Level 2: Trees and lists

Counting and combinations · level 2 of 8 · rough age 7-8 (a guide for parents; anyone can start anywhere)

In level 1 you counted with tidy lists and boxes. In this level the lists grow into tree diagrams, and the trees turn into a quick multiplication. You learn when to multiply and when to add, count codes and locks, find the handshake numbers hiding in the diagonals of a shape, and hunt down every triangle and rectangle in a picture. Each time, you also learn why the count is right.

Lesson	You will be able to
Tree diagrams	Draw a tree for choices made in steps, read a path as one result, and explain why counting tips counts results
From trees to multiplying	Count the tips of an even tree by multiplying (3 × 2 × 2 = 12), and spot an uneven tree where you must add
"And" multiplies, "or" adds	Decide between adding and multiplying from the words of a problem, use both together, and avoid double counting
Codes and locks	Count codes with repeats (100 two-digit codes, 27 three-letter words) and without, and see why each dial multiplies by 10
Handshakes and diagonals	Find the handshake numbers by multiplying and halving, and use them to count the lines between points and the diagonals of any shape
Counting shapes in a picture	Count every triangle and rectangle in a picture by size, and check the count by choosing lines

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