Repeating Patterns: a week of ready-to-teach maths

Five days of lessons for Year 1 Algebra, the next step toward thinking in patterns. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus cut-out shape and number 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 shape tiles, number 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 repeating unit — the chunk — in shapes and in numbers; Day 2 stamps the unit again to copy and continue a pattern; Day 3 works out what comes next; Day 4 sees that different patterns can share the same skeleton, like AB or ABB; and Day 5 fixes a broken pattern and lets each child make one of their own. It grows out of the patterns children met in Foundation and opens the way to number patterns and skip counting.

Materials for the week (one trip)

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

Dear families

This week in maths, Year 1 explores repeating patterns. We find the chunk that repeats, continue and create patterns with shapes, objects and numbers, and learn to name the repeating unit. This is early algebra: seeing the structure inside a pattern.

Try this at home

• Go on a pattern hunt: stripes on a jumper, tiles on a floor, a fence, a footpath. Point and say the chunk that repeats.
• Make a pattern with spoons and forks, or buttons and pegs, and ask your child what comes next.
• Say a number pattern together — one, two, one, two — and clap the beat of it.
• Start a pattern with two or three kinds of thing and let your child keep it going, then name the unit.

My patterns this week

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

Printed from the free seegongsik Repeating Patterns teaching pack · seegongsik.com/au/y1/algebra/AC9M1A02/pack

Find the chunk

A repeating pattern is built from one small chunk, said again and again. The whole week rests on finding that chunk — the repeating unit — so today we point to it, loop it, and say it aloud, in rows of shapes and in rows of numbers.

We are learning to

• see when a row of shapes or numbers makes a repeating pattern,
• find the chunk that repeats and loop it,
• notice a row that does not repeat.

Success criteria

• I can loop the chunk that repeats.
• I can say the repeating unit out loud.

You need

The shape tiles and the number 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 chunk on the tiles.

Watch for these ideas

• Looping the whole row instead of the smallest chunk that repeats.
• Starting the loop in the middle of the chunk, so it does not rebuild the row.
• Calling a row a pattern when nothing comes back — one, two, three, four is not repeating.

Answers

• Row a unit is circle, triangle. Row b unit is square, square, triangle. Row c unit is 1, 2.
• The pattern to tick is Row 1 (unit circle, circle, square). Row 2 never repeats.
• Own pattern varies: check the same chunk comes back at least twice.

Find the chunk that repeats

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

Which one is not a pattern?

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

Your own pattern

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

Stamp the pattern

A repeating pattern is one unit, stamped again and again. Today children treat the unit like a stamp: they copy a pattern by stamping its unit, then stamp it two more times to keep it going. It is where they first hold the whole unit in mind instead of grabbing any shape.

We are learning to

• find the unit of a pattern and treat it as a stamp,
• copy a pattern by stamping the unit again in the right order,
• continue the pattern by stamping the unit two more times.

Success criteria

• I can copy a pattern by stamping its unit.
• I can continue it by stamping the unit again.

You need

The shape 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 clapping. Start Session B with the tile stamps.

Watch for these ideas

• Copying only the first shape and then improvising the rest.
• Changing the unit partway, so a new stamp appears.
• Copying the right shapes but losing the order.

Answers

• Pattern 1 stamp is circle, square: the whole row is circle, square, circle, square, then two more make circle, square, circle, square again.
• Pattern 2 stamp is triangle, triangle, circle: copy and both extra stamps are triangle, triangle, circle each time.
• Pattern 3 stamp is square, circle: copy and both extra stamps are square, circle each time.

Stamp the pattern

The stamp is the unit that repeats. Copy the pattern, then stamp the unit two more times.

Read it back

Point to each box and say the shape. Does every stamp match the first one?

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 works out the unit first, then asks where the row is up to inside it. Today they do it with shapes and with numbers.

We are learning to

• work out the unit of a pattern,
• say what comes next in shapes and in numbers,
• 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 shape tiles, the number 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 thing they see instead of continuing the whole unit.
• Guessing without working out the unit first.
• Doing only one more when the question asks for two or three.

Answers

• Row a next is square (unit circle, square). Row b next is circle (unit triangle, triangle, circle). Row c next is circle (unit square, circle, circle).
• Number row next two are 2, 3 (unit 2, 3).
• Keep it going: circle, triangle, circle (unit circle, 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.

