§Your child is working hard, attending every lesson, and trying their best. But when mock results come back, they're stuck on a grade 3 when they need a 4 to pass, or hovering at grade 4 when a grade 5 would open up sixth form options.
I'm Aadam, and I've been tutoring Foundation tier students for over five years at SHLC. Here's what I've learned: most Foundation students aren't held back by a lack of effort. They're held back by specific topics that create bottlenecks in their understanding.
Master these ten topics, and grade 4 or 5 becomes genuinely achievable. Continue struggling with them, and you'll stay stuck regardless of how many hours you revise.
Understanding Foundation Tier: What You're Actually Aiming For
Before we dive into specific topics, let's be clear about what Foundation tier means.
Foundation tier allows grades 1 to 5. You cannot get a grade 6 or above on Foundation papers, no matter how well you perform. The content focuses more heavily on number and proportion (roughly 50% of marks) with less emphasis on complex algebra compared to Higher tier.
Why grade 4 matters so much: Grade 4 is the government pass standard. It's what most employers and sixth forms require. Research shows that achieving grade 4 in English and Maths typically adds around £2,000 to annual earnings, compounding to significant sums over a working life.
Why grade 5 matters even more: Many schools and colleges actually require grade 5 for sixth form entry, particularly for A level Maths or STEM subjects. Moving from grade 4 to grade 5 could be worth around £23,000 in lifetime earnings.
These topics genuinely matter for your child's future.
Topic 1: Fractions (All Operations)
Why it holds students back: Fractions appear everywhere in Foundation papers. They're tested directly, but they also appear hidden within ratio, proportion, algebra and geometry questions. If fraction skills are shaky, students lose marks across the entire paper.
Research shows fractions are the number one topic Foundation students struggle with, with over 40% of students losing marks on basic fraction calculations.
What Foundation students must know:
- Converting between mixed numbers and improper fractions
- Adding and subtracting fractions (finding common denominators)
- Multiplying fractions (multiply numerators, multiply denominators)
- Dividing fractions (keep, change, flip method)
- Finding fractions of amounts
- Expressing one number as a fraction of another
- Simplifying fractions fully
Common mistakes:
- Adding fractions without finding common denominators (trying to do 1/3 + 1/4 = 2/7)
- Dividing the wrong way when converting fractions to decimals
- Not simplifying final answers
- Mixing up multiplication and division rules
How to master it: Start with equivalent fractions. If you can't generate equivalent fractions fluently, everything else breaks down.
Use Corbett Maths 5-a-Day Foundation which includes fraction practice daily. Consistency beats cramming.
Practice with real contexts. Sharing pizza, measuring ingredients for recipes, working out sale discounts. When fractions feel real, they stick better.
Use SHLC past papers to see exactly how fractions appear in Foundation exams. Mark carefully to identify which operation causes you most trouble.
Topic 2: Percentages (Especially Percentage Change)
Why it holds students back: Percentage questions are worth roughly 10-15% of Foundation paper marks. They test whether students understand proportional reasoning, which underpins so much of GCSE Maths.
What Foundation students must know:
- Finding a percentage of an amount (e.g., 30% of £80)
- Expressing one amount as a percentage of another (e.g., 15 out of 60 as a percentage)
- Percentage increase and decrease
- Finding the original amount after a percentage change (reverse percentages)
- Simple interest calculations
- Real world applications (VAT, discounts, profit and loss)
The killer question type: "A jacket costs £45 after a 25% discount. What was the original price?"
This reverse percentage question requires understanding that £45 represents 75% (not 100%). Many Foundation students try to increase £45 by 25%, getting the wrong answer.
Common mistakes:
- Using the wrong base (increasing/decreasing from the new value instead of original)
- Forgetting to convert percentages to decimals (calculating 15% as ×15 instead of ×0.15)
- Not showing method (percentage questions have multiple method marks)
How to master it: Create a formula card:
- Find % of amount: Amount × (percentage ÷ 100)
- Express as %: (Part ÷ Whole) × 100
- % increase: Original × (1 + percentage as decimal)
- % decrease: Original × (1 - percentage as decimal)
For reverse percentages, always identify what percentage the new amount represents first.
Use Maths Genie to work through every percentage question type systematically.
Topic 3: Ratio and Proportion
Why it holds students back: Ratio makes up roughly 25% of Foundation paper content. It connects to fractions, percentages, and real world problem solving. Students who struggle with ratio struggle with proportional reasoning generally.
