Patterns That Repeat: a week of ready-to-teach maths

Five days of lessons for Foundation Algebra, the first step toward algebra. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus cut-out tiles, a mini-check and every answer.

Start here: five minutes to Monday

1. Skim the week at a glance on the next page.
2. Print the five days. Each day is two A4 sheets: a plan and a worksheet.
3. Cut out the two card sheets once; the tiles and strips are reused all week.
4. Open the free interactive unit on your board. Every plan tells you which picture to show and when.
5. 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 model answers, so you can walk in and teach it.

One day, one lesson

The five lessons fill a week of maths, one short lesson of about 40 minutes a day. Run them in order: each day stands on the one before. Every lesson can also split into a carpet warm-up and a table task if your timetable runs small blocks.

The week at a glance

One short lesson a day for a week. Each day stands on the day before, so run them in order.

How the week builds

Day 1 finds the part that repeats; Day 2 copies a pattern; Day 3 continues one; Day 4 shows that the same pattern can wear colours, shapes or sounds; and Day 5 lets each child make their own. It grows out of the patterns children already know — the days of the week, the beat of a song — and it opens the way to repeating patterns with numbers in Year 1.

Materials for the week (one trip)

• From the classroom: scissors, pencils or crayons, this pack printed.
• From the collage box: anything that comes in two or three kinds — buttons, bottle tops, leaves, pegs — to build patterns with hands before pencils.
• Cut out once, use all week: the pattern tiles and the blank strips in this pack. No maths equipment to buy.

Dear families

This week in maths, Foundation explores patterns that repeat. We find the part that repeats, copy patterns, work out what comes next, and see that the same pattern can be shown in different ways. This is the very first step toward algebra.

Try this at home

• Go on a pattern hunt: stripes on a jumper, tiles on a floor, a fence, a footpath. Point and say it aloud.
• Make a pattern with spoons and forks, or socks and shoes, and ask your child what comes next.
• Clap a pattern — loud, soft, soft — and have your child clap it back.
• Start a pattern with two kinds of thing and let your child keep it going.

My patterns this week

Fill one row a day. Tick when you have found a pattern and made one.

Printed from the free seegongsik Patterns That Repeat teaching pack · seegongsik.com/au/foundation/algebra/AC9MFA01/pack

Find the repeat

Children learn that a repeating pattern is built from one small part, said again and again. The whole week rests on finding that part — the unit — so today we point to it and say it aloud.

We are learning to

• see when a row of things makes a repeating pattern,
• find the part that repeats and say it,
• notice a row that does not repeat.

Success criteria

• I can point to the part that repeats.
• I can say the repeating part out loud.

You need

The pattern tiles (cut-out sheet 1), one set per pair. The worksheet, one per child. A few things from the collage box that come in two kinds, to lay a pattern on the carpet.

Lesson flow (about 40 minutes)

Two half-sessions instead? End Session A after the carpet chant. Start Session B by looping the unit on the tiles.

Watch for these ideas

• Looping the whole row instead of the smallest part that repeats.
• Calling a row a pattern when nothing comes back — red, blue, green, yellow is not repeating.
• Starting the loop in the middle of the unit, so it does not rebuild the row.

Answers

• Row a repeats circle, triangle. Row b repeats square, square, triangle. Row c repeats circle, square, triangle.
• The not-a-pattern row is the one where nothing comes back.
• Own pattern varies: check the same part comes back at least twice.

Find the part that repeats

Each row is a repeating pattern. Draw a loop around the smallest part that repeats.

Which one is not a pattern?

One row keeps saying the same part. One row never repeats. Tick the pattern.

Your own pattern

Choose two shapes and draw a repeating pattern in the boxes.

Copy a pattern

Copying a pattern means rebuilding the same unit yourself, in the same order, beside the model. It sounds easy, yet it is where children first practise holding the whole unit in mind instead of grabbing any shape.

We are learning to

• look at a pattern and find its unit,
• copy the pattern shape by shape in the right order,
• check my copy matches the model.

Success criteria

• I can copy a pattern in the same order.
• I can check my copy against the model.

You need

The pattern tiles (cut-out sheet 1) and the blank strips (cut-out sheet 2), one set per pair. The worksheet, one per child.

Lesson flow (about 40 minutes)

Two half-sessions instead? End Session A after the clapping. Start Session B with the tile copies.

Watch for these ideas

• Copying the right shapes but losing the order.
• Stopping partway through the unit, so the copy is shorter than the model.
• Matching only the first shape and then improvising the rest.

Answers

• Pattern 1 copy: circle, square, circle, square, circle, square.
• Pattern 2 copy: triangle, triangle, circle, triangle, triangle, circle.
• Pattern 3 copy: square, circle, triangle, square, circle, triangle.

Copy the pattern

The top row is the model. Draw the same pattern in the empty boxes below it.

Read it back

Point to each box and say the shape. Does your copy match the model, box for box?

What comes next

Continuing a pattern is a small act of prediction, and it is where the algebra hides. To say what comes next, a child holds the unit in mind and asks where the row is up to inside it.

We are learning to

• work out the unit of a pattern,
• say what comes next,
• keep a pattern going for two or three more.

Success criteria

• I can say what comes next in a pattern.
• I can say why, by naming the unit.

You need

The pattern tiles and the blank strips (cut-out sheets 1 and 2), one set per pair. The worksheet, one per child.

Lesson flow (about 40 minutes)

Two half-sessions instead? End Session A after the first next-tile task; start Session B with keeping it going.

