Number and Algebra
This subtopic covers fundamental mathematical concepts including arithmetic operations, fractions, decimals, percentages, ratios, and basic algebraic manipulation. Practical application in service industries includes calculating costs, pricing, discounts, and interpreting data for business decisions.
Assessment criteria
Learning Objectives
What you need to know and understand
- Perform arithmetic operations accurately with integers, fractions, and decimals
- Convert between fractions, decimals, and percentages
- Calculate percentages including increases and decreases
- Use ratios and proportions to solve real-world problems
- Simplify algebraic expressions and solve linear equations
- Apply mathematical reasoning to service industry scenarios
Assessment Criteria
Key criteria assessors look for in your portfolio
- Award credit for correct use of BODMAS/BIDMAS in calculations
- Award credit for accurate conversion between fractions, decimals, and percentages
- Award credit for correct calculation of percentage change
- Award credit for setting up and solving ratio problems correctly
- Award credit for correct simplification of algebraic expressions
- Award credit for solving linear equations with one unknown
Assessment Guidance
Guidance for achieving higher grades
- 💡Show all working steps clearly to gain method marks even if the final answer is wrong
- 💡Check your answers by substituting back into the original problem
- 💡Practice mental arithmetic to speed up calculations
- 💡Read the question carefully to identify whether a percentage increase or decrease is required
- 💡Use estimation to check the reasonableness of your answers
Common Mistakes
Common errors to avoid in your coursework
- Misapplying the order of operations (e.g., calculating addition before multiplication)
- Confusing fractions and decimals when converting
- Forgetting to convert percentages to decimals before multiplying
- Setting up ratios incorrectly (e.g., reversing the order)
- Making errors when simplifying algebraic expressions (e.g., combining unlike terms)
Pass / Merit / Distinction Evidence Checklist
How your portfolio evidence is graded for ACTIVE IQ Number and Algebra
Every vocational unit is marked against named criteria rather than an exam percentage. Your tutor's brief lists the exact codes for this unit — here is what each band is asking you to do.
Demonstrate baseline knowledge, accurate terminology, and core practical application.
Provide detailed analysis, structured explanations, and clear workplace reasoning.
Deliver thorough evaluation, original problem solving, and fully justified recommendations.
Coursework AI Review
Paste your assignment brief and check your draft against its P/M/D criteria
Key Terminology
Essential terms to know
- Arithmetic operations
- Fractions, decimals, and percentages
- Ratios and proportions
- Basic algebra
- Problem-solving in context
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