arithmetic and relational operations
4 detailed 50-minute lessons with teaching scripts, worked examples, parent guides, and assessment criteria.
Lesson Overview
Total Lessons: 4
Tier: Foundation and Higher
Duration: 50 minutes per lesson (200 minutes total)
Exam Boards: AQA, Edexcel, OCR, Eduqas, CCEA
Tier: Foundation and Higher
Duration: 50 minutes per lesson (200 minutes total)
Exam Boards: AQA, Edexcel, OCR, Eduqas, CCEA
Learning Objectives
- Explain the key ideas of arithmetic and relational operations
- Apply arithmetic and relational operations to exam-style questions
- Develop independent study skills
- Build cross-topic connections
Prerequisites
- Read the revision notes for arithmetic and relational operations first (GCSE Revise summary)
- Key vocab to pre-teach: Arithmetic operators, DIV, Relational operators
- Basic skills: reading the summary notes and answering the practice questions there
Materials & Equipment
- Exercise book, coloured pens
- Ruler
- Printed revision notes (link below)
- Internet for videos (see Resources)
Lesson 1: Introduction: arithmetic and relational operations
Duration: 50 minutes
Starter Activity (5 minutes)
Quick Recall
Write down everything you already know about arithmetic and relational operations. Then check against the key terms: Arithmetic operators, DIV, Relational operators. Use a mini-whiteboard or paper.
Main Content (35 minutes)
Parent/Teacher Guide:
Before lesson: Read the script below. Pre-teach key vocab: Arithmetic operators, DIV, Relational operators.
If stuck: Re-read the revision notes (link above), then break the content into smaller steps.
Extension: See the Stretch & Challenge ideas in Lesson 4.
Before lesson: Read the script below. Pre-teach key vocab: Arithmetic operators, DIV, Relational operators.
If stuck: Re-read the revision notes (link above), then break the content into smaller steps.
Extension: See the Stretch & Challenge ideas in Lesson 4.
Teaching Script (35 mins):
Mins 0-5 - Hook: "Today: arithmetic and relational operations. By the end you will be able to answer exam questions on it unaided. It connects to the rest of Computer Science because the ideas here recur across the spec."
Mins 5-20 - Direct Instruction: Work through the core ideas below one at a time; after each, ask your student to explain it back in their own words.
Mins 20-30 - Guided Practice: Model the worked example together, then let your student attempt the first practice question with guidance.
Mins 30-35 - Independent Practice: 2-3 practice questions from Lesson 3 below, with immediate feedback.
Mins 0-5 - Hook: "Today: arithmetic and relational operations. By the end you will be able to answer exam questions on it unaided. It connects to the rest of Computer Science because the ideas here recur across the spec."
Mins 5-20 - Direct Instruction: Work through the core ideas below one at a time; after each, ask your student to explain it back in their own words.
Mins 20-30 - Guided Practice: Model the worked example together, then let your student attempt the first practice question with guidance.
Mins 30-35 - Independent Practice: 2-3 practice questions from Lesson 3 below, with immediate feedback.
First Look
Start with the revision notes summary, then attempt: Evaluate: 17 DIV 5 and 17 MOD 5
Plenary (5 minutes)
Check Out
Your student states one thing they learned and one question they still have about arithmetic and relational operations.
Lesson 2: Core Concepts: arithmetic and relational operations
Duration: 50 minutes
Starter Activity (5 minutes)
Review Previous Lesson
Quick recap: write 3 key points from Lesson 1 on arithmetic and relational operations. Check them against the notes below.
Main Content (35 minutes)
Arithmetic operators: perform mathematical calculations on numeric values. At GCSE, you need to know seven operators including DIV and MOD.
DIV: gives the whole number result of division (quotient). MOD gives the remainder. Together they describe any division completely: for a / b, the quotient is a DIV b and the remainder is a MOD b.
Relational operators: compare two values and return a Boolean result (TRUE or FALSE). They are used in IF conditions and WHILE loop conditions.
Exam Warning: In pseudo-code, = means "equal to" (comparison), NOT assignment. Assignment uses the left-arrow (←). This is different from languages like Python where = is assignment and == is comparison.
BODMAS/BIAS: applies in programming just as in maths. Operations are evaluated in a specific order: Brackets first, then exponents, then division/multiplication, then addition/subtraction.
GCSE Computer Science Exam Tips: Know your operators: +, -, *, /, DIV, MOD, ^ for arithmetic; =, <>, , = for comparison; AND, OR, NOT for logic. MOD is essential for divisibility checks and wrapping values. DIV for integer division. Always use brackets to clarify order of operations. In pseudo-code, ← is assignment; = is equality comparison. Remember BODMAS applies in expressions.
| Term | Meaning | Example |
|---|---|---|
| Addition | + | Add two values |
| Subtraction | - | Subtract second from first |
| Multiplication | * | Multiply two values |
| Real division | / | Divide, returns decimal |
| Integer division | DIV | Divide, returns whole number only |
| Modulo (remainder) | MOD | Returns the remainder after division |
| Exponent | ^ | Raises to a power |
| 10 DIV 3 | 3 | 10 / 3 = 3.33..., whole number part = 3 |
Practice (10 minutes)
Q: Evaluate: 17 DIV 5 and 17 MOD 5
Answer: 17 DIV 5 = 3 (17 / 5 = 3.4, whole number part = 3). 17 MOD 5 = 2 (remainder = 17 - 5*3 = 2).
