Growing and shrinking patterns: a week of ready-to-teach maths

Five days of lessons for Year 2 Algebra. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus cut-out cards, 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; they 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 lesson of about 50 minutes a day. Run them in order: each day stands on the one before. Every lesson can also split into a short warm-up and a main session if your timetable runs small blocks.

The week at a glance

One 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 a growing pattern in objects and keeps it going; Day 2 turns it around and counts down; Day 3 names the constant jump and tests that one rule fits; Day 4 uses the jump to repair a missing number; and Day 5 lets children build patterns of their own. It builds on skip-counting and repeating patterns from Year 1, and it opens the way to describing number rules in later years.

Materials for the week (one trip)

• From the classroom: scissors, pencils, this pack printed.
• From home or the craft box: a handful of counters — dried pasta, buttons, bottle caps or blocks — to build growing and shrinking stacks.
• Cut out once, use all week: the number cards, jump cards, shape-pattern tiles, step strips and what-comes-next cards in this pack. No maths equipment to buy.

Dear families

This week in maths, Year 2 explores growing and shrinking patterns. We find the jump that repeats, keep patterns going, count them down, repair a missing number, and make patterns of our own with numbers, shapes and objects.

Try this at home

• Spot a growing pattern out and about: house numbers on one side of the street, seats in a row, the twos on a scoreboard. Say the jump.
• Count down together by the same jump: 20, 17, 14 and on. How low can you go?
• Lay out spoons or blocks in a growing pattern and ask what comes next, and how they know.
• Hide one number in a short pattern with your finger and let your child work it out.

My patterns this week

Fill one row a day. Tick when you have said the jump and found what comes next.

Printed from the free seegongsik Growing and Shrinking Patterns teaching pack · seegongsik.com/au/y2/algebra/AC9M2A01/pack

Patterns that grow

A pattern keeps one promise: the same jump, every time. Today children spot a growing pattern in objects, keep it going, and say the jump in their own words. Objects come first all week, because a jump you can stack is a jump you believe.

We are learning to

• spot a growing pattern made of objects,
• find the jump that repeats and keep the pattern going,
• say where a pattern starts and how it jumps.

Success criteria

• I can write the next few numbers in a growing pattern.
• I can say the jump that made it.

You need

A handful of counters — dried pasta, buttons or blocks — to build growing stacks. The shape-pattern tiles and number cards (cut-out sheets 1 and 2), one set per pair. The what-comes-next cards for early finishers. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? End Session A after the staircase. Start Session B by rebuilding 3, 7, 11 from memory, then keep it going.

Watch for these ideas

• Adding a different amount each time and still calling it a pattern: the jump must be the same every time.
• Continuing by copying the last number instead of adding the jump on.
• Counting every object again each step, instead of adding the constant jump to the last total.

Answers

• 6, 9, 12, 15, 18, 21 (the jump is +3).
• Row 4 has 8 dots; the rows grow by 2, so the drawing shows eight dots.
• The tower blocks are 4, 7, 10, 13, 16 (three more each time), and the jump is +3.

Grow the pattern

Each pattern grows by the same jump. Find the jump, then keep it going.

Keep it going

Write the next three numbers. 6, 9, 12, ____, ____, ____

Growing dots

These dot rows grow by the same jump: 2 dots, 4 dots, 6 dots. Row 4 has ____ dots.

Fill the tower table

Each tower has 3 more blocks than the one before. Fill in the blocks.

Name the jump

The tower jump is + ____

Patterns that shrink

A pattern can go down as well as up. Today children count back by the same jump on a number line, and meet the quiet limit a shrinking pattern carries: sooner or later it runs out of room near zero.

We are learning to

• count down by the same jump each time,
• keep a shrinking pattern going on a number line,
• notice when a shrinking pattern runs out of room.

Success criteria

• I can write the next few numbers in a shrinking pattern.
• I can say the jump that made it go down.

You need

Counters for counting back, and the number cards (cut-out sheet 1). A number line on the board or drawn on the floor with chalk or tape. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? End Session A after the count back. Start Session B with the floor line.

