Rounding Decimal Numbers

Overview

Students use place value, number lines and physical digit models to round decimals to the nearest tenth and hundredth. The lesson builds on understanding that each decimal place is ten times smaller than the place to its left, with substantial teacher modelling and guided practice.

Learning intentions

• WALT identify the place value of digits in decimals to thousandths.
• WALT round decimals to the nearest tenth and hundredth.
• WALT use a number line and place value reasoning to explain rounding.
• WALT estimate decimal values to check whether an answer is reasonable.

Success criteria

• I can find the digit in the place I am rounding to.
• I can look at the digit immediately to the right and decide whether to round up or leave it.
• I can represent a decimal on a number line and identify the closest benchmark.
• I can explain why my rounded answer is reasonable.

Curriculum links

• Number — interpret, compare and order decimals with more than two decimal places using place value and number lines.
• Number — check and explain the reasonableness of solutions using estimation strategies.
• Mathematics progression — connects prior rounding work with whole numbers and supports later work with more complex decimal estimation.
• Measurement — applies rounding to decimal measures such as length, mass and capacity.

Lesson structure (40 minutes)

1. 0–5 min · Hook and prior knowledge. Display the question, “Is 3.746 closer to 3.7 or 3.8?” using the opening comparison slide. Students make a quiet estimate, show their choice with fingers or mini-whiteboards, then explain what they already know about rounding whole numbers.

2. 5–12 min · Model place value. Use the Place Value Mat and digit cards to build 3.746, then display the place value teaching slides. Teacher highlights the ones, tenths, hundredths and thousandths columns, stating: “To round to the nearest tenth, look at the hundredths digit.” Model:

• 3.746 → 3.7 because 4 is less than 5
• 3.756 → 3.8 because 5 means round up Students build each number with a partner, point to the rounding digit and say the checking digit aloud.

3. 12–20 min · Hands-on guided investigation. Give pairs a place value mat, digit cards and a counter. Teacher slowly guides students through the routine: build the number, circle the target place, look one place right, decide, and record. Use the guided investigation instructions and complete 4.263, 5.718 and 2.995 together. Students physically move the counter to the digit being checked and explain their decision using the sentence frame: “I am rounding ___ to the nearest ___. The ___ digit is ___. Therefore, my answer is ___.”

4. 20–29 min · Number-line rounding. Open the number-line demonstration and draw benchmark tenths on the board. Model placing 4.36 between 4.3 and 4.4; discuss why it is closer to 4.4. Repeat with 6.241 rounded to the nearest tenth and hundredth. Students use mini-whiteboards to mark the two benchmarks, place the decimal and write the rounded value. Pause after each example for a thumbs-up check and re-model using the place value mat where needed.

5. 29–36 min · Supported worksheet practice. Distribute the decimal rounding practice worksheet. Students complete the first section with a partner and the teacher works with a focus group requiring additional support. The worksheet should include colour-coded place-value columns, partially completed number lines and questions rounding decimals to the nearest tenth and hundredth. Encourage students to use the five-step routine displayed on the practice and estimation slides. Early finishers solve the challenge: “Find three different decimals that round to 4.7 to the nearest tenth. Explain how you know.”

6. 36–40 min · Review and exit check. Revisit the final reasoning prompts. Students answer orally: “Why do we look at only the digit immediately to the right?” Collect a quick exit response: round 7.364 to the nearest tenth and nearest hundredth, then complete the sentence, “My answer is reasonable because…”.

Resources

• the decimal rounding slide deck
• the decimal rounding practice worksheet
• the Place Value Mat
• Digit cards 0–9
• Counters or small connecting cubes
• Mini-whiteboards and markers
• Board or interactive display
• Pencils and coloured pencils
• Prepared focus-group examples

Assessment

• Listen for correct use of place-value language during partner modelling and guided questioning.
• Check mini-whiteboards for accurate benchmark numbers, decimal placement and rounding decisions.
• Use the exit response to identify whether students can round to both requested places and justify reasonableness. Record students needing further practice with place value or the “look next door” rule.

Differentiation

• Support: seat students with a confident partner; provide the place-value mat, digit cards and the sentence frame throughout; use numbers with one or two decimal places before introducing thousandths. Explicitly rehearse the routine with concrete models and colour coding.
• Additional support for EAL/D and students requiring adjustments: pre-teach “nearest”, “digit”, “round up”, “round down” and “between”; use gestures, oral repetition and worked examples. Permit students to explain orally, point to models or use a scribed response.
• Core learners: round decimals including numbers greater than one to the nearest tenth and hundredth, using either a place-value or number-line method.
• Extension: students find several decimals with the same rounded value, compare which is closest to the midpoint, and explain why a number such as 2.995 may cause a change across the whole-number boundary.