C. Algebra · Patterns, Equations, Coding and ModellingWhat Repeats? Elements and Operations in Patterns
C1.1 A1About 35 minutes
Learning goals- I can find the core (the part that repeats) in a repeating pattern.
- I can find the operation that repeats in a growing or shrinking pattern, like add 4 or subtract 10.
- I can describe a pattern of movements, like a shape that turns a quarter turn each time.
- I can find and describe patterns in real life, like on a calendar.
Words to know
element
One part of a pattern: one shape, one number, one sound or one action.
core
The group of elements that repeats over and over in a repeating pattern.
operation
Something we do to numbers: add (+), subtract (−), multiply (×) or divide (÷).
growing pattern
A pattern where the numbers or shapes get bigger each time.
shrinking pattern
A pattern where the numbers or shapes get smaller each time.
quarter turn
One fourth of a full turn, like the hand of a clock moving from 12 to 3.
Remember from Grade 2
In Grade 2 you found repeating, growing and shrinking patterns. You looked at shapes, colours and numbers, and you said the rule of a pattern.
In Grade 3 we become pattern detectives. In every pattern, something repeats. Our job is to find out what repeats.
A calendar mystery
Today is a holiday Monday: Thanksgiving, October 12, 2026. Look at all the Mondays in October 2026:
5, 12, 19, 26
What do you notice? Each Monday is 7 days after the one before. The numbers change, but the adding 7 stays the same every time. The thing that repeats is an operation: add 7.
| Sun | Mon | Tue | Wed | Thu | Fri | Sat |
|---|
| | | | 1 | 2 | 3 |
| 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 11 | 12 | 13 | 14 | 15 | 16 | 17 |
| 18 | 19 | 20 | 21 | 22 | 23 | 24 |
| 25 | 26 | 27 | 28 | 29 | 30 | 31 |
Kind 1: Repeating elements
In a repeating pattern, a group of elements repeats again and again. That group is called the core.
🍁 🍁 🍂 🍁 🍁 🍂 🍁 🍁 🍂
The core is 🍁 🍁 🍂: two maple leaves, then one fallen leaf. It has 3 elements. We can also call it an AAB pattern.
The days of the week are a real-life repeating pattern: Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, then Sunday again. The core has 7 elements.
Kind 2: Repeating operations
In a growing or shrinking pattern, the numbers change. But the operation we do each time stays the same. The operation is what repeats.
- 3, 7, 11, 15, 19 → add 4 repeats. It is a growing pattern.
- 60, 50, 40, 30, 20 → subtract 10 repeats. It is a shrinking pattern.
- 2, 4, 8, 16, 32 → double (multiply by 2) repeats. 2 × 2 = 4, 4 × 2 = 8, 8 × 2 = 16, 16 × 2 = 32. It grows faster and faster!
Kind 3: Repeating movements
Some patterns are made by moving a shape. Look at this arrow. Each time, it makes a quarter turn to the right (the way clock hands move).
The movement turn a quarter turn to the right repeats. After 4 quarter turns, the arrow is back where it started, so the arrows also make a repeating pattern with a core of 4: up, right, down, left.
Movements can also be slides (moving a shape over without turning it) and flips (like seeing it in a mirror).
Worked exampleExample 1: Find the core
Describe this pattern: 🔴 🔵 🔵 🔴 🔵 🔵 🔴 🔵 🔵
- Look for where the pattern starts again. After 🔴 🔵 🔵, we see 🔴 again.
- So the core is 🔴 🔵 🔵.
- Count the elements in the core: 1 red circle, 2 blue circles = 3 elements.
- Check: the core repeats 3 times with no extra pieces.
The core is 🔴 🔵 🔵. It is an ABB pattern with 3 elements in the core.
Worked exampleExample 2: Find the repeating operation
Describe this pattern: 5, 9, 13, 17, 21
- The numbers get bigger, so it is a growing pattern.
- Find the change from each number to the next: 5 to 9 is +4, 9 to 13 is +4, 13 to 17 is +4, 17 to 21 is +4.
- The same operation happens every time.
It starts at 5 and adds 4 each time. The operation add 4 repeats.
Worked exampleExample 3: A shrinking pattern
Describe this pattern: 45, 40, 35, 30, 25
- The numbers get smaller, so it is a shrinking pattern.
- 45 − 5 = 40, 40 − 5 = 35, 35 − 5 = 30, 30 − 5 = 25.
- Each time we subtract 5.
It starts at 45 and subtracts 5 each time.
Worked exampleExample 4: A pattern in real life
At the park there are tricycles in a row. 1 tricycle has 3 wheels. 2 tricycles have 6 wheels. 3 tricycles have 9 wheels. What repeats?
- Write the wheel numbers in order: 3, 6, 9.
- 3 to 6 is +3. 6 to 9 is +3.
- Each new tricycle brings 3 more wheels.
The operation add 3 repeats, because every tricycle has 3 wheels. 4 tricycles would have 12 wheels.
Just for funFunny but true: Because the days of the week have a core of 7, if today is a Monday, then 7 days from now is a Monday, and so is 70 days from now. Your calendar is one giant repeating pattern!
| Pattern | What repeats? | Kind |
|---|
| Winter, spring, summer, fall, winter, spring, … | The 4 seasons (the core) | Repeating elements |
| Clap, stomp, stomp, clap, stomp, stomp, … | Clap, stomp, stomp (the core) | Repeating elements |
| 10, 20, 30, 40, … | Add 10 | Growing (repeating operation) |
| 24, 21, 18, 15, … | Subtract 3 | Shrinking (repeating operation) |
| 1, 2, 4, 8, 16, … | Double (× 2) | Growing (repeating operation) |
| Arrow turns up, right, down, left, … | A quarter turn to the right | Repeating movement |
Look for patterns in art
Many artists use repeating patterns. Many First Nations and Métis artists, for example, make beadwork with designs that repeat. Quilts, tiles, fences and knitted sweaters often have patterns too. Whenever you see a pattern, ask: What repeats? Is it an element, an operation or a movement?
