Algorithms & Patterns
Follow the Rule: Add 3
Start at the given number and add 3 each time.
Follow the Rule: Add 5
Start at the given number and add 5 each time.
Follow the Rule: Subtract 4
Start at the given number and subtract 4 each time.
Follow the Rule: Subtract 3
Subtract 3 each time.
What Is the Rule?
Look at the pattern and circle the rule.
5, 10, 15, 20, 25
30, 27, 24, 21, 18
4, 8, 12, 16, 20
100, 90, 80, 70, 60
More Rules
Circle the rule.
2, 9, 16, 23, 30
50, 44, 38, 32, 26
1, 3, 5, 7, 9
Match Patterns to Rules
Match.
Continue the Shape Pattern
What comes next in each pattern?
More Shape Patterns
What comes next?
Write the Algorithm
Write the step-by-step rule for each pattern.
Pattern: 2, 5, 8, 11, 14 Algorithm: Start at ___, add ___ each time
Pattern: 50, 45, 40, 35, 30 Algorithm: Start at ___, subtract ___ each time
Pattern: 1, 4, 7, 10, 13 Algorithm: Start at ___, add ___ each time
Match Algorithms to Patterns
Match.
What Comes Next?
Follow the algorithm. What is the next number?
Start at 6, add 5: 6, 11, 16, 21, ___
Start at 80, subtract 7: 80, 73, 66, 59, ___
Start at 3, add 6: 3, 9, 15, 21, ___
Start at 99, subtract 9: 99, 90, 81, 72, ___
Follow My Algorithm
Follow the algorithm and write the first 6 numbers.
Algorithm: Start at 4, add 6 each time. Pattern: 4, ___, ___, ___, ___, ___
Algorithm: Start at 75, subtract 8 each time. Pattern: 75, ___, ___, ___, ___, ___
Two-Step Patterns
Fill in the missing numbers.
Create Your Own Algorithm
Write an algorithm and then follow it to create a pattern.
My algorithm: Start at ___, add ___ each time. My pattern: ___, ___, ___, ___, ___, ___
My algorithm: Start at ___, subtract ___ each time. My pattern: ___, ___, ___, ___, ___, ___
Guess My Rule
Look at the pattern. Write the rule and the next 3 numbers.
Pattern: 7, 14, 21, 28, 35 Rule: ___ Next 3: ___, ___, ___
Pattern: 64, 56, 48, 40, 32 Rule: ___ Next 3: ___, ___, ___
Odd One Out
Which number does NOT follow the pattern?
Pattern: 5, 10, 15, 20, 26, 30
Pattern: 3, 6, 9, 11, 15, 18
Pattern Investigation
Investigate these patterns.
Start at 1, add 2 each time: 1, 3, 5, 7, 9... Are these numbers odd or even? ___ Will 20 appear in this pattern? Why? ___
Start at 2, add 2 each time: 2, 4, 6, 8, 10... Are these numbers odd or even? ___ Will 15 appear in this pattern? Why? ___
Home Activity: Pattern Machines
Build your own pattern machines!
- 1Write an algorithm: 'Start at 2, add 3 each time.' Follow it for 10 steps.
- 2Ask a family member to follow your algorithm. Do they get the same pattern?
- 3Make a mystery pattern. Can someone work out your rule?
- 4Try a two-step algorithm: 'Start at 1, double it, then add 1.' What happens?
Follow the Rule: Add 7
Add 7 each time.
Follow the Rule: Add 9
Add 9 each time.
Follow the Rule: Subtract 6
Subtract 6 each time.
Follow the Rule: Subtract 8
Subtract 8 each time.
Multiplication Patterns: ×2
Each term doubles. Fill in the missing numbers.
Multiplication Patterns: ×3
Each term is multiplied by 3. Fill in the missing numbers.
ABCABC Shape Pattern
Continue the pattern.
AABB Shape Pattern
Continue the pattern.
What Is the Rule? — Set A
Circle the rule for each pattern.
12, 19, 26, 33, 40
95, 86, 77, 68, 59
1, 2, 4, 8, 16
What Is the Rule? — Set B
Circle the rule.
100, 93, 86, 79, 72
5, 15, 25, 35, 45
1, 10, 100
Write the Algorithm — Set A
Write the algorithm for each pattern.
11, 18, 25, 32, 39 Algorithm: ___
90, 82, 74, 66, 58 Algorithm: ___
3, 6, 12, 24, 48 Algorithm: ___
Write the Algorithm — Set B
Write the algorithm and the next 3 numbers.
7, 14, 21, 28, 35 Algorithm: ___ Next 3: ___, ___, ___
100, 95, 90, 85, 80 Algorithm: ___ Next 3: ___, ___, ___
Continue the Pattern — Set A
Write the next 5 terms.
Algorithm: Start at 8, add 11. 8, 19, 30, ___, ___, ___, ___, ___
Algorithm: Start at 100, subtract 12. 100, 88, 76, ___, ___, ___, ___, ___
Continue the Pattern — Set B
Write the next 5 terms.
