Did you know? The most common difficulty in a Secondary 1 G2 Mathematics ratio or percentage question is often not the arithmetic. It is deciding which amount is the whole, which amount is a part, and what the word ‘per’ means. For families looking for a Secondary 1 G2 Mathematics tutor in Bukit Timah, that is a useful place to begin.
Quick answer: label ratio parts in the correct order, identify the original quantity for percentage change, divide by the remaining percentage when working backwards, and attach units to every rate and speed. Learn those distinctions and many intimidating word problems become manageable relationships.
This reader-friendly guide follows the MOE G2 Mathematics syllabus for Secondary 1, together with the unchanged eduKateSG small-group tutorial model. It uses worked questions, common mistakes and a short weekly improvement routine rather than promising a score or treating G2 as identical to G3.
The one-minute summary
- For a ratio a:b, write labels for a and b before calculating.
- When the total is given, add ratio parts; when the difference is given, subtract the appropriate parts.
- Percentage means per hundred; write down ‘percent of what?’
- Reverse a discount by dividing the final price by the fraction remaining.
- A rate must carry units: dollars per item, kilometres per hour or metres per second.
- Average speed = total distance divided by total time.
- Check whether a result grows or shrinks as the story requires.
Why word problems can defeat otherwise capable students
A student can calculate 20% of 300 perfectly and still answer the wrong question when asked for the original amount after a 20% discount. The calculation is not the central issue. The issue is identifying the reference base. In a ratio problem, the same student might divide a given difference by the sum of the ratio parts when the difference should be divided by the gap between those parts.
A reliable tutor therefore asks the student to translate the story before calculating. What two groups are compared? What quantity is the base? What is one part worth? What unit is being measured? Is the change from original to final, or final back to original? These questions give the student a route that is still useful when the numbers and context change.
Children travelling to tuition around Bukit Timah and Sixth Avenue may come from schools that sequence topics differently. That is expected. The maths should be aligned with each child’s actual G2 course. A small group can support careful reasoning and correction while avoiding a constant race toward harder questions that the student has not yet learned to model.
Seventeen essential ideas explained without jargon
1. A ratio compares quantities in the same order
The ratio 2:3 means the first quantity corresponds to two parts and the second to three parts. The order matters: 2:3 is not the same description as 3:2. Always name what the first and second quantities stand for.
Worked illustration: If a bag contains red and blue counters in ratio 2:3, there are two red for every three blue, giving five total parts.
A mistake worth noticing: Some students write 2:3 without identifying red and blue, and later reverse the values when interpreting the answer.
How to make it stick: Write ‘red:blue’ directly above the ratio and check that the answer respects this label.
2. Equivalent ratios scale both parts together
Multiplying each part of a ratio by the same nonzero factor keeps the comparison unchanged. This works because the underlying relationship remains proportional.
Worked illustration: 2:5 = 4:10 = 6:15. Every new pair preserves the same relationship, even as the quantities grow.
A mistake worth noticing: Changing only one part, as in 2:5 becoming 4:5, alters the comparison and is not equivalent.
How to make it stick: Ask the student to explain what ‘two times as many groups’ means before multiplying both parts.
3. A ratio is not automatically a fraction of the total
For a ratio of 3:5, the first quantity is 3/5 of the second, but 3/8 of the total. These are different denominators because they refer to different wholes.
Worked illustration: If boys:girls = 3:5, boys form 3 out of the combined 8 parts, or 3/8 of the group.
A mistake worth noticing: Calling the first share 3/5 of the total confuses comparing two groups with sharing the combined group.
How to make it stick: Draw eight equal blocks and colour three. Identify the reference whole aloud.
4. A total can be divided by the number of parts
When a sum is shared in ratio 2:3:5, there are ten parts altogether. Find the value of one part, then multiply by the number of parts assigned to each person.
Worked illustration: If $200 is shared 2:3:5, one part is $20 and the shares are $40, $60 and $100.
A mistake worth noticing: Dividing the total by the first ratio number, rather than by the sum, produces an incorrect unit part.
How to make it stick: Label one part and confirm all shares add back to the original total.
5. A difference can also reveal the value of one part
Not every ratio question provides a total. Sometimes the larger amount exceeds the smaller by a known difference. Subtract the number of ratio parts first.
Worked illustration: If a:b = 3:7 and b exceeds a by 20, four parts equal 20 and one part equals 5. Therefore a = 15 and b = 35.