Watch for these ideas

• Thinking a pattern can only grow: counting down by the same jump is a pattern too.
• Losing the jump on the way down, hopping back 4 and then back 3.
• Not noticing a shrinking pattern runs out of room near zero.

Answers

• 20, 17, 14, 11, 8, 5 (the jump is -3).
• Count down three more: from 40 by 4 gives 36, 32, 28; from 25 by 5 gives 20, 15, 10; from 18 by 3 gives 15, 12, 9.
• From 15 by 5: 15, 10, 5, 0. After 0 the next jump of 5 would go below zero, so the shrinking pattern runs out of room.

Count it down

Each pattern shrinks by the same jump. Find the jump, then keep counting down.

Keep counting down

Write the next three numbers. 20, 17, 14, ____, ____, ____

Count down three more

Write the next three numbers in each row.

How low can it go?

Count down from 15 by 5: 15, 10, 5, ____

Draw the hops back on the line, then say what happens after 0.

Name the jump

To describe a pattern, name two things: where it starts and how it jumps. Today children read the gaps between neighbours to find the constant jump, and learn the discipline that matters most: a rule must survive every gap, not just the first.

We are learning to

• read the gaps between numbers to find the jump,
• write a rule as + or - a number,
• check that the same jump fits every gap.

Success criteria

• I can write the rule for a pattern.
• I can tell a real pattern from one whose jumps change.

You need

The number cards and jump cards (cut-out sheet 1), one set per pair. A board for the class write. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? End Session A after reading gaps. Start Session B with the jump-card match.

Watch for these ideas

• Reading only the first gap and not checking the rest.
• Calling any regular-looking list a pattern; the gaps must all match. 5, 10, 20, 40 doubles, so it is a pretender.
• Writing the rule without its direction, forgetting the minus for a shrinking pattern.

Answers

• Rules: 8, 13, 18, 23 is +5; 30, 24, 18, 12 is -6; 11, 20, 29, 38 is +9; 50, 45, 40, 35 is -5.
• 5, 10, 20, 40 is not an additive pattern: the gaps are +5, +10, +20, so it doubles rather than adding the same jump.
• Following + 4 from 7 gives 7, 11, 15, 19.

What is the rule?

Read the gaps between the numbers. Write each rule as + or - a number.

Name the rule

Pattern or pretender?

Is 5, 10, 20, 40 an additive pattern? Yes □    No □

Why or why not?

Build it

Follow the rule + 4 from a start of 7. 7, ____, ____, ____

The missing number

A missing number is not a mystery; it is a held place. The gaps on either side still speak. Today children read a neighbouring jump and apply it into the hole, and learn the reverse trick for a missing first number: step back by the jump.

We are learning to

• find a missing number in the middle of a pattern,
• find a missing first number by stepping back,
• check the answer fits the jump on both sides.

Success criteria

• I can fill a gap using the jump.
• I can check my answer against both sides.

You need

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

Lesson flow (about 50 minutes)

Two half-sessions instead? End Session A after the hidden card. Start Session B with the gap cards.

Watch for these ideas

• Guessing the missing number from how big its neighbours look, instead of using the jump.
• Using the number on only one side of the gap.
• Getting stuck when the first number is missing; you step back by the jump.

Answers

• The worked example is 12.
• 9, 14, 19, 24, 29: the missing number is 19. 38, 32, 26, 20, 14: the missing number is 26.
• 9, 15, 21, 27: the missing first number is 9. 4, 10, 16, 22, 28: the next two numbers are 22 and 28.
• The missing tower has 7 blocks (3, 7, 11, 15, growing by 4).

Fill the gap

One number is missing. Use the jump on both sides to find it.

Find the gap

9, 14, ____, 24, 29. The missing number is ____

38, 32, ____, 20, 14. The missing number is ____

The missing start

____, 15, 21, 27. The missing first number is ____

The next two

4, 10, 16, ____, ____. The next two numbers are ____, ____

The missing tower

A tower pattern grows by 4: 3 blocks, ____ blocks, 11 blocks, 15 blocks. The missing tower has ____ blocks.

Make your own pattern

Making a pattern is the strongest test of understanding, and it asks for only two decisions: pick a start, pick a jump. Today children build their own growing and shrinking patterns with numbers, shapes and objects, and meet the awkward case worth meeting on purpose.

