How to Get Better at Maths: A Practical Study Plan

Functional Skills

To get better at maths, identify one specific gap, learn the underlying idea from a clear worked example, practise varied questions, analyse each error and revisit the skill after a delay. Short, focused sessions with feedback are usually more useful than completing large sets of nearly identical questions without checking why answers are right or wrong.

This guide is primarily for UK learners preparing for GCSE Maths, Functional Skills Maths or a return to everyday numeracy. It provides an educational study framework rather than a promise of instant improvement. Your timetable will depend on your starting point, goal, available support and any learning needs.

The quick improvement plan

Use this six-stage cycle whenever you begin a new topic or discover a weakness:

Diagnose: answer a small selection of questions without notes so that you can see exactly where understanding breaks down.
Select: choose one manageable prerequisite gap rather than trying to repair an entire subject at once.
Study: examine a worked example and explain what happens at each step and why.
Practise: move from supported questions to independent, varied problems.
Check: mark your work, classify errors and obtain feedback where necessary.
Revisit and transfer: return to the skill after increasing intervals, then apply it to an unfamiliar problem.

This structure reflects the broad aims of mathematics education in England. The Department for Education’s national curriculum for mathematics emphasises fluency, mathematical reasoning and solving problems—not speed or repetition alone.

Improvement is therefore broader than memorising a procedure. You should aim to calculate accurately, understand relationships, choose an appropriate method and explain why it works.

1. Diagnose the real gap

A disappointing test result may reveal a gap, but the final topic named on the paper is not always the root problem. Difficulty solving equations, for example, might come from weak negative-number arithmetic, fraction operations or the meaning of the equals sign.

Take a short diagnostic

Choose six to ten questions covering the topic at more than one level. Attempt them independently and show every step. Record each result as:

Secure: correct, with a method you can explain.
Partly secure: correct with a hint, or correct despite uncertainty.
Gap: incorrect, unfinished or not attempted.

Do not use one total score as your only diagnosis. Look for patterns. If you can find 10% of an amount but cannot increase an amount by 10%, your gap concerns how percentages change a whole—not necessarily percentage calculation in general.

Diagnostic assessment should inform the next teaching or study step. The Education Endowment Foundation’s guidance on improving mathematics in Key Stages 2 and 3 recommends using assessment to identify pupils’ strengths and weaknesses and then deciding how to respond.

Trace prerequisite knowledge

Ask, “What must I already know to solve this?” A GCSE question involving the area of a compound shape may depend on multiplication, unit conversion and identifying rectangles before it depends on a complicated formula. Repair the earliest missing link first.

Use your exam board specification, course outline or teacher’s topic list to avoid random study. For Functional Skills, consult the Department for Education’s official Functional Skills mathematics subject content. If you are preparing for GCSE, use the specification and assessment materials published by your awarding organisation.

2. Understand concepts and worked examples

A rule is easier to apply flexibly when you understand the quantities and relationships behind it. Memorisation still has a role—for multiplication facts and standard formulae, for example—but it should support understanding rather than replace it.

How to study a worked example

Do more than read the finished solution. Cover each line below the one you are examining and ask:

What information is given?
What is the question asking me to find?
Why is this operation appropriate?
Which fact, definition or rule justifies this step?
What common mistake could occur here?
Can I estimate the answer before calculating?

Then close the example and reproduce it from memory. Change one feature—a number, unit or context—and solve the new version. The EEF guidance linked above discusses worked examples as a way to model successful problem-solving and make mathematical thinking visible.

A complete algebra example

Consider this practice problem:

A school club books a minibus for a fixed charge of £48 and then pays £3 per passenger. The total charge is £93. How many passengers travelled?

Let p be the number of passengers.

Step 1: Represent the charges.
The fixed charge is £48. The passenger charge is £3 × p, so:
£48 + £3p = £93

Step 2: Remove the fixed charge from both sides.
£3p = £93 − £48
£3p = £45

Step 3: Divide both sides by £3 per passenger.
p = £45 ÷ £3 per passenger
p = 15 passengers

Answer: 15 passengers travelled.

Check the result by substituting it into the original relationship: £48 + (15 × £3) = £48 + £45 = £93. The units also make sense: dividing a charge in pounds by a rate in pounds per passenger gives a number of passengers.