What Foundation students must know:
- Simplifying ratios to their simplest form
- Sharing amounts in given ratios
- Using ratios to find quantities
- Scale drawings and maps
- Direct proportion problems
- Best buy calculations (comparing value)
- Recipe and mixture problems
- Converting between units using ratio
Common question types: "Mix paint in the ratio blue:yellow = 2:3. You have 8 litres of blue paint. How much yellow paint do you need?"
Many students struggle because they try to work with the parts rather than understanding the scaling factor.
Common mistakes:
- Not simplifying ratios fully (writing 4:6 instead of 2:3)
- Mixing up the order (if ratio is 2:3, putting the wrong amount with the wrong part)
- Not finding the multiplier when scaling ratios
- Forgetting units in final answers
How to master it: Use the bar model method. Draw bars representing each part of the ratio. This visual approach helps students see what the ratio actually means.
Practice finding "one part" first, then multiplying to find other parts.
For best buy questions, always calculate cost per unit (cost ÷ quantity) for each option, then compare.
Topic 4: Basic Algebra (Collecting Terms, Expanding Brackets, Factorising)
Why it holds students back: Foundation students often develop algebra phobia. But roughly 20% of Foundation marks come from algebra, and these are often "easier" marks if students build confidence.
What Foundation students must know:
- Understanding algebraic notation (3a means 3×a, 2a+5 cannot be simplified further)
- Collecting like terms (2a+3b+4a = 6a+3b)
- Multiplying terms (3a × 4b = 12ab)
- Expanding single brackets (3(2a+5) = 6a+15)
- Factorising simple expressions (6a+9 = 3(2a+3))
- Substituting values into formulas
- Writing expressions from word problems
Common mistakes:
- Trying to add unlike terms (2a+3b does not equal 5ab)
- Sign errors when expanding brackets with negatives
- Forgetting to multiply everything inside brackets
- Not fully factorising (taking out 2 when you could take out 4)
How to master it: Start concrete before abstract. Use number bonds and balance problems to build algebraic thinking before introducing letters.
Think of letters as mystery numbers, not as scary algebra. If 3 × mystery number + 5 = 20, what's the mystery number? This builds intuition.
Practice expanding brackets with positive numbers first, then introduce negatives only after the method is secure.
My digital revision planner helps track which algebraic skills are secure and which need more work.
Topic 5: Solving Linear Equations
Why it holds students back: Equation solving appears directly (worth 5-8 marks) but also appears within other topics. You might need to solve an equation hidden in a geometry problem or word problem.
What Foundation students must know:
- Solving one step equations (x+5=12, 3x=15)
- Solving two step equations (3x+5=20)
- Equations with x on both sides (5x+3=2x+15)
- Equations with brackets (3(x+2)=18)
- Forming and solving equations from word problems
Common mistakes:
- Not doing the same thing to both sides
- Sign errors (especially when subtracting from both sides)
- Not showing working (equation questions have method marks)
- Dividing when they should multiply, or vice versa
How to master it: Think of equations as balanced scales. Whatever you do to one side, you must do to the other to keep it balanced.
Always write out each step. Don't try to do multiple steps in your head, even if it seems easy.
Check your answer by substituting back into the original equation. This catches errors.
Use Physics and Maths Tutor to find all past paper equation questions. Pattern recognition comes from volume practice.
Topic 6: Area and Perimeter (Including Compound Shapes)
Why it holds students back: Area and perimeter questions account for roughly 8-12% of Foundation marks. They test whether students can apply formulas in various contexts, including breaking down complex shapes.
What Foundation students must know:
- Perimeter of rectangles, triangles and compound shapes
- Area of rectangles, triangles, parallelograms and trapeziums
- Area of circles and circumference
- Breaking compound shapes into rectangles and triangles
- Finding missing dimensions when area is given
- Real world problems (carpets, fences, paint coverage)
The formulas you must memorise:
- Rectangle: Area = length × width
- Triangle: Area = ½ × base × height
- Parallelogram: Area = base × height
- Trapezium: Area = ½(a+b)h
- Circle: Area = πr², Circumference = 2πr or πd
Common mistakes:
- Mixing up area and perimeter (calculating area when asked for perimeter)
- Forgetting units or using wrong units (cm instead of cm²)
- Not breaking compound shapes into manageable parts
- Mixing up radius and diameter in circle calculations
- Using wrong formula for triangles (doing base×height instead of ½×base×height)
How to master it: Create formula flashcards with diagrams showing what each letter means.
