Primary 4 Maths: Equivalent Fractions and Decimals

Primary 4 Maths: Equivalent Fractions and Decimals — Tutor Lesson Plan

2026-10-27

Tutor lesson-prep guides · Primary maths

The classic error is adding the same number to top and bottom. This lesson shows the same quantity cut differently, so only multiplying or dividing survives.

Objectives — the student can expand and simplify fractions, convert between fractions and decimals, and compare two fractions by common denominators or decimals.

01 Prerequisites (3-minute check)

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

Skill	Quick check	Pass mark
Meaning of a fraction	What does 3/4 mean?	Three of four equal parts
Multiplication and division	3 × 5, 20 ÷ 4	15, 5
Decimal place value	What is 0.7 as a fraction?	7/10

02 Lesson flow (45 minutes)

Time	Stage	Tutor does	Student does
0-6 min	Paper strips	Compare 1/2 and 2/4	Say the strips are the same length
6-16 min	Expand and simplify	Show 3/4 = 15/20 and 18/24 = 3/4	Two of each
16-26 min	Fraction to decimal	3/8 becomes 3 ÷ 8	Do 5/8
26-34 min	Decimal to fraction	0.6 = 6/10 = 3/5	Do 0.45
34-42 min	Compare	Common denominator or decimals	Compare 2/5 and 3/8
42-45 min	Exit check	Three questions marked at once	Finish alone

03 Teaching script (read it out)

Scene 1: Same amount, different cuts

1/2 and 2/4 look different but the strips are equal.
Cut every part in half: twice as many parts, twice as many taken, same amount.

Student says “multiply top and bottom by the same number”.

Scene 2: Simplifying runs backwards

18/24: divide both by 6, giving 3/4.
Simplify until no common factor is left.

Warn: adding 1 to both numbers is not equivalent, and it is the most common error.

Scene 3: Fractions and decimals are two names

3/8 means 3 ÷ 8 = 0.375. In reverse, 0.6 is six tenths, 6/10 = 3/5.
Denominators of 10 or 100 convert straight to decimals.

Student does 5/8 = 0.625 and 0.45 = 9/20.

04 Question types and worked steps

Type	Example	Steps	Answer
Expand	3/4 = ?/20	Multiply both by 5	15/20
Simplify	18/24	Divide both by 6	3/4
Fraction to decimal	3/8	3 ÷ 8	0.375
Compare	2/5 and 3/8	0.4 against 0.375	2/5 is larger

Sanity check (teach this): A proper fraction is below 1 and so is its decimal; an answer of 3.8 for 3/8 means the division was inverted.

05 Independent practice (3 questions)

Question	Answer	What to watch
5/8 as a decimal	0.625	Doing 5 ÷ 8
0.45 as a simplified fraction	9/20	Fully simplified
Compare 3/7 and 4/9	4/9 is larger	Common denominator or decimals

06 Common mistakes and what to say

Mistake	Student writes	Say this
Adding to both numbers	3/4 becomes 4/5	Only multiplying or dividing keeps the value.
Not fully simplified	18/24 = 9/12	Divide by 3 again: 3/4.
Comparing numerators only	3/7 and 4/9 compared by 3 and 4	Denominators differ, so convert first.
Dividing the wrong way	3/8 computed as 8 ÷ 3	The numerator is divided by the denominator.

07 Homework (paper, section and question numbers)

Primary 4 first-term paper — Section A, questions 1 to 5
Primary 4 first-term paper — Section B, questions 5 to 8

08 Exit check (last 5 minutes)

Question	Answer	Decision
5/8 as a decimal	0.625	All right: move to decimal operations
0.45 as a simplified fraction	9/20	One wrong: re-teach simplifying
Compare 3/7 and 4/9	4/9 is larger	Two wrong: repeat the paper strips

09 Tutor FAQ

Should they memorise common decimals?

The eighths family is useful, but they must know it comes from dividing.

Common denominator or decimals?

Teach both and let them choose; eighths often favour decimals.

Students simplify slowly.

Ask for common factors 2, 3, 5 in order instead of guessing.

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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.