ACARA. Curriculum content descriptors are (c) ACARA, licensed under CC BY 4.0. Free to print and use in class.

The week at a glance5 lessons

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	Slide it	Slide shapes across a grid, describe each slide by how far every corner moves, and see what stays the same	Translations slide a shape
2	Flip it	Flip shapes in upright and flat mirror lines, find a mirror line, and see that a flip reverses the way a shape faces	Reflections flip a shape
3	Turn it	Turn shapes a quarter or a half turn about a point with tracing paper, and sort before-and-after cards by the move	Rotations turn a shape
4	Lines of symmetry	Fold twelve shape cards to count their lines of symmetry, and finish pictures across a mirror line	Lines of symmetry
5	Turning symmetry	Turn the shape cards on their outlines to find the order of turning symmetry, sort them both ways, and play the unit quiz	Rotational symmetry

How the week builds

Days 1 to 3 take the three moves one at a time and end with a sort of all three; Days 4 and 5 turn the moves back on a shape itself, as lines of symmetry and turning symmetry. It builds on Year 4’s line and rotational symmetry (AC9M4SP03), and it leads to Year 6, where combined moves make tessellations (AC9M6SP03).

Materials for the week (one trip)

From the classroom: tracing paper or baking paper, scissors, rulers, a small mirror per group if you have them, this pack printed.
Print once per pair: the move cards (Day 3). Print once per child: the shape cards (Days 4 and 5).

Words for the word wall

translation, slide, reflection, flip, mirror line, rotation, turn, centre of rotation, clockwise, anticlockwise, line of symmetry, rotational symmetry, order

A note homeHome practice

Dear families

This week in maths, Year 5 moves shapes in three ways: a slide (translation), a flip (reflection) and a turn (rotation). None of them changes a shape’s size or shape. We also look for symmetry: a shape has a line of symmetry when folding it makes the halves match.

Try this at home

Fold a paper napkin or a leaf in half. Do the halves match?
Look at road signs and window patterns. Which have lines of symmetry? Which look the same after a turn?
Stand beside a mirror and raise your right hand. Which hand does your reflection raise?

Symmetry I spotted this week

Fill one row a day. Write what you saw and how many lines of symmetry it has.

Day	What I saw	Lines of symmetry
Monday
Tuesday
Wednesday
Thursday
Friday

Printed from the free seegongsik Transformations and Symmetry teaching pack · seegongsik.com/au/y5/space/AC9M5SP03/pack

Day 1 · Teacher planDay 1 of 5

Slide it

A translation slides a shape without turning or flipping it. Every corner moves the same distance in the same direction, so one move describes the whole slide, such as 3 right and 1 up: count from a corner to the same corner of the image. The image is the same size and shape and faces the same way; only its position changes.

We are learning to

slide a shape on a grid by a given move,
describe a slide by counting from a corner to the same corner of the image,
say what a slide changes and what it keeps.

Success criteria

I can slide a shape exactly and describe a slide.
I can explain that a slide changes only where a shape is.

You need

A grid on the board (or a grid sheet under a visualiser) and a paper L-shape to slide on it. The worksheet, one per child.

Lesson flow (about 50 minutes)

10 min	Slide the triangle Show the board (see the box). Children say where each corner will land before each press. Ask: “Are all the dotted lines the same length? Why must they be?”
25 min	Slide and describe Model sliding the L 3 right and 1 up, one corner at a time, then joining the corners. Children do Parts A and B. Ask: “Where do you count from: the gap between the shapes, or a corner and its image?”
15 min	What stays the same Children do Part C. Ask: “Could a slide ever make a shape face the other way?”

Two half-sessions instead? Split after Part A; start Session B by describing the slides in Part B.

On the board

Show “Translations slide a shape”: a right-angled triangle on a grid. Press “Right 1” three times and “Up 1” once: dotted lines join each corner to where it lands, all the same length. “Start again” puts it back.

seegongsik.com/au/y5/space/AC9M5SP03

Watch for these ideas

Counting the empty squares between the shapes instead of from a corner to its image.
Moving one corner and redrawing the rest by eye, so the image stretches.
Confusing up with down, or left with right, when describing the slide.

Answers

Part A:
Part B: 5 right and 3 up; 4 left and 1 down. Part C: only its position changes; its size, its side lengths, its angles, the way it faces and its shape stay the same.