A mistake worth noticing: Adding the parts and dividing the difference by the total number of parts uses the wrong reference quantity.
How to make it stick: Compare the difference between the final values with the given difference.
6. Ratios with fractions can still be simplified
The entries of a ratio are quantities, not necessarily whole numbers. Multiply both entries by a common denominator to clear fractional forms before simplifying.
Worked illustration: (1/2):(3/4) becomes 2:3 after multiplying both entries by four.
A mistake worth noticing: Students may divide the numerators directly and ignore the denominators, losing the comparison.
How to make it stick: Convert to a common unit, then check the two ratios with a calculator if necessary.
7. Percentage means parts per hundred
A percentage expresses a quantity relative to a reference whole of one hundred equal parts. It can be written as a fraction or decimal, but the chosen base must remain clear.
Worked illustration: 35% = 35/100 = 0.35. Thirty-five percent of 200 is 70, whereas thirty-five percent of 80 is 28.
A mistake worth noticing: A familiar percent figure can tempt students to forget what quantity it is applied to.
How to make it stick: Underline ‘of what?’ before performing any percentage calculation.
8. Percentage change uses the original value
To describe how much a quantity increases or decreases, divide the amount of change by the original quantity, then multiply by 100%. The starting value provides the base.
Worked illustration: From 80 to 100, the increase is 20, so percentage increase is 20/80 × 100% = 25%.
A mistake worth noticing: Dividing by the new value would give 20%, a different comparison.
How to make it stick: Circle the original amount before writing the percentage-change fraction.
9. An increase and a reversal do not cancel symmetrically
A rise of 20% followed by a fall of 20% does not return to the original amount. The second percentage uses a new base. Percentages are multiplicative transformations, not simply detachable points.
Worked illustration: Starting from $100, a 20% increase gives $120; a 20% fall from $120 gives $96.
A mistake worth noticing: Students subtract twenty percentage points from twenty and assume the original value is restored.
How to make it stick: Use multipliers 1.20 and 0.80; their product is 0.96, not 1.
10. Reverse percentage starts from a known result
When a final price is given after a discount, the final price is a stated fraction of the original. Divide by the remaining multiplier to recover the unknown starting value.
Worked illustration: If $120 is 80% of the original after a 20% discount, original = 120 ÷ 0.80 = $150.
A mistake worth noticing: Adding 20% of $120 gives $144, which mistakenly takes the discount from the reduced base.
How to make it stick: Check by calculating 20% of the recovered original and subtracting it.
11. Percentage points are not percentage change
When a rate moves from 10% to 15%, it has increased by 5 percentage points, but its relative percentage increase is 50%. The two statements measure different things.
Worked illustration: Five percentage points is 15% – 10%. Relative increase is 5/10 × 100% = 50%.
A mistake worth noticing: Using ‘five percent’ ambiguously can make financial or data statements misleading.
How to make it stick: Always state whether the comparison is in percentage points or a percentage of the starting rate.
12. Rate is one quantity per unit of another
A rate relates different units, such as dollars per kilogram or pages per minute. The ‘per’ describes division. Reliable working begins by naming both quantities and the unit.
Worked illustration: If six kilograms of rice cost $24, the price is $4 per kilogram. Four kilograms then cost $16 at that constant rate.
A mistake worth noticing: Dividing kilograms by dollars instead yields kg per dollar, which may be mathematically valid but answers the wrong question.
How to make it stick: Write units beside the division before calculating; use them to check the answer.
13. Speed is distance per unit time
Speed relates distance travelled to time taken. Distance = speed × time; time = distance ÷ speed. Each version represents the same relationship, but the units must match.
Worked illustration: At 60 kilometres per hour for two hours, distance = 60 × 2 = 120 kilometres.
A mistake worth noticing: Multiplying when the problem needs a time, or combining hours with minutes without conversion, gives wrong dimensions.
How to make it stick: Write km, h or m/s next to every numerical value and cancel units as appropriate.
14. Unit conversions are part of solving, not an afterthought
One hour contains 3,600 seconds and one kilometre contains 1,000 metres. Converting km/h to m/s therefore multiplies by 1000/3600, equivalent to dividing by 3.6.
Worked illustration: 36 km/h = 10 m/s. In the opposite direction, 12 m/s = 43.2 km/h.
A mistake worth noticing: Multiplying by 3.6 when converting from km/h to m/s reverses the operation.
