Discover that mathematics is really the study of patterns — in numbers, shapes, and everyday sequences.
Many sequences of numbers follow a hidden rule. Once you spot the rule — like always adding the same amount, or following the shape of triangular or square numbers — you can predict what comes next.
What are the first 5 triangular numbers (1, 3, 6, 10, ...)? What is the rule?
1, 3, 6, 10, 15 — each number adds one more than the previous addition (add 2, then 3, then 4, then 5)
What comes next in the sequence 1, 4, 9, 16, 25, ...?
36 — these are square numbers (1², 2², 3², 4², 5², 6²)
Patterns aren't just about numbers — shapes made of dots or tiles can also follow a growing rule, and counting how many dots or tiles are added at each step reveals the pattern.
A pattern of dots forms triangles: 1 dot, then 3 dots, then 6 dots. How many dots in the next triangle?
10 dots — each triangle adds one more row than the last
A pattern of squares uses 4, 8, 12 matchsticks for 1, 2, 3 squares in a row. How many matchsticks for 4 squares?
16 matchsticks — following the rule of adding 4 more each time
1. What comes next in 2, 4, 8, 16, ...?
2. What are the first 4 triangular numbers?
3. What comes next in 1, 8, 27, 64, ...?
4. A pattern uses 3 matchsticks for 1 triangle, then adds 2 more matchsticks for each extra triangle in a row. How many matchsticks for 5 triangles?
5. What comes next in 5, 10, 15, 20, ...?