A ratio describes a relationship between quantities. Red to blue in the ratio 2:1 means two equal-sized parts of red for every one part of blue, not necessarily two red items and one blue item.
For families exploring schools in Dover, this guide connects verified local mathematics context with an independent counter-drawing activity. It focuses on identifying what each number compares and how the parts make a total.
Start with eighteen fictional counters in two colours. Draw the ratio parts, find the value of one part and check that the quantities preserve both the relationship and the total.
eduKateSG · Neighbourhood education
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1 · Local context · 2 · Worked example · 3 · Family practice
Contents
Explore, practise and connect · Four chapters
CHAPTER 1 OF 4
1. Connect local mathematics with clear representations
Fairfield Methodist School (Primary)’s department overview describes mathematics learning through hands-on activities and real-life problem-solving across the primary years. This offers local context for representing a numerical relationship before calculating.
The exercise below is independently written by eduKateSG. It is not a Fairfield worksheet or a report of school learning outcomes. Draw marks on paper rather than using small loose objects around younger children.
Name the order: red to blue. In 2:1, the first number belongs to red and the second to blue. Reversing the names without reversing the ratio changes the statement.
CHAPTER 2 OF 4
2. Find the total number of equal parts
Imagine eighteen counters, all red or blue, with red to blue in the ratio 2:1. Draw two equal boxes for red and one equal box for blue. Each box represents the same number of counters.
There are three parts altogether, not two. Since all eighteen counters are included, one part represents 18 ÷ 3 = 6 counters.
Red therefore has 2 × 6 = 12 counters and blue has 1 × 6 = 6 counters. Check the total: 12 + 6 = 18.
The ratio does not give the size of a part by itself. A total of nine counters with the same ratio would produce six red and three blue. The relationship stays the same while the quantities change.
CHAPTER 3 OF 4
3. Keep part-to-part and part-to-whole comparisons distinct
The red-to-blue ratio is 2:1, but the red-to-total ratio is 2:3. The whole contains both the red parts and the blue part.
This means red accounts for two thirds of these eighteen counters, not two halves. Ask the child to point to the parts included in the denominator before writing a fraction.
The actual quantities 12:6 simplify to 2:1 because both are divided by the same positive number, six. Multiplying both ratio terms by the same positive factor likewise preserves the relationship.
Adding the same number to both terms does not generally preserve a ratio. Starting from 2:1 and adding one gives 3:2, which is a different relationship. Equal addition and equal scaling are different operations.
CHAPTER 4 OF 4
4. Check a new total and explain the result
Try a red-to-blue ratio of 3:2 with twenty counters altogether. Five equal parts share the total, so one part is four counters. Red has twelve and blue has eight.
Ask for two checks: the quantities add to twenty, and 12:8 simplifies to 3:2. Matching only the total is not enough to establish that the ratio is correct.
If the learner divides twenty by three, return to the diagram and count all the parts. The three describes red’s share of the ratio, not the total number of shares.
Finish by stating the named ratio, the total parts, one part’s value and the two quantities. A clear representation helps the child explain what the calculation means.
Sources and scope
School information checked on 16 October 2026 (Singapore time): Fairfield Methodist School (Primary) department overview. Programmes may change. Family activities are independently written by eduKateSG, not official school tasks. This article does not imply school endorsement, rank schools or guarantee admission or learning results.