Day 1 · Worksheet

Slide it

NameClassDate

A. Slide each shape and draw its image

1. Slide it 5 right and 2 down.

2. Slide it 5 left and 1 down.

B. Describe each slide from the shaded shape to its image

1. It slid ________________________

2. It slid ________________________

C. After a slide, what is the same and what has changed? Tick one box each.

The shape’s...	Same	Changed
its size
its position
its side lengths
its angles
the way it faces
its shape

Day 2 · Teacher planDay 2 of 5

Flip it

A reflection flips a shape over a mirror line. Each corner lands on the other side of the line, the same number of squares away, straight across at right angles to the line. The image is the same size and shape, but it is a mirror image: it faces the other way, as a right hand does in a mirror.

We are learning to

flip a shape in an upright or a flat mirror line on a grid,
find the mirror line between a shape and its image,
say what a flip changes and what it keeps.

Success criteria

I can flip a shape by counting each corner’s squares to the mirror line.
I can find the mirror line between a shape and its image.

You need

A small mirror per group if you have them, or tracing paper. The paper L from Day 1. The worksheet, one per child.

Lesson flow (about 50 minutes)

10 min	Choose a mirror line Show the board (see the box). Children point to where the image will land before each press. Ask: “Count from the square corner to the line, then from the line to its image. What do you notice?”
25 min	Flip and check Model flipping the L in an upright line, one corner at a time, then stand a mirror on the line to check. Children do Part A and check with a mirror or by folding along the line. Ask: “The image faces the other way. Could a slide have made it?”
15 min	Find the mirror Children do Parts B and C. Ask: “With only the two shapes, how can you find where the mirror line must be?”

Two half-sessions instead? Split after Part A; start Session B with the hidden mirror in Part B.

On the board

Show “Reflections flip a shape”: a triangle beside two dashed mirror lines. Press “Flip over the upright line”: the image lands on the other side, each corner the same number of squares away. Then press “Flip over the flat line”. “Start again” clears it.

seegongsik.com/au/y5/space/AC9M5SP03

Watch for these ideas

Sliding the shape across the line instead of flipping it, so it still faces the same way.
Counting from the edge of the grid instead of from the mirror line.
Drawing the image against the line when the shape sits a gap away from it.

Answers

Part A:
(the flag hangs upside down, its pennant still to the right)
Part B: the upright line through 4, halfway between each corner and its image. Part C: 1. 3 squares to the right of the line. 2. the way it faces and its position changed; its size and its side lengths stayed the same.

Day 2 · Worksheet

Flip it

NameClassDate

A. Flip each shape in the dashed mirror line

1. An upright mirror line

2. A flat mirror line

B. Where is the mirror line?

The outlined shape is the shaded one flipped in an upright mirror line. Draw the line.
It is on the number ______

C. Think about flips

1. A corner is 3 squares to the left of an upright mirror line. Where is its image?

2. When you flipped the triangle in A1, what changed? Tick one box each.

The shape’s...	Same	Changed
its size
the way it faces
its side lengths
its position

Day 3 · Teacher planDay 3 of 5

Turn it

A rotation turns a shape about a fixed point, the centre of rotation, which stays still. A quarter turn is 90° and a half turn 180°, clockwise or anticlockwise. With tracing paper: trace the shape and the dot, hold a pencil point on the dot, turn the paper, then press through at the corners. The image is the same size and shape but faces a new way.

We are learning to

turn a shape a quarter or a half turn about a point,
name a turn by its size and direction,
tell a slide, a flip and a turn apart.

Success criteria

I can turn a shape about a point with tracing paper.
I can say which move made an image.

You need

Tracing paper (or baking paper) and a sharp pencil. The Which move? cards (cut-out sheet 1), one set per pair, cut out. The worksheet, one per child.

Lesson flow (about 50 minutes)

10 min	Quarter turns Show the board (see the box). Children sketch the next position in the air before each press. Ask: “Which point never moves? Where is the triangle after four quarter turns?”
25 min	Turn with tracing paper Model a quarter turn clockwise of the paper L about its bottom-left corner, with tracing paper. Children do Parts A and B. Ask: “On paper lying flat, which way is clockwise? How do you check?”
15 min	Which move? Pairs sort the nine cards into slides, flips and turns, then fill Part C. Ask: “Which card was hardest to sort? What settled it?”

Two half-sessions instead? Split after Part A; start Session B with Part B and the card sort.

On the board

Show “Rotations turn a shape”: a triangle with a dot at its square corner. Press “Quarter turn clockwise”: it turns 90° about the dot; press again for 180°, 270° and a full turn of 360°. “Start again” brings it back.

seegongsik.com/au/y5/space/AC9M5SP03

Watch for these ideas

Turning about the middle of the shape instead of about the dot.
Turning anticlockwise for clockwise. Clockwise is the way a clock’s hands go.
Sorting a turn as a flip because the image faces a new way. Tracing paper turned, not flipped over, fits a turn.

