A pattern is not just something that repeats. It is a structure generated by a rule. Primary 1 learners begin with visible repetitions and simple number sequences, then learn to identify what changes, what stays the same, and how to predict what comes next.
This laboratory extends Number Patterns, Sequences, Rules and Pattern Recognition, the Hundred Chart Laboratory, and the Equal Groups & Arrays Laboratory.
The useful question is not only “what comes next?” but “what rule makes the next term inevitable?”
Session 1 | Repeating Patterns
Build red-blue-red-blue-red-blue with counters. Ask what repeats. The repeating unit is red-blue. The child should identify the smallest useful repeat rather than describe the whole visible string.
Then extend the pattern beyond what is already shown. Prediction becomes evidence that the rule has been understood.
Worked Example 1 | Find the Repeating Unit
Circle, square, triangle, circle, square, triangle… repeats in groups of three. The next term is circle.
Session 2 | Growing Patterns
Show towers with 1 cube, 2 cubes, 3 cubes, 4 cubes. The pattern grows by one cube each step. The fifth tower should contain 5 cubes.
Contrast this with a repeating colour pattern. In a growing pattern, the quantity changes according to a rule rather than returning to the same small cycle.
Worked Example 2 | Add Two Each Time
2, 4, 6, 8, __ follows a +2 rule. The next number is 10. The rule explains every step, not only the last pair.
Session 3 | Missing Terms
Give 5, 10, __, 20, 25. The missing term is 15 because the sequence increases by 5 every time.
A learner should check both neighbours. Fifteen is 5 more than 10 and 5 less than 20.
Worked Example 3 | Two Missing Terms
12, 14, __, __, 20 uses a +2 rule. The missing terms are 16 and 18.
Session 4 | Skip Counting as a Pattern
Skip-counting by 2 produces 2, 4, 6, 8, 10. By 5: 5, 10, 15, 20. By 10: 10, 20, 30, 40. Connect these sequences to equal groups and hundred-chart movement.
The child should know what each jump adds. Skip counting is stronger when it represents repeated equal change rather than a memorised chant.
Worked Example 4 | Tens on the Hundred Chart
23, 33, 43, 53… increases by 10. The ones digit stays 3 while the tens increase by one.
Session 5 | Detect the Rule From Differences
For 18, 21, 24, 27, compare consecutive terms. Each increase is 3. Therefore the rule is +3.
For 40, 35, 30, 25, each change is −5. Patterns can decrease as well as increase.
Worked Example 5 | Decreasing Sequence
30, 27, 24, 21 follows −3. The next term is 18.
Session 6 | Rule Machines
Use a simple input-output machine. Input 4 becomes 6; input 7 becomes 9; input 10 becomes 12. The rule is “add 2”.
Then reverse the task: if the rule is +2 and the output is 15, the input must have been 13. This introduces inverse thinking without formal function notation.
Worked Example 6 | Input and Output
| Input | Output |
|---|---|
| 3 | 8 |
| 5 | 10 |
| 9 | 14 |
Every output is 5 more than the input, so the rule is +5.
Visual Patterns and Number Patterns Can Connect
A staircase of 1, 2, 3, 4 cubes produces the number sequence 1, 2, 3, 4. A row of growing pairs might produce 2, 4, 6, 8. Recording the visible growth numerically helps transfer between representations.
Not Every List Has a Unique Rule
A short list such as 2, 4, 6 may fit more than one imaginable rule. At Primary 1, use clear intended rules and enough terms to make the pattern reasonable. Do not present ambiguous sequences as if only one sophisticated rule could exist.
The learning goal is to identify and apply a stated or strongly supported simple rule.
Check a Claimed Rule
If a child says the rule for 7, 10, 13, 16 is +2, test the rule against more than one transition. Seven plus two is 9, not 10, so the claim fails immediately. The correct rule is +3.
Common Pattern Errors
| Error | Likely weak link |
|---|---|
| predicts next term without stating rule | pattern recognition may be superficial |
| checks only final pair | rule consistency not tested |
| confuses repeating with growing pattern | type of change not identified |
| skip-count chant breaks when starting point changes | equal-step structure weak |
| cannot work backwards through rule machine | inverse relationship weak |
| copies visual pattern but cannot record number sequence | representation transfer weak |
Twenty Practice Questions
- Continue: red, blue, red, blue, __.
- Continue: circle, square, triangle, circle, square, triangle, __.
- Continue: 2, 4, 6, 8, __.
- Continue: 5, 10, 15, __, __.
- Fill the blank: 12, 14, __, 18.
- Fill two blanks: 21, __, __, 27.
- Continue: 40, 35, 30, __.
- What is the rule: 18, 21, 24, 27?
- What is the rule: 50, 40, 30, 20?
- Continue: 23, 33, 43, __.
- Which digit stays the same in 23, 33, 43, 53?
- A tower pattern has 1, 2, 3, 4 cubes. How many in the next tower?
- A pattern has 2, 4, 6, 8 objects. How many are added each stage?
- Rule machine +2: input 7. Output?
- Rule machine +5: input 9. Output?
- Rule machine +3: output 12. What input?
- Is +2 a correct rule for 7, 10, 13, 16?
- Give the correct rule for 7, 10, 13, 16.
- Create a four-term increasing pattern with rule +4.
- Create a four-term decreasing pattern with rule −2.
Explained Answers
1. red. 2. circle. 3. 10. Rule +2. 4. 20, 25. Rule +5. 5. 16. 6. 23, 25. Rule +2.
7. 25. Rule −5. 8. +3. 9. −10. 10. 53. 11. The ones digit 3. 12. 5 cubes. 13. 2 objects.
14. 9. 15. 14. 16. 9. Nine plus three gives twelve. 17. No. Seven plus two is nine, not ten. 18. +3. 19–20. Many answers are valid if the same stated rule is used consistently.
A Strong Practice Progression
- Copy and extend repeating patterns.
- Identify the repeating unit.
- Build simple growing patterns.
- Record visual growth numerically.
- Fill one missing term.
- Fill several missing terms.
- Skip count by equal steps.
- Detect increase or decrease rules.
- Use simple input-output machines.
- Work backwards through a known rule.
What Adults Can Ask
- “What repeats?”
- “What changes each time?”
- “How much does it change by?”
- “Does your rule work for every step?”
- “Can you show the same pattern with objects and numbers?”
- “Can you reverse the rule?”
Return to the Primary 1 Mathematics Learning Hub.
