Secondary 1 G3 Mathematics Tutor Bukit Timah | Unitary Method, Ratios and Recipe Scaling

Did you know? If a recipe for four people needs 300 grams of flour, a recipe for ten people needs 750 grams—not 300 + 10 grams. The difference is understanding how the amount changes per person. This is what the unitary method makes visible: find the amount corresponding to one unit, then build the quantity you need.

For families looking for a Secondary 1 G3 Mathematics tutor in Bukit Timah, ratio and the unitary method are useful bridges between Primary 6 bar models and Secondary 1 algebra. A learner may solve a straightforward sharing ratio but struggle with recipe quantities, unit prices and questions that reverse the unknown.

This guide gives easy worked examples, a quick-answer method and self-tests. All costs and recipes here are fictional Mathematics examples, not real quotations, prices or nutritional advice.

The quick answer: divide to one, multiply to many

Suppose four identical notebooks cost $10 in total. The price per notebook is $10 ÷ 4 = $2.50.

Seven notebooks cost 7 × $2.50 = $17.50, assuming every notebook has the same unit price and no extra fees.

The method is total for a known number of units ÷ number of units = amount per one unit. Then multiply by the new number of units.

It works because, in this model, the total amount is directly proportional to the quantity. Double the number of identical notebooks and the total price doubles. A fixed delivery fee would change that relationship, as we’ll see.

What is the “one” in the unitary method?

The word “unitary” points to one unit of the right quantity. If six exercise books require 240 sheets of paper, the unit is one exercise book and the amount per unit is 240 ÷ 6 = 40 sheets.

If eight fictional study kits take 24 pencils in total, one kit takes three pencils. Fifteen identical kits take 45 pencils.

Before doing the division, ask what the known total is being shared among. The unit might be one student, one printed item, one serving, one metre or one hour. Using the wrong unit can produce a neat number that answers the wrong question.

A useful tutor asks the learner to complete this sentence: “For one ______, the amount is ______.” It makes the denominator explicit.

Worked example 1: scale a recipe up

A fictional recipe serves four and uses 300 g of flour, 200 mL of milk and 2 eggs. Scale it to ten servings using a simple proportional model.

The number of servings scales by 10 ÷ 4 = 2.5. Multiply each original ingredient amount by 2.5.

Flour becomes 300 × 2.5 = 750 g. Milk becomes 200 × 2.5 = 500 mL. Eggs become 2 × 2.5 = 5.

Check with the unitary route: flour per serving = 300 ÷ 4 = 75 g, so ten servings require 750 g. Milk per serving = 50 mL, so ten servings require 500 mL. The answers agree.

The Mathematics assumes all ingredients scale linearly. Real cooking may require adjustments to baking time or equipment, but the numerical model is clear.

Worked example 2: scale a recipe down

A recipe for twelve fictional muffins uses 480 g of flour. How much flour is needed for five muffins at the same ratio?

Find flour per muffin: 480 ÷ 12 = 40 g. For five muffins, multiply 40 × 5 = 200 g.

Alternatively, use the scale factor 5/12: 480 × (5/12) = 200.

Both methods express the same relationship. The first exposes the one-unit amount; the second is an equivalent ratio calculation.

An incorrect answer of 480 ÷ 5 = 96 g mistakes the new number of muffins for the number to which the original flour amount corresponded. Label the known pairing first: 12 muffins ↔ 480 g.

Worked example 3: use ratios when you know one part

A model drink mixture contains water and syrup in the ratio 5:2. If 750 mL of water is used, how much syrup is required?

Five parts correspond to 750 mL. One part is 750 ÷ 5 = 150 mL. Syrup has two parts, so 2 × 150 = 300 mL.

The total mixture is 750 + 300 = 1050 mL in this model. Check the ratio 750:300. Divide both values by 150 and obtain 5:2.

The common wrong step is dividing 750 by seven. Seven is the total number of parts, but the known 750 mL refers only to water’s five parts.

Ask “Which part-count represents the given measurement?” before calculating.

Worked example 4: a total is given instead

Now imagine the same water:syrup ratio 5:2, but the total mixture is 1050 mL. Find each amount.