Answers

Part A:
Part B: a quarter turn anticlockwise.
Part C: slides 2, 6, 9; flips 3, 4, 8; turns 1, 5, 7. Flips and turns change the way the shape faces; slides do not.

Day 3 · Worksheet

Turn it

NameClassDate

A. Turn each shape about the dot. Use tracing paper.

1. Turn it a quarter turn clockwise.

2. Turn it a half turn.

B. Which turn made the outlined image? Circle one.

a quarter turn clockwise

a half turn

a quarter turn anticlockwise

C. Which move? Sort the cards, then write their numbers.

Slide	Flip	Turn

Which moves change the way a shape faces? ______________________

Day 4 · Teacher planDay 4 of 5

Lines of symmetry

A line of symmetry is a mirror line that flips a shape back onto itself: fold along it and the two halves match exactly. A shape can have none, one or many. A rectangle has two, through the middles of its sides; its diagonals are not lines of symmetry, because folding along one leaves two corners sticking out.

We are learning to

find the lines of symmetry of a shape by folding,
use a mirror line to finish a symmetric picture,
see a line of symmetry as a flip that puts a shape back on itself.

Success criteria

I can find every line of symmetry of a shape card.
I can finish a picture so that it is symmetric about a line.

You need

The shape cards (cut-out sheet 2), one set per child, cut out. A sheet of A4 paper. Mirrors if you have them. The worksheet.

Lesson flow (about 50 minutes)

10 min	How many lines? Show the board (see the box). Children choose before you press. Ask: “Is a diagonal of the rectangle a line of symmetry? How could we test it?”
25 min	Fold the cards Model with an A4 sheet: fold it in half both ways and the halves match; fold it along a diagonal and they do not. Children fold each card and fill Part A. Ask: “Look at the regular shapes. How many lines does each one have? What do you notice?”
15 min	Finish the picture Children do Parts B and C. Ask: “How can a mirror stood on the line check your picture?”

Two half-sessions instead? Split after Part A; start Session B with the pictures in Part B.

On the board

Show “Lines of symmetry”: a square with the buttons 2, 4 and 1. A right answer draws the dashed lines of symmetry. “New shape” brings a rectangle, then an equilateral triangle.

seegongsik.com/au/y5/space/AC9M5SP03

Watch for these ideas

Counting the diagonals of a rectangle or a parallelogram as lines of symmetry.
Missing the slanted lines of a regular shape. Turn the card and fold again.
Copying the half beside the line in Part B instead of flipping it.

Answers

Part A: A 4, B 8, C 3, D 1, E 0, F 0, G 2, H 1, I 6, J 1, K 0, L 5. A regular shape has as many lines as sides.
Part B:
Part C: shapes vary, such as a kite or an isosceles triangle.

Day 4 · Worksheet

Lines of symmetry

NameClassDate

A. Fold each shape card. How many lines of symmetry does it have?

Card	A	B	C	D	E	F
Lines of symmetry

Card	G	H	I	J	K	L
Lines of symmetry

B. Finish each picture so that the dashed line is a line of symmetry

C. Draw a shape with exactly one line of symmetry. Mark the line.

Day 5 · Teacher planDay 5 of 5

Turning symmetry

A shape has turning (rotational) symmetry when it fits its own outline after less than a full turn about its centre. Its order is how many times it fits in one full turn, the full turn included: a rectangle fits twice, so its order is 2. A shape that fits only after the full turn has order 1, no turning symmetry. Line and turning symmetry are separate: a shape can have either without the other.

We are learning to

find the order of turning symmetry of a shape,
sort shapes by line symmetry and turning symmetry,
use what we know about slides, flips and turns in the unit quiz.

Success criteria

I can find the order of turning symmetry by turning a card on its outline.
I can sort shapes by both kinds of symmetry.

You need

The shape cards from Day 4 and a sheet of A4 paper. Scrap paper to trace on. The worksheet, one per child.

Lesson flow (about 50 minutes)

10 min	How many fits? Show the board (see the box). Children choose before you press. Ask: “Why does the full turn count as one of the fits?”
25 min	Turn the cards Model with an A4 sheet: trace round it, mark a top corner, and turn the sheet on its outline, counting the fits in one full turn. Children trace each card, turn it on its outline and do Parts A and B. Ask: “Does a shape with more lines of symmetry always have a higher order? Check the cards.”
15 min	Last card and quiz Children do Part C. Then run the unit’s self-check quiz as a class game, teams showing answers on mini whiteboards. Ask: “Which question split the class? Who can convince the others?”

