Year 4 Maths | Learn, see, try
Year 4 Maths: break a problem into useful parts
Larger calculations do not always need a completely new method. Partitioning a number into manageable parts lets students use known multiplication facts and place value. Fractions and decimals also become clearer when the whole and its equal parts are kept visible.
What to notice
Choose a split that makes the calculation easier. Twenty-three is twenty and three, not two and three. Keep track of the value of each part when reading or writing a number.
What to do
For 6 × 23, calculate six groups of twenty and six groups of three. A partitioned rectangle or two arrays can show that every item is included once. Add the two partial totals at the end.
Why it works
Every group of twenty-three contains a group of twenty and a group of three. Splitting all six groups in the same way preserves the total while making the facts easier to calculate.
Work through an example
A class has 6 trays with 23 counters on each. How many counters are there?
- Split 23 into 20 + 3.
- Six groups of twenty make 120; six groups of three make 18.
- Combine the parts: 120 + 18 = 138 counters. Check that the result is a little more than 6 × 20.
Read decimals by place, not by digit count
Thirty-four hundredths is 0.34. A hundred-square model shows three full tenths and four more hundredths. When comparing 0.6 and 0.45, rename six tenths as sixty hundredths before deciding which is greater.
Compare fractions with the same whole
One half covers the same length as two quarters when both bars start with the same whole. The number of marked pieces changes because the pieces became smaller. Do not compare a half of one-sized object with a quarter of a much larger object without considering their sizes.
Keep measurement units consistent
Before adding lengths, check whether every value is in centimetres or metres. A drawing with labelled sides can reveal a missing side and make the difference between distance around a shape and covered surface easier to discuss.
A common mistake
6 × 23 is not 6 × 20 + 3. The three extra counters appear on every tray, so they must be counted six times as well.
A strategy to try
Estimate before calculating, then ask whether the answer fits. Six groups of a number just above twenty should total just above one hundred and twenty. An estimate can catch a missing place-value digit.
For parents and carers
Encourage two ways of showing one problem rather than many calculations with no explanation. The decimal lesson provides a visual starting point when tenths and hundredths are being confused.
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