Grade by Grade
C. Algebra · Patterns, Equality and Coding

Pattern Rules, Predictions and Missing Parts

C1.3About 35 minutes
Learning goals
  • I can say the rule of a pattern.
  • I can extend a pattern (make it longer).
  • I can predict what will come later in a pattern and explain why.
  • I can find a missing part of a pattern.
  • I can tell a repeating pattern from a growing pattern.

Words to know

pattern rule
Words that tell exactly how a pattern works, like "the core is circle, square and it repeats" or "start at 2 and add 2 each time".
extend
To make a pattern longer by following its rule.
predict
To use what you know to say what will happen, before you see it.
justify
To explain why your answer makes sense.
growing pattern
A pattern that gets bigger (or smaller) by the same amount each time.
term
One thing (one step) in a pattern. The first term, the second term, and so on.

Pattern detectives need clues

A detective uses clues to solve mysteries. A pattern rule is your best clue! Once you know the rule, you can:

  1. Extend the pattern (keep it going).
  2. Predict what comes far along the pattern.
  3. Find a missing piece.

Writing a pattern rule

For a repeating pattern, the rule tells the core.

🟢 🟢 🟣 🟢 🟢 🟣 🟢 🟢 🟣

Rule: The core is green, green, purple. It repeats.

For a growing pattern, the rule tells where to start and what to add each time.

2, 4, 6, 8, 10

Rule: Start at 2. Add 2 each time.

Growing patterns

A growing pattern does not repeat. It gets bigger by the same amount each time. Look at these block towers.

1357
Towers with 1, 3, 5 and 7 blocks. Each tower has 2 more blocks than the one before.
Worked example

Extend a growing pattern

The towers have 1, 3, 5, 7 blocks. How many blocks will the next tower have?

  1. Compare each tower with the next: 1 to 3 is 2 more. 3 to 5 is 2 more. 5 to 7 is 2 more.
  2. The rule is: Start at 1. Add 2 each time.
  3. Use the rule: 7 + 2 = 9.

The next tower has 9 blocks.

012345678910+2+2+2+2
The tower pattern on a number line: 1, 3, 5, 7, 9. Each jump is +2.

Finding a missing part

Sometimes a piece of the pattern is hidden. Use the rule to find it!

?
circle, square, circle, ?, circle, square, circle, square
Worked example

What is missing?

circle, square, circle, ?, circle, square, circle, square. What shape is missing?

  1. Find the core using the parts you can see: circle, square, circle, square... The core is circle, square.
  2. Say the pattern out loud, pointing to each shape: circle, square, circle, square, circle, square, circle, square.
  3. Check: a square fits between the 2nd circle and the 3rd circle. The pattern still works.

The missing shape is a square.

Worked example

Missing number

5, 10, 15, ?, 25, 30. What number is missing?

  1. Look at how the numbers change: 5 to 10 is 5 more. 10 to 15 is 5 more.
  2. The rule is: Start at 5. Add 5 each time. This is counting by 5s!
  3. 15 + 5 = 20.
  4. Check: 20 + 5 = 25. Yes, 25 is the next number shown.

The missing number is 20.

Making predictions

A prediction is a smart guess using the rule. You can predict without drawing the whole pattern!

Look at this AB pattern: 🔴 🔵 🔴 🔵 🔴 🔵 ...

What will the 10th term be?

Term12345678910
Colour🔴🔵🔴🔵🔴🔵🔴🔵🔴🔵
In this AB pattern, red is on 1, 3, 5, 7, 9. Blue is on 2, 4, 6, 8, 10.
Worked example

Predict and justify

In the pattern 🔴 🔵 🔴 🔵 ..., what colour is the 10th term? Explain how you know.

  1. Blue is on terms 2, 4, 6, 8... These are the numbers we say when we count by 2s.
  2. Count by 2s: 2, 4, 6, 8, 10. The number 10 is in our count!
  3. So term 10 is blue.

The 10th term is blue 🔵, because blue is on every number when you count by 2s, and 10 is one of those numbers.

