Year 4 · Short Multiplication and Short Division · Summary

Year 4 Short Multiplication and Short Division: summary and key words

Part of the Year 4 short multiplication and short division chapter. Chapter overview · whole chapter on one page

Chapter summary

Skill	Method
× and ÷ by 10, 100	Digits move 1 place (10) or 2 places (100): left to multiply, right to divide. Zeros are place holders. 35 × 100 = 3,500; 3,500 ÷ 10 = 350.
Distributive law	34 × 6 = (30 + 4) × 6 = 30 × 6 + 4 × 6 = 180 + 24 = 204. Near a round number: 29 × 6 = 30 × 6 − 6.
Grid method	Partition into hundreds, tens and ones. Multiply each part. Add the partial products. Keep the zeros.
Expanded column	Multiply each digit by its value: 7 × 6, 40 × 6, 300 × 6. Write each on its own line. Add.
Short multiplication	Start with the ones. Write the ones digit of each answer, carry the tens digit and add it in the next column. Estimate to check.
Division with place value	Split into chunks: 84 ÷ 4 = 80 ÷ 4 + 4 ÷ 4. Use known facts: 2,400 ÷ 6 = 400.
Short division (bus stop)	Start on the left. Divide each digit, carry the remainder to the next digit. Write 0 when a step is too small. Check by multiplying back.
Remainders	The remainder is what is left over and is smaller than the divisor. Check: answer × divisor + remainder = start.
Remainders in context	Left over: the remainder. Full groups: ignore it. Enough for everyone: round up. Sharing: say both parts.
Scaling	“n times as many”: multiply. To go back, divide. Do not confuse with “n more” (add).
Correspondence	n things each connected to m things make n × m combinations (3 hats and 5 tops: 15 outfits). Three groups: multiply all three.
Three numbers	Multiply in any order. Look for a pair that makes 10 or 100 first.
Word problems	Read, draw a bar model, choose the operations, work one step at a time, check the answer fits the question.

Can you…?

I can multiply and divide whole numbers by 10 and 100 by moving the digits.
I can use partitioning and the distributive law to multiply a two-digit number by a one-digit number in my head.
I can use the grid method and the expanded method to multiply two-digit and three-digit numbers by one digit.
I can use short multiplication with carrying, and check with an estimate.
I can divide using place value and known facts.
I can use the bus stop method to divide two-digit and three-digit numbers by one digit, with and without a remainder.
I can decide what a remainder means in a story.
I can solve problems with “n times as many”.
I can solve problems like 3 hats and 5 tops (correspondence).
I can multiply three numbers by choosing an easy pair first.
I can solve multi-step word problems with a bar model.

Key terms

Digit: One of the symbols 0 to 9 used to write numbers.
Place holder: A zero that keeps other digits in the right columns, as in 340.
Partition: To split a number into parts, such as 347 = 300 + 40 + 7.
Partial product: The answer to one part of a multiplication, such as 40 × 6 = 240.
Distributive law: Splitting a number and multiplying each part: (30 + 4) × 6 = 30 × 6 + 4 × 6.
Grid method: Putting the parts of a number in a table and multiplying each part.
Carry: Moving the tens digit of an answer into the next column.
Short multiplication: A written method for multiplying by a one-digit number, column by column.
Short division: The bus stop method for dividing a number by a one-digit number.
Divisor: The number you divide by.
Remainder: What is left over when a number does not divide exactly.
Exchange: Swapping 1 of a place for 10 of the next place down, such as 1 ten for 10 ones.
Scaling: Making an amount a number of times bigger or smaller, such as 4 times as many.
Correspondence: Pairing each object in one group with each object in another group to count the combinations.
Combination: One choice from each group put together, such as one hat and one top.
Estimate: A quick answer that is close, found by rounding.
Bar model: A drawing of boxes that shows the numbers in a problem.
Inverse: The opposite operation. Multiplying and dividing undo each other.