A number pattern

Work out the unit, then write the next two numbers.

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 skeleton

The deepest idea in this topic: a pattern is its skeleton, not the things in it. The skeleton AB can wear shapes (circle, square), or numbers (1, 2), or a clap and a stamp — and it is still the same pattern. We name skeletons with letters: AB, ABB, ABC.

We are learning to

• name the skeleton of a pattern with letters, like AB or ABB,
• see that different patterns can share the same skeleton,
• make a new pattern on a given skeleton.

Success criteria

• I can name a skeleton like AB or ABB.
• I can show two patterns that share a skeleton.

You need

The shape tiles, the number 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 naming the skeleton; start Session B with new clothes.

Watch for these ideas

• Thinking two patterns are different just because the things in them are different.
• Muddling AB with ABB — missing that ABB has the second thing twice.
• Naming by the shape or number rather than by the skeleton.

Answers

• Row a skeleton AB. Row b skeleton AB. Row c skeleton ABB. Row d skeleton ABC.
• Rows a and b share the skeleton AB (one in shapes, one in numbers).
• Own rows vary: an ABB row goes X, Y, Y (like circle, square, square or 1, 2, 2); an AB number row goes X, Y.

Same skeleton

A skeleton is the shape of a pattern, said in letters: AB, ABB, ABC.

One skeleton, different clothes

All three rows go AB. The clothes change, but the skeleton stays the same.

What is the skeleton?

Write AB, ABB or ABC on the line for each row.

Which two share a skeleton?

Two rows above have the same skeleton. Write the two rows:

Write your own

Here is a skeleton: ABB. Draw a row of shapes that fits it.

Here is a skeleton: AB. Write a row of numbers that fits it.

Fix the line

To fix a broken pattern, a child must hold the unit in mind and check the whole row against it. Today they spot the item that does not fit, fix it, then make a repeating pattern of their own and name its unit. The week ends with a short mini-check.

We are learning to

• work out the unit and check a whole row against it,
• find the item that does not fit and fix it,
• make a repeating pattern of my own and name its unit.

Success criteria

• I can find and fix the mistake in a pattern.
• I can make my own pattern and name its unit.

You need

The shape tiles, the number tiles and the blank strips (cut-out sheets 1 and 2), one set per pair. The worksheet, one per child. 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 find it and fix it; start Session B with the mini-check.

Watch for these ideas

• Fixing to a different unit, so the whole row changes.
• Not checking the whole row, so a second mistake slips past.
• Changing more than one item when only one is wrong.

Answers

• Row a: the wrong one is the 5th (triangle); it should be a circle (unit circle, square).
• Row b: the wrong one is the 5th (circle); it should be a triangle (unit triangle, triangle, circle).
• Number row: the wrong one is the last (3); it should be a 2 (unit 1, 2).
• Own pattern varies: check the unit repeats unbroken and the child names it. Mini-check answers are on the answers-and-marking sheet.

Fix the line

Each row should repeat, but one item is wrong. Say the unit, mark the wrong one, and write the fix.

Now make your own

Draw a repeating pattern in the boxes. Make sure the same unit comes back at least three times.

My unit is: ____________________.

Shape and number tiles

Cut out the tiles. There are three shapes in three colours — a blue circle, a green square and a gold triangle — and number tiles for 1, 2 and 3. Use them to build, copy, continue and fix patterns all week. One set per pair is plenty.

Teacher note: these are the same shapes and numbers 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), build a skeleton (Day 4) or fix and make your own (Day 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: Repeating Patterns

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

1. Draw a loop around the unit that repeats:
2. Draw the next two shapes:
3. What is the repeating unit? Write or draw it.
4. Continue this number pattern. Write the next two numbers.
   1212
5. One shape is wrong. Mark it and write what it should be.

Answers and marking guide

Answers

1. The repeating unit is circle, triangle.
2. Next two are circle, square (unit circle, square).
3. The repeating unit is circle, circle, square.
4. Next two are 1, 2 (unit 1, 2).
5. The wrong one is the last shape (triangle); it should be a circle (unit triangle, circle).

A quick three-level guide

Five questions, four ideas. A child at standard finds the unit, continues a pattern in shapes and numbers, and fixes a broken row.

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 chunk, stamp the pattern, what comes next, same skeleton, and fix the line.