Practice compound shapes specifically. Draw lines to split them into rectangles and triangles before calculating.
Always label diagrams clearly with all dimensions before starting calculations.
Topic 7: Interpreting Graphs and Charts
Why it holds students back: Foundation papers include substantial data handling content. Students must read information from bar charts, pie charts, line graphs, scatter graphs and frequency tables.
What Foundation students must know:
- Reading values from bar charts and pictograms
- Drawing and interpreting pie charts
- Reading coordinates from scatter graphs
- Understanding correlation (positive, negative, none)
- Drawing lines of best fit
- Reading conversion graphs (currency, temperature)
- Distance time graphs (including calculating speed)
- Frequency tables and grouped data
- Finding mean, median, mode and range
Common mistakes:
- Misreading scales (especially when 1 square = 2 or 5 units)
- Drawing pie charts with wrong angles
- Not using a ruler for lines of best fit
- Mixing up positive and negative correlation
- Calculating mean incorrectly from frequency tables
- Finding mode from grouped data (you can only identify the modal class)
How to master it: Practice reading scales carefully. This basic skill causes surprising numbers of errors.
For pie charts, remember: 360° = 100%, so each 1% = 3.6°
When calculating mean from frequency tables, remember: mean = (sum of f×x) ÷ (sum of f)
Topic 8: Transformations and Coordinates
Why it holds students back: Transformations combine visualisation, accuracy and following rules. They're worth 5-8 marks and students either find them easy or completely confusing.
What Foundation students must know:
- Plotting and reading coordinates (including negative coordinates)
- Translations using column vectors
- Reflections in vertical, horizontal and diagonal lines
- Rotations about a point (90° and 180°)
- Enlargements with positive scale factors
- Describing transformations fully
Common mistakes:
- Mixing up x and y coordinates (writing y first)
- Not describing transformations fully (saying "reflection" without stating the mirror line)
- Rotating the wrong way (clockwise vs anticlockwise)
- Not using the correct centre for rotations
- Mixing up object and image
How to master it: Use tracing paper for transformations. It's allowed in exams and makes rotations and reflections much clearer.
When describing transformations, always include all necessary details:
- Translation: column vector
- Reflection: equation of mirror line
- Rotation: angle, direction, centre
- Enlargement: scale factor, centre
Practice on graph paper initially to build accuracy, then practice on blank paper to develop visualisation skills.
Topic 9: Units and Conversions
Why it holds students back: Unit conversion appears throughout Foundation papers, hidden in measurement, ratio and problem solving questions. Students lose marks not through calculation errors but through using wrong units.
What Foundation students must know:
- Converting between metric units (mm, cm, m, km for length; g, kg for mass; ml, litres for capacity)
- Converting between units of area (cm² to m²)
- Converting between units of volume (cm³ to litres)
- Converting between 12 and 24 hour times
- Reading scales and measuring accurately
- Understanding compound units (speed, density)
Common conversion errors:
- Dividing when they should multiply (or vice versa)
- Not squaring when converting area units (1m² = 100cm² is wrong, should be 10,000cm²)
- Mixing up volume and capacity conversions
- Forgetting to include units in final answers
How to master it: Create a conversion ladder for each measurement type:
km ×1000→ m ×100→ cm ×10→ mm
←÷1000 ←÷100 ←÷10
Remember: when converting area units, square the conversion factor. When converting volume units, cube it.
Practice compound measures separately. Speed = distance ÷ time needs automatic recall.
Topic 10: Probability (Including Tree Diagrams)
Why it holds students back: Probability questions test logical thinking under pressure. Foundation probability is worth 4-6 marks but students either get them all or lose them all.
What Foundation students must know:
- Probability scale from 0 to 1
- Finding probability of single events
- Listing outcomes systematically
- Using two way tables
- Simple tree diagrams
- Combined probabilities (AND means multiply, OR means add)
- Experimental vs theoretical probability
- Expected frequency
Common mistakes:
- Writing probabilities greater than 1 or less than 0
- Adding probabilities when they should multiply
- Not simplifying probability fractions
- Forgetting to multiply along branches in tree diagrams
- Not checking probabilities sum to 1
How to master it: Start with the probability scale. Every probability must be between 0 and 1 inclusive. If your answer is 1.3 or negative, something's wrong.