Move from supported to independent work

Start with a fully explained example. Next, complete a similar question with prompts. Then solve one without prompts. Finally, try a question that looks different but relies on the same concept. This gradual removal of support helps reveal whether you understand the method or have merely copied its surface pattern.

3. Practise effectively

Practice matters, but quantity alone is not a reliable measure of quality. Twenty carefully checked questions can teach more than a hundred rushed ones.

Use short, regular sessions

A workable session might last 20 to 40 minutes:

five minutes retrieving previously learned facts or methods;
ten minutes reviewing one concept or worked example;
ten to twenty minutes solving varied questions;
five minutes marking, correcting and planning the next review.

This is an example, not a compulsory schedule. Some learners benefit from shorter sessions, breaks, assistive technology or additional processing time. Regular study reduces the need for last-minute cramming, but daily practice is not a magic condition for progress.

Space and mix your review

Return to a topic after a delay instead of completing it once and abandoning it. You might review a new skill the next day, three days later, a week later and then during cumulative revision. These intervals are a practical starting point rather than a universal formula; shorten or lengthen them according to what you can retrieve independently.

Mix some previously learned material into each session. If all ten questions use the same method and appear under a heading that names it, you are not practising the decision about which method to choose. A mixed set might include percentages, fractions and ratio so that you must interpret each question first.

Vary the examples

Variation helps you notice what matters. When studying linear equations, include unknowns on either side, brackets, negative numbers and fractional coefficients—but increase complexity gradually. When studying area, vary orientation and missing dimensions rather than relying only on identical rectangles.

Estimate before calculating

An estimate helps detect impossible answers. For 19.8 × 5.1, 20 × 5 gives an estimate of 100. An answer of 1,009 should therefore prompt you to inspect decimal placement.

Estimation is especially useful with calculators. A calculator can execute an entered operation accurately, but it cannot decide whether you selected the right operation or entered the intended values.

4. Use feedback and an error log

Marking an answer wrong is not enough. An error becomes useful when you identify its cause and change what you do next.

Classify each mistake

Concept error: you misunderstood an idea, such as treating the denominator as the number of selected parts.
Method error: you chose an unsuitable process or used the right process in the wrong order.
Arithmetic error: the plan was correct but a calculation failed.
Reading error: you missed a unit, condition, scale or instruction.
Notation error: your symbols were ambiguous or incorrect.
Checking error: you did not compare the result with an estimate or substitute it back.

A worked error-log entry

Prompt	Example entry
Question	Find 15% of £60.
My answer	£90.
Error type	Place-value and reasonableness error.
Cause	I calculated 15 × 60 and did not divide by 100.
Correction	10% of £60 is £6 and 5% is £3, so 15% is £9.
Check	15% is less than 100%, so the result must be less than £60.
Next action	Practise finding 5%, 10%, 15% and percentage multipliers; review in three days.

Feedback should tell you what to do next. The EEF’s guidance on teacher feedback stresses laying suitable foundations and planning how learners will receive and use feedback. When studying alone, model this by correcting your reasoning, not merely copying an answer.

5. Strengthen essential foundations

The right foundations depend on your goal, but the following areas frequently support GCSE and Functional Skills work.

Order of operations

BIDMAS or BODMAS reminds you to handle brackets and indices or orders before multiplication and division, followed by addition and subtraction. Operations at the same level are normally completed from left to right. Therefore, 20 ÷ 5 × 2 = 4 × 2 = 8; multiplication does not automatically come before division.

The four operations and number sense

Build accurate methods for addition, subtraction, multiplication and division, alongside estimation. Mental strategies can make calculation efficient. For example:

14 × 9 = 14 × (10 − 1) = 140 − 14 = 126.

You do not need to reject calculators. Learn when mental calculation, written methods or a calculator is most appropriate, and always consider the expected size of the answer.

Fractions, decimals and ratios

A fraction is a number written as one integer divided by another non-zero integer. It can represent division, a point on the number line, an operator or parts of a whole. For example, 3/4 means 3 ÷ 4 and equals 0.75.

A decimal is a base-ten representation of a number. Digits to the right of the decimal point represent tenths, hundredths, thousandths and so on. Fractions and decimals can therefore be alternative representations of the same number.