How to make it stick: Think physically: ten metres per second is about thirty-six kilometres per hour, not 129.6 m/s.
15. Average speed is total distance over total time
When the speed changes during a trip, average speed is not necessarily the arithmetic mean of the separate speeds. The distances and durations determine the true rate.
Worked illustration: A 120 km outward trip at 60 km/h takes two hours; a 120 km return at 40 km/h takes three. Total 240 km in five hours means average speed 48 km/h.
A mistake worth noticing: Averaging 60 and 40 to obtain 50 ignores how long the traveller spent at each speed.
How to make it stick: Build a distance-time table, total each column and divide total distance by total time.
16. Real word problems require modelling
The hard step is often choosing what the quantities mean, not pressing calculator buttons. Underline the unknown, identify the reference whole or unit and form a relationship before calculating.
Worked illustration: A transport schedule, a recipe scale-up or a sale price can all be represented by a ratio, a percentage multiplier or a rate equation.
A mistake worth noticing: Students look for a keyword such as ‘discount’ and perform a memorised operation without checking which value is known.
How to make it stick: Read the problem twice: first for the story, second to label each quantity and relationship.
17. A reasonable answer check saves marks
If a shirt is discounted, its final price should usually be below its original price. If a recipe is scaled up, the ingredients should increase. If speed is positive and time is longer, a fixed-speed distance should grow.
Worked illustration: For a 25% discount from $80, the final price is $60. A result of $100 signals the operation has been reversed.
A mistake worth noticing: Focusing entirely on arithmetic can cause students to accept a value that contradicts the story.
How to make it stick: Write one reasonableness sentence after the answer: ‘The amount is smaller because this is a discount.’
32 mini-clinics for ratio, percentage and speed
Try the question before opening the explanation. For every word problem, say the relationship in one sentence. For example, ‘the final price is 80% of the original’ is a stronger start than ‘I think I should divide by something’. These short clinics mix the topic types so the student must select a method rather than copy one.
Mini-clinic 1: Simplify 12:18
Answer: 2:3. Reasoning: Divide both parts by their HCF, six.
Common wrong turn: Dividing only the first term alters the ratio. When this happens, return to the labelled whole, the unit or the comparison being made. Ask the student to identify the first decision rather than copying the complete answer from a worked solution.
Self-check: Scale 2:3 back up by six. A good check should test the relationship in the original story, not just repeat the last arithmetic operation. This is the habit that helps a learner work independently on an unfamiliar question.
Mini-clinic 2: Find an equivalent ratio for 3:7 with first term 15
Answer: 15:35. Reasoning: Multiply both terms by five.
Common wrong turn: Writing 15:7 changes the relationship. When this happens, return to the labelled whole, the unit or the comparison being made. Ask the student to identify the first decision rather than copying the complete answer from a worked solution.
Self-check: Reduce the answer to 3:7. A good check should test the relationship in the original story, not just repeat the last arithmetic operation. This is the habit that helps a learner work independently on an unfamiliar question.
Mini-clinic 3: Find the fraction of the total represented by the first term in 2:5
Answer: 2/7. Reasoning: There are seven combined parts.
Common wrong turn: 2/5 compares the two groups, not the whole. When this happens, return to the labelled whole, the unit or the comparison being made. Ask the student to identify the first decision rather than copying the complete answer from a worked solution.
Self-check: Draw seven equal parts. A good check should test the relationship in the original story, not just repeat the last arithmetic operation. This is the habit that helps a learner work independently on an unfamiliar question.
Mini-clinic 4: Share 80 in ratio 3:5
Answer: 30 and 50. Reasoning: Eight parts total, worth ten each.
Common wrong turn: Dividing by three alone ignores the second share. When this happens, return to the labelled whole, the unit or the comparison being made. Ask the student to identify the first decision rather than copying the complete answer from a worked solution.
Self-check: Check 30 + 50 = 80. A good check should test the relationship in the original story, not just repeat the last arithmetic operation. This is the habit that helps a learner work independently on an unfamiliar question.
Mini-clinic 5: Share $150 in ratio 2:3:5
Answer: $30, $45, $75. Reasoning: Ten parts total, each worth fifteen dollars.
Common wrong turn: Using ten as a share rather than a count of parts is a scale error. When this happens, return to the labelled whole, the unit or the comparison being made. Ask the student to identify the first decision rather than copying the complete answer from a worked solution.
