Year 5 · Long Multiplication · Summary

Year 5 Long Multiplication: summary and key words

Part of the Year 5 long multiplication chapter. Chapter overview · whole chapter on one page

Chapter summary

Skill	Method
Multiply by 10, 100, 1,000	Every digit moves 1, 2 or 3 places to the LEFT. Fill empty places with zeros. The decimal point does not move: 4.07 × 100 = 407.
Known facts and zeros	Use 6 × 7 = 42 to get 60 × 70 = 4,200. Count ALL the zeros from both numbers.
Mental strategies	Partition; double one and halve the other; multiply by factors (× 12 = × 3 × 4); × 5 = × 10 then halve; × 25 = × 100 then halve twice; × 9 = × 10 − one lot; × 19 = × 20 − one lot.
The equals sign	It means “is the same value as”. Work out the side you can, then find the missing number that balances the other side: 3 × 4 = 6 × 2.
Grid method	Partition both numbers. Multiply every part by every part (one box each). Add all the boxes.
Short multiplication	Write in columns. Start with the ones. Multiply, add the carry, write the ones digit, carry the tens digit. Write any final carry as the next digit.
Long multiplication	Row 1: number × ones digit. Row 2: write a 0 place holder, then number × tens digit. Add the two rows.
Estimating and checking	Round each number to one digit followed by zeros and multiply. Check the last digit. Use known facts and inverse operations.
Scaling and rates	“n times as many” → × n. “Half / a quarter” → ÷ 2 / 4. Rates: scale both amounts by the same number; cost = price of one × number.
Combinations	Choices in group 1 × choices in group 2 (× group 3). 3 tops and 4 skirts: 12 outfits.
Area, squares and cubes	Area = length × width (cm²). n² = n × n. n³ = n × n × n.
Reasoning	Spot the mistake by working it out yourself. “Always” needs a reason. One counter-example breaks “always”. Puzzles: list all the possibilities.

Can you…?

I can multiply whole numbers and decimals by 10, 100 and 1,000 by moving the digits.
I can multiply in my head using known facts, partitioning, doubling and halving, factors and compensation.
I can multiply a number with up to 4 digits by a one-digit number using short multiplication.
I can multiply a number with up to 4 digits by a two-digit number using the grid method and long multiplication.
I can estimate by rounding and check my answers.
I can solve scaling problems with whole numbers and simple fractions, and problems about rates.
I can count combinations by multiplying.
I can find areas of rectangles, and work out squares and cubes.
I understand the equals sign and can find missing numbers.
I can solve multi-step problems and explain my reasoning.

Key terms

Product: The answer to a multiplication. The product of 6 and 7 is 42.
Multiple: A number in the times table of another number.
Factor: A whole number that divides exactly into another number.
Place holder: A zero that keeps the other digits in the right columns, such as the 0 in 60.
Partition: To split a number into parts, such as 47 = 40 + 7.
Partial product: The answer to one part of a multiplication, such as 40 × 6 in 47 × 6.
Grid method: A way to multiply by partitioning both numbers and filling a grid of boxes.
Short multiplication: A written method for multiplying by a one-digit number, with carrying.
Long multiplication: A written method for multiplying by a number with two or more digits.
Carry: A digit you move to the next column when a column makes 10 or more.
Estimate: An answer that is close, found by rounding. Written with ≈.
Round: To change a number to a nearby number that is easier to use, such as 347 to 300.
Compensate: To multiply by an easy number, then correct the answer: × 19 is × 20 then take away one lot.
Equals sign: The symbol = which means “is the same value as”. Both sides must balance.
Scaling: Making an amount bigger or smaller by multiplying, such as “3 times as long”.
Rate: A comparison of two amounts, such as £3 for 5 apples or 12 km each hour.
Combination: One choice from each group, such as one top and one skirt.
Area: The amount of flat space inside a shape, measured in square units such as cm².
Square number: A number multiplied by itself, such as 36 = 6 × 6. Written 6².
Cube number: A number multiplied by itself twice, such as 64 = 4 × 4 × 4. Written 4³.
Counter-example: One example that shows a statement is false.