Not every fraction has a terminating decimal representation. For example, 1/3 = 0.333… where the 3 recurs. Likewise, 2/3 = 0.666… . By contrast, 1/8 = 0.125 terminates.

A ratio compares quantities. The ratio 1:2 means one quantity corresponds to two units of another. Ratios can be related to fractions, but they are not simply the same concept. In a group with a red-to-blue ratio of 1:2, red items are 1/3 of the whole because there are three equal ratio parts altogether.

Practise translating among representations. For instance, 1/4 = 0.25 = 25%, while a ratio of one red item to three other items makes red 1/4 of the total.

Percentages

A percentage is a quantity expressed per hundred. To find 15% of £80, you can calculate 0.15 × £80 = £12. To increase £80 by 15%, add £12 or multiply by 1.15, giving £92. Distinguish “15% of”, “increase by 15%” and “15 percentage points”; they ask different things.

Units, measures and data

Write units throughout a calculation and convert them before combining quantities. One metre is 100 centimetres, but one square metre is 10,000 square centimetres because both dimensions are converted.

When reading graphs, inspect the title, axis labels, units, intervals and whether an axis starts at zero. For averages, decide whether mean, median or mode answers the actual question, and consider the effect of outliers.

Algebra and the equals sign

Letters represent numbers or quantities, and the equals sign states that two expressions have the same value. It does not merely mean “write the answer next”. Preserve equality by performing equivalent operations on both sides.

For 3x + 5 = 20, subtract 5 from both sides to obtain 3x = 15, then divide both sides by 3: x = 5. Check by substitution: 3 × 5 + 5 = 20.

A seven-day diagnostic-and-practice plan

This restrained one-week plan gives you a repeatable mechanism for one topic. Use 20 to 40 minutes per day if that is manageable, or spread the same stages across a longer period.

Day	Main task	Evidence to record
1	Complete a short diagnostic without notes. Choose one prerequisite gap.	Questions attempted, accuracy and error categories.
2	Study one or two worked examples. Explain every step aloud or in writing.	A short explanation of why the method works.
3	Complete supported examples, then three independent questions.	Which prompts were still needed.
4	Retrieve the method without notes and solve a varied set.	Accuracy by question type, not just total score.
5	Mix the topic with two older skills. Update your error log.	Whether you selected methods correctly.
6	Attempt an unfamiliar or contextual problem and explain your reasoning.	Your model, units, estimate and final check.
7	Take a short retest and compare it with Day 1. Schedule another review.	Independent accuracy, recurring errors and next review date.

If the retest shows little improvement, do not simply repeat more questions at the same level. Return to the prerequisite, use a different explanation or ask a teacher or tutor for targeted feedback.

What to do when you are stuck

Being stuck provides information; it is not evidence that you are incapable of learning the topic. Use a planned sequence:

Rewrite what the question gives you and what it asks you to find.
Draw a diagram, table, number line or bar model where appropriate.
Label units and estimate the likely answer range.
Try a simpler case or use smaller numbers to expose the structure.
Find a worked example involving the same relationship, not merely similar words.
Ask for a hint before requesting the complete solution.
After receiving help, close the solution and complete the question again independently.

You can ask questions through whichever channel is comfortable: in class, privately after a lesson, by email, through an approved learning platform or with a constructive study partner. Choose people who help you examine the mathematics rather than dismissing your concerns or doing the work for you.

If difficulties are persistent, broad or causing significant distress, speak to your teacher, college learning-support team or an appropriately qualified tutor. Learners with dyscalculia, language needs, visual impairments, attention differences or other support needs may benefit from tailored teaching and reasonable adjustments. Schools, colleges and awarding organisations can advise on support and assessment arrangements; eligibility is determined individually rather than by this article.

How to measure progress

Do not define mastery as answering several identical questions immediately after seeing an example. Use a stronger progression check.

A skill is ready for progression when you can:

solve a varied set accurately without prompts;
explain the reasoning or justify the method;
recognise when the method does and does not apply;
check the answer using estimation, substitution or another representation;
repeat the performance after a delay; and
apply the idea within at least one unfamiliar problem.

This is not a permanent finish line. Continue occasional cumulative practice after moving to the next topic. If later review exposes a weakness, return to it.