Self-check: Check sum and ratio. A good check should test the relationship in the original story, not just repeat the last arithmetic operation. This is the habit that helps a learner work independently on an unfamiliar question.
Mini-clinic 6: Two amounts have ratio 4:9 and differ by 25. Find both
Answer: 20 and 45. Reasoning: Five parts represent twenty-five, so one part is five.
Common wrong turn: Using thirteen parts corresponds to a total, not a difference. When this happens, return to the labelled whole, the unit or the comparison being made. Ask the student to identify the first decision rather than copying the complete answer from a worked solution.
Self-check: Check 45 – 20 = 25. A good check should test the relationship in the original story, not just repeat the last arithmetic operation. This is the habit that helps a learner work independently on an unfamiliar question.
Mini-clinic 7: Simplify 0.5:1.5
Answer: 1:3. Reasoning: Multiply both quantities by two, then simplify.
Common wrong turn: Treating decimal places independently breaks equivalence. When this happens, return to the labelled whole, the unit or the comparison being made. Ask the student to identify the first decision rather than copying the complete answer from a worked solution.
Self-check: Check each ratio has first term one-third of second. A good check should test the relationship in the original story, not just repeat the last arithmetic operation. This is the habit that helps a learner work independently on an unfamiliar question.
Mini-clinic 8: Simplify (1/2):(3/4)
Answer: 2:3. Reasoning: Multiply both terms by four.
Common wrong turn: Crossing out numerators without considering denominators is invalid. When this happens, return to the labelled whole, the unit or the comparison being made. Ask the student to identify the first decision rather than copying the complete answer from a worked solution.
Self-check: Compare numerical quotient (1/2)/(3/4) = 2/3. A good check should test the relationship in the original story, not just repeat the last arithmetic operation. This is the habit that helps a learner work independently on an unfamiliar question.
Mini-clinic 9: Find 25% of 320
Answer: 80. Reasoning: One quarter of 320 is eighty.
Common wrong turn: 25 × 320 without dividing by 100 gives a hundredfold error. When this happens, return to the labelled whole, the unit or the comparison being made. Ask the student to identify the first decision rather than copying the complete answer from a worked solution.
Self-check: Check eighty is one quarter of 320. A good check should test the relationship in the original story, not just repeat the last arithmetic operation. This is the habit that helps a learner work independently on an unfamiliar question.
Mini-clinic 10: Express 18 out of 60 as a percentage
Answer: 30%. Reasoning: Eighteen divided by sixty equals 0.30.
Common wrong turn: Multiplying sixty by eighteen reverses the reference. When this happens, return to the labelled whole, the unit or the comparison being made. Ask the student to identify the first decision rather than copying the complete answer from a worked solution.
Self-check: Check 30% of 60 is 18. A good check should test the relationship in the original story, not just repeat the last arithmetic operation. This is the habit that helps a learner work independently on an unfamiliar question.
Mini-clinic 11: Increase $80 by 15%
Answer: $92. Reasoning: 15% of 80 is twelve, then add it.
Common wrong turn: Subtracting twelve treats an increase as a discount. When this happens, return to the labelled whole, the unit or the comparison being made. Ask the student to identify the first decision rather than copying the complete answer from a worked solution.
Self-check: Check the answer exceeds eighty. A good check should test the relationship in the original story, not just repeat the last arithmetic operation. This is the habit that helps a learner work independently on an unfamiliar question.
Mini-clinic 12: Decrease $240 by 25%
Answer: $180. Reasoning: Keep 75% of the original: 0.75 × 240.
Common wrong turn: Subtracting 25 as dollars confuses units. When this happens, return to the labelled whole, the unit or the comparison being made. Ask the student to identify the first decision rather than copying the complete answer from a worked solution.
Self-check: A quarter of 240 is sixty. A good check should test the relationship in the original story, not just repeat the last arithmetic operation. This is the habit that helps a learner work independently on an unfamiliar question.
Mini-clinic 13: Find percentage increase from 50 to 65
Answer: 30%. Reasoning: Increase fifteen divided by original fifty.
Common wrong turn: Dividing by final sixty-five uses the wrong base. When this happens, return to the labelled whole, the unit or the comparison being made. Ask the student to identify the first decision rather than copying the complete answer from a worked solution.
Self-check: Check 1.30 × 50 = 65. A good check should test the relationship in the original story, not just repeat the last arithmetic operation. This is the habit that helps a learner work independently on an unfamiliar question.
