ACARA v9 CONTENT DESCRIPTION “solve problems involving multiplication of larger numbers by one- or two-digit numbers, choosing efficient calculation strategies and using digital tools where appropriate; check the reasonableness of answers”
Builds on multiplication facts and place value. Year 5 multiplies larger numbers by one- or two-digit numbers, using efficient strategies such as partitioning and the area model, using a calculator where it makes sense, and always checking that the answer is reasonable by estimating first. Multiplying larger numbers is a matter of breaking the work into manageable parts and putting them back together.
Multiplying by partitioning
One efficient way to multiply a larger number is to partition it by place value and multiply each part. To work out twenty-three times four, split twenty-three into twenty and three: twenty times four is eighty, three times four is twelve, and eighty plus twelve is ninety-two. Partitioning turns a hard multiplication into a few easy ones using known facts, then adds the results. For a three-digit number the same idea applies, splitting into hundreds, tens and ones, so any larger number can be multiplied by a single digit this way.
Multiplying by partitioning
Split by place value, multiply each part, then add.
Multiply 23 by 4 by partitioning.
The area model
The area model lays the same partitioning out as a grid, which is especially helpful for multiplying two two-digit numbers. To find twenty-three times fourteen, both numbers are split by place value: twenty and three across the top, ten and four down the side. Each cell of the grid is one partial product, twenty times ten is two hundred, twenty times four is eighty, three times ten is thirty, and three times four is twelve. Adding the four partial products, two hundred plus eighty plus thirty plus twelve, gives three hundred and twenty-two. The grid makes sure no part is missed.
The area model
Each cell is a partial product; add them all.
Use the area model for 23 x 14.
Choosing an efficient strategy
Choosing an efficient strategy makes multiplication quicker and less error-prone. Partitioning and the area model suit most problems, but some numbers invite a shortcut: ninety-nine times six is easiest as one hundred times six, six hundred, minus six, giving five hundred and ninety-four. A calculator is the right tool when the numbers are large or the multiplication is one step inside a bigger problem. The skill is to look at the numbers first and pick the method that fits them, rather than always using the same one.
Choosing an efficient strategy
Match the method to the numbers.
Choose the strategy that fits the numbers.
Checking the answer is reasonable
Before trusting an answer, it is worth checking that it is reasonable by estimating. Rounding each number to a convenient value gives a quick approximate answer: forty-eight times twenty-one is about fifty times twenty, which is one thousand, so a result near one thousand is sensible and a result of one hundred or ten thousand is not. Estimating first, or checking afterwards, catches mistakes such as a misplaced digit. A reasonable answer is close to the estimate; one far from it is a signal to check the working again.
Checking the answer is reasonable
Round, estimate, and compare to the result.
Estimate by rounding to check the answer.
Solving multiplication problems
Multiplication solves many everyday problems: the total cost of several identical items, the number of objects in equal rows, or the distance of several equal stages. The steps are the same each time: decide that multiplication is needed, choose an efficient strategy, carry it out, and check the answer against an estimate. Setting the problem out clearly, with the numbers and the operation, helps avoid slips. The same partitioning and area-model methods that work for bare calculations work just as well inside word problems.
Solving multiplication problems
Choose a strategy, calculate, then check.
Multiply, then check against an estimate.
Multiplying with confidence
Multiplying larger numbers confidently comes down to breaking the work into parts and recombining them: partition by place value, or lay the parts out as an area model, choose the strategy that fits the numbers, use a calculator when it helps, and always check the answer against an estimate. These habits make multiplication by one- and two-digit multipliers reliable, and they prepare a child for the division, the larger calculations and the multi-step problems of later years.
Quick self-check
1. To multiply 23 x 4 by partitioning, you work out...
2. In the area model for 23 x 14, the four parts are...
3. An efficient strategy for 99 x 6 is...
4. A good estimate for 48 x 21 is...
5. If 23 x 4 is calculated as 920, the answer is...