Show Your Working

Overview

Students develop reliable written subtraction by connecting concrete place-value exchanges to pictorial representations and the column algorithm. They build on understanding of three- and four-digit place value, subtraction without regrouping, and the idea that equal quantities can be renamed in different ways.

Learning intentions

• WALT explain regrouping as exchanging one place-value unit for ten of the next smaller unit.
• WALT use concrete materials, drawings and the column algorithm to subtract.
• WALT subtract when a zero in the minuend requires more than one exchange.
• WALT check that our answer and working are reasonable.

Success criteria

• I can line up digits by place value.
• I can exchange one ten for ten ones, or one hundred for ten tens, without changing the total value.
• I can show my working with place-value language, drawings or the column algorithm.
• I can check my answer using addition or estimation.

Curriculum links

• Te Mātaiaho Mathematics and Statistics, Phase 2, Years 4–6 Number: standard written algorithms rely on place value, regrouping and renaming.
• Addition and subtraction can be solved using place value, partitioning or column methods.
• Mathsteasers resources support higher-order thinking, challenge and deeper understanding for advanced learners.

Prior knowledge: reading and partitioning four-digit numbers; place-value columns; subtraction within each place; addition facts to 10; inverse relationships.

Vocabulary: minuend, subtrahend, difference, ones, tens, hundreds, thousands, exchange, regroup, rename, estimate, algorithm.

Lesson structure (60 minutes)

1. 0–7 min · Engaging launch. Teacher displays 500 − 268 on the launch and teaching slides and asks, “Can we subtract 8 ones from 0 ones? What could we rename?” Students make an estimate, discuss with a partner, and explain what might need to change. Emphasise that regrouping does not take value away: one hundred is exchanged for ten tens, and one ten for ten ones.

2. 7–18 min · Concrete and pictorial modelling. Teacher builds 500 with place-value blocks or counters, recording 5 hundreds, 0 tens and 0 ones. Model exchanging one hundred for ten tens, then one ten for ten ones, leaving 4 hundreds, 9 tens and 10 ones. Subtract 268 physically, draw the representation, and state each action aloud: “I cannot subtract 8 ones from 0 ones, so I rename one ten as ten ones. There are no tens, so I first rename one hundred as ten tens.” Students use their own place-value materials or sketch a place-value chart, then explain why the total remains 500.

3. 18–28 min · Explicit connection to the algorithm. Teacher records the same example in aligned columns, showing crossed-out digits and their replacements clearly. Model a second example, 742 − 385, linking each written step to the blocks and language: “4 tens becomes 3 tens and 10 ones.” Then model 603 − 278, carefully exchanging one hundred through the zero tens: 6 hundreds becomes 5 hundreds and 10 tens; 10 tens becomes 9 tens and 10 ones. Students echo the language and identify the value before and after each exchange.

4. 28–40 min · Guided practice and gradual release. Teacher and students solve 821 − 457 together, first with a place-value chart and then using the algorithm. Ask: “Which column must we begin with?”, “What can we exchange?”, “How do we know the value has stayed the same?”, and “How could we check?” Pairs then solve 930 − 486 and 704 − 259, choosing blocks, drawings or the algorithm. Teacher checks alignment and listens for accurate place-value explanations, pausing for a quick reteach where needed.

5. 40–53 min · Independent application. Distribute the regrouping subtraction practice worksheet. Core learners solve six four-digit subtraction problems, including 500 − 268, 603 − 278 and 704 − 259, and show one solution with a drawing or place-value explanation. Support learners complete three carefully scaffolded problems with pre-drawn columns, colour-coded place values and optional blocks; the teacher or peer reads instructions aloud. Extension learners solve an open task: find three different minuends that give a difference of 425 when subtracting a four-digit number, then prove each solution and explain which exchanges were needed.

6. 53–60 min · Plenary and exit ticket. Teacher revisits the launch on the discussion and plenary slides and invites students to compare their first idea with their final method. Students complete an exit ticket: solve 800 − 356, draw or describe the exchanges, and answer, “Why does regrouping leave the total value unchanged?” Invite two students to share different representations.

Resources

• the launch and teaching slides
• the regrouping subtraction practice worksheet
• Place-value blocks, counters or bundled sticks
• Place-value charts and mini-whiteboards
• Pencils, coloured pencils and erasers
• Exit-ticket slips
• Enlarged teacher modelling grid

Assessment

• During modelling, check whether students can explain that one unit is exchanged for ten smaller units, rather than “borrowing”.
• During guided practice, use questioning and observation to identify errors with column alignment, zeroes and crossed-out values; provide immediate concrete re-modelling.
• Use the worksheet and exit ticket to assess accurate calculation, visible working, place-value reasoning and checking.

Differentiation

• Support: use manipulatives, enlarged place-value charts, colour-coded columns and partially completed examples. Keep numbers smaller initially, then move to four digits when ready. Provide the sentence frame: “I exchanged ___ for ___ because ___.”
• Dyslexia-friendly access: use a clear sans-serif font, large spacing, uncluttered questions, one problem per line and high-contrast place-value columns. Read directions aloud, allow oral explanations, and accept drawings or photographed practical work.
• Diverse learners: pair students strategically, rehearse vocabulary orally and display the words with place-value images. Allow students to choose blocks, drawings or the algorithm while maintaining the same mathematical goal.
• Advanced learners: require the extension proof to include an estimate, an inverse check and an explanation of how changing the minuend or subtrahend affects the difference.