Multi-step Number Problems

Overview

Students solve multi-step word problems that integrate addition, subtraction, multiplication and (where appropriate) division. They practise choosing efficient strategies, recording working clearly, and checking that answers make sense.

Learning intentions

• Students will solve multi-step problems involving whole numbers using addition and subtraction.
• Students will solve multi-step problems involving equal groups using multiplication and division (where numbers allow).
• Students will explain how they decided what operation to use at each step.
• Students will check solutions using estimation, inverse operations, or reasonableness.

Success criteria

• I can identify the important numbers and what the question is asking.
• I can choose the correct operations in the right order to solve the problem.
• I can show my working using drawings, number sentences, or concrete strategies.
• I can check my answer using an inverse operation or sensible estimation.

Curriculum links

• Number and Algebra: using efficient mental and written strategies for addition and subtraction of whole numbers, and building automaticity with number facts.
• Number and Algebra: using multiplication as equal groups and division as sharing or grouping, and relating them to each other.
• Mathematical Reasoning: interpreting and solving word problems, explaining strategies, and checking results for reasonableness.

Lesson structure (45 minutes)

1. 0–5 min: Warm-up fluency

• Do a quick class routine: 4 short questions on the board (2 addition/subtraction, 2 multiplication/division).
• Students answer on mini-whiteboards and share one strategy each (e.g., counting on, doubles, making 10, equal groups).

2. 5–12 min: Problem-solving model (teacher guided)

• Teacher models one integrated multi-step problem using think-alouds.
• Example: “There are 3 bags with 4 apples in each. You eat 5 apples. How many apples are left?”
• Steps: find total (multiplication as equal groups), then subtract (remaining), then check with addition (5 more equals total).

3. 12–22 min: Guided practice in pairs

• Provide 3 problem cards of increasing complexity (same topic, slightly different structures).
• Students work in pairs to solve, record a number sentence for each step, and include a quick check.
• Teacher circulates, prompting: “What does this step mean?” and “How do you know this operation fits?”

4. 22–30 min: Strategy share and select “best method”

• Whole class discussion of one or two student solutions (chosen to show different correct strategies).
• Students vote/justify which method is most efficient (e.g., using known facts, partitioning, arrays/equal groups, compensation).

5. 30–40 min: Independent multi-step challenge

• Students complete a worksheet (or task sheet) with 2 multi-step problems.
• Expectation: show working clearly (drawing and/or number sentences), and complete a final check.
• Differentiation built in by having “Support” and “Extension” versions on the same sheet.

6. 40–45 min: Exit check

• Students answer one quick “final-check” question: give an incorrect example solution and ask them to find the mistake or verify the result.
• Collect responses to guide next lesson or intervention.

Resources

• Mini-whiteboards, markers, erasers
• Problem cards with multi-step word problems (addition/subtraction + multiplication/division)
• Student worksheets (Support and Extension options)
• Base-ten blocks or counters (for arrays/equal groups where needed)
• Number line (large class display or printed copies)
• Think-aloud chart headings: “What do I know?”, “What do I need?”, “What operation?”, “How can I check?”
• Pencils, coloured pencils for highlighting key numbers
• Timer for independent work segments

Assessment

• Formative: teacher observation during pair work (operation choice, clarity of steps, use of checks).
• Monitoring task: collect the independent challenge for written evidence of correct multi-step reasoning.
• Exit check: identify whether students can verify answers using inverse operations or reasonableness.

Differentiation

• Support
• Provide a “step scaffold” on the worksheet: Step 1 (find total/equal groups), Step 2 (add/subtract), Step 3 (check).
• Offer manipulatives (counters, base-ten blocks) and a number line for students who need concrete support.
• Reduce cognitive load by using smaller numbers while keeping the same multi-step structure.
• Extension
• Include problems that require either two different representations (equal groups and array, or number line and number sentence) or a more efficient strategy (e.g., using known facts like doubles).
• Add one question that asks students to write their own multi-step word problem for a given number sentence.
• EAL/SEN considerations
• Pre-teach key words in context (e.g., “left”, “altogether”, “each”, “in every group”, “share”, “how many more”).
• Use sentence frames for explanations: “First I…, because… Next I… because… I checked by…”
• Allow oral responses or drawing as part of the working shown.