Multiplication
Lessons in this chapter
About Multiplication
Multiplication is the chapter that completes the times tables and, more importantly, gives kids the properties that let them work around a fact they have forgotten.
Multiply Single-Digit Numbers Using Equal Groups, Arrays, Number Lines offers three pictures of the same operation. The number line is the new one, and it is the one that carries furthest, because it is how multiplication will later be shown for fractions and negatives.
The table lessons work outward from the easy sets: 2, 5 and 10 first, then 3 and 4, then 6 and 8, then 7 and 9. Leaving 7 until last is deliberate, since by then every other table has already supplied most of its facts.
Understand the Zero, Identity, and Commutative Properties of Multiplication is where the tables get cheaper. Commutativity alone halves what has to be memorized, because knowing 7 × 3 means knowing 3 × 7.
Understand the Distributive Property of Multiplication and Multiply Single-Digit Numbers by Multiples of 10 using the Associative Property give kids a route to any forgotten fact. A child who cannot recall 7 × 8 can take 7 × 4 twice, and that is a far better position than being stuck.
Build multiplication tables of 2, 5, and 10, Build Multiplication Tables of 6 and 8 and Understand the Distributive Property of Multiplication each open as a worksheet in the page, scored as your child works. Four of the eight lessons are times tables practice, taught in order of difficulty, and the properties lessons give a child a route to any fact they cannot recall. All eight are free.
Frequently asked questions
Multiplying with equal groups, arrays and number lines, then building the tables in order of difficulty: 2, 5 and 10, then 3 and 4, then 6 and 8, then 7 and 9. The zero, identity, commutative, distributive and associative properties are taught alongside them, the last one for multiplying by multiples of 10. It sits in Operations and Algebraic Thinking (3.OA).
All of them from 2 to 10. The chapter builds them in order of difficulty: 2, 5 and 10, then 3 and 4, then 6 and 8, then 7 and 9.
It halves them. 7 × 3 and 3 × 7 give the same answer, so learning one gives you the other free.
Splitting one factor and multiplying each part. 7 × 8 can be done as 7 × 4 plus 7 × 4, which gives a route to any fact a child cannot recall.
Because by the time you get there, the other tables have already covered most of its facts. 7 × 2, 7 × 5, 7 × 3 and so on are all already known through commutativity.
Multiplying any number by 1 leaves it unchanged, since 1 is the multiplicative identity. It is a simple rule, but it still catches kids out when it appears inside a longer calculation.