Multiplication and division
When every group holds the same amount, how do two numbers decide the total, and how do you work backward from a total?
Where you are 16 inside
What this area is about
Multiplication counts equal groups: when every group is the same size, the number of groups and the size of each decide the total. Division runs the other way, from a total back to the size of a group or the number of groups. Here the numbers are whole numbers.
How these fit together
Meanings. What multiplication means, rows and columns of objects, arrays, the area model, times as many and what division means.
Results. Properties of multiplication, the distributive property (splitting a factor into parts), and how multiplying and dividing undo each other.
Facts and methods. Multiplication facts through 10 \times 10, division facts, multi-digit multiplication and long division.
Stories. Equal group problems, what a remainder means and problems using several operations.
A path through it
Start with what multiplication means, then arrays and the properties, and the distributive property before the facts. The area model and the facts lead to multi-digit multiplication. On the division side: what division means, then division facts (after the multiplication facts), then undoing, equal group stories and multi-step problems. Remainders and multi-digit multiplication come before long division, which comes last. Times as many fits anywhere after the first star.
Next come fractions, divisibility and primes, exponents and the order of operations.