C. Algebra · Patterns, Equations, Inequalities, Coding and Modelling

Repeating and Growing Patterns in Real Life

C1.1 A1About 35 minutes

Learning goals

I can tell whether a pattern is repeating or growing.
I can name the core of a repeating pattern.
I can describe how a growing pattern grows, using a start number and the change each time.
I can find repeating and growing patterns in real life.

Words to know

repeating pattern
A pattern where the same core repeats again and again.

core
The part of a repeating pattern that repeats, like 🍁❄️❄️.

growing pattern
A pattern where each term gets bigger by following a rule.

shrinking pattern
A pattern where each term gets smaller by following a rule.

term
One item in a pattern. In 4, 7, 10, 13 each number is a term.

term number
The position of a term: 1st, 2nd, 3rd and so on.

Remember from Grade 3

In Grade 3 you looked for what repeats in a pattern: a core of shapes, a math operation like add 4, or a movement like a quarter turn. In Grade 4 you will sort patterns into repeating and growing patterns, describe exactly how they change, and spot them in the world around you.

Let's start with a story

It is a snowy January morning. Amira looks out her window and sees two things:

Her neighbour's fence: post, board, board, post, board, board, post, board, board.
Her little brother building a snow wall. Day 1: 4 blocks. Day 2: 6 blocks. Day 3: 8 blocks. Each day he adds 2 more blocks.

The fence is a repeating pattern. The snow wall is a growing pattern. Can you tell why?

A wooden fence with snow-capped posts runs along a snowy backyard in front of houses. — A fence is a real-life repeating pattern: a post, then a section of boards, then a post again. The core repeats and the fence never changes its rule. AI-generated image

Amira's two patterns. The fence repeats the same 3-element core. The snow wall grows: 4, 6, 8 blocks, adding 2 each day.

Repeating patterns

A repeating pattern has a core. The core repeats again and again, and the pattern never gets bigger or smaller.

🍁❄️❄️🍁❄️❄️🍁❄️❄️

The core is 🍁❄️❄️. It has 3 elements (3 pictures). To describe a repeating pattern, say what is in the core and how many elements it has.

Real-life repeating patterns: the days of the week, the four seasons (winter, spring, summer, fall), the tiles on a floor, the beads on a bracelet.

Growing patterns

In a growing pattern, each term gets bigger by following a rule. Look at these figures made of toothpicks.

Figure 1 has 4 sticks, Figure 2 has 7, Figure 3 has 10 and Figure 4 has 13. Each new figure adds one square on the right using 3 more sticks.

To describe a growing pattern, tell:

Where it starts (the first term): 4 sticks.
How it changes each time: add 3 sticks.

So we say: Start at 4 and add 3 each time. The terms are 4, 7, 10, 13, ...

The term number tells the position. Figure 1 is term number 1, Figure 2 is term number 2, and so on.

Shrinking patterns

Some patterns get smaller each time. A carton holds 24 eggs. The family uses 3 eggs every morning: 24, 21, 18, 15, ... This is a shrinking pattern: start at 24 and subtract 3 each time.

Not every growing pattern grows by the same amount

Look at 1, 3, 6, 10, 15. The jumps are +2, +3, +4, +5. The pattern still grows, but the jump gets 1 bigger each time. Always check every jump before you describe a pattern.

Pattern	Repeating or growing?	How to describe it
Mon, Tue, Wed, Thu, Fri, Sat, Sun, Mon, ...	Repeating	The core is the 7 days of the week.
4, 7, 10, 13, ...	Growing	Start at 4, add 3 each time.
24, 21, 18, 15, ...	Shrinking	Start at 24, subtract 3 each time.
1, 3, 6, 10, 15, ...	Growing	Start at 1, add 2, then 3, then 4, then 5 ...

Four patterns, described.

Worked example

Example 1: Describe a repeating pattern

Describe this pattern: clap, snap, snap, stomp, clap, snap, snap, stomp, clap, snap, snap, stomp

Look for the part that starts again. After stomp, the pattern starts again with clap.
So the core is clap, snap, snap, stomp.
Count the elements in the core: clap (1), snap (2), snap (3), stomp (4).
The pattern does not get bigger. The same core just repeats.

It is a repeating pattern. The core is clap, snap, snap, stomp, with 4 elements. It repeats 3 times here.

Worked example

Example 2: Describe a growing pattern from real life

Noah puts money in his piggy bank every week. Week 1: $12. Week 2: $17. Week 3: $22. Week 4: $27. Describe the pattern.

The amounts get bigger, so it is not a repeating pattern.
Find each jump: 17 − 12 = 5, 22 − 17 = 5, 27 − 22 = 5.
Every jump is the same: +5.
It starts at $12.

It is a growing pattern: start at $12 and add $5 each week.

Worked example

Example 3: Repeating or growing?

