Rules for Growing Patterns
Continue the Addition Pattern
Find the rule and fill in the missing numbers.
Continue the Multiplication Pattern
Find the rule and fill in the missing numbers.
Subtraction Patterns
Fill in the missing numbers in each decreasing pattern.
Match the Pattern to the Rule
Draw a line to match each pattern to its rule.
Match More Patterns to Rules
Draw a line to match each pattern to its rule.
What Is the Rule?
Circle the rule for each pattern.
4, 7, 10, 13, 16, ...
2, 6, 18, 54, ...
80, 70, 60, 50, ...
1, 4, 16, 64, ...
Write the Next Three Numbers
Identify the rule and write the next 3 numbers in each pattern.
6, 11, 16, 21, ___, ___, ___. Rule: ___
3, 6, 12, 24, ___, ___, ___. Rule: ___
500, 450, 400, 350, ___, ___, ___. Rule: ___
1, 5, 25, 125, ___, ___, ___. Rule: ___
Describe the Rule
Look at each pattern. Write the rule and find the next two numbers.
4, 8, 12, 16, 20, ___, ___ Rule: ___
1, 3, 9, 27, 81, ___, ___ Rule: ___
100, 90, 80, 70, 60, ___, ___ Rule: ___
2, 5, 8, 11, 14, ___, ___ Rule: ___
Describe More Rules
Write the rule and find the next two numbers.
7, 14, 28, 56, ___, ___ Rule: ___
1000, 800, 600, 400, ___, ___ Rule: ___
3, 5, 9, 15, 23, ___, ___ Rule: ___
What Comes Next?
Circle the next number in each pattern.
1, 2, 4, 8, 16, ?
50, 45, 40, 35, ?
3, 6, 12, 24, ?
7, 11, 15, 19, ?
More Next Numbers
Circle the next number in each pattern.
5, 8, 11, 14, ?
2, 10, 50, 250, ?
1000, 900, 800, 700, ?
1, 4, 9, 16, ?
Input-Output Tables
Complete each input-output table and write the rule.
Input: 1→4, 2→7, 3→10, 4→?, 5→? Rule: ___
Input: 1→3, 2→6, 3→12, 4→?, 5→? Rule: ___
Input: 2→5, 4→9, 6→13, 8→?, 10→? Rule: ___
Growing Shape Patterns
A pattern grows like this: Step 1 = 1 square, Step 2 = 3 squares, Step 3 = 5 squares. Answer the questions.
How many squares at Step 4? ___
How many squares at Step 5? ___
What is the rule? ___
How many squares at Step 10? ___
Another Growing Pattern
A pattern grows: Step 1 = 4 dots, Step 2 = 7 dots, Step 3 = 10 dots.
How many dots at Step 4? ___
How many dots at Step 6? ___
Write a rule to find the number of dots for any step: ___
How many dots at Step 20? ___
Create Your Own Growing Pattern
Design your own growing pattern.
My rule: ___ Step 1: ___ Step 2: ___ Step 3: ___ Step 4: ___ Step 5: ___
How many at Step 10? ___ How did you work it out? ___
Two-Step Rule Patterns
Some patterns use a two-step rule (e.g. multiply by 2 then add 1).
Pattern: 1, 3, 7, 15, 31, ___. Rule: ___
Pattern: 2, 5, 11, 23, 47, ___. Rule: ___
Pattern: 0, 1, 4, 13, 40, ___. Rule: ___
Home Activity: Pattern Creator
Create your own growing patterns!
- 1Use blocks or counters to build a growing pattern. Draw each step.
- 2Make a pattern that starts at 2 and doubles each time. How big does it get after 8 steps?
- 3Create a decreasing pattern that starts at 1,000 and subtracts 75 each time.
- 4Find a growing pattern in nature (e.g. petals on flowers, spirals in shells).
- 5Challenge a family member with a pattern and see if they can find the rule.
Fibonacci-Like Sequences
In this sequence, each term = the two before it added together. Fill the missing numbers.
Arithmetic Sequences
An arithmetic sequence has a constant difference. Find the rule and complete each sequence.
