Patterns — Grade 2 Mathematics
In Grade 2, we move from simple colour/shape repeating patterns to number patterns. We find the rule that links numbers in a sequence and use it to extend or complete the pattern. We also use input/output tables to represent rules with larger numbers.
Number Sequences and Skip Counting
Common rules:
- + rule: Add the same amount each time (e.g., +3, +5, +10)
- − rule: Subtract the same amount (e.g., −2, −4)
- × rule: Double each time (×2), triple (×3), etc.
Sequence Examples
Rule: +5
Rule: −4
Input/Output Tables
If the input is in and the output is out, then the rule might be: out = in + 7 or out = in × 3, etc.
Example table (rule: ×2 + 1)
| Input (in) | Output (out) |
|---|---|
| 1 | 3 |
| 2 | 5 |
| 3 | 7 |
| 4 | 9 |
| 5 | ? |
Rule: out = in × 2 + 1. So when in = 5: out = 5 × 2 + 1 = 11.
Worked Examples
Find the rule and fill in the missing number:
- 7 − 3 = 4, 11 − 7 = 4 → Rule: +4
- 11 + 4 = 15
- Check: 15 + 4 = 19 ✓
| In | Out |
|---|---|
| 4 | 12 |
| 6 | 18 |
| 8 | 24 |
| 10 | ? |
- 12 ÷ 4 = 3; 18 ÷ 6 = 3; 24 ÷ 8 = 3 → Rule: out = in × 3
- 10 × 3 = 30
Amir saves 8 stickers every week. He starts with 4. How many does he have after 5 weeks?
4
12
20
28
36
44
After 5 weeks: 44 stickers.
Practice Questions
Try each question. Show the answer when ready.
1. What is the next number? 10, 17, 24, 31, ___
2. What is the missing number? 50, 44, 38, ___, 26
3. Complete the table: In = 5, rule = in × 4. Out = ?
4. Find the rule: In = 3 → Out = 9; In = 5 → Out = 15; In = 7 → Out = 21.
5. A baker bakes 12 cookies each hour. How many cookies after 4 hours?
Key Points to Remember
- Find the rule by subtracting or dividing consecutive terms.
- A + rule means the sequence increases; a − rule means it decreases.
- An input/output table applies the same rule to every input number.
- Always check your rule works for all given pairs.
- Patterns help us predict without counting every single step.