Different ways to check

You can check a prediction by extending the pattern with objects and counting, or by touching and counting each term out loud. Both ways are good math!

Your turn

1

Extend the pattern. Draw the next 3: ⭐ 🌙 🌙 ⭐ 🌙 🌙 ___ ___ ___

2

Write the rule: 3, 4, 5, 6, 7

3

What is missing? 🍎 🍌 🍇 🍎 ___ 🍇 🍎 🍌 🍇

4

What is missing? 10, 20, ___, 40, 50

5

Towers have 2, 4, 6 blocks. How many blocks in the next tower?

6

In the pattern clap, stomp, clap, stomp ... is the 7th action a clap or a stomp?

7

Is 1, 2, 1, 2, 1, 2 a repeating pattern or a growing pattern?

8

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

Just for fun

Why are pattern detectives never surprised?

Because they always know what comes next!

Hands-on activity

Hide the piece

You need: about 20 small things in two or three kinds (coins, buttons, pasta, LEGO bricks).

  1. A grown-up makes a repeating pattern in a line, at least 3 cores long.
  2. Close your eyes. The grown-up takes away one piece and leaves a gap.
  3. Open your eyes. Which piece is missing? Say the rule to explain how you know.
  4. Now make a growing pattern with towers of 1, 2, 3 blocks. Ask your grown-up to predict how many blocks tower number 6 needs. Build it to check!
  5. Switch jobs.

More practice: warm-up

1

Extend the pattern. Draw the next 2: 🟡 🟣 🟡 🟣 🟡 🟣 ___ ___

2

What comes next? 5, 6, 7, 8, ___

3

What is missing? 🐶 🐱 🐶 ___ 🐶 🐱

4

Is 4, 4, 9, 4, 4, 9 a repeating pattern or a growing pattern?

5

Write the rule: 🍎 🍎 🍐 🍎 🍎 🍐

More practice: on your own

1

What is missing? 2, 4, ___, 8, 10, 12

2

Write the rule. Then find the next number: 4, 6, 8, 10, ___

3

In the pattern 🍁 ⛄ 🍁 ⛄ ..., is the 9th picture 🍁 or ⛄? How do you know?

4

What comes next? 50, 40, 30, 20, ___

5

What is missing? 🔺 🟦 🟦 🔺 🟦 ___ 🔺 🟦 🟦

Challenge

1

Find the mistake! Jay says the next number in 1, 3, 5, 7 is 8, because numbers go up by 1. Is he right? Explain.

2

In the pattern clap, clap, stomp, clap, clap, stomp ..., what is the 9th action? Show how you know.

3

Towers have 1, 2, 3, 4 blocks. Predict how many blocks tower number 8 will have. Explain your prediction.

Check your understanding

Quiz

1.

What comes next? 1, 3, 5, 7, ___

2.

What is missing? 🟥 🟦 🟦 🟥 ___ 🟦 🟥 🟦 🟦

3.

Which is the rule for 10, 20, 30, 40?

4.

In the pattern 🐶 🐱 🐶 🐱 ..., what is the 8th animal?

5.

Which is a growing pattern?

6.

What is missing? 🌙 ⭐ ⭐ 🌙 ___ ⭐ 🌙 ⭐ ⭐

7.

What comes next? 40, 35, 30, 25, ___

For parents and teachers

Your child is moving from seeing patterns to using the rule to reason: extending, predicting and finding missing pieces.

Common mistakes

  • Guessing the next term from only the last one or two terms. Encourage looking at the whole pattern to find the core or the change.
  • Mixing up repeating and growing patterns. Ask: Does it repeat the same thing, or does it get bigger each time?
  • Losing count when predicting. Have your child point to each term and count aloud, or build the pattern with objects.
  • Stating a rule that is too vague ("it goes up"). Help them say how much it goes up and where it starts.

How to help

  • Play "What's missing?" with objects or drawings.
  • Ask how do you know? after each answer so your child practises justifying.
  • Celebrate persistence: predictions are allowed to be wrong; checking them is the important part.