Primary 3 Maths | Introduction to Fractions (Teacher Lesson Guide)

2026-11-08

Tutor lesson-prep guides · Primary Maths

Fractions in P3 are not arithmetic. They are about cutting something into equal parts. A student who writes one quarter wrongly usually does not misunderstand the four, but has no idea of equal shares. Open by cutting a cake, and cut it unevenly on purpose.

Objectives — Students can: (1) explain that the denominator is how many equal parts the whole is cut into and the numerator is how many parts are taken; (2) write the fraction shown in a diagram and draw a diagram for a given fraction; (3) find a fraction of a quantity, such as one quarter of 12; (4) build equivalent fractions by multiplying and compare fractions with the same denominator.

01 Prerequisites (3-minute check)

If any of these fails, fix it before the lesson starts.

Skill	Quick check	Pass mark
Equal sharing	Share 12 sweets equally among 4 children	3 each
Times tables	What is 4 x 3?	12
Division	What is 12 / 4?	3
Comparing numbers	Which is larger, 3 or 5?	5

02 Lesson flow (45 minutes)

Time	Stage	Tutor does	Student does
0-9 min	Entry: cut it badly	Cut a cake into four pieces, one obviously larger, and ask whether it is one quarter	They say the parts must be equal
9-18 min	What the numbers mean	Write 1/4 and 3/4 and point to the denominator and numerator in turn	They say “bottom is how many parts, top is how many taken”
18-27 min	Diagram to fraction and back	Model three shapes: a circle, a strip, a grid	They draw and write three fractions
27-36 min	Fraction of a quantity	Model one quarter of 12 sweets as divide then multiply	Five questions, working shown
36-43 min	Equivalent and comparing	Model 1/2 = 2/4, then compare 3/8 with 5/8	Five questions with a stated reason
43-45 min	Exit check	Three quick oral questions	Answered independently

03 Teaching script (read it out)

Scene 1: Equal parts first, fractions second

Students call any random slice a quarter. Make equal sharing something they can check: stack the four pieces and compare. If the stack is uneven, the cut was wrong.
Then use a counterexample: one big piece plus three small ones still makes one whole cake, but it is not four equal parts, so it is not 1/4 and 3/4. Skip this step and every later fraction floats in the air.

Student does: stacks the four pieces and judges equal or not.

Scene 2: Denominator below, telling how many parts

Students read three quarters correctly but write 4/3, because the two numbers swap places. Fix the reading and the writing together: first how many parts it is cut into (denominator, below), then how many are taken (numerator, above).
Colour code it: denominator blue, numerator red. Have them read each fraction as “three out of four parts”, so a swap is audible straight away.

Student says: “so many out of so many parts” for every fraction written.

Scene 3: Like denominators: only the numerators matter

Comparing 3/8 with 5/8, students stall because the 8 matches, and some compare the denominators instead. Say it plainly: when the number of parts is the same, every part is the same size, so the fraction with more parts is larger.
Prove it with strips: two equal strips, shade 3 squares and 5 squares. With the same numerator and different denominators the reverse holds: a bigger denominator means smaller parts, so 1/4 is larger than 1/8.

Student does: shades two equal strips and states the reason out loud.

04 Question types and worked steps

Type	Example	Steps	Answer
Diagram to fraction	A circle cut into 6 equal parts, 2 shaded	Count total parts for the denominator, shaded parts for the numerator	2/6
Fraction to diagram	Draw 3/5	Five equal parts, shade three	Five equal squares, three shaded
Fraction of a quantity	One quarter of 12 sweets	Divide by the denominator, multiply by the numerator	3 sweets
Equivalent and comparing	1/2 = ?/4; compare 3/8 and 5/8	Multiply both parts; same denominator means compare numerators	2/4; 5/8 is larger

Sanity check (teach this): Reasonableness checks: a fraction only exists on top of equal parts, so every region in the diagram must be the same size; a denominator cannot be zero; the numerator does not exceed the denominator at this stage; a fraction of a quantity must come out as a whole number smaller than the whole; like denominators are compared by numerator only; equivalent fractions multiply both parts by the same number.

05 Independent practice (3 questions)

Question	Answer	What to watch
5 diagram questions	Circle, strip and grid, plus two where a fraction is drawn	Checks the parts are equal
5 fraction-of-a-quantity questions	One half, one quarter and three quarters of 12, 20 and 24	Checks divide then multiply
4 comparing and equivalent questions	Two like-denominator comparisons, two equivalent fractions	Checks numerators and denominators are not swapped

06 Common mistakes and what to say

Mistake	Student writes	Say this
Calling an unequal slice a fraction	A random slice named one quarter	“Four parts have to be equal to be quarters. Stack them and look: this one is bigger.”
Swapping numerator and denominator	Three quarters written as 4/3	“The bottom is how many parts you cut, which is 4. The top is how many you take, which is 3.”
Comparing the denominators	3/8 against 5/8, answering 3/8	“Same number of parts, so each part is the same size. Five parts is more than three.”
Thinking 1/4 is bigger than 1/2	Answering 1/4 because 4 beats 2	“Cut into four and each piece is small; cut into two and each piece is big. A bigger denominator means smaller parts.”

07 Homework (paper, section and question numbers)

Primary 1 to 6 Maths test papers with answers — Do the P3 fraction questions, drawing a diagram each time
Primary Maths chapter index — All chapters in the subject
Redo this chapter — Redo five fraction-of-a-quantity questions, writing divide then multiply

08 Exit check (last 5 minutes)

Question	Answer	Decision
What the denominator means	How many equal parts the whole is cut into	Answering “how many taken” means going back to the third stage
What the numerator means	How many parts are taken	Answering “how many parts” means going back to the third stage
One quarter of 12	3	Answering 4 means going back to the fifth stage
Which is larger, 3/8 or 5/8	5/8	Answering 3/8 means going back to the sixth stage

09 Tutor FAQ

Should adding unlike denominators be taught?

Not in P3. Make equal parts and “so many out of so many” solid first; unlike denominators belong to P4.

What if a student insists 1/4 is larger than 1/2?

Do not argue. Fold two equal strips once and twice, then stack them and let the eyes decide.

How should the fraction bar be drawn?

With a ruler: denominator under the bar, numerator above, always starting from the bar so the two numbers cannot drift.

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A TutorZone lesson-prep guide. Written by the TutorZone team; questions and lesson flow are original and are not taken from any school or publisher material.