Track useful measures

Record more than a percentage score:

independent accuracy;
number and type of hints needed;
error categories;
time taken, where speed is relevant;
ability to explain and check;
performance after a delay;
success on an unfamiliar application.

Use timed work selectively. It can help with exam pacing once methods are secure, but applying time pressure too early may conceal the concept you need to learn.

A simple progress calculation

To compare two short tests fairly, use equivalent sets covering the same skill and difficulty. Calculate independent accuracy as:

Independent accuracy = independently correct answers ÷ questions attempted × 100%

For example, 6 independently correct answers from 8 attempted questions gives 6 ÷ 8 × 100% = 75%. Record prompted answers separately: counting a question completed after a substantial hint as fully independent can hide the support you still need. A percentage from a tiny set is volatile, so combine it with your error types, explanation and delayed performance rather than treating it as a definitive measure.

Use mock tests and courses purposefully

A mock test is most useful when you review it question by question, identify patterns and turn them into a study plan. Learners considering Functional Skills Maths Level 1 can take this free mock test to sample questions and identify areas for further study. Check the course page for its current format and terms.

If you enrol on a course or work with a tutor, look for clear explanations, diagnostic assessment, opportunities for independent practice and specific feedback. A tutor can organise learning and respond to misconceptions, but no course removes the need to think through problems and review mistakes.

For a wider choice of study options, explore Lead Academy’s Functional Skills courses:

Top Courses of this Category

Digital Functional Skills Level 1 Online Course and Exam

Functional Skills English Entry Level 3 Course

Functional Skills Entry Level 1 English Course Online

Functional Skills Entry Level 2 Maths Online Course

Functional Skills Maths Entry Level 3 Online Course

Frequently asked questions

How long does it take to get better at maths?

There is no universal timescale. A narrow procedural gap may improve after several focused sessions, while rebuilding number knowledge or preparing for a qualification can take months. Compare performance on equivalent questions over time rather than expecting a fixed number of days.

Should I practise maths every day?

Daily practice can suit some schedules, but quality, spacing, feedback and sufficient rest matter more than maintaining an unbroken streak. Three or four focused sessions each week may be effective if you revisit material and act on errors.

What should I do if I understand examples but cannot answer questions alone?

You may still depend on the example’s prompts. Try partially completed questions, then remove one prompt at a time. Reproduce the method from memory and practise questions with different wording, layouts and values. If the difficulty remains, seek feedback on the exact step where you stop.

Is memorising formulas enough?

No. You also need to know what each symbol means, which units are required, when the formula applies and how to rearrange or check it. Learn a formula alongside a diagram, derivation or worked application where appropriate.

Should I use a calculator?

Use one when it is permitted and appropriate, but retain estimation and core number skills. Write the calculation you intend to perform, enter it carefully and check whether the result is reasonable. Follow the calculator rules for your particular assessment.

How can I reduce maths anxiety?

Begin with a manageable task, allow enough time, record small improvements and ask for support through a comfortable channel. Focus on the next mathematical step rather than judging yourself. If anxiety is severe or affects daily life, speak to a teacher, pastoral lead, GP or qualified mental-health professional as appropriate.

Are past papers the best way to revise?

Past papers are valuable for checking coverage, interpreting exam wording and practising timing, but they are not a complete teaching method. Use topic practice to repair identified gaps, then return to a paper to test whether the skill transfers.

Conclusion

Getting better at maths is a cycle: diagnose, learn, practise, check, revisit and transfer. Begin with one clearly defined gap. Study the reasoning behind a worked example, complete varied questions, classify mistakes and return to the skill after a delay. Progress when you can work independently across different forms of the problem—and keep older material in cumulative review.

Confidence can grow from evidence: a corrected misconception, a method you can explain or a question you can now solve without a prompt. If progress stalls, change the explanation or level of support rather than assuming that more undirected repetition will solve the problem.

About this guide

This educational guide is published by Lead Academy’s editorial team. It was prepared by comparing its study advice with current Department for Education mathematics curriculum and Functional Skills documents and relevant Education Endowment Foundation guidance. The worked calculations were checked line by line for arithmetic, units and interpretation. No named maths educator or external specialist review is claimed. Learners should use the current specification, assessment rules and authorised materials from their school, college or awarding organisation for qualification-specific decisions.

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