AC9M4N06 · YEAR 4 · NUMBER

Efficient Strategies

ACARA v9 CONTENT DESCRIPTION develop efficient strategies and use appropriate digital tools for solving problems involving addition and subtraction, and multiplication and division where there is no remainder
Builds on: Multiplying and Dividing by 10, 100 and 1000 (AC9M4N05). This unit develops efficient mental strategies for addition, subtraction, multiplication and division where the answer comes out exactly.

Splitting into tens and ones

An efficient way to add two-digit numbers in your head is to split each into tens and ones. For 38 + 47, add the tens (30 + 40 = 70), then the ones (8 + 7 = 15), then combine: 70 + 15 = 85. Breaking numbers up by place value keeps each step small and avoids slow counting or column writing. This splitting strategy is one of the most useful for mental addition, and it builds directly on understanding place value. Year 4 develops several such strategies, choosing the one that fits the numbers rather than always working the same way.

Split into tens and ones
Splitting numbers into tens and ones is an efficient way to add mentally.
Add 38 + 47 by splitting each number into tens and ones. Step through it.

Rounding and adjusting

When a number is close to a ten, rounding then adjusting is fast. For 47 + 19, round 19 up to 20, add to get 67, then take back the extra 1 for 66. For subtraction it works the same way: round, subtract, then correct. This strategy turns an awkward calculation into an easy one plus a small fix-up. Recognising when a number is near a friendly ten, and adjusting afterwards, is an efficient habit, and it shows that good calculators choose a route that suits the numbers in front of them.

Round, then adjust
Rounding to a friendly number, then adjusting, makes near-ten sums quick.
For 47 + 19, round 19 to 20 first. Then adjust.

Multiplying by parts

Multiplication becomes manageable by splitting a number using place value. For 6 x 30, do 6 x 3 = 18 then multiply by 10 to get 180; for 4 x 23, do 4 x 20 = 80 and 4 x 3 = 12, then add to make 92. Breaking one factor into tens and ones turns a hard product into easy known facts that are added. This part-by-part strategy, resting on the multiplication facts and place value, lets a child multiply larger numbers mentally and accurately, and it is far quicker than repeated addition.

Multiply by parts
Splitting a number by place value turns a hard multiplication into easy ones.
Work out 6 x 30 by splitting 30 using place value.

Dividing with no remainder

When a division comes out exactly, the quickest way is to use the matching multiplication fact. For 84 / 4, ask what times 4 makes 84: since 21 x 4 = 84, the answer is 21 with no remainder. Division and multiplication are inverses, so a known fact answers the division directly. This unit deals with division where there is no remainder, exactly the case the descriptor names, so a child can rely on the times tables to divide efficiently rather than sharing out one at a time.

Divide with no remainder
Division with no remainder is solved by the matching multiplication fact.
84 divided by 4 shares exactly. Use a known fact: what times 4 gives 84?

Choosing a strategy

The real skill is choosing a strategy that fits the numbers. Splitting suits 38 + 47; rounding and adjusting suits 47 + 19; multiplying by parts suits 6 x 30; a known fact suits 84 / 4. There is rarely just one right method, but some are far quicker than others for a given problem, and counting one by one is almost always the slowest. Learning to look at the numbers and pick an efficient approach — sometimes with a digital tool for checking — is what the descriptor means by developing efficient strategies, and it matters more than any single trick.

Pick the strategy
The skill is choosing a strategy that fits the numbers, not counting one by one.
Which is the most efficient strategy for 47 + 19?

Strategies at a glance

Pulling the unit together, efficient calculation means having a toolkit of strategies and matching each to the problem. A table makes the pairings clear: split tens and ones for 38 + 47, round and adjust for 47 + 19, multiply by parts for 6 x 30, use a known fact for 84 / 4. Each rests on place value and the number facts, and each beats counting one by one. With splitting, rounding and adjusting, multiplying by parts and dividing by known facts, a child can solve addition, subtraction, multiplication and exact division problems efficiently and accurately, the goal of this part of Year 4 number.

Strategies at a glance
Matching an efficient strategy to each kind of problem is the heart of mental calculation.
Each kind of problem has an efficient strategy. Reveal each.
Quick self-check
1. An efficient way to work out 38 + 47 in your head is to...
2. To work out 47 + 19 quickly, a good strategy is to...
3. A neat way to find 6 x 30 is...
4. Because 21 x 4 = 84, the division 84 / 4 equals...
5. The main idea of efficient strategies is to...
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