Level 1: How many ways?

Counting and combinations · level 1 of 8 · rough age 5-6 (a guide for parents; anyone can start anywhere)

Counting one, two, three is easy. Counting ways is a puzzle: how many outfits, how many line-ups, how many paths? In this level you count them with your hands, with cut-out pictures and with tidy lists, and for every answer you learn how to be sure that nothing is missing and nothing is counted twice. You also meet the question that runs through this whole topic: does the order matter?

Lesson	You will be able to
Dressing a teddy	Lay out every outfit in a box of rows and columns, and explain why 2 shirts and 3 pants make 6 outfits, not 5
Ice-cream towers	Tell when the order matters (towers) and when it does not (cups), and see why towers are double the cups
Lining up	Find all 6 line-ups of 3 friends by keeping the front person still, and use that to get 24 for 4 friends
Handshakes	Count handshakes with dots and lines, explain why "each shakes 3, so 12" counts everything twice
Paths to the playground	Trace every right-and-up path on a small grid, and count paths fast with the corner trick
Being organised	Make a tidy list in a fixed order, use it to find a missing or repeated item, and check a count two ways

Next: Level 2: Trees and lists · Back to the topic: Counting and combinations