Mini-clinic 14: Find percentage decrease from 120 to 90
Answer: 25%. Reasoning: Decrease thirty divided by original 120.
Common wrong turn: Using the new ninety as denominator yields 33.3%. When this happens, return to the labelled whole, the unit or the comparison being made. Ask the student to identify the first decision rather than copying the complete answer from a worked solution.
Self-check: Check 0.75 × 120 = 90. A good check should test the relationship in the original story, not just repeat the last arithmetic operation. This is the habit that helps a learner work independently on an unfamiliar question.
Mini-clinic 15: After a 20% discount, a bag costs $64. Find the original
Answer: $80. Reasoning: Sixty-four is 80% of the original.
Common wrong turn: Adding 20% of sixty-four gives $76.80, not the original. When this happens, return to the labelled whole, the unit or the comparison being made. Ask the student to identify the first decision rather than copying the complete answer from a worked solution.
Self-check: Check 80 – 16 = 64. A good check should test the relationship in the original story, not just repeat the last arithmetic operation. This is the habit that helps a learner work independently on an unfamiliar question.
Mini-clinic 16: After a 10% increase, a price is $99. Find its original
Answer: $90. Reasoning: Ninety-nine represents 110% of the original.
Common wrong turn: Subtracting ten percent of ninety-nine starts from the wrong base. When this happens, return to the labelled whole, the unit or the comparison being made. Ask the student to identify the first decision rather than copying the complete answer from a worked solution.
Self-check: Check 90 × 1.10 = 99. A good check should test the relationship in the original story, not just repeat the last arithmetic operation. This is the habit that helps a learner work independently on an unfamiliar question.
Mini-clinic 17: A success rate rises from 40% to 45%. Find change in percentage points
Answer: 5 percentage points. Reasoning: Subtract the rate values directly for points.
Common wrong turn: Calling this a five percent relative increase confuses comparisons. When this happens, return to the labelled whole, the unit or the comparison being made. Ask the student to identify the first decision rather than copying the complete answer from a worked solution.
Self-check: The relative increase is 12.5%; identify the requested measure. A good check should test the relationship in the original story, not just repeat the last arithmetic operation. This is the habit that helps a learner work independently on an unfamiliar question.
Mini-clinic 18: A quantity increases by 50%, then decreases by 50%, starting at 100
Answer: 75. Reasoning: 100 × 1.5 × 0.5 = 75.
Common wrong turn: Treating the changes as cancelling gives one hundred. When this happens, return to the labelled whole, the unit or the comparison being made. Ask the student to identify the first decision rather than copying the complete answer from a worked solution.
Self-check: Track the new base after the first change. A good check should test the relationship in the original story, not just repeat the last arithmetic operation. This is the habit that helps a learner work independently on an unfamiliar question.
Mini-clinic 19: Six notebooks cost $18. Find cost per notebook
Answer: $3. Reasoning: Divide total dollars by notebook count.
Common wrong turn: Dividing six by eighteen produces notebooks per dollar. When this happens, return to the labelled whole, the unit or the comparison being made. Ask the student to identify the first decision rather than copying the complete answer from a worked solution.
Self-check: Check six times three equals eighteen. A good check should test the relationship in the original story, not just repeat the last arithmetic operation. This is the habit that helps a learner work independently on an unfamiliar question.
Mini-clinic 20: At $4 per kg, find the price of 2.5 kg
Answer: $10. Reasoning: Multiply rate by quantity.
Common wrong turn: Dividing the rate by mass reverses dimensions. When this happens, return to the labelled whole, the unit or the comparison being made. Ask the student to identify the first decision rather than copying the complete answer from a worked solution.
Self-check: Check two kilograms costs eight dollars. A good check should test the relationship in the original story, not just repeat the last arithmetic operation. This is the habit that helps a learner work independently on an unfamiliar question.
Mini-clinic 21: A cyclist covers 45 km in 1.5 h. Find speed
Answer: 30 km/h. Reasoning: Speed = distance ÷ time.
Common wrong turn: Multiplying 45 and 1.5 gives the wrong unit. When this happens, return to the labelled whole, the unit or the comparison being made. Ask the student to identify the first decision rather than copying the complete answer from a worked solution.
Self-check: Check 30 × 1.5 = 45. A good check should test the relationship in the original story, not just repeat the last arithmetic operation. This is the habit that helps a learner work independently on an unfamiliar question.
