Algorithms & Number Patterns
Follow the Rule: Add 3
The rule is 'add 3'. Fill in the missing numbers.
Follow the Rule: Add 4
The rule is 'add 4'. Fill in the missing numbers.
Follow the Rule: Add 5
The rule is 'add 5'. Fill in the missing numbers.
Follow the Rule: Subtract 3
The rule is 'subtract 3'. Fill in the missing numbers.
Follow the Rule: Multiply by 2
The rule is 'multiply by 2'. Fill in the missing numbers.
Follow the Rule: Multiply by 3
The rule is 'multiply by 3'. Fill in the missing numbers.
Match the Rule to the Pattern (Set A)
Draw a line from each rule to the pattern it creates.
Match the Rule to the Pattern (Set B)
Draw a line from each rule to the number pattern.
What Comes Next? (Set A)
Look at the pattern and circle what comes next.
7, 14, 21, 28, ___
2, 6, 18, 54, ___
100, 90, 81, 73, ___
1, 4, 9, 16, ___
What Comes Next? (Set B)
Circle what comes next.
5, 10, 20, 40, ___
3, 7, 11, 15, ___
64, 32, 16, 8, ___
1, 1, 2, 3, 5, ___
What Is the Rule? (Set A)
Look at the pattern and circle the rule.
3, 6, 9, 12, 15
2, 4, 8, 16, 32
50, 45, 40, 35, 30
1, 4, 16, 64
What Is the Rule? (Set B)
Circle the rule.
10, 17, 24, 31, 38
100, 91, 82, 73, 64
2, 6, 18, 54, 162
What Is the Rule? (Set C)
Circle the rule.
5, 10, 15, 20, 25
1,000, 900, 800, 700
3, 9, 27, 81, 243
64, 32, 16, 8, 4
What Is the Rule? (Set D)
Circle the rule.
12, 24, 36, 48, 60
200, 180, 160, 140
1, 5, 25, 125, 625
100, 50, 25
Continue the Pattern (Set C)
Find the rule and continue.
Continue the Pattern (Set D)
Continue the pattern.
Continue the Pattern (Set E)
Continue the pattern.
Match Patterns to Rules (Set A)
Draw a line from each pattern to its rule.
Match Patterns to Rules (Set B)
Draw a line to match.
Sort: Addition or Multiplication Pattern?
Sort each pattern.
Sort: Growing or Shrinking Pattern?
Sort each pattern.
Pattern Step Sizes (Set A)
The total is the next number in the pattern. Find the step size (partB).
Pattern Step Sizes (Set B)
Find the missing value.
Describe the Pattern
Describe the rule for each pattern in words.
4, 8, 12, 16, 20 — Rule:
2, 4, 8, 16, 32 — Rule:
100, 85, 70, 55, 40 — Rule:
1, 3, 9, 27, 81 — Rule:
Create Your Own Patterns
Make up your own number patterns.
Write an addition pattern starting at 7:
Write a subtraction pattern starting at 100:
Write a multiplication pattern starting at 2:
What is the rule for each pattern you created?
What Comes Next? (Set A)
Circle what comes next in the pattern.
8, 16, 24, 32, ___
1, 2, 4, 8, 16, ___
90, 80, 70, 60, ___
5, 25, 125, ___
What Comes Next? (Set B)
Circle what comes next.
6, 12, 18, 24, ___
200, 175, 150, 125, ___
3, 12, 48, ___
1, 1, 2, 3, 5, ___
Sort: Growing or Shrinking Pattern?
Sort each pattern.
Create Your Own Pattern (Set A)
Create a number pattern using the given rule. Write the first 5 numbers.
Rule: Start at 7, add 6. Pattern: 7, ___, ___, ___, ___
Rule: Start at 2, multiply by 2. Pattern: 2, ___, ___, ___, ___
Rule: Start at 50, subtract 7. Pattern: 50, ___, ___, ___, ___
Create Your Own Pattern (Set B)
Create the pattern.
Rule: Start at 100, subtract 11. Pattern: 100, ___, ___, ___, ___
Rule: Start at 3, multiply by 3. Pattern: 3, ___, ___, ___, ___
Rule: Start at 1, add 8. Pattern: 1, ___, ___, ___, ___
Describe the Pattern
Look at each pattern and describe the rule in words.
4, 8, 12, 16, 20 — The rule is: ___
3, 6, 12, 24, 48 — The rule is: ___
80, 72, 64, 56, 48 — The rule is: ___
1, 4, 9, 16, 25 — The rule is: ___
Continue the Pattern
Work out the rule, then write the next 3 numbers.