Two half-sessions instead? Split after Part A; start Session B with the sort in Part B.

On the board

Show “Rotational symmetry”: a square with a dot at its centre and the buttons 2, 4 and 1. A right answer shows “order 4”. “New shape” brings an equilateral triangle, then a rectangle.

seegongsik.com/au/y5/space/AC9M5SP03

Watch for these ideas

Counting the start and the full turn as two fits. They are the same position.
Turning the card about a corner instead of about its centre.
Thinking a shape needs a line of symmetry to have turning symmetry.

Answers

Part A: A 4, B 8, C 3, D 1, E 1, F 2, G 2, H 1, I 6, J 1, K 2, L 5.
Part B: lines yes and turning yes: A, B, C, G, I, L; lines yes and turning no: D, H, J; lines no and turning yes: F, K; lines no and turning no: E. Part C: F, K; drawings vary.

Day 5 · Worksheet

Turning symmetry

NameClassDate

A. Trace each card, then turn it on its outline. How many times does it fit in one full turn?

Card	A	B	C	D	E	F
Order

Card	G	H	I	J	K	L
Order

B. Sort the cards. Write each letter in one box.

Use your Day 4 sheet for the lines of symmetry. Turning symmetry means an order of 2 or more.

	Has turning symmetry	No turning symmetry
Has a line of symmetry
No line of symmetry

C. Turning symmetry but no line of symmetry

Which cards have turning symmetry but no line of symmetry? __________ Draw one more shape like them.

Cut-out cards 1 of 2Which move?

Which move? cards

One set per pair (Day 3). Each card shows a shaded shape and its image after one move: a slide, a flip or a turn. Cut them out and sort them into three piles.

1Which move?

2Which move?

3Which move?

4Which move?

5Which move?

6Which move?

7Which move?

8Which move?

9Which move?

Teacher note: no card shows its mirror line or centre of turning; tracing paper settles any argument.

Cut-out cards 2 of 2Shape cards

Shape cards

One set per child (Days 4 and 5). Cut along the dashed lines. Keep the cards for both days.

square

regular octagon

equilateral triangle

isosceles triangle

right-angled triangle

parallelogram

rhombus

kite

regular hexagon

isosceles trapezium

step shape

regular pentagon

Teacher note: fold a card to test a line of symmetry; trace its outline and turn it on top to test turning symmetry.

Mini-check · End of the weekTransformations and Symmetry

What we know: Transformations and Symmetry

NameClassDate

Work on your own. You may use tracing paper.

Describe the slide from the shaded shape to its image. ______________
Flip the shape in the dashed mirror line.
Turn the flag a quarter turn clockwise about the dot.
Name each move: a slide, a flip or a turn.
a. __________
b. __________
c. __________
After any slide, flip or turn, which stay the same? Circle them.
sizepositionshapeanglesthe way it facesside lengths
How many lines of symmetry does this shape have? ______
What is the order of turning symmetry of this shape? ______
Finish the picture so that the dashed line is a line of symmetry.

How did this week feel? Circle one: I can teach it · I am getting there · I need more help

Mini-check · Answers and markingFor the teacher

Answers and marking guide

Answers

5 right and 2 up
a. a flip; b. a turn; c. a slide
size, shape, angles and side lengths
1
4 (it also has 4 lines of symmetry)

A quick three-level guide

Idea	Working towards	At standard	Beyond
Slides and flips (Q1, Q2, Q8)	counts the gap between shapes, or slides instead of flipping	slides, flips and describes on a grid	finds a mirror line from a shape and its image
Turns (Q3)	turns about the wrong point	turns a shape a quarter or a half turn with tracing paper	turns without tracing paper
Naming moves (Q4, Q5)	mixes up flips and turns	names each move and what it keeps	explains why only a slide keeps the way a shape faces
Symmetry (Q6, Q7)	counts diagonals as lines of symmetry	finds lines of symmetry and the order of turning symmetry	links a regular shape to its number of lines

Eight questions, four ideas. A child at standard answers most questions and can say why, by following each corner of a shape to its image and by testing a shape against its own outline.

Weekly recordClass checklist

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	Slides	Flips	Turns	Lines of symmetry	Turning symmetry

The five columns are the five days: slides, flips, turns, lines of symmetry and turning symmetry.