There are 5 + 2 = 7 parts in the whole mixture. Each part is 1050 ÷ 7 = 150 mL. Water is 5 × 150 = 750 mL; syrup is 2 × 150 = 300 mL.

The answers match the previous example, but the starting operation differed. When the known amount is the whole, add parts. When it is one component, use that component’s part-count.

A child who automatically adds the parts in every ratio problem may know a procedure without knowing when it applies.

Worked example 5: unit price comparison

Fictional Shop A offers five identical exercise books for $12.50. Fictional Shop B offers eight identical exercise books for $18.40. Which has the lower price per book?

Shop A costs 12.50 ÷ 5 = $2.50 per book. Shop B costs 18.40 ÷ 8 = $2.30 per book.

Shop B has the lower unit price by $0.20 per book.

That doesn’t automatically establish which entire purchase is preferable for a household. If a buyer needs only five books, the minimum bundle sizes, unused books or other conditions may matter. But it correctly compares each bundle’s unit cost.

State what the unit is. “Shop B is $0.20 cheaper” is ambiguous; “$0.20 less per notebook” is precise.

Worked example 6: reverse the recipe question

A fictional recipe uses 210 g of flour for seven servings. You have 840 g available. How many servings can you model at the same ingredient rate?

Flour per serving is 210 ÷ 7 = 30 g. The available 840 g can support 840 ÷ 30 = 28 servings, assuming flour is the limiting ingredient and the recipe scales exactly.

Check: 28 servings × 30 g = 840 g. That is four times the original seven servings, matching the fact that 840 g is four times 210 g.

The unknown is a number of servings this time, not a quantity of flour. It is important to identify which direction the problem is asking you to work.

Worked example 7: fractions in a scaling relationship

A batch of 6 model snack packs uses 3/4 kg of one ingredient. How many kilograms are required for 10 packs at the same rate?

The amount per pack is (3/4) ÷ 6 = 3/24 = 1/8 kg. Ten packs need 10/8 kg = 5/4 kg, or 1.25 kg.

Check by scale factor: 10/6 × 3/4 = 30/24 = 5/4 kg.

This is a good connection to fraction division. Students who find the ratio idea easy but freeze at 3/4 ÷ 6 may need a separate arithmetic correction. The relationship itself has not changed.

When the unitary method does not apply to the whole price

Imagine a fictional service charges $10 per box plus one fixed delivery charge of $4. Three boxes cost 3 × $10 + $4 = $34. Six boxes cost 6 × $10 + $4 = $64.

A student might double $34 and predict $68. That fails because the $4 delivery fee is charged once, not once per box.

The amount per box before delivery is directly proportional to the box count. The complete total with a fixed charge is not proportional to the count.

A good teaching question is “Which part scales when the quantity changes, and which part stays constant?” This insight prepares students for function machines and linear tables.

Distinguish direct and inverse relationships

If every fictional student receives exactly three pencils, doubling the number of students doubles the pencils needed. This is a direct relationship.

If four people share twelve identical tasks equally, each does three tasks. If six people share the same twelve tasks equally, each does two. Increasing the number of workers decreases the number assigned to each, under the simple assumption of equal sharing.

The two situations are not the same proportional rule. Avoid multiplying when the story requires a fixed total to be divided differently.

Formal direct and inverse proportion methods develop further in lower-secondary Mathematics. The immediate Secondary 1 goal is to read the situation and preserve the stated relationship.

Ratios with inconsistent units

Simplify 1.5 litres : 600 millilitres.

Convert to the same units: 1.5 litres = 1500 mL. Then 1500:600 simplifies to 5:2.

If the student writes 1.5:600 and compares the raw numbers, they have changed the physical relationship. A litre is a thousand millilitres; the units cannot be ignored.

This is especially important in recipe-style examples because one quantity might be measured in kilograms and another in grams. Consistent units are necessary before simplifying a ratio of like quantities.

Read a ratio question before choosing a method

There are three frequent starting points: a total, a difference, or one known component.