Mini-clinic 22: At 6 m/s for 80 s, find distance
Answer: 480 m. Reasoning: Multiply speed and time with matching seconds.
Common wrong turn: Dividing produces a time-like unit, not metres. When this happens, return to the labelled whole, the unit or the comparison being made. Ask the student to identify the first decision rather than copying the complete answer from a worked solution.
Self-check: Check 480 ÷ 80 = 6. A good check should test the relationship in the original story, not just repeat the last arithmetic operation. This is the habit that helps a learner work independently on an unfamiliar question.
Mini-clinic 23: A car covers 150 km at 50 km/h. Find time
Answer: 3 h. Reasoning: Divide distance by speed.
Common wrong turn: Multiplying makes the result much too large. When this happens, return to the labelled whole, the unit or the comparison being made. Ask the student to identify the first decision rather than copying the complete answer from a worked solution.
Self-check: Check 50 × 3 = 150. A good check should test the relationship in the original story, not just repeat the last arithmetic operation. This is the habit that helps a learner work independently on an unfamiliar question.
Mini-clinic 24: Convert 72 km/h to m/s
Answer: 20 m/s. Reasoning: Divide seventy-two by 3.6.
Common wrong turn: Multiplying gives a value that is too large. When this happens, return to the labelled whole, the unit or the comparison being made. Ask the student to identify the first decision rather than copying the complete answer from a worked solution.
Self-check: Check 20 × 3.6 = 72. A good check should test the relationship in the original story, not just repeat the last arithmetic operation. This is the habit that helps a learner work independently on an unfamiliar question.
Mini-clinic 25: Convert 8 m/s to km/h
Answer: 28.8 km/h. Reasoning: Multiply eight by 3.6.
Common wrong turn: Dividing makes an implausibly small hourly speed. When this happens, return to the labelled whole, the unit or the comparison being made. Ask the student to identify the first decision rather than copying the complete answer from a worked solution.
Self-check: Check 28.8 ÷ 3.6 = 8. A good check should test the relationship in the original story, not just repeat the last arithmetic operation. This is the habit that helps a learner work independently on an unfamiliar question.
Mini-clinic 26: Convert 1 h 30 min into hours
Answer: 1.5 h. Reasoning: Thirty minutes is half of an hour.
Common wrong turn: Reading 1 h 30 min as 1.30 h mistakes base sixty for base ten. When this happens, return to the labelled whole, the unit or the comparison being made. Ask the student to identify the first decision rather than copying the complete answer from a worked solution.
Self-check: Check 1.5 × 60 = 90 minutes. A good check should test the relationship in the original story, not just repeat the last arithmetic operation. This is the habit that helps a learner work independently on an unfamiliar question.
Mini-clinic 27: Two buses leave together every 12 and 18 minutes. When next together?
Answer: 36 minutes. Reasoning: Use LCM for repeating schedules.
Common wrong turn: HCF six cannot be a common recurrence. When this happens, return to the labelled whole, the unit or the comparison being made. Ask the student to identify the first decision rather than copying the complete answer from a worked solution.
Self-check: List multiples to thirty-six. A good check should test the relationship in the original story, not just repeat the last arithmetic operation. This is the habit that helps a learner work independently on an unfamiliar question.
Mini-clinic 28: A train covers 120 km in 2 h then 60 km in 1.5 h. Find average speed
Answer: about 51.43 km/h. Reasoning: Total distance 180 km divided by total time 3.5 h.
Common wrong turn: Simple average of segment speeds ignores different durations. When this happens, return to the labelled whole, the unit or the comparison being made. Ask the student to identify the first decision rather than copying the complete answer from a worked solution.
Self-check: Estimate about fifty km/h before rounding. A good check should test the relationship in the original story, not just repeat the last arithmetic operation. This is the habit that helps a learner work independently on an unfamiliar question.
Mini-clinic 29: A shopper pays $135 after a 10% discount. Original price?
Answer: $150. Reasoning: Divide 135 by 0.9.
Common wrong turn: Adding $13.50 to the reduced price is not reversing a ten percent discount. When this happens, return to the labelled whole, the unit or the comparison being made. Ask the student to identify the first decision rather than copying the complete answer from a worked solution.
Self-check: Check ten percent of 150 is fifteen. A good check should test the relationship in the original story, not just repeat the last arithmetic operation. This is the habit that helps a learner work independently on an unfamiliar question.
