KPSEA Mathematics: 8 Grade 6 Worked Examples Every Learner Should Master

Mathematics can lift a Grade 6 learner's KPSEA result more than almost any other subject, because it rewards method you can practise. A child who shows clear working earns marks even when the final answer slips. This guide walks through worked examples across every strand KPSEA returns to, place value, fractions, percentages, measurement, geometry, data and simple algebra, with the full method for each. Work each one on paper first, then check your steps against ours. The examples are drawn from our KPSEA Grade 4 to 6 Complete Revision Course, and you can see a free sample before you buy anything.

The five strands KPSEA Mathematics draws from

Grade 6 Mathematics under the CBC is organised into strands, and KPSEA questions are spread across them rather than concentrated in one. Knowing the map helps you revise evenly instead of over-practising the topics your child already enjoys. The five strands are:

• Numbers, the largest strand: place value, operations, fractions, decimals, percentages, ratio, and number patterns.
• Measurement: length, mass, capacity, area, perimeter, volume, money and time.
• Geometry: lines, angles, shapes and their properties.
• Data handling: reading and interpreting tables, bar graphs and pictographs, and finding the mean, mode and median.
• Algebra: simple expressions and equations, forming and solving them.

A learner who is comfortable across all five walks into the paper without nasty surprises. The worked examples below are grouped the same way, so you can target a strand your child finds shaky.

How marks are actually awarded

Here is the single most important idea in KPSEA Mathematics, and the reason so many able children score below their ability: most of the marks in a multi-step question are for the method, not the final answer. A learner who writes only the answer, even the right one, can leave marks on the table, while a learner who shows every step earns method marks even when the final figure is wrong.

So the rule your child should carry into every question is simple: show every step, write the units, and underline the final answer. Now to the examples.

Numbers

1. Place value. Write the place value of 7 in 4,703,158. Counting from the right, the 7 sits in the hundred thousands place, so its value is 700,000. A quick check: label each digit's place under it before answering, and place-value questions become automatic.

2. Fractions. Work out 3/4 + 1/8. Use a common denominator of 8: 3/4 becomes 6/8, so 6/8 + 1/8 = 7/8. The key step is finding the common denominator; write it down even if you can do it in your head, because that is where the method mark lives.

3. Percentages. Find 25% of 240. Percent means "out of 100", so 25% is 25/100. Then (25 ÷ 100) × 240 = 60. Learners who remember that "of" means multiply rarely lose these marks.

4. Ratio. Share KSH 500 between two children in the ratio 2:3. Add the parts: 2 + 3 = 5 parts. One part is 500 ÷ 5 = 100. So the shares are 2 × 100 = KSH 200 and 3 × 100 = KSH 300. Always check the shares add back to the total: 200 + 300 = 500. Correct.

5. LCM and HCF. Find the LCM of 6 and 8. List multiples: 6, 12, 18, 24 and 8, 16, 24. The lowest common one is 24. For the HCF of 12 and 18, list factors and take the highest shared one, which is 6. Writing the lists out is the working the scheme rewards.

6. Decimals. Work out 4.6 + 2.75. Line up the decimal points and fill a gap with zero: 4.60 + 2.75 = 7.35. The single most common error here is misaligned decimal points, so line them up before adding.

Measurement

7. Perimeter and area. A rectangle is 8 cm long and 5 cm wide. Perimeter = 2 × (8 + 5) = 2 × 13 = 26 cm. Area = 8 × 5 = 40 cm². Note the units carefully: length in cm, area in cm². A missing or wrong unit can cost a mark even when the number is right.

8. Length conversion. Convert 3.5 km to metres. Since 1 km = 1,000 m, 3.5 × 1,000 = 3,500 m. For conversions, first write the fact you are using (1 km = 1,000 m); that line is often worth a mark on its own.

9. Volume of a cuboid. Find the volume of a box 4 cm by 3 cm by 2 cm. Volume = length × width × height = 4 × 3 × 2 = 24 cm³. Remember volume is in cubic units (cm³), not square units.

10. Time and money. A book costs KSH 120; find the change from KSH 200. 200 − 120 = KSH 80. Now a time example: a bus leaves at 8:45 am and travels for 2 hours 30 minutes. It arrives at 11:15 am. Add the hours first (8:45 + 2 h = 10:45), then the minutes (10:45 + 30 min = 11:15).

Geometry

11. Angles on a straight line. Two angles sit on a straight line. One is 110°. Find the other. Angles on a straight line add up to 180°, so 180 − 110 = 70°. Stating the rule ("angles on a straight line = 180°") earns the method mark.

12. Area of a triangle. A triangle has a base of 10 cm and a height of 6 cm. Area = ½ × base × height = ½ × 10 × 6 = 30 cm². The half is the step learners forget; write the formula first every time.

Data handling and algebra

13. Mean (average). Find the mean of 4, 7, 9 and 10. Add them: 4 + 7 + 9 + 10 = 30. Divide by how many there are: 30 ÷ 4 = 7.5. The mean can be a decimal; that is normal and correct.

14. Mode and median. For the numbers 2, 3, 3, 5, 7, the mode is the most frequent value, which is 3. The median is the middle value when they are in order, also 3. Teach your child to write the numbers in order first; the median follows easily.

