Ordering and Rounding Decimals

1. 1 Write on the board: 'Put in order: 0.6, 0.12, 0.9'. Many students will write 0.12 as largest (three digits). Ask for a volunteer order. Discuss why this is a common error — digits after the decimal do not work like whole numbers.
2. 2 Write 3.47 in a place value chart: 3 ones, 4 tenths, 7 hundredths. 'A tenth is bigger than a hundredth — just as tens are bigger than ones.' Revisit 0.6 vs 0.12: 0.6 = 0.60 > 0.12.
3. 3 Mark 0.6, 0.12, 0.9 on a number line from 0 to 1. Students position them. Which comes first? 'The number line proves it: 0.12 is less than 0.6.'
4. 4 Model rounding 3.67 to the nearest whole: '3.67 is between 3 and 4. Is it closer to 3 or 4? The tenths digit is 6 — that is ≥ 5, so we round up to 4.' Rule: look at the digit to the right of where you are rounding.
5. 5 Round 2.47 to 1 decimal place. 'Look at the hundredths digit: 7 ≥ 5, so the tenths digit rounds up from 4 to 5. Answer: 2.5.' Students practise five examples.
6. 6 A runner's time is 9.87 seconds. 'Round to the nearest second.' A price is £4.36. 'Round to the nearest £1.' 'Which rounded down and which rounded up?'
7. 7 Students order five decimals from smallest to largest and round two numbers to 1 d.p. and to the nearest whole number.

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