Number Operations
Lessons in this chapter
About Number Operations
Number Operations is where whole-number arithmetic is finished. After this chapter the rest of 5th grade is fractions, decimals and geometry.
Apply the Properties of Multiplication puts the commutative, associative and distributive properties to work as tools rather than facts. Distributivity in particular is what makes multi-digit multiplication possible, since 24 × 36 is really 24 × 30 plus 24 × 6.
Multiply a Number by Multiples of 10 is the pattern the long method depends on, and it is worth being explicit about why appending a zero works: multiplying by 10 shifts every digit one place left.
Multiply Multi-Digit Numbers extends to numbers of any length, where the discipline is keeping the partial products aligned. Divide Multi-Digit Numbers brings long division with multi-digit divisors, which is the hardest procedure in elementary arithmetic because each digit of the answer has to be estimated and then checked.
Estimation is what makes long division survivable. A child who expects a two-digit quotient will notice immediately when they produce a three-digit one, and catching it there is far cheaper than discovering it at the end.
Apply the Properties of Multiplication, Multiply Multi-Digit Numbers and Divide Multi-Digit Numbers each open as a worksheet inside the page. These are the math sheets for 5th graders that carry the long division work, and every question is marked as you answer it. All four lessons are free to try, with no login needed for your first 3.
Frequently asked questions
Apply the Properties of Multiplication puts the commutative, associative and distributive properties to work as tools, since distributivity is what makes multi-digit multiplication possible at all. Multiply a Number by Multiples of 10 is the pattern the long method depends on, Multiply Multi-Digit Numbers extends it to any length, and Divide Multi-Digit Numbers brings long division with multi-digit divisors, the hardest procedure in elementary arithmetic. The chapter sits in the Common Core domain Number and Operations in Base Ten (5.NBT).
Because every digit of the answer has to be estimated before it can be checked, and a wrong estimate means backing up. No other arithmetic procedure asks for that.
It is what the long method does. 24 × 36 is 24 × 30 plus 24 × 6, which is exactly the two rows of a long multiplication.
Because every digit shifts one place left, and the ones place is left empty. The zero is a placeholder, not an extra digit stuck on the end.
Round the divisor and dividend to friendly numbers. 3,847 ÷ 62 is roughly 3,600 ÷ 60, so about 60, which tells you to expect a two-digit answer.
Commutative, the order does not matter. Associative, the grouping does not matter. Distributive, multiplication spreads over addition. The third is the one that does the most work.