Algorithm: Start at 2, multiply by 2. 2, 4, 8, ___, ___, ___, ___, ___
Algorithm: Start at 3, add 4, then subtract 1 alternately. 3, 7, 6, 10, 9, ___, ___, ___, ___, ___
Pattern Investigation — Odds and Evens
Investigate odd and even patterns.
Start at 1, add 2 each time: 1, 3, 5, 7, 9... Are these odd or even? ___ Will 101 be in this pattern? ___
Start at 0, add 2 each time: 0, 2, 4, 6, 8... Are these odd or even? ___ Will 99 be in this pattern? ___
Pattern Investigation — Multiples
Investigate multiple patterns.
Write the multiples of 3 from 3 to 36. Do they increase by the same amount each time? ___
Write the multiples of 4 from 4 to 48. What is the rule? ___
Match Algorithms to Outputs — Set A
Match each algorithm to its sequence.
Match Algorithms to Outputs — Set B
Match.
Sort: Increasing or Decreasing Pattern?
Sort each pattern.
Create and Share an Algorithm
Create your own algorithm and test it.
My algorithm: Start at ___, (add/subtract/multiply) ___ each time. First 8 terms: ___, ___, ___, ___, ___, ___, ___, ___
A challenge question based on my pattern: ___
Answer: ___
Spot the Error
Each pattern has one number that doesn't belong. Find it and correct it.
5, 10, 15, 20, 26, 30 Error: ___ should be ___
3, 6, 9, 11, 15, 18 Error: ___ should be ___
100, 90, 80, 71, 60 Error: ___ should be ___
Pattern Rules Tally
Tally how many students used each rule in their pattern.
| Item | Tally | Total |
|---|---|---|
Add 2 or 3 | ||
Add 5 or 10 | ||
Subtract | ||
Multiply |
Pattern Types Graph
This graph shows which types of patterns were made in class.
| Number patterns | |
| Shape patterns | |
| Colour patterns | |
| Multiplication patterns |
Which type of pattern was most popular?
How many more number than shape patterns?
How many students made patterns in total?
Fibonacci-Style Pattern
Each term is the sum of the two before it. Fill in the gaps.
What Comes After? — Set A
Circle the next number.
12, 19, 26, 33, ___
64, 56, 48, 40, ___
1, 2, 4, 7, 11, ___
100, 95, 85, 70, ___
Describe the Rule in Words
Write the rule for each pattern using words.
8, 16, 24, 32, 40. Rule: ___
81, 72, 63, 54, 45. Rule: ___
1, 4, 9, 16, 25. Rule: ___
Tables as Patterns
Recognise multiplication tables as patterns.
Write the 6 times table as a pattern: 6, 12, ___, ___, ___, ___, ___, ___, ___, ___, ___, ___
What is the rule? ___
Does 90 appear in this pattern? ___ How do you know? ___
Make a Two-Rule Pattern
Create a pattern with two alternating rules.
My pattern uses two rules: add ___ then subtract ___. My pattern: ___, ___, ___, ___, ___, ___, ___, ___
Describe your pattern: ___
Growing Pattern
Describe how each pattern grows.
Pattern and Prediction
Investigate the pattern and predict.
Pattern: 2, 5, 8, 11, 14, 17... What will the 10th term be? ___ How did you work it out? ___
Pattern: 100, 93, 86, 79, 72... What will the 8th term be? ___ Will the pattern reach 0? ___
Home Activity: Pattern Everywhere
Find patterns in daily life!
- 1Look at a calendar. What patterns do you see in the numbers?
- 2Listen to music. Can you hear a repeating pattern?
- 3Look at wallpaper, tiles or fabric. Describe the pattern.
- 4Make a skip counting pattern while bouncing a ball.
Pattern Number Bonds
Find the missing number to complete each pattern bond.
Add 7 Pattern
Fill in the missing numbers.
Add 9 Pattern
Fill in the missing numbers.
Subtract 6 Pattern
Fill in the missing numbers counting backwards.
Multiply by 2 Pattern
Fill in the missing numbers.
Identify the Rule — Set A
What is the rule for each pattern?
5, 10, 15, 20, 25
50, 44, 38, 32, 26
3, 6, 12, 24, 48
Identify the Rule — Set B
What is the rule?
100, 91, 82, 73, 64
2, 6, 18, 54, 162
64, 32, 16, 8, 4
Continue the Pattern
Circle the next term.
4, 9, 14, 19, 24, ?
100, 90, 80, 70, 60, ?
1, 2, 4, 8, 16, ?
60, 53, 46, 39, 32, ?
Match Pattern to Rule
Match each pattern to its rule.
Match Algorithm to Output
Follow the algorithm and match to the output.
Sort: Increasing or Decreasing?
Sort each pattern.
Sort: Repeating or Growing Pattern?
Sort each pattern type.
Object Repeating Pattern — Set A
Continue the pattern.
Object Repeating Pattern — Set B
Continue the pattern.
Write the Next Three Terms
Write the rule and the next three terms.
5, 8, 11, 14, ___ Rule: ___
96, 90, 84, 78, ___ Rule: ___
3, 9, 27, 81, ___ Rule: ___
500, 250, 125, ___ Rule: ___
Write the Algorithm
Write an algorithm that produces each pattern.
