Integer Operations Practice

Overview

This 60-minute consolidation lesson gives First Year students structured practice multiplying and dividing integers. Students revisit sign rules, use patterns and estimation to check answers, and apply their skills to increasingly challenging calculations and short problems.

Learning intentions

Students will:

• multiply and divide positive and negative integers accurately;
• explain how the signs of the numbers affect the sign of the answer;
• use inverse operations and estimation to check calculations;
• apply integer operations in simple real-life contexts.

Success criteria

• I can multiply and divide integers using the correct sign rule.
• I can explain why my answer is positive or negative.
• I can check a calculation using the inverse operation or estimation.
• I can show clear working and correct mathematical notation.

Curriculum links

• Number — perform multiplication and division in the integers and maintain the properties of operations.
• Number — use models, patterns and the number line to make sense of arithmetic operations.
• Number — interpret and solve problems involving integers in everyday contexts.
• Number — use brackets and order of operations correctly when appropriate.

Lesson structure (60 minutes)

1. 0–5 min · Retrieval hook. Display the first question on the integer operations practice deck: “A temperature falls by 4°C every hour for 3 hours. What is the total change?” Students answer independently on mini-whiteboards, then compare answers and explain the sign.

2. 5–13 min · Revisit the rules. Use the sign-rule and worked-example slides to review: same signs give a positive product or quotient, different signs give a negative product or quotient. Model examples such as ( (-6)\times(-3)=18 ), ( (-24)\div6=-4 ), and ( 35\div(-5)=-7 ), emphasising that the number calculation and sign decision are separate steps. Students annotate the two-step method in their copies.

3. 13–23 min · Guided practice. Present the “sign first, numbers second” examples from the guided-practice slides. Students solve six questions on mini-whiteboards, showing the sign and numerical calculation separately. Pause after each pair to check responses, address misconceptions, and ask students to justify one answer to a partner.

4. 23–43 min · Independent practice. Distribute the integer multiplication and division practice worksheet. Students complete the core questions independently: sign-only decisions, straightforward calculations, missing-number questions, and calculations involving brackets and order of operations. Circulate with a focus group for students who need support, while other students progress to the reasoning questions.

5. 43–53 min · Check and correct. Display the answers and checking prompts on the checking and reasoning slides. Students use a different-coloured pen to correct their work and must investigate one error by explaining whether it came from the sign, the numerical calculation, or the order of operations. In pairs, students check selected answers using multiplication and division as inverse operations.

6. 53–60 min · Plenary and exit check. Show the final prompts on the plenary slides. Students complete the three-question exit check in their copies: ( (-8)\times7 ), ( (-45)\div(-9) ), and “Explain why multiplying two negative integers gives a positive result.” Invite two students to share different checking strategies before collecting responses.

Resources

• Slides deck covering the hook, sign rules, worked examples, guided practice, checking prompts and plenary
• One-page integer multiplication and division worksheet
• Mini-whiteboards, markers and erasers
• Student copies and pens
• Calculators for checking only, if appropriate
• Board or projector
• Different-coloured correction pens

Assessment

• Use mini-whiteboard responses during the hook and guided practice to identify sign-rule misconceptions immediately.
• During worksheet circulation, question students individually: “What is the sign?”, “What is the numerical calculation?”, and “How can you check it?”
• Collect the exit check to identify students who need further practice with negative signs, inverse operations or brackets.

Differentiation

• Support students with a visible sign-rule reference, a two-step scaffold (“choose the sign; calculate the numbers”), multiplication facts, and paired verbal rehearsal before writing.
• Provide a number line or integer counters to students who need a concrete representation, and reduce the number of core questions while maintaining a mixture of positive and negative examples.
• Use sentence starters such as “The answer is ___ because the signs are ___” and “I checked this by ___” for students who need language support, including EAL learners.
• Challenge confident students with missing-number questions, mixed operations and explanations of why the sign rules work, without allowing calculators for the initial calculations.