15. Percentage profit. A trader buys goods for KSH 3,200 and sells for KSH 3,600. Profit = 3,600 − 3,200 = 400. Percentage profit = (400 ÷ 3,200) × 100 = 12.5%. The profit is always worked out against the buying (cost) price, not the selling price.

16. Simple equations. Solve x + 7 = 12. Take 7 from both sides: x = 12 − 7 = 5. Solve 3x = 21 by dividing both sides by 3: x = 7. Show the "do the same to both sides" step; it is the heart of the method.

Reading the question is half the battle

A surprising number of marks are lost before any calculation begins, simply because the child answered a slightly different question from the one on the paper. KPSEA Mathematics leans heavily on word problems, where the sum is wrapped inside a short story about shopping, sharing, travelling or measuring. The skill of pulling the numbers and the operation out of the words is one you can teach directly, and it pays off across every strand.

Train your child to do three things with every word problem. First, underline the numbers and the units as they read, so nothing is missed. Second, decide what the question is actually asking for, the change, the total, the area, the average, and write that word down before calculating. Third, choose the operation on purpose: words like "altogether" and "in total" usually mean addition, "left" or "change" mean subtraction, "each" and "per" often mean multiplication or division. When a child names the operation deliberately rather than guessing, careless errors fall away and the working becomes clear enough to earn every method mark.

It also helps to read the question twice: once for the story, once for the maths. The first read builds the picture, the second pulls out the figures. This habit costs a few seconds and saves whole questions, especially the multi-step ones near the end of the paper where the marks are richest and the pressure is highest.

A parent's playbook for the final weeks

You do not need to be a mathematician to help your child improve. The most valuable thing a parent brings is a steady routine and honest marking, and both are entirely within reach. Start by setting a fixed short slot most days, the same time each evening if you can, because a predictable rhythm removes the daily argument about when to study and quietly builds the hours.

Keep every session active. Passive re-reading of notes feels productive but changes very little; working through problems and then marking them is what moves the result. After each short set, sit together and mark against the answers, and when a mark is lost, ask your child to explain where the method went wrong rather than simply writing the correct figure. That single conversation, repeated over a few weeks, is worth more than any amount of silent practice.

Keep a running list of the mistakes that come back again and again, the missing units, the forgotten half in the triangle area, the decimal points out of line. A short, personal list of recurring slips is far more useful than a general textbook, because it targets exactly where your child is leaking marks. Revisit that list every week, and watch it shrink. Finally, protect sleep and some downtime in the run-up; a rested mind recalls method under exam pressure far better than a tired one that crammed the night before.

Quick-reference: method and common mistake by topic

How marks are earned in KPSEA Maths

• Show every step. Working earns method marks even if the final answer is wrong.
• Write units (cm, cm², cm³, KSH). A missing unit can quietly cost a mark.
• Check the answer makes sense before moving on, for example that a change is smaller than the amount paid.
• Underline the final answer so the marker sees it clearly.

A simple practice rhythm that works

These sixteen examples are a start, not the whole job. A strong result comes from practising every strand and marking honestly against a scheme. A short daily session beats a long weekly one: twenty focused minutes, then mark it together, builds real confidence over a few weeks. Rotate the strands so no topic is neglected, and keep a list of the mistakes that recur so you can target them directly. Every subject in our KPSEA course includes a detachable answer booklet, so you can print the questions for your child and keep the answers to mark later.

Frequently asked questions

My child gets answers right but loses marks. Why?
Usually because the working or the units the scheme rewards are missing. Teach them to show every step and write units every time, and the lost marks come back.

How often should we practise Maths?
A short daily session beats a long weekly one. Twenty minutes of practice, then marking it together, builds real confidence faster than a single long stretch at the weekend.

Which strand should we start with?
Start with Numbers, since it is the largest strand and underpins the others, then move to whichever of Measurement, Geometry or Data your child finds hardest. Use the quick-reference table above to spot the recurring mistakes.

Is it worth learning the formulas by heart?
Yes, for perimeter, area, volume and the triangle's half. Writing the correct formula first is often worth a method mark on its own, and it steadies the whole answer.

What if my child freezes on a hard question?
Teach a simple rule: if a question will not come after a fair try, mark it lightly, move on, and return at the end. Sitting stuck on one hard question while easier marks wait further down the paper is one of the most common ways able children lose marks. Coming back with a fresh mind, once the easier questions have built some confidence, often unlocks it.

Does my child need to memorise everything, or understand it?
Both, in the right places. The formulas for area, perimeter, volume and the triangle's half are worth learning by heart, because writing them down earns method marks and steadies the answer. Everything else, though, is better understood than memorised: a child who understands why you find a common denominator will handle any fraction question, not just the ones they have seen before. Aim for understanding first, then memorise the handful of formulas on top.

Revise the whole subject

The KPSEA Grade 4 to 6 Complete Revision Course covers Mathematics and all five core subjects: notes, topical questions with marking schemes, and mock papers, for KSH 300 (or KSH 150 per subject). Fit it into a routine with our August holiday revision plan, see exactly how marks are awarded in our marking-scheme guide, and check the timeline in our KJSEA and KPSEA 2026 dates and countdown. See the free sample, and join our free Facebook community.