We are learning to

• make a growing pattern from a start and a jump,
• make a shrinking pattern that does not fall below zero,
• build a pattern with numbers, shapes and objects.

Success criteria

• I can make a pattern and say its rule.
• I can find a friend’s rule from their pattern.

You need

The pattern-step strips and shape-pattern tiles (cut-out sheet 2), the number cards and jump cards (cut-out sheet 1), and counters. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? End Session A after building on the strip. Start Session B with swap-and-solve and the class quiz.

Watch for these ideas

• Choosing a small start with a backwards jump, so the pattern collapses in a step or two; a shrinking pattern needs headroom.
• Changing the jump partway through the pattern.
• Building numbers that grow by a widening gap (doubling) instead of one constant jump.

Answers

• Growing, start 4 and jump + 5: 4, 9, 14, 19, 24, 29.
• Shrinking, start 28 and jump - 4: 28, 24, 20, 16, 12, 8, 4, 0.
• Shape pattern: 1, 3, 5 dots (two more each time); accept any shapes drawn, as long as each has two more than the last.
• Invent-your-own varies: check every gap is the same and matches the stated jump, and that a shrinking pattern starts high enough not to fall below 0.

Your pattern machine

You are the pattern machine. Choose a start and a jump, then build.

A growing pattern

Start at 4, jump + 5. Write six numbers: ____, ____, ____, ____, ____, ____

A shrinking pattern

Start at 28, jump - 4. Write the numbers until you reach 0: ____

A shape pattern

Draw a growing shape pattern. Each shape has 2 more dots than the last. Start with 1 dot, then draw three shapes.

Invent your own

Number and jump cards

Cut out the cards. Use the number cards to build, continue and order patterns. Use the jump cards to name the rule and to set the pattern machine going. One set per pair is plenty.

Number cards

Jump cards

Teacher note: the number cards make and continue patterns all week; the jump cards name the rule on Day 3 and drive the pattern machine on Day 5. These are the same jumps the screen offers.

Shape tiles, step strips and next cards

Cut out the tiles and cards. Lay the shape tiles in a row to make a growing or shrinking pattern of objects. Use the step strips to build your own pattern, or to lay cards and find a missing one. On the what-comes-next cards, write the number that finishes the pattern.

Shape-pattern tiles

Pattern-step strips

Start on the left. Write your first number, then add or take the same jump across the six boxes.

What-comes-next cards

Teacher note: the what-comes-next cards continue by +3, +5, -4 and -2, so the next numbers are 13, 25, 10 and 8. The shape tiles and step strips are the hands-on version of the pattern machine on screen.

What we know: growing and shrinking patterns

Work on your own. Show your thinking if you can.

1. Continue the growing pattern: 3, 9, 15, 21, ____, ____
2. Continue the shrinking pattern: 34, 30, 26, 22, ____, ____
3. Write the rule for 7, 14, 21, 28 (like +5 or -5): ____
4. Write the rule for 60, 52, 44, 36: ____
5. Find the missing number: 5, 11, ____, 23, 29
6. Find the missing first number: ____, 16, 24, 32
7. Which one is NOT an additive pattern? (a) 4, 8, 12, 16   (b) 3, 6, 12, 24   (c) 50, 45, 40, 35
8. Make a pattern. Start at 6 and add 5 each time. Write five numbers: ____, ____, ____, ____, ____

Answers and marking guide

Answers

1. 27, 33 (the jump is +6).
2. 18, 14 (the jump is -4).
3. +7 (it adds 7 each time).
4. -8 (it subtracts 8 each time).
5. 17 (the jump is +6, so 11 + 6 = 17).
6. 8 (the jump is +8, so step back 8 from 16).
7. (b) 3, 6, 12, 24 (it doubles: the gaps are +3, +6, +12, not one constant jump).
8. 6, 11, 16, 21, 26.

A quick three-level guide

Eight questions, four ideas. A child at standard continues, names, repairs and makes an additive pattern, and can say the rule.

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: grow, shrink, name the rule, find the missing number, and make a pattern.