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Numeracy involves understanding numbers and using them to make sense of everyday situations: working out a cost, judging a quantity or reading a timetable. The most useful starting point is a task the learner wants to manage. That might be a school question, a workplace calculation or something at home.

Here are three illustrative worked examples, from adding whole numbers to checking a sale price. Choose a starting point the learner is ready to tackle.

Addition: make the next ten

For 28 + 17, a learner who counts on one at a time may lose their place. Split 17 into 2 and 15. Adding 2 takes 28 to 30; adding the remaining 15 gives 45. A number line can show those two jumps.

The explanation matters: “I still added 17, but I used 2 of it to reach 30 first.” For a follow-up, try 38 + 17: reach 40 with 2, then add 15 to get 55. This checks whether the learner can reuse the idea.

Decimals: compare the value, not the number of digits

Suppose a learner says 0.35 is larger than 0.5 because 35 is larger than 5. Write 0.5 as 0.50. Five tenths is the same as fifty hundredths, so the comparison is between 50 hundredths and 35 hundredths. 0.5 is larger.

A stronger answer is: “The extra digit does not make the number bigger; I need to compare equal place values.” Try 0.6 and 0.42 next: 0.60 is 60 hundredths, which is more than 42 hundredths.

Percentages: separate the saving from the price paid

An item costs £40 with 20% off. Taking away £20 would confuse a percentage with a fixed amount of money. First find 10% of £40: £4. Double it to get 20%: £8. That is the saving; the price paid is £40 − £8 = £32.

Now change the original price to £60. Ten per cent is £6, so the saving is £12 and the price paid is £48. The percentage stays the same while the money saved changes with the starting price.

A correct-looking number can still answer the wrong question. For example, a task takes 1 hour 30 minutes. Writing 1.30 hours in a box that requires decimal hours treats minutes as hundredths of an hour.

Convert the whole hour to 60 minutes, then add 30: the duration is 90 minutes. Half of 60 minutes is 30 minutes, so the same duration is 1.5 hours. By comparison, 0.30 of an hour is 0.30 × 60 = 18 minutes; 1.30 decimal hours would mean 1 hour 18 minutes.

For practice, convert 1 hour 45 minutes. It is 105 minutes, or 1 + 45 ÷ 60 = 1.75 hours. Keeping “minutes” and “hours” beside the working makes the change of unit visible. This is an illustrative task that can connect school time problems with an adult timesheet or timetable.

Look for relevant teaching experience and an explanation the learner can follow. A useful tutor discussion should leave you with a specific first priority, such as understanding decimal place value, rather than only a broad promise to improve confidence.

A useful plan connects an initial attempt, a teaching priority and something the learner can later do with less help. Here is one way to organise that conversation with a tutor.