Level 2: Boxes and machines

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

In level 1 the mystery number hid under a cup. In this level it hides in a box, in bigger number sentences, inside number machines and inside stories. You learn to find it with fact families, to keep both sides of the equal sign in balance, to find a machine's secret rule, and to run a machine backwards. You also learn to tell whether a number sentence is true without working it out, which is the first step towards real algebra.

Lesson	You will be able to
Missing numbers with bigger numbers	Find the box in 8 + ? = 15, 20 − ? = 12 and ? − 6 = 9 using fact families and jumps on a number line
The equal sign as a balance	Solve 8 + 4 = ? + 5, and explain why 12 is the wrong answer
Number machines	Find a machine's rule (add 3, double, ...) from in-out pairs, and know when one pair is not enough
Working backwards	Find what went into a two-step machine by undoing its steps in reverse order
True or false number sentences	Decide if sentences like 7 + 5 = 6 + 6 are true by reasoning, without adding up
Unknowns in stories	Turn a story like "Sam gets 7 more marbles and has 12" into ? + 7 = 12, solve it and check it in the story

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