One half and two quarters have different names but can represent the same amount of the same whole. For families exploring schools in Hougang, drawing equivalent fractions helps make that relationship visible before introducing a rule.
Holy Innocents’ Primary School’s Mathematics page describes the Concrete-Pictorial-Abstract approach, fraction representations and discussion that develops mathematical reasoning. The paper-strip examples below are independent eduKateSG activities, not official school worksheets or claims about a particular lesson.
Use equal-length rectangles to represent the same whole. The important idea is that dividing the parts more finely changes the number of pieces, while the selected amount can remain unchanged.
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Contents
Explore, practise and connect · Four chapters
CHAPTER 1 OF 4
1. Keep the shaded amount unchanged
Draw a rectangle divided into two equal parts and shade one part. Label it 1/2. Copy the same-sized rectangle, divide it into four equal parts, and shade two parts covering the same proportion.
The second picture represents 2/4. Its pieces are smaller, but there are twice as many shaded pieces. Both pictures show half of an equal-sized whole, so 1/2 = 2/4.
Ask the child what changed and what stayed the same. The number and size of the equal parts changed; the shaded proportion did not. This explanation is more useful than saying only that both pictures have some shading.
CHAPTER 2 OF 4
2. Connect the picture with multiplication
Start again with one of two equal parts shaded. Divide every part into three equal smaller parts. There are now six parts altogether and three shaded parts, so the same shaded amount is represented by 3/6.
In the fraction notation, both numerator and denominator were multiplied by 3: 1/2 = 3/6. For these positive fractions, multiplying both by the same positive whole number preserves the value because the whole and the selected parts are subdivided consistently.
Multiplying just the numerator changes the value. For example, changing 1/2 to 2/2 selects the entire whole. Ask the child to draw that difference rather than accepting a rule about “making the numbers bigger” without checking the amount.
CHAPTER 3 OF 4
3. Test an incorrect shortcut
Consider the claim “Add one to the top and bottom, so 1/2 equals 2/3.” Draw equal-sized rectangles showing those fractions. Two thirds covers more of its rectangle than one half does, so the claim fails.
Adding the same number is not the same operation as multiplying both numbers by the same factor. Use a familiar correct pair, such as 2/3 and 4/6, to show how doubling the count of equal subdivisions preserves the proportion.
Equivalent fractions have equal numerical value even when they describe different objects. However, half of a large cake and half of a small cake need not be equal physical amounts. Equal-sized wholes matter when comparing the actual shaded areas in this drawing activity.
CHAPTER 4 OF 4
4. Match, justify and simplify
Write cards showing 1/2, 2/4, 3/6, 2/3 and 4/6. Make two groups of equal values. The first three belong together; the last two form another group. Ask for a picture or multiplication explanation for each match.
Read the relationship backwards as well. Since numerator and denominator of 4/6 can both be divided by 2, it simplifies to 2/3. Dividing both by a common non-zero factor preserves the value.
Finish with 3/4 and ask for an equivalent fraction in eighths. The answer is 6/8 because each original quarter is split into two equal parts. Let the child explain why the shaded amount stayed unchanged before moving to more difficult numbers.
Sources and scope
School information checked on 17 October 2026 (Singapore time): Holy Innocents’ Primary School: Mathematics Department. 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.
For more local learning connections, explore the neighbourhood school and family learning guide.