Decimal Detective

Overview

A one-to-one tutoring session developing confidence with decimals to three decimal places. The pupil uses place-value representations to read, write, order and compare decimals, then rounds decimals to the nearest whole number and one decimal place before applying these skills to practical money and measurement problems.

Learning intentions

• Students will read, write, order and compare decimals with up to three decimal places.
• Students will use place value to round decimals with two decimal places to the nearest whole number and one decimal place.
• Students will solve short practical problems involving decimals.
• Students will explain their reasoning using place-value language and appropriate symbols.

Success criteria

• I can identify the value of each digit in a decimal.
• I can compare decimals by checking digits from left to right.
• I can round using the digit immediately to the right of the rounding place.
• I can choose a sensible operation and show my working in a decimal problem.

Curriculum links

• Number — number and place value: read, write, order and compare numbers to at least 1,000,000 and determine the value of each digit.
• Number — fractions, including decimals and percentages: read, write, order and compare numbers with up to three decimal places.
• Number — fractions, including decimals and percentages: read and write decimal numbers as fractions.
• Number — number and place value: solve number and practical problems involving these skills.

Lesson structure (45 minutes)

1. 0–6 min · Diagnostic hook. Open with the decimal detective introduction slides and ask, “Which is greater: 0.7 or 0.65? How do you know?” The pupil answers without being corrected immediately, then explains the comparison. Ask: “What is the value of the 6 in 0.65?” and “How could we write 0.7 with two decimal places?” Expected responses: “0.7 is greater because 70 hundredths is greater than 65 hundredths”; “the 6 is six tenths”; “0.70”. Note whether the pupil treats 0.65 as larger because 65 is greater than 7.

2. 6–15 min · Model place value. Display the place-value chart in the place value mat and build 3.406 with digit cards or counters. Model reading it as “three and four hundred and six thousandths”, writing it in words and partitioning it as 3 + 0.4 + 0.006. Ask the pupil to build 5.270 and explain why 5.27 and 5.270 have the same value. Tutor prompt: “Which place should we compare first?” Expected response: “Ones, then tenths, then hundredths, then thousandths if needed.” Emphasise that zero is a place-holder and does not change the value when added at the end.

3. 15–23 min · Guided compare and order. Use the chart and a marked number line on the slides. Compare 2.407 and 2.47, first matching decimal places as 2.407 and 2.470. Then order 0.908, 0.89 and 0.9 from least to greatest. The pupil places digits, says each number aloud and records <, > or =. Tutor prompts: “Do we compare the whole string of digits?” and “What is 0.9 equivalent to?” Expected responses: “No, we compare place by place”; “0.900.” Correct immediately by rebuilding the numbers if necessary. Reinforce that 0.908 is greater than 0.89 because 908 thousandths is greater than 890 thousandths.

4. 23–31 min · Explicit rounding model. Show 6.74 on the rounding examples and number-line slides. To round to one decimal place, identify the tenths digit, look at the hundredths digit and decide whether to keep or increase the tenths. Model 6.74 → 6.7, then 6.75 → 6.8. Repeat for 8.36 to the nearest whole number: the tenths digit is 3, so the answer is 8. Use a number line or counters to confirm. The pupil completes 4.28 to one decimal place and 4.28 to the nearest whole number, explaining each decision. Expected answers: 4.3 and 4. Ask, “Which digit tells us what to do?” Address the misconception that the rounding digit itself must always increase.

5. 31–39 min · Guided practical practice. Give the pupil one or two suitable scenarios from the budgeting scenario cards and ask them to estimate before calculating. For example: “A drink costs £1.35 and a snack costs £2.40. What is the total?” and “A runner completes 2.76 km. Round this to the nearest kilometre and nearest tenth of a kilometre.” The pupil records a number sentence and explains whether the answer is reasonable. Expected answers: £3.75; 3 km and 2.8 km. Prompt: “What information matters? Which operation will you use?” Support the pupil to align decimal points when adding.

6. 39–43 min · Independent check. Distribute the decimal practice worksheet. The pupil completes the short mixed set independently, while the tutor observes strategy rather than supplying answers. Pause after each item for immediate feedback using “check the place value” or “look at the next digit” prompts, then ask the pupil to correct errors in a different colour.

7. 43–45 min · Exit assessment. Ask the pupil to answer orally or on a clean section of the worksheet: (a) write 0.506 in words; (b) put 1.2, 1.020 and 1.12 in ascending order; (c) round 7.46 to one decimal place and the nearest whole number; (d) £5.00 − £1.75. Expected answers: five hundred and six thousandths; 1.020, 1.12, 1.2; 7.5 and 7; £3.25. Ask the pupil to state one strategy they will remember.

Resources

• the decimal detective slide deck
• the decimal practice worksheet
• the place value mat
• the budgeting scenario cards
• Digit cards 0–9 and small counters
• Mini-whiteboard and pen
• Ruler or number line
• Pencil and different-coloured pen for corrections

Assessment

• Diagnostic questions reveal misconceptions about trailing zeroes, digit value and comparing digits as whole numbers.
• Observe whether the pupil compares from left to right, rounds using the next digit and aligns decimal points when adding or subtracting.
• Use the four-question exit assessment: aim for at least three correct answers, with explanations, before moving to more complex decimal problems.

Differentiation

• Support with the place-value mat, counters, colour-coded columns, expanded form and sentence starters: “I compared the ___ place first because…” and “The next digit is ___, so…”.
• If the pupil is insecure, use decimals with two places first, add a zero to show equivalent forms, and calculate practical totals with a written column method.
• For extension, ask the pupil to create two different decimals between 3.4 and 3.5, order them, and explain why 3.49 rounds to 3.5 to one decimal place but 3.49 rounds to 3 to the nearest whole number.
• Read every question aloud where helpful, allow thinking time, and accept spoken explanations alongside written work. Avoid introducing unnecessary vocabulary before the pupil has modelled the idea.