Plenary (5 minutes)
Explain Back
Your student teaches the key points back to you without looking. Fill any gaps immediately.
Lesson 3: Application: arithmetic and relational operations
Duration: 50 minutes
Starter Activity (5 minutes)
Quick Recall
Recall the key terms: Arithmetic operators, DIV, Relational operators. Define each in one sentence.
Main Content (35 minutes)
Parent/Teacher Guide: Let your student attempt each question alone first, then compare with the model answer. Award method marks for correct working even if the final answer is wrong.
Q1: Evaluate: 17 DIV 5 and 17 MOD 5
Answer: 17 DIV 5 = 3 (17 / 5 = 3.4, whole number part = 3). 17 MOD 5 = 2 (remainder = 17 - 5*3 = 2).
Q2: Write pseudo-code that checks if a number is divisible by 3.
Answer: INPUT number IF number MOD 3 = 0 THEN OUTPUT number, " is divisible by 3" ELSE OUTPUT number, " is not divisible by 3" ENDIF
Q3: Evaluate step by step: 3 + 4 * 2 - 1
Answer: Step 1: 4 * 2 = 8. Step 2: 3 + 8 = 11. Step 3: 11 - 1 = 10.
Q4: Write pseudo-code that takes a number of minutes and outputs the hours and remaining minutes.
Answer: INPUT totalMinutes hours ← totalMinutes DIV 60 minutes ← totalMinutes MOD 60 OUTPUT hours, " hours and ", minutes, " minutes"
Q5: What is the result of (10 + 5) / 3? What about 10 + 5 / 3?
Answer: (10 + 5) / 3 = 15 / 3 = 5.0. 10 + 5 / 3 = 10 + 1.67 = 11.67. Brackets change the result!
Plenary (5 minutes)
Error Review
Review any questions answered incorrectly. Identify whether the error was knowledge, method, or reading the question.
Lesson 4: Exam Practice: arithmetic and relational operations
Duration: 50 minutes
Starter Activity (5 minutes)
Command Words
Review what these command words require: state (one point), describe (say what happens), explain (say why), compare (both sides), evaluate (judgement).
Main Content (35 minutes)
Extended Answer
Extended question: Full-Mark Response Write pseudo-code that inputs a number and determines whether it is divisible by both 3 and 5, divisible by 3 only, divisible by 5 only, or neither. Output an appropriate message for each case. [4 marks] <div class="
INPUT number IF number MOD 3 = 0 AND number MOD 5 = 0 THEN OUTPUT 'Divisible by both 3 and 5' ELSE IF number MOD 3 = 0 THEN OUTPUT 'Divisible by 3 only' ELSE IF number MOD 5 = 0 THEN OUTPUT 'Divisible by 5 only' ELSE OUTPUT 'Not divisible by 3 or 5' ENDIF
Exam Tips: DIV gives the whole number part of division; MOD gives the remainder | Use MOD 2 = 0 to check for even numbers | Use MOD 10 to get the last digit of a number | Always use brackets to make order of operations clear | In pseudo-code, = means "is equal to" (comparison), not assignment | Practise DIV and MOD calculations - they appear frequently in exams
Common Errors: ✗ Confusing = (assignment) with == (comparison) ✓ A single = assigns a value to a variable; == compares two values for equality. In pseudo-code, ← is assignment and = is comparison. ✗ Forgetting operator precedence — assuming left-to-right evaluation always applies ✓ BODMAS/BIDMAS rules apply: brackets first, then multiplication/division, then addition/subtraction. Use brackets to make order explicit. ✗ Using DIV when MOD is needed (or vice versa) ✓ DIV gives the integer quotient (7 DIV 2 = 3); MOD gives the remainder (7 MOD 2 = 1). MOD is used to check divisibility (e.g. n MOD 2 = 0 means n is even). ✗ Confusing <> (not equal) with (greater than) ✓ In pseudo-code, <> means 'not equal to'. m
Stretch & Challenge (Grade 8-9):
- Synoptic links: explain how arithmetic and relational operations connects to another Computer Science topic you have studied
- Real-world: research one real-world use or example of arithmetic and relational operations
- Critical: "What are the limitations of the models used in arithmetic and relational operations?"
Plenary (5 minutes)
Assessment Criteria
- Got it: Confident explanation + correct worked examples
- Getting there: Main points OK, needs support with detail
- Not yet: Confused on key concepts - re-run Lesson 2
Homework & Consolidation
- Consolidation: Re-answer any Lesson 3 practice questions answered incorrectly (20 mins)
- Retrieval: Write flashcards for the key terms: Arithmetic operators, DIV, Relational operators (10 mins)
- Exam practice: One past-paper question on arithmetic and relational operations from the board websites (15 mins)
- Extension: Explain arithmetic and relational operations to someone else in your own words (10 mins)