Four Operations, Many Strategies

Overview

In this 45-minute workshop, Year 4 students apply place-value understanding to solve column addition, subtraction, multiplication and division problems. They explain regrouping, compare efficient strategies and check whether answers are reasonable, building on prior work with number facts and written algorithms.

Learning intentions

• WALT use place value to solve written problems involving all four operations.
• WALT explain what happens when we regroup.
• WALT choose a suitable strategy and check our answer.
• WALT work independently and discuss mathematical thinking with others.

Success criteria

• I can line up digits according to their place value.
• I can show or explain regrouping when I need it.
• I can solve a problem and check my answer using another strategy.
• I can explain why my answer is reasonable.

Curriculum links

• Mathematics and Statistics — using place value and written strategies to solve number problems.
• Mathematics and Statistics — communicating mathematical thinking, reasoning and checking solutions.
• Mathsteasers — challenging learners with higher-order thinking questions and opportunities to deepen understanding.
• Mathsteasers / Alignment — connecting challenge problems with familiar mathematical content and strategies.

Lesson structure (45 minutes)

1. 0–5 min · Number hook. Display a deliberately incorrect calculation on the opening hook slide: 402 − 178 = 376. Ask, “How can we prove this answer is not correct?” Students estimate, use a quick mental check and share what the digits tell them. Emphasise that mathematicians explain and check, rather than simply record an answer.

2. 5–13 min · Teacher model. Use the worked-example slides to model 268 + 157, 402 − 178, 24 × 6 and 84 ÷ 4, selecting examples that show regrouping or place-value partitioning. Think aloud: “I am exchanging one hundred for ten tens,” or “I know 84 divided by 4 means sharing 84 into four equal groups.” Students use mini-whiteboards to identify the place value being regrouped and suggest one checking strategy, such as inverse operations, estimation or an array.

3. 13–16 min · Explain the workshop. Display the task and discussion slides and distribute the differentiated four-operations practice sheet. Explain that students begin at the set that matches their confidence; the teacher may move them during the workshop. Students read the success criteria, choose a starting strategy and underline where they will show their reasoning.

4. 16–31 min · Differentiated practice. Supported learners solve smaller two-digit addition and subtraction problems and simple multiplication or division problems using place-value charts, drawn groups and guided steps on the worksheet. Developing learners solve mixed two- and three-digit problems, including regrouping, and record a check for each operation. Extending learners solve larger problems, multi-step situations and error-analysis questions, explaining which step is incorrect and how to repair it. Students work independently first, then compare one solution with a partner. Confer with individuals and ask, “What does this digit represent?”, “Why did you regroup?” and “How could you check it?”

5. 31–39 min · Strategy conference. Pause the class and show two different solutions from the worksheet on the strategy-comparison slides. Students decide whether each is correct, identify the strategy used and discuss which representation makes the thinking clearest. Partners explain one completed problem using the sentence frame: “I ___ because ___. I checked by ___.” Invite selected students to share; address errors by returning to place-value language rather than only correcting the answer.

6. 39–45 min · Exit ticket and reflection. Display the plenary and exit-ticket slide and give each student one prompt: 306 − 148 = ___. Students must show working and write one sentence explaining the regrouping or their checking method. Collect responses as they leave. If time permits, students compare their estimate with their exact answer and describe whether the result is reasonable.

Resources

• the Four Operations, Many Strategies slide deck
• the differentiated four-operations practice sheet
• Mini-whiteboards, pens and erasers
• Place-value charts and base-ten blocks or bundled sticks
• Pencils, rulers and highlighters
• Enlarged model calculations for teacher demonstration

Assessment

• Observe alignment of digits, use of place-value language and accurate regrouping during modelling and independent practice.
• Confer with a range of learners, recording whether each student can solve accurately, explain a step and select an appropriate checking strategy.
• Use the exit ticket to identify students needing further support with subtraction regrouping, written explanation or checking. Retain examples of misconceptions for the next teaching session.

Differentiation

• Support learners with a place-value chart, base-ten materials, smaller numbers, colour-coded columns and the prompts “I exchanged ___ for ___” and “I checked by ___”.
• Read word problems aloud where needed, reduce copying demands and allow students to explain orally before writing. Pair EAL learners with a supportive peer and pre-teach exchange, regroup, inverse and estimate using examples.
• For learners ready for challenge, provide larger numbers, multi-step problems and incorrect worked examples to analyse; require more than one strategy or a written comparison of efficiency.
• Accept drawings, equations and oral explanations as evidence of reasoning, while continuing to model precise mathematical vocabulary.