8, 13, 18, 23, ___, ___. Common difference: ___
100, 85, 70, 55, ___, ___. Common difference: ___
-5, -1, 3, 7, ___, ___. Common difference: ___
Geometric Sequences
A geometric sequence multiplies by the same ratio each time. Complete each sequence.
3, 6, 12, 24, ___, ___. Common ratio: ___
500, 100, 20, 4, ___, ___. Common ratio: ___
2, 6, 18, 54, ___, ___. Common ratio: ___
Match Sequence Type to Rule
Draw a line to match each sequence to its rule type.
Pattern Tables
Complete each pattern table.
Position: 1, 2, 3, 4, 5, 10. Term (×4 + 1): 5, ___, ___, ___, ___, ___
Position: 1, 2, 3, 4, 5, 10. Term (3n − 2): ___, ___, ___, ___, ___, ___
Position: 1, 2, 3, 4, 5. Term (n²): ___, ___, ___, ___, ___
Generalising Patterns with Algebra
Write an algebraic rule for the nth term of each pattern.
Pattern: 5, 10, 15, 20. nth term = ___
Pattern: 7, 9, 11, 13. nth term = ___
Pattern: 2, 5, 8, 11. nth term = ___
Pattern: 0, 3, 8, 15, 24. nth term = ___
Which Term Comes Next?
Circle the next term in each sequence.
Fibonacci: 13, 21, 34, ?
Arithmetic: -8, -3, 2, 7, ?
Geometric: 1,000, 500, 250, ?
Square: 1, 4, 9, 16, 25, ?
Sort Sequences by Type
Sort each sequence into the correct type.
Pattern Investigation: Square Numbers
Investigate the pattern of square numbers.
First differences of 1, 4, 9, 16, 25: ___
Second differences of those: ___
What do you notice about the second differences? ___
Predict the next square number using this pattern: ___
Counting Patterns in Shapes
Patterns of squares: Step 1 = 1 square, Step 2 = 5 squares, Step 3 = 13 squares. Each icon = 1 square.
| Step 1 | |
| Step 2 | |
| Step 3 | |
| Step 4 |
What is the rule for this pattern?
How many squares at Step 5?
Write an algebraic rule for the nth term.
Patterns in Nature
Answer these questions about mathematical patterns in nature.
Sunflower seeds follow a Fibonacci spiral. The Fibonacci sequence starts 1, 1, 2, 3, 5, 8... List the next 5 terms: ___
The ratio of consecutive Fibonacci numbers approaches 1.618. This is called the ___
Find an example of a growing pattern in real life and describe the rule: ___
How Quickly Does It Grow?
Track how fast each sequence grows. Tally the size of terms 1-5.
| Item | Tally | Total |
|---|---|---|
Add 3 (e.g. 3,6,9,12,15) | ||
Multiply by 2 (e.g. 1,2,4,8,16) | ||
Square (1,4,9,16,25) |
Creating Pattern Rules
Create a growing pattern that meets each condition.
Pattern that starts at 3 and grows by multiplying by 3: ___
Pattern where the 10th term is exactly 100: ___
Pattern where the differences are 2, 4, 6, 8 (triangle numbers): ___
Predicting with Patterns
Use the pattern rule to predict terms far in the sequence.
Rule: 2n + 3. What is the 20th term? ___. The 100th term? ___
Rule: 5n − 2. What is the 15th term? ___. The 50th term? ___
Arithmetic sequence: first term 4, common difference 7. What is the 12th term? ___
Comparing Two Growing Patterns
Compare these two patterns.
Pattern A: 2, 5, 8, 11 (add 3). Pattern B: 1, 3, 9, 27 (multiply by 3). Which is larger at term 5? ___. At term 10? ___
Which pattern grows faster in the long run? ___. Why? ___
nth Term Calculations
Calculate each term using the formula given.
Formula 3n + 1. Term 6 = ?
Formula 4n − 3. Term 5 = ?
Formula n². Term 8 = ?
Formula 2n². Term 4 = ?
Patterns with Ratios and Proportions
Investigate patterns involving ratios.
Ratio of 3:5 grows as 6:10, 9:15, 12:___, ___:25
A pattern where every term is 3/4 of the previous: Start at 256. List 5 terms: ___
If the ratio of boys:girls is 2:3 in every class, and there are 120 students total, how many girls? ___