Mini-clinic 30: A recipe 2:3 sugar:flour uses 450 g flour. Find sugar
Answer: 300 g. Reasoning: Three parts are 450 g, so one part is 150 g; sugar is two parts.
Common wrong turn: Dividing 450 by two uses the wrong part count. When this happens, return to the labelled whole, the unit or the comparison being made. Ask the student to identify the first decision rather than copying the complete answer from a worked solution.
Self-check: Check 300:450 simplifies to 2:3. A good check should test the relationship in the original story, not just repeat the last arithmetic operation. This is the habit that helps a learner work independently on an unfamiliar question.
Mini-clinic 31: Price rises $75 to $90 and then falls to $81. Find each percentage change
Answer: 20% rise, then 10% fall. Reasoning: The first base is 75; the second base is 90.
Common wrong turn: Calling the fall twelve percent by using the original base is wrong. When this happens, return to the labelled whole, the unit or the comparison being made. Ask the student to identify the first decision rather than copying the complete answer from a worked solution.
Self-check: Check 75 × 1.2 × 0.9 = 81. A good check should test the relationship in the original story, not just repeat the last arithmetic operation. This is the habit that helps a learner work independently on an unfamiliar question.
Mini-clinic 32: A 3 km walk at 4 km/h. Find time in minutes
Answer: 45 minutes. Reasoning: Time = 3/4 hour = 0.75 hour = 45 minutes.
Common wrong turn: Treating 0.75 as 75 minutes confuses decimals and clocks. When this happens, return to the labelled whole, the unit or the comparison being made. Ask the student to identify the first decision rather than copying the complete answer from a worked solution.
Self-check: Check four kilometres per hour covers three in three-quarters of an hour. A good check should test the relationship in the original story, not just repeat the last arithmetic operation. This is the habit that helps a learner work independently on an unfamiliar question.
A four-week practice plan that fits schoolwork
Week 1: ratio meaning and part diagrams
Start with labelled ratios, equivalent comparisons and sharing given totals. Then add one difference-based question and one fractional ratio. Use two colours in a bar diagram if helpful. The success condition is that the student can say what one part represents before finding any final amount.
Keep each home session short enough to review the answers properly. A child who can solve six varied problems, explain the chosen relationships and catch an error independently has produced valuable evidence of learning. The purpose of a practice schedule is to build durable understanding while leaving room for school, rest and other commitments.
Week 2: percentages and changing reference bases
Review fraction–decimal–percent conversion, then work on percentage increase and decrease. Contrast percentage points with relative percentage change. Introduce reverse percentages only after students can explain what fraction of the original remains. Test one question with a discount and another with a price increase.
Keep each home session short enough to review the answers properly. A child who can solve six varied problems, explain the chosen relationships and catch an error independently has produced valuable evidence of learning. The purpose of a practice schedule is to build durable understanding while leaving room for school, rest and other commitments.
Week 3: rates, speed and units
Make a small conversion reference in the student’s own handwriting. Practise dollars per unit, distance = speed × time and mixed units. Derive the relationship between km/h and m/s rather than relying solely on a memorised rule. Finish with one average-speed question based on total distance and total time.
Keep each home session short enough to review the answers properly. A child who can solve six varied problems, explain the chosen relationships and catch an error independently has produced valuable evidence of learning. The purpose of a practice schedule is to build durable understanding while leaving room for school, rest and other commitments.
Week 4: mixed modelling and assessment practice
Mix ratio, percentage, rates and speed without giving chapter labels. Before each calculation, ask for a one-line explanation of the relationship and the unit. Review the error ledger, revisit a question several days after the correction and compare independent working with the first attempt.
Keep each home session short enough to review the answers properly. A child who can solve six varied problems, explain the chosen relationships and catch an error independently has produced valuable evidence of learning. The purpose of a practice schedule is to build durable understanding while leaving room for school, rest and other commitments.
A 90-minute tutorial, viewed from the student’s desk
A useful session begins with two short retrieval questions from older topics. The tutor then presents a word problem and asks everyone to identify the reference whole or unit before any numbers are multiplied. One student might draw a ratio bar; another might write a percentage multiplier; a third might check an answer against the real context. Each method is inspected for mathematical validity.
The next stage is guided practice. The tutor observes whether a child mixes up a total and a difference, treats a 20% discount as a twenty-dollar discount or converts hours to decimal form incorrectly. In a three-student group, the feedback can be immediate and specific. The lesson should end with a fresh question that students complete without the model visible.
