Compensation Makes It Easy

Overview

Lesson 6 of 16 in Mastering Addition and Subtraction. In a structured, hands-on lesson, students use compensation to make subtraction calculations easier, then adjust their answer to keep it accurate. The lesson is suitable for a mixed Year 2–4 group, with numbers adjusted to each student’s readiness.

Learning intentions

Students will:

• Understand compensation as changing a number to create a friendlier subtraction problem.
• Use mental strategies to subtract from multiples of 10 or 100.
• Compensate correctly after adjusting a number.
• Explain and compare different subtraction strategies.

Success criteria

• I can change a number to make a subtraction easier.
• I can explain how I compensated.
• I can adjust my answer to match the original problem.
• I can check whether my answer is reasonable.

Curriculum links

• Additive strategies: use mental strategies and written methods to solve addition and subtraction problems.
• Number and place value: recognise the value of digits and use multiples of 10 and 100.
• Mathematical reasoning: explain strategies, compare methods and justify answers.
• General capabilities: Critical and Creative Thinking through selecting efficient strategies; Personal and Social Capability through turn-taking and collaborative discussion.

Lesson structure (45 minutes)

1. 0–5 minutes – Settle, connect and review

Open with the hook and learning intention slides. State: “Today we will make subtraction easier by changing a number, then compensating.” Display and read the routine: Listen – Think – Explain – Check.

Write 52 − 19. Ask students to solve it silently using any known strategy. Invite brief responses and identify that 19 is close to 20.

2. 5–13 minutes – Explicit teaching and modelling

Use the compensation modelling slides to model:

• 52 − 19 = 52 − 20 + 1 = 33
• 73 − 29 = 73 − 30 + 1 = 44

Emphasise that subtracting an extra 1 makes the answer 1 too small, so 1 must be added back. Use the language: “I changed 19 to 20, subtracted 20, then compensated by adding 1.”

For students working at an earlier level, model 42 − 9 = 42 − 10 + 1. For students ready for extension, model 326 − 198 = 326 − 200 + 2.

3. 13–20 minutes – Concrete exploration

Give each student place-value blocks, counters or numeral cards. Present one problem at a time: 61 − 19, 84 − 29 and 150 − 98. Students physically represent the subtraction, change the subtrahend to a friendly number, and show the compensation with counters or a number line.

Use the subtraction strategies strategy mat as a visual prompt for students who need help selecting or describing a strategy. Pause after each example and ask: “What changed? What must we do to keep the answer correct?”

4. 20–32 minutes – Guided partner practice

Distribute the differentiated compensation practice worksheet. Students work in pairs, taking turns as Solver and Checker. The Solver explains the calculation; the Checker asks, “Did you compensate?” and checks using estimation or the inverse operation.

Suggested levels:

• Year 2: two-digit problems involving subtracting 9 or 19, such as 45 − 9 and 67 − 19.
• Year 3: two- and three-digit problems involving 9, 19, 29, 99 or 199.
• Year 4: three-digit problems involving numbers close to 100 or 200, including 402 − 198 and 735 − 299.

Confer with each student and provide only one prompt at a time: “What friendly number is close?” or “You changed the number—how will you compensate?”

5. 32–39 minutes – Strategy sort and discussion

Display four problems from the guided practice and discussion slides: 56 − 19, 92 − 29, 300 − 98 and 421 − 199. Students choose one, solve it on a mini-whiteboard and place it under the most suitable friendly number: 10, 20, 30, 100 or 200.

Each student explains one solution using the sentence stem: “I changed ___ to ___ because ___. I then compensated by ___.” Compare two methods and discuss which is most efficient and why.

6. 39–45 minutes – Independent check and exit reflection

Return to the plenary and exit-question slides. Students complete three quick responses on the bottom of the worksheet:

• 64 − 19
• 250 − 98
• “Explain why 80 − 29 is the same as 80 − 30 + 1.”

Collect responses as an exit check. Finish with a one-word or short verbal reflection: “Compensation helps me because…”

Resources

• the complete compensation lesson deck
• the differentiated compensation practice worksheet
• the subtraction strategies strategy mat
• Place-value blocks, counters or linking cubes
• Numeral cards showing multiples of 10 and 100
• Mini-whiteboards and markers
• Pencils and erasers
• Visual timer
• Individual “Listen – Think – Explain – Check” prompt cards

Assessment

• Observe whether students select a nearby friendly number and compensate in the correct direction.
• Listen for accurate explanations using change, subtract, add back and compensate.
• Use worksheet and exit responses to identify whether students can apply compensation independently and check reasonableness.

Differentiation

• Support students with smaller numbers, concrete materials, a number line and the structure: “Changed ___ to ___; compensated by ___.”
• Present one problem at a time, use a visual timer, reduce copying and allow students to point, draw or explain orally.
• Pair students strategically and maintain consistent Solver/Checker roles to support predictable interaction.
• Extend confident students to compare compensation with partitioning or written subtraction and justify which method is more efficient.