Sort these: (a) 2, 9, 2, 9, 2, 9 (b) 50, 45, 40, 35 (c) 3, 6, 12, 24

(a) 2, 9 comes back again and again. The numbers never get bigger overall. Repeating, core 2, 9.
(b) The jumps are −5, −5, −5. Shrinking: start at 50, subtract 5 each time.
(c) The jumps are +3, +6, +12. They are not the same. Look again: 3 × 2 = 6, 6 × 2 = 12, 12 × 2 = 24. Growing: start at 3, multiply by 2 each time.

(a) repeating, (b) shrinking, (c) growing (double each time).

Math talk: how do you know?

When you say It is a growing pattern, also say how you know: "I found the jumps. They were all +5." If you are not sure, that's okay! Try another way, like building the pattern or making a table. Trying again is part of being a mathematician.

Just for fun

My socks have a repeating pattern: left, right, left, right... except on laundry day, when the core is just one lonely sock.

Hands-on activity

Pattern hunt and build

You need: paper, a pencil, and about 30 toothpicks, cotton swabs or pennies.

Part 1: Pattern hunt (10 minutes). Walk around your home with a grown-up. Look for 3 repeating patterns (floor tiles, a striped shirt, a fence, a calendar, a placemat) and 1 growing or shrinking pattern (stairs going up, a stack of cups getting taller, pages left in a book as you read). Draw or write each one. For each repeating pattern, circle the core.

Part 2: Build a growing pattern. Build Figures 1, 2 and 3 of the toothpick squares above. Count the sticks in each. Now build Figure 4. Was it 13? Describe the pattern out loud: Start at ___, add ___ each time.

Part 3: Make your own. Build a different growing pattern (for example, triangles in a row). Ask your grown-up to describe it.

What to look for: your child names the core of each repeating pattern, and says the start and the change for each growing pattern.

Grown-up note: keep small items like these away from babies and toddlers, and watch that toothpicks are handled carefully (their ends are sharp; cotton swabs are a safer swap).

Your turn

What is the core of this pattern? 🌲🌲⛄🌲🌲⛄🌲🌲⛄

Is 8, 16, 24, 32, 40 a repeating, growing or shrinking pattern? Describe it.

Is 100, 90, 80, 70 a repeating, growing or shrinking pattern? Describe it.

How many elements are in the core of A B C C A B C C A B C C?

Leila reads 15 pages of her book every day. After day 1 she is at page 15, after day 2 at page 30, then page 45, then page 60. Describe the pattern.

Give one repeating pattern you can find in a calendar.

Look at 1, 2, 4, 7, 11. Are the jumps all the same?

More practice: warm-up

What is the core of red, blue, red, blue, red, blue?

Repeating or growing: 5, 10, 15, 20?

Repeating or growing: 1, 0, 0, 1, 0, 0, 1, 0, 0?

What comes next: 20, 18, 16, 14, ?

How many elements are in the core of winter, spring, summer, fall?

More practice: on your own

Describe the pattern 7, 11, 15, 19, 23.

A pattern of stacked chairs: 1 chair is 80 cm tall, 2 stacked chairs are 90 cm, 3 are 100 cm. Describe the pattern.

Describe this pattern and say how many elements are in the core: ⬆️➡️➡️⬇️⬆️➡️➡️⬇️

A bag has 36 apples. Each day the family eats 4. Write the first 5 terms and describe the pattern.

Is 2, 4, 8, 16 growing by the same amount each time? Describe it.

Challenge

Mika says 3, 5, 3, 5, 3, 5 is a growing pattern because 5 is bigger than 3. Is she right? Explain.

Make up a real-life growing pattern and a real-life shrinking pattern. Describe each with a start number and a change.

Look at 1, 3, 6, 10, 15. Predict the next two terms and explain.

Check your understanding

Quiz

What is the core of 🍁🍁❄️🍁🍁❄️🍁🍁❄️?

Which is a growing pattern?

How would you describe 12, 20, 28, 36?

Which is a repeating pattern in real life?

What kind of pattern is 45, 40, 35, 30?

The toothpick pattern goes 4, 7, 10, 13 sticks. What does term number 3 mean?

For parents and teachers

Big idea: The Ontario curriculum (C1.1) asks Grade 4 students to identify and describe repeating and growing patterns, including patterns found in real-life contexts. Describing a pattern with a start and a change gets your child ready for pattern rules, tables of values and graphs later in this unit.

Common difficulties:

Calling any pattern with bigger numbers "growing" (3, 5, 3, 5). Ask: "Does every term get bigger?"
Checking only the first jump. In 1, 3, 6, 10, the first jump is +2 but the next is +3. Ask your child to write every jump.
Naming a core that is too short or too long (saying 🍁❄️ instead of 🍁🍁❄️). Have your child point to where the pattern starts over.

How to help: Go on pattern hunts during everyday life: floor tiles, knitting, fences, the bus schedule, the weekly recycling day. Ask "Is it repeating or growing? How do you know?" Praise your child for explaining and for trying again after a mistake (Strand A: perseverance and communicating).