The eduKateSG reference tutorial describes weekly 90-minute 3-pax support, feedback and focused continuation work near Sixth Avenue MRT. That is a format, not a guarantee of outcomes. The practical test of any approach is whether the child can read an unfamiliar question, choose a relationship and verify a reasonable answer without hints.
How to spot the real cause of a low assessment score
Read through a marked paper and code each mistake. R means the wrong ratio reference, P means a percentage base error, U means inconsistent units, M means an incorrect model and A means arithmetic. The same child may have five wrong answers because of only one recurring modelling decision. Fixing that root cause is usually more productive than redoing every problem indiscriminately.
When the student corrects a question, require a sentence before the calculation: ‘There are eight parts altogether,’ ‘the final price is ninety percent of the original,’ or ‘the time must first be converted to hours.’ This sentence exposes whether the child has chosen the right mathematical structure. Then the arithmetic can be checked separately.
For parents, a useful monthly comparison is not merely a change in raw marks. Look at how many problems the child began with the correct model, how many mistakes were self-corrected and whether the same weakness reappeared after a week. This evidence gives a tutor or school teacher a concrete starting point.
Questions parents commonly ask
What is covered in Secondary 1 G2 ratio and percentage?
The official syllabus includes equivalent ratios, division of quantities in ratios, percentages, percentage change, reverse percentages and contextual problems. It also includes rates and speed. Exact teaching order depends on the school and assessment calendar.
Why does my child divide by the wrong number in ratio questions?
Often the child has not identified what the known amount represents: a total, one share or a difference. Draw a part diagram and label the whole or difference before doing arithmetic.
How do I explain reverse percentage without a formula?
Use a simple hundred-dollar comparison. If a 20% discount leaves 80% of the original, the final amount is eight-tenths of the starting amount. Work backwards from that relationship. The essential question is ‘What percentage of the original remains?’.
Why does 20% up and 20% down not cancel?
The two percentages apply to different bases. After a rise from 100 to 120, the subsequent 20% decrease uses 120 as its base. This leaves 96, not 100.
Does G2 Secondary 1 already include speed?
Yes. Rate and speed are part of the G2 Secondary 1 syllabus. Students need to understand distance, time, unit rates, average speed and unit conversion at the level set out in the current teaching sequence.
How can my child remember km/h to m/s?
Derive the conversion from one kilometre being 1,000 metres and one hour being 3,600 seconds. Then 1 km/h is 1000/3600 m/s. This explains dividing by 3.6 and makes it easier to reconstruct the rule.
What is the difference between a rate and a ratio?
A ratio usually compares quantities of the same kind or provides a proportional comparison; a rate expresses one quantity per unit of another, often with different units. Both are forms of comparison, but their labels and interpretation matter.
What if a child has good arithmetic but cannot start word problems?
Use a modelling routine: read the context, label units, underline the unknown, decide what total or base is being compared, draw a diagram if useful and only then choose a calculation. Practice starting the question before attempting the entire solution.
Do repeated full papers help with these topics?
They can help with mixed application and timing after concepts are stable. If the child keeps making the same ratio-base mistake, short targeted corrections and delayed retesting are often a more efficient first step.
What should a Bukit Timah family look for in a mathematics tutor?
Ask for evidence of precise diagnosis, clear worked explanations, practice matched to the student’s G2 syllabus and checks for independent transfer. The eduKateSG reference describes three students per weekly 90-minute session near Sixth Avenue MRT; parents can confirm details directly.
Will G2 Mathematics affect later study options?
Subject-level decisions and pathways depend on current MOE rules, school advice and student performance over time. In Secondary 1, the useful immediate priority is strong mathematical understanding and consistent learning habits rather than predictions about later admissions.
Useful local and official reading
Compare the official MOE G2 syllabus, the G2 Mathematics in Bukit Timah explainer and the eduKateSG 3-pax tutorial overview. The syllabus defines the learning content; tuition should respond to an individual student’s evidence and school sequence.
- Negative numbers, fractions and estimation
- Algebra notation and linear equations
- Geometry, mensuration and data interpretation
The final lesson is simple: word problems become easier when a child can identify the story’s relationships before reaching for an operation. Ratio, percentage and speed are not three unrelated chapters. They are three ways of describing how quantities connect.