Number and Algebra
This subtopic covers fundamental mathematical concepts in number and algebra, including arithmetic operations, fractions, decimals, percentages, ratios, and algebraic expressions. It provides the essential quantitative skills required for solving real-world problems in computing and vocational contexts, such as data analysis, algorithm design, and financial calculations.
Assessment criteria
Learning Objectives
What you need to know and understand
- Perform arithmetic operations with integers, fractions, and decimals accurately
- Convert between fractions, decimals, and percentages
- Apply ratio and proportion to solve practical problems
- Simplify algebraic expressions by collecting like terms and expanding brackets
- Solve linear equations in one variable
- Solve linear inequalities and represent solutions on a number line
- Use algebraic methods to solve word problems
- Evaluate expressions by substituting numerical values
Assessment Criteria
Key criteria assessors look for in your portfolio
- Award credit for correct application of the order of operations (BIDMAS/BODMAS) in multi-step calculations
- Award credit for accurate conversion between fractions, decimals, and percentages in given contexts
- Award credit for setting up and solving ratio problems, including sharing quantities in a given ratio
- Award credit for correctly simplifying algebraic expressions, including expanding single brackets and collecting like terms
- Award credit for solving linear equations with unknown on one side, showing clear steps
- Award credit for solving inequalities and correctly representing the solution set on a number line
- Award credit for translating real-world scenarios into algebraic equations and solving them
- Award credit for accurate substitution into algebraic expressions, including use of negative numbers
Assessment Guidance
Guidance for achieving higher grades
- 💡Always show your working out clearly, as method marks are often awarded even if the final answer is incorrect
- 💡Check your answers by substituting back into the original equation or problem
- 💡Practice mental arithmetic to improve speed and accuracy in non-calculator sections
- 💡When solving word problems, define your variables and write down the equation before solving
- 💡Use a calculator effectively, but be aware of when it is allowed and when it is not
- 💡Revise key formulas and rules, such as the order of operations and fraction operations
Common Mistakes
Common errors to avoid in your coursework
- Misapplying the order of operations, e.g., calculating addition before multiplication
- Confusing the rules for multiplying and dividing fractions, e.g., not inverting the second fraction when dividing
- Incorrectly converting percentages to decimals, e.g., dividing by 100 instead of moving the decimal point
- Forgetting to reverse the inequality sign when multiplying or dividing by a negative number
- Losing track of negative signs when expanding brackets
- Not simplifying fractions or ratios to their lowest terms
Pass / Merit / Distinction Evidence Checklist
How your portfolio evidence is graded for PROQUAL AWARDING BODY 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 and order of operations
- Fractions, decimals, and percentages
- Ratios and proportions
- Algebraic expressions and simplification
- Linear equations and inequalities
- Problem-solving with real-world applications
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