Understanding fractions
🧩 Let’s Start with a Problem
Emma is making a colorful ribbon for her school project. She has a ruler marked only in whole centimeters. She needs to cut a ribbon that is exactly $3\frac{1}{3}$ cm long. But her ruler only shows whole numbers: $0, 1, 2, 3, 4$ ...
She knows the mark for $3$ cm, but where is the point that is $\frac{1}{3}$ cm after $3$ cm? How can she find it without guessing?
💡 What Do You Notice?
If $1$ cm is divided into $3$ equal parts, how long is one small part? And where would that small part land on the ruler after the $3$ cm mark?
🧠 Why This Matters
Fractions aren’t just for pizza and cake—they help us measure things precisely! When you build, sew, or draw, you often need lengths that are between whole numbers. Understanding fractions on a ruler will help you measure anything, exactly.
✏️ Quick Warm-Up Activities
Activity 1: Partition a Strip
Draw a line that is $12$ cm long. Divide it into $3$ equal parts. How long is each part?
Think about it: If $12$ is divided into $3$ equal groups, you use division. But what if you only have $1$ cm and you divide it into $3$ equal parts? Then you are working with fractions like $\frac{1}{3}$.
Activity 2: Compare Unit Fractions
Which is larger: $\frac{1}{2}$ or $\frac{1}{3}$? Which is larger: $\frac{1}{4}$ or $\frac{1}{5}$?
Think about it: The denominator tells how many equal parts the whole is split into. More parts means each part is smaller.
Activity 3: Estimate on a Number Line
Draw a number line from $0$ to $1$. Mark $\frac{1}{3}$, $\frac{1}{2}$, and $\frac{3}{4}$ on it.
Think about it: Where do these fractions sit between $0$ and $1$? How can you check if your estimates are reasonable?
🚀 Ready to Learn
Now let’s discover how to name, compare, and use fractions like $\frac{1}{3}$ when measuring real things!
🎯 In this topic you will
- Explain that dividing a whole into more equal parts produces smaller fractions.
- Represent a fraction as division: numerator ÷ denominator.
🧠 Key Words
- denominator
- fraction
- numerator
Show Definitions
- denominator: The bottom number in a fraction that shows how many equal parts the whole is divided into.
- fraction: A number that represents part of a whole (or part of a group), written as one number over another.
- numerator: The top number in a fraction that shows how many parts are being counted.
📘 Getting Started with Fractions
In this unit you will write fractions with numerators and denominators and learn how to read fractions in words, for example $\dfrac{3}{4}$ is ‘three-quarters’.
✂️ Splitting Shapes into Equal Parts
You will learn how to divide a shape into fractions. When you divide a shape into lots of the same fraction you must divide the shape into equal parts. Each of these parts must be the same size but the parts can be in different positions.
❓ EXERCISES
1. Look at the number wall. It is not complete.
Copy this number sentence and use the number wall to help you complete it.
$\frac{1}{2} > \_\_\_ > \frac{1}{4} > \_\_\_ > \frac{1}{12}$
👀 Show answer
Completed sentence: $\frac{1}{2} > \frac{1}{3} > \frac{1}{4} > \frac{1}{6} > \frac{1}{12}$
On a fraction wall, $\frac{1}{3}$ lies between $\frac{1}{2}$ and $\frac{1}{4}$, and $\frac{1}{6}$ lies between $\frac{1}{4}$ and $\frac{1}{12}$.
2. Eight people share one cake.
How much of the cake does each person get when they share it equally?
👀 Show answer
Each person gets $\frac{1}{8}$ of the cake.
3. Part of a floor is covered with matting.
What fraction of the floor is covered with matting?
A $\frac{1}{2}$ B $\frac{1}{3}$ C $\frac{1}{4}$ D $\frac{1}{6}$
Compare your answer with your partner's answer.
👀 Show answer
$\frac{1}{3}$ (option B).
The floor is split into $6$ equal parts and $2$ are covered, so the fraction covered is $\frac{2}{6}=\frac{1}{3}$.
4. Fatima says, ‘The square is divided into four equal parts.’
Do you agree with Fatima?
Explain your reasons to your partner, then write them down.
👀 Show answer
No. The square is divided into $4$ parts, but the parts are not equal in area, so it is not divided into four equal parts.
5. Four shapes are divided into parts.
Arun chooses a shape.
Which shape is Arun describing?
My shape is
divided into equal parts.
Less than half my shape is
shaded. My shape has no
curved lines.
👀 Show answer
B.
Shape B has no curved lines, it is divided into equal parts, and less than $\frac{1}{2}$ of it is shaded.
6. Look at these diagrams.
What is the same? What is different?
👀 Show answer
The same: Each diagram shows a shape divided into parts, with some parts shaded.
Different: The shapes are different, the number of parts is different, and the fraction shaded is different. The parts are arranged differently (triangular regions in A, horizontal strips in B, and rectangular sections in C).
7. These diagrams shows four fractions with the same numerator.
Write the fractions in order of size. Start with the smallest fraction.
👀 Show answer
$\frac{3}{12},\ \frac{3}{8},\ \frac{3}{6},\ \frac{3}{4}$
All the fractions have the same numerator ($3$). The larger the denominator, the smaller the fraction.
🧠 Think like a Mathematician
Hexagons
This hexagon is divided into four equal parts. It is divided into quarters.
$1 \div 4 = \frac{1}{4}$
Question: How can you divide a regular hexagon into equal parts and represent each division as a fraction?
Equipment: A sheet of regular hexagons, pencil, ruler, and coloured pencils (optional).
Method:
- Get a sheet of regular hexagons.
- Choose one hexagon and decide how many equal parts you want to divide it into.
- Use a ruler to divide the hexagon into equal parts.
- Write the division as a fraction (for example, if there are 4 equal parts, each part is $\frac{1}{4}$).
- Repeat with other hexagons, each time dividing into a different number of equal parts so that each hexagon is different.
Follow-up Questions:
👀 show answer
- 1: One part is $\frac{1}{4}$, because the whole is split into 4 equal pieces.
- 2: Each part is $\frac{1}{6}$. As a division statement: $1 \div 6 = \frac{1}{6}$.
- 3:
- 3 equal parts: one part is $\frac{1}{3}$.
- 5 equal parts: one part is $\frac{1}{5}$.
- 8 equal parts: one part is $\frac{1}{8}$.