Your turn
1What is the core of this pattern? ⭐ ⭐ 🌙 ⭐ ⭐ 🌙 ⭐ ⭐ 🌙
⭐ ⭐ 🌙. It has 3 elements (an AAB pattern).
2What operation repeats? 2, 4, 6, 8, 10
Add 2. Each number is 2 more than the one before.
3What operation repeats? 50, 45, 40, 35
Subtract 5. It is a shrinking pattern.
4Is 12, 22, 32, 42 growing or shrinking? What repeats?
5What operation repeats? 3, 6, 12, 24
Double (multiply by 2). 3 × 2 = 6, 6 × 2 = 12, 12 × 2 = 24.
6How many elements are in the core of the days of the week?
7: Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday.
7An arrow points up, then right, then down. It keeps turning a quarter turn to the right. Which way does it point next?
Left. Up, right, down, left, then up again.
Hands-on activityPattern hunt at home
You need: paper, a pencil and a grown-up helper.
- Walk around your home and look for 3 patterns. Ideas: floor tiles, a striped shirt, a fence, a calendar, buttons on a phone, stairs.
- Draw or write each pattern on your paper.
- Beside each one, write what repeats: a core of elements, an operation (like add 7 on a calendar), or a movement.
- Bonus: look at a calendar. Pick a day, like Saturday. Write the dates of all the Saturdays this month. What operation repeats?
Math talk: Tell your grown-up, "I know this is a pattern because ___ repeats."
Grown-up note: keep small items away from younger children who might put them in their mouths.
More practice: warm-up
1What is the core? A B C A B C A B C
A B C. It has 3 elements.
2What operation repeats? 1, 2, 3, 4, 5
3What operation repeats? 100, 90, 80, 70
4Is 5, 10, 15, 20 growing or shrinking?
Growing. It adds 5 each time.
5Name a pattern that repeats in real life.
Many answers. For example: the days of the week, the seasons, the months of the year, or a striped shirt.
More practice: on your own
1Describe this pattern: 🐟 🐟 🐟 🦆 🐟 🐟 🐟 🦆. What is the core and how many elements does it have?
The core is 🐟 🐟 🐟 🦆: 3 fish and 1 duck. It has 4 elements (an AAAB pattern).
2Describe this pattern: 7, 16, 25, 34. Show how you know.
It starts at 7 and adds 9 each time. 7 + 9 = 16, 16 + 9 = 25, 25 + 9 = 34.
3Describe this pattern: 64, 32, 16, 8. (Hint: it is not subtracting the same number each time.)
It halves (divides by 2) each time. 64 ÷ 2 = 32, 32 ÷ 2 = 16, 16 ÷ 2 = 8. The subtraction changes (−32, −16, −8), but divide by 2 stays the same.
4The Saturdays in a month are 3, 10, 17, 24 and 31. What operation repeats? Why does that make sense?
Add 7. It makes sense because there are 7 days in a week, so each Saturday is 7 days after the last one.
5Each dog has 4 legs. Write the number of legs for 1, 2, 3, 4 and 5 dogs. What repeats?
4, 8, 12, 16, 20. The operation add 4 repeats, because each new dog brings 4 more legs.
Challenge
1Is 2, 5, 2, 5, 2, 5 a repeating pattern or a growing pattern? Explain.
It is a repeating pattern. The numbers do not keep getting bigger. The core 2, 5 repeats. (You could also say +3, −3 repeats, but the numbers go back and forth instead of growing.)
2Mia says 1, 3, 6, 10 is a growing pattern where add 2 repeats. Is she right? Explain.
No. 1 + 2 = 3, but 3 + 3 = 6 and 6 + 4 = 10. The amount added goes up by 1 each time: +2, +3, +4. It is a growing pattern, but the adding is not the same each time. The next number would be 10 + 5 = 15.
3A shape turns a quarter turn to the right each time. How many quarter turns does it take to get back to where it started? What about two full times around?
4 quarter turns make one full turn back to the start. Two full times around would be 4 + 4 = 8 quarter turns.
Quiz
1. What is the core of 🍎 🍐 🍐 🍎 🍐 🍐 🍎 🍐 🍐?
2. What operation repeats in 4, 8, 12, 16?
3. Which pattern is shrinking?
4. What repeats in 5, 10, 20, 40?
5. The Mondays in October 2026 are 5, 12, 19 and 26. What repeats?
6. An arrow points right. It turns a quarter turn to the right. Where does it point now?
Big idea: In Grade 3 (C1.1), children look closely at what repeats in a pattern. In a repeating pattern it is a group of elements (the core). In a growing or shrinking pattern it is an operation, like add 4 or subtract 10, or even double. Some patterns repeat a movement, like a quarter turn.
Common difficulties:
- Naming a core that is too short or too long. For 🔴 🔵 🔵 🔴 🔵 🔵, some children say the core is 🔴 🔵. Ask them to find where the pattern starts over.
- Describing only the first jump. Encourage checking every jump: "Is it +4 every time?"
- Mixing up "grows" and "repeats". A growing pattern still has something that repeats: the operation.
- Quarter turns. Use a toy or your child's own body: stand up and make quarter turns to the right.
How to help: Look at calendars, house numbers on one side of the street (they often go up by 2), stairs and tiles. Ask: "What repeats here?" Accept an explanation in your child's own words.