Level 2: Factors and multiples

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

In level 1 you made pairs, shared things out and built rectangles from counters. In this level those ideas get their real names. Rectangles become factors, skip counting becomes multiples, and the line-only numbers become primes. You will find out why odd plus odd is always even, find every prime up to 100 with a 2,000-year-old method, and solve a famous puzzle about 100 lockers.

Lesson	You will be able to
Odd and even sums	Say whether a sum is odd or even without adding, and explain why with pairs of blocks
Multiples	List multiples, find their patterns on a hundred chart, and find where two skip counts land together
Factors with arrays	Find every factor of a number with rectangles, and list factors in pairs without missing any
Primes and composites	Tell primes from composites, explain why 1 is not prime, and know the primes up to 50
The sieve of Eratosthenes	Find all the primes up to 100 on a hundred chart, and explain why you can stop after crossing out the 7s
Square numbers and the locker puzzle	Explain why square numbers have an odd number of factors, and solve the 100 lockers puzzle

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