Handout: Pattern Detective Agency
Your mission is to crack the code behind these patterns!
Case #1: The Growing Shapes
1. Draw the next two shapes in the pattern.
2. How many triangles will be in the 6th shape? _________
3. What is the rule for this pattern? _________________________
Case #2: The Skipping Numbers
1. What are the next two numbers in the sequence?
2. What is the rule for this pattern? _________________________
Case #3: The Mirrored Pattern
1. What are the next three numbers in this sequence?
2. Describe the pattern in your own words. _________________________
Extra Challenge: The Two-Step
Can you figure out the two-step rule and find the next number?
Rule: _________________________
🔑 Kaiako answer key
Case #1 — The Growing Shapes
- The next two shapes have 4 triangles and 5 triangles.
- The 6th shape has 6 triangles.
- Rule: n — the shape number is the number of triangles.
Case #2 — The Skipping Numbers
- 19, 23
- Rule: add 4 each time. As an expression for the nth term: 4n − 1 (check: 4(1) − 1 = 3 ✓).
Case #3 — The Mirrored Pattern
- 2, 3, 2
- The block 1, 2, 3, 2 repeats over and over. It climbs to 3 and comes back down. The tenth term is 2, the eleventh is 3, the twelfth is 2.
Extra Challenge — The Two-Step
- Rule: double it and add 1. Check: 2×2 + 1 = 5, 5×2 + 1 = 11, 11×2 + 1 = 23 ✓.
- Next number: 47.
Watch for: in Case #2 many ākonga will answer “add 4” and stop. That is a correct rule — accept it, then ask what the 100th number would be, which is what forces 4n − 1.
📋 Teacher Planning Snapshot
Ngā Whāinga Ako — Learning Intentions
A worksheet for Lesson 1. Ākonga meet several kinds of sequence — arithmetic, geometric and repeating — and work out the rule for each.
Ngā Paearu Angitū — Success Criteria
- ✅ I can continue an arithmetic, a geometric and a repeating pattern.
- ✅ I can describe each rule in my own words.
- ✅ I can find a two-step rule such as "double it and add 1".
Differentiation & Inclusion
The four cases are different kinds of pattern on purpose, so a struggle with Case #3 says nothing about Case #2. Offer counters for Case #1 and a number line for Case #2. The Extra Challenge is genuinely hard — treat it as optional.