For a ratio A:B = 2:5 and a total of 70, seven equal parts represent 70. Therefore A = 20 and B = 50.

If the same ratio has a difference of 30, the difference is three parts. One part is 10, giving A = 20 and B = 50.

If instead A is 20, the two parts represent 20. One part is 10 and B is 50.

These examples happen to produce the same final values, but the starting information and calculation differ. A good learner names the relationship before dividing.

For a broader look at ratio sharing, see ratio, fractions and sharing quantities.

Ten-question mini diagnostic

• A. Four notebooks cost $10. What does one cost?
• B. At the same unit price, what do seven notebooks cost?
• C. Twelve fictional muffins require 480 g of flour. How many grams per muffin?
• D. How much flour for five muffins at that rate?
• E. Water:syrup = 5:2. If water is 750 mL, find syrup.
• F. Water:syrup = 5:2. If total is 1050 mL, find water.
• G. A recipe uses 210 g for seven servings. How many servings can 840 g support in the same model?
• H. Five books cost $12.50; eight cost $18.40. Which bundle has the lower cost per book?
• I. Three boxes cost $10 each plus a fixed $4 delivery fee. What do six boxes cost with the same fee?
• J. A ratio A:B = 3:4 and A = 21. Find B.

Answers and one-line reasons

A. $2.50 each.

B. $17.50.

C. 40 g per muffin.

D. 200 g.

E. 300 mL; each of the five water parts is 150 mL.

F. 750 mL; each of the seven total parts is 150 mL.

G. 28 servings; each uses 30 g.

H. The eight-book bundle, at $2.30 per book versus $2.50.

I. $64; 6 × $10 + $4, because delivery is fixed.

J. B = 28; one ratio part is 21 ÷ 3 = 7.

Ask the learner which quantities represent totals and which represent per-unit amounts. Explaining that difference is more useful than completing ten sums without interpretation.

A fifteen-minute revision routine

Begin with a three-line unitary table: known number of units, total amount, and amount for one unit. Ask the student to complete the missing entry before calculating a new total.

Then present a ratio where one part is known and another where the total is known. Change the wording without changing the mathematics so the child has to identify the correct denominator.

Finish with a fixed-fee question. If the student automatically doubles the full total, explain which part is actually proportional. Revisit another changed question after a few days without prompts.

What Bukit Timah parents should ask a tutor

A useful Secondary 1 G3 Mathematics tutor checks whether the child understands what a ratio part, total and one unit represent. The tutor should also notice weak fraction arithmetic, unit conversions and incomplete reading of fixed charges.

The original eduKateSG Secondary 1 Mathematics small-group tutorial reference describes close feedback in three-student tutorials near Sixth Avenue MRT. The Bukit Timah G3 Mathematics tuition overview provides related programme context. Families should verify lesson availability, fit and their school’s topic sequence directly.

The MOE G2 and G3 Mathematics syllabus covers ratio, proportion and problems in real-world contexts. A recipe is a model of a proportional relationship, not a promise that every real-world preparation scales without adjustment.

Frequently asked questions

### Is the unitary method only for Primary School?

No. Finding a per-unit amount is a useful strategy across Secondary Mathematics, including ratios, rates, percentages and modelling. Students build on it with algebra.

### Why divide first?

Dividing by the known number of units tells us the amount per one unit. Multiplying that result gives the amount for any other number of equivalent units, assuming a proportional relationship.

### Can I scale every real recipe perfectly?

The mathematical model assumes linear scaling. Real recipes may involve different oven sizes, mixing times or other constraints, so practical adjustments can be needed.

### Why does a fixed fee break simple doubling?

Because the fixed fee is added once regardless of the quantity. Only the variable amount scales with the number of items.

### When do I add ratio parts?

Add them when the given quantity is the total of all the represented parts. If one component alone is given, use that component’s part-count.

Read the next guides

• Ratio, fractions and sharing quantities
• Fractions, decimals and percentages
• Function machines and linear rules
• Reading distance-time and speed-time graphs

The next time a child sees “six packs need 240 grams,” ask what one pack needs first. That small pause makes proportion easier to understand and harder to misapply.