Compensating to Add

Overview

Lesson 5 of 16 in Mastering Addition and Subtraction. Students learn to adjust one addend to create a friendly number, then compensate by adjusting the total. The lesson uses explicit instruction, concrete materials, visual models and short, predictable practice cycles for a class of four Year 2–4 students.

Curriculum links

• Use place value understanding to represent, partition and recombine two- and three-digit numbers.
• Apply flexible mental strategies to solve addition problems efficiently.
• Explain and justify a chosen calculation strategy using materials, drawings, equations and mathematical language.
• Develop critical and creative thinking by comparing strategies and deciding when compensation is useful.

Learning intentions

Students will:

• recognise when an addend can be adjusted to make a friendly ten or hundred;
• use compensation to solve addition problems mentally;
• represent compensation with counters, place-value materials, drawings and equations;
• explain why the total must be adjusted after changing an addend.

Success criteria

• I can make one addend easier to work with.
• I can show what I added or subtracted to compensate.
• I can solve and check an addition problem using compensation.
• I can explain my strategy using words, materials or a drawing.

Lesson structure (45 minutes)

1. 0–5 min – Settle, connect and hook Display the opening question in the introduction slides: “Which is easier to calculate: 39 + 26 or 40 + 26?” Students silently choose, then share with a partner or teacher. State: “Today we will make a number friendlier, then fix the answer so it stays accurate.”

2. 5–12 min – Explicit teacher model Build 39 + 26 with place-value blocks or counters. Move one from 26 to 39 to make 40, explaining: “I added 1 to 39, so I must subtract 1 from the total.” Record: 39 + 26 = 40 + 26 − 1 = 65. Repeat with 198 + 34 = 200 + 34 − 2 = 232. Use the worked-example slides to show the adjustment arrow and compensation step.

3. 12–18 min – Guided concrete practice Give each student place-value blocks, counters or an open number line. Work through 48 + 25 and 299 + 16 together. Students physically adjust the first addend, calculate the friendly-number total, and remove the adjustment from the answer. Prompt: “What changed? What must we do to keep the equation balanced?”

4. 18–28 min – Strategy sort and explain Introduce the addition strategies task cards. Select the Compensate card and compare it with Make 10, Partition/Break Apart and Use a Model. Students match each worked example to a strategy, then explain why compensation is appropriate for 59 + 23 but may not be the quickest choice for 42 + 17. Keep language precise: “adjust, friendly number, compensate, total, equivalent.”

5. 28–38 min – Individual practice with teacher conferencing Distribute the compensation practice worksheet. Students solve six questions, drawing a model for at least two. Suggested progression: 29 + 34, 58 + 27, 97 + 16, 198 + 25, 299 + 37 and one choice problem. The teacher works beside one student at a time, using the same prompts: “Which number will you adjust?” “By how much?” “How will you compensate?” Students may use materials throughout.

6. 38–43 min – Share, check and correct Display the discussion and checking slides. Invite two students to show different methods for one problem. Check answers by estimation, inverse thinking or a second strategy. Address the common error of adjusting an addend but forgetting to compensate.

7. 43–45 min – Exit response and preview Students complete the final prompt on the compensation practice worksheet: “Solve 68 + 25 using compensation. Show the adjustment and explain the correction.” Collect responses and preview that the next lesson will compare compensation with other addition strategies.

Resources

• the introduction, modelling, practice and discussion slide deck
• the compensation practice worksheet
• the addition strategies task cards
• Place-value blocks, counters or connecting cubes
• Mini-whiteboards and markers
• Open number lines
• Pencils and erasers
• Visual timer and individual workspaces

Assessment

• Observe whether students identify a suitable addend, state the adjustment and compensate accurately during guided practice.
• Check worksheet representations and equations, especially whether the correction is made in the correct direction.
• Use the exit response to group students for the next lesson: secure, developing or requiring concrete-material support.

Differentiation

• Support: use two-digit numbers first, provide pre-drawn number lines and an equation frame: ___ + ___ = friendly number + ___ − ___. Model one step at a time and reduce visual clutter.
• Support for ADHD and autistic learners: use the same low-variance routine for each problem—Build, Adjust, Add, Compensate, Check. Give one instruction at a time, use a visual timer and offer brief movement or sensory breaks.
• EAL/D and language support: display visuals and sentence stems: “I adjusted ___ by ___.” “I compensated by ___.” “The total is ___ because ___.”
• Extension: students choose whether to adjust the first or second addend, solve a three-digit example, and justify which strategy is most efficient.