Watch for these ideas

• Repeating the last shape they see instead of continuing the whole unit.
• Losing the place inside the unit, so the pattern jumps.
• Guessing without saying the unit first.

Answers

• Row a next is square (unit circle, square). Row b next is circle (unit triangle, circle, circle). Row c next is triangle (unit square, triangle, triangle).
• Two more: a square then circle; b then triangle then circle; c then square then triangle.
• Own pattern varies: check each next tile continues the unit.

What comes next

Say the unit, then draw the shape that comes next in the empty box.

Keep it going

Draw the next three shapes to keep this pattern going.

Your own pattern

Start a pattern in the first three boxes, then keep it going in the rest.

Same pattern, new clothes

The deepest idea in this topic: a pattern is its structure, not the things in it. The pattern A, B, B can wear shapes, or two colours, or a loud clap and a soft tap — and it is still the same pattern.

We are learning to

• see that one pattern can be shown in different ways,
• match a pattern of sounds to a pattern of shapes,
• show the same pattern with new clothes.

Success criteria

• I can show one pattern two ways.
• I can say why they are the same pattern.

You need

The pattern tiles and the blank strips (cut-out sheets 1 and 2), one set per pair. The worksheet, one per child. Crayons in two colours.

Lesson flow (about 40 minutes)

Two half-sessions instead? End Session A after clap it, build it; start Session B with new clothes.

Watch for these ideas

• Thinking two patterns are different just because the things in them are different.
• Matching by the colour or shape rather than by the structure.
• Hearing loud, soft, soft but building loud, soft only.

Answers

• The claps CLAP, tap, tap go A, B, B, the same as circle, square, square and blue, yellow, yellow.
• The matching shape row is the one that goes A, B, B.
• Own three ways vary: check each row keeps the same A, B, B structure.

Same pattern, new clothes

This pattern goes A, B, B. Here it is three ways. Fill the missing clothes.

Sounds to shapes

Here is a clap pattern. Draw it with shapes below.

Colours to shapes

Here is a colour pattern. Draw it with shapes below.

Shapes to colours

Here is a shape pattern. Colour the circles below to match, using two colours.

They are all the same

Every row goes A, B, B. The clothes change, but the pattern stays the same.

Make your own (the footy scarf)

A team scarf repeats the same band of colours along its whole length. Today children choose a unit — two colours or three — and repeat it to make a scarf of their own. The week ends with a short mini-check.

We are learning to

• choose a unit of two or three,
• repeat the unit to make a pattern,
• check my pattern really repeats.

Success criteria

• I can make my own repeating pattern.
• I can point to my unit and show it repeat.

You need

The pattern tiles and the blank strips (cut-out sheets 1 and 2), one set per pair. The worksheet, one per child. Crayons. The mini-check (back of the pack) for the last few minutes.

Lesson flow (about 40 minutes)

Two half-sessions instead? End Session A after the scarves; start Session B with the mini-check.

Watch for these ideas

• Colouring at random, so no band comes back.
• Starting a repeat but changing the band partway.
• Making the unit but stopping after one band, so nothing repeats.

Answers

• Scarves vary: check the same band of colours repeats along the whole scarf.
• A good scarf shows the unit at least three times, unbroken.
• Mini-check answers are on the answers-and-marking sheet.

Make your own footy scarf

A scarf that repeats

This scarf repeats a band of two colours: navy, gold, navy, gold.

A longer band

This scarf repeats a band of three colours: navy, gold, green.

Now make your own

Choose a band of two or three colours. Colour it again and again down the whole scarf.

My unit is: ____________________. It repeats ____ times.

Pattern tiles

Cut out the tiles. There are three shapes in three colours: a blue circle, a green square and a gold triangle. Use them to build, copy and continue patterns all week. One set per pair is plenty.

Teacher note: these are the same three shapes and colours the children see on screen, so the tiles on the table and the pictures on the board tell one story.

Blank pattern strips

Cut out the strips. Lay tiles along a strip to copy a pattern (Day 2), continue one (Day 3) or make your own (Days 4 and 5). Each strip has eight boxes.

Teacher note: line up the model strip above an empty strip so children can match box for box as they copy.

What we know: Patterns That Repeat

Work on your own. Point and say the pattern if it helps.

1. Draw a loop around the part that repeats:
2. One row is a pattern and one is not. Tick the pattern.
   A:
   B:
3. Copy this pattern in the empty boxes:
4. Draw what comes next:
5. Draw what comes next:
6. Draw the next two:
7. These claps go CLAP, CLAP, tap. Draw them with shapes:
8. Make your own repeating pattern:

Answers and marking guide

Answers

1. The repeating part is circle, circle, triangle.
2. Tick Row A (square, circle over and over). Row B never repeats.
3. Copy: circle, triangle, square, circle, triangle, square.
4. Next is a circle (unit square, square, circle).
5. Next is a triangle (unit circle, square, triangle).
6. Next two are triangle then circle (unit triangle, circle).
7. Shapes go A, A, B, for example circle, circle, square: the same beat as CLAP, CLAP, tap.
8. Own pattern varies: check the same unit comes back at least twice.

A quick three-level guide

Eight questions, four ideas. A child at standard finds the unit, copies and continues a pattern, and can say the repeating part aloud.

Weekly class record

Jot a tick as you move around the room; the mini-check fills any gaps. A tick a day is plenty.

The five columns are the five days: find the unit, copy, continue, one pattern in new clothes, and make your own.