Level 3: Sequences and their positions

Patterns and sequences · level 3 of 8 · rough age 9-10 (a guide for parents; anyone can start anywhere)

In level 2 you wrote rules like "start at 3 and add 2 each time". In this level every number in a pattern gets a position, 1st, 2nd, 3rd, and you learn to jump straight to the 10th or the 100th without writing out all the ones before. You meet three famous families of numbers (square, triangular and Fibonacci), find hidden patterns in the times tables, and finish with a warning: a pattern that works for a few numbers can still trick you.

Lesson	You will be able to
Terms and positions	Put a sequence in a position table and find the 10th or 100th term without drawing them all
Square numbers	Draw square numbers as dots, and explain why adding the next odd number makes the next square
Triangular numbers	Draw triangular numbers, and find the 10th or 100th one by fitting two triangles into a rectangle
The Fibonacci sequence	Continue the Fibonacci sequence, solve the rabbit and staircase puzzles, and check claims about sunflowers
Patterns in the multiplication table	Explain why the last digits of the 4s and 6s repeat, and why the table is the same flipped over its diagonal
Patterns that trick you	Show that 1, 2, 4, 8 can go on in more than one way, and explain why a few terms are not a proof

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