Pattern: 4, 7, 10, 13, 16 Algorithm: Start at ___, then ___
Pattern: 64, 56, 48, 40, 32 Algorithm: Start at ___, then ___
Pattern: 2, 6, 18, 54 Algorithm: Start at ___, then ___
Design Your Own Growing Pattern
Create and describe your own growing pattern.
My rule: ___ My pattern (first 6 terms): ___, ___, ___, ___, ___, ___
What will the 10th term be? ___ How do you know? ___
Algorithm Investigation
Follow each algorithm and record the output.
Algorithm A: Start at 1. Add 5 each time. Stop at 10 steps. Output: ___
Algorithm B: Start at 100. Subtract 7 each time. Stop when below 50. Output: ___
Tally: Types of Patterns Found
Count how many of each pattern type the class found.
| Item | Tally | Total |
|---|---|---|
Number pattern | ||
Shape pattern | ||
Colour pattern | ||
Sound pattern |
Pattern Quiz Results
How many questions did students get right?
| All 5 right | |
| 3-4 right | |
| 1-2 right | |
| 0 right |
How many students got all 5 right?
How many students got at least 3 right?
How many students took the quiz?
Patterns in the Calendar
Look at a monthly calendar and investigate.
What pattern do you notice in the column of Mondays? ___
What is the difference between any date and the same date in the row below? ___
What patterns can you see diagonally? ___
Home Activity: Pattern Detective
Be a pattern detective in your world!
- 1Count every second fence post on a walk. What number pattern does this make?
- 2Look at the numbers on houses in your street. Is there a pattern? Why?
- 3Find a recipe and double all the quantities. What pattern do you notice?
- 4Listen to a song. Clap out the rhythm pattern.
Identify the Rule
Circle the rule that creates each pattern.
5, 10, 15, 20, 25 ...
3, 6, 12, 24, 48 ...
100, 90, 80, 70, 60 ...
2, 5, 8, 11, 14 ...
Two-Step Algorithm Patterns
Follow the two-step rule to complete each sequence.
Pattern Differences
Find the difference between consecutive terms.
Match Algorithm to Its Pattern
Match each algorithm to the pattern it creates.
Create an Algorithm
Write your own algorithm and show the pattern it creates.
My algorithm: Start at ___, then ___ each time. First 6 terms: ___, ___, ___, ___, ___, ___
A pattern your algorithm creates that surprises you:
Error in the Pattern — Find and Fix
Each pattern has one wrong number. Find it and fix it.
4, 8, 12, 17, 20, 24 Wrong number: ___ Corrected: ___
50, 45, 40, 36, 30, 25 Wrong number: ___ Corrected: ___
2, 4, 8, 16, 31, 64 Wrong number: ___ Corrected: ___
Sort: Increasing or Decreasing Pattern?
Sort each pattern into the correct column.
Pattern Types in a Survey
Record how many students chose each pattern type as their favourite.
| Item | Tally | Total |
|---|---|---|
Adding patterns | ||
Subtracting patterns | ||
Doubling patterns | ||
Object patterns |
Patterns in Nature
Explore patterns found in nature and mathematics.
A sunflower has 34 seeds in one ring and 55 in the next. What pattern might this follow?
Describe a pattern you have noticed in the real world:
Home Activity: Pattern Creator
Create and share your own mathematical patterns!
- 1Make up 3 different algorithms. Show the first 6 terms for each.
- 2Challenge a family member to guess your rule from just the first 3 terms.
- 3Find a pattern in nature (e.g., leaves, seeds, tiles). Describe it in numbers.
- 4Use a calculator: start at any number and keep adding the same amount. What do you notice?
Which Algorithm Produces This Pattern?
Circle the algorithm that produces each pattern.
1, 3, 9, 27, 81 ...
100, 95, 90, 85, 80 ...
1, 4, 9, 16, 25 ...
Fibonacci-Like Sequences
In these sequences, each term equals the sum of the two before it.
Pattern Differences — Step Up
The differences between terms increase by 1 each time. Find the missing term.
Match Pattern Type to Description
Match each pattern to its type.
Patterns in a Hundred Chart
Use a hundred chart to explore patterns.
Colour multiples of 3 in the chart. What diagonal patterns do you see?
Colour multiples of 5. What vertical patterns do you see?
Which numbers are multiples of both 3 and 5? List them:
Sort: Multiplicative or Additive Pattern?
Sort each pattern by whether it grows by adding or multiplying.
Pattern to Prediction
Use a pattern to make a prediction.
Pattern: 5, 10, 15, 20 ... What is the 20th term? ___ How did you work it out?
If the rule is 'add 7', and the 1st term is 3, what is the 10th term? ___
Home Activity: Pattern in Numbers
Investigate number patterns at home!
- 1Write the multiplication table for 9. Look at the digits. What pattern do you notice?
- 2Add consecutive odd numbers: 1, 1+3, 1+3+5 ... What do you get?
- 3Look at a clock face. What patterns do you see in the numbers?
- 4Create a new sequence and challenge a family member to find the rule.