For combined events: AND means multiply (probability of A AND B = P(A) × P(B)) OR means add (probability of A OR B = P(A) + P(B))
Tree diagrams must have all branches at each stage summing to 1. Use this to check your work.
Get professional feedback on probability through my mock exam marking service. These questions require precise notation that's hard to self mark.
How to Systematically Master These Topics
Knowing which topics cause problems is useless without a plan. Here's the system I use with Foundation students at SHLC:
Step 1: Diagnostic (Weeks 1-2) Complete a full Foundation paper under timed conditions. Mark it carefully. For each lost mark, identify which of these ten topics caused it.
Rank these topics from weakest (loses most marks) to strongest (loses fewest marks).
Step 2: Targeted Practice (Weeks 3-24) Target topics in order of weakness. For each topic:
- Watch explanation videos on Maths Genie
- Complete 20-30 questions of increasing difficulty
- Attempt past paper questions specifically on that topic
- Review every mistake using worked solutions
Use my digital revision planner to track progress from red (struggling) to amber (improving) to green (confident).
Aim to move at least two topics from red to amber each month.
Step 3: Integration Practice (Weeks 25-30) Now these topics must connect. Complete mixed topic questions and full papers.
Complete at least one Foundation paper per week. Track scores over time. You should see steady improvement.
Target: Paper 1 (non calculator) 50+ marks, Papers 2&3 (calculator) 55+ marks for grade 4. For grade 5: Paper 1 target 60+ marks, Papers 2&3 target 65+ marks.
Step 4: Professional Feedback Self marking misses subtle errors. Every 4-6 weeks, use my mock exam marking service to get expert analysis showing exactly where marks are being lost.
Common Mistakes Foundation Students Make
Mistake 1: Neglecting Basics Long multiplication, long division, decimal addition. These seem too simple to practise, but foundation students who've forgotten the basics lose marks throughout papers.
Spend time on Peter Robson style foundation building if these skills are shaky.
Mistake 2: Starting Past Papers Too Early If you can't do individual topics, full papers are overwhelming and demotivating. Master topics first, then move to full papers.
Mistake 3: Only Practising Calculator Skills Paper 1 is non calculator. It's worth 80 marks. Students who rely on calculators for everything struggle badly on Paper 1.
Practice non calculator methods separately. Use Corbett Maths 5-a-Day Foundation which focuses on non calculator skills.
Mistake 4: Not Reading Questions Carefully Over 30% of Foundation students lose marks simply through misreading what questions ask for. Practice highlighting key instruction words before starting.
Mistake 5: Leaving Questions Blank A blank answer gets zero marks. Even wrong working might earn method marks. Attempt everything.
For Parents: Supporting Foundation Students
Understand That Foundation Isn't "Easy" The current Foundation tier is significantly harder than previous versions. Students aren't lazy if they're finding it challenging.
Focus on Grade 4 First If your child is hovering at grade 3, focus all energy on securing grade 4. That pass opens doors. Grade 5 can come later if time allows.
Celebrate Small Wins Moving from 30% to 40% on fractions practice deserves celebration, even if the overall grade hasn't changed yet. Progress in topics leads to grade improvements, but it takes time.
Consider Professional Support Foundation students often have gaps from Year 7-9 that need filling before current content makes sense.
At SHLC, I specialise in identifying and filling these gaps systematically. I've helped dozens of students move from grade 3 to grade 4 or 5, achieving that crucial pass that changes their options.
Monitor Confidence Foundation students often have mathematical anxiety from years of struggle. Building confidence matters as much as building skills.
The Bottom Line
These ten topics consistently hold Foundation students back from achieving grade 4 or 5. They account for roughly 70-80% of Foundation paper marks.
Master them systematically, and passing becomes genuinely achievable. Continue struggling with them, and you'll stay stuck at grade 2-3 regardless of how many practice papers you complete.
The students I work with who move from grade 3 to grade 4-5 have three things in common:
- They identify their specific weak topics early
- They practise those topics systematically with clear tracking
- They seek help when self study isn't working
You now know which topics cause the most problems. The question is: will you address them systematically?
Remember: achieving grade 4 in Maths typically adds £2,000 to annual earnings. Moving to grade 5 adds thousands more. These topics genuinely affect your child's future opportunities and financial security.
Start today. Master these ten topics. Pass your GCSE Maths.
Struggling with Foundation tier topics? Get in touch with SHLC to discuss how targeted tutoring can help you master these topics and achieve grade 4 or 5.