6, 11, 16, 21, ___, ___, ___
2, 6, 18, 54, ___, ___, ___
95, 86, 77, 68, ___, ___, ___
1, 2, 4, 7, 11, ___, ___, ___
Shape Patterns (Set A)
What comes next? Fill in the blank shapes.
Shape Patterns (Set B)
Fill in the missing shapes.
Two-Step Rules
Follow the two-step rule to generate the pattern.
Rule: Multiply by 2, then add 1. Start at 1: ___, ___, ___, ___, ___
Rule: Add 3, then multiply by 2. Start at 1: ___, ___, ___, ___
Rule: Double, then subtract 1. Start at 2: ___, ___, ___, ___, ___
Find the Hidden Rule
These patterns have tricky rules. Work them out.
1, 1, 2, 3, 5, 8, 13 — What is the rule? Write the next two numbers.
1, 4, 9, 16, 25 — What is the rule? Write the next two numbers.
2, 3, 5, 8, 12, 17 — What is the rule? Write the next two numbers.
Make Up Your Own Rule and Pattern
Be creative!
Write your own rule: ___
Write the first 6 numbers of your pattern: ___
Challenge: write a two-step rule and its first 5 numbers:
Home Activity: Pattern Detectives
Find and create patterns at home!
- 1Count tiles in your bathroom. How does the pattern grow row by row?
- 2Write a 'secret code' using a number pattern rule. Can your family crack it?
- 3Stack blocks following a rule (e.g. each layer has 2 more). Draw the pattern.
- 4Find patterns in house numbers on your street. What is the rule?
Fibonacci-Style Pattern
Each number is the sum of the two before it. Fill in the missing values.
Multiplication Patterns
Fill in the missing values in each multiplication pattern.
Identify the Rule (Set A)
Circle the rule that matches each pattern.
5, 10, 20, 40, 80 …
100, 90, 80, 70, 60 …
3, 6, 9, 12, 15 …
1, 4, 9, 16, 25 …
Create an Algorithm
Write the steps of your algorithm, then use it to generate a number pattern.
Start with 4. Rule: multiply by 3 then subtract 2. Generate the first 6 values:
Start with 100. Rule: divide by 2 then add 5. Generate the first 5 values:
Create your own algorithm and list the first 6 values:
Match Pattern to Its Rule
Draw a line from each pattern to its rule.
What Comes Next? (Set A)
Extend each pattern by 4 more terms and write the rule.
7, 14, 21, 28 → Rule: ___, Next: ___, ___, ___, ___
256, 128, 64, 32 → Rule: ___, Next: ___, ___, ___, ___
2, 5, 10, 17, 26 → Rule: ___, Next: ___, ___, ___, ___
Sort Patterns: Increasing or Decreasing?
Sort each pattern into the correct column.
Two-Operation Patterns
Each pattern uses two operations. Find the rule and continue.
3, 7, 15, 31 → Rule: ×2+1 each time. Next: ___
100, 52, 28, 16 → Rule: ___, Next: ___
2, 5, 11, 23 → Rule: ×2+1 each time. Next: ___
Number Patterns Survey
Students vote for their favourite type of number pattern.
| Item | Tally | Total |
|---|---|---|
Add/subtract pattern | ||
Multiply/divide pattern | ||
Square number pattern | ||
Two-operation pattern |
Pattern Puzzles
Solve each pattern puzzle.
___, 15, ___, 45, 60. Rule: add 15. Find the missing values.
___, 6, ___, 24, 48. Rule: double each time. Find the missing values.
100, ___, 84, ___, 68. Rule: subtract ___. Find the rule and missing values.
Pascal's Triangle Pattern
Each number in Pascal's Triangle is the sum of the two numbers above it.
Fill in row 5: 1, ___, ___, ___, ___, 1
What are the row sums for rows 1 to 5? 1, 2, ___, ___, ___
What pattern do you notice in the row sums?
Number Pattern in Tables
Use a table to record and describe the pattern.
Input: 1, 2, 3, 4, 5. Rule ×4: Output: ___, ___, ___, ___, ___
Input: 2, 4, 6, 8, 10. Rule ÷2+3: Output: ___, ___, ___, ___, ___
Describe the relationship between input and output for rule ×4:
Predicting Large Terms
Use the pattern rule to predict specific terms.
Pattern: 5, 10, 15, 20 … What is the 10th term? The 20th term?
Pattern: 3, 6, 12, 24 … What is the 8th term?
Pattern: 1, 4, 9, 16, 25 … What is the 10th term? What type of numbers are these?
Challenge: Reverse Engineering a Pattern
Work backwards to find the start of each pattern.
The 5th term in a +7 pattern is 35. What is the 1st term?
The 4th term in a ×3 pattern is 81. What is the 1st term?
Write a pattern where the 6th term is 100. What is the rule?