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Thirds & Fifths

Maths · Y3 Fractions
Year 3
Lesson Guide
Explanation
So far we've folded things in half — but what if THREE people share? Cut the whole into 3 equal parts: each part is one third, 1/3. Two parts are 2/3, and all three make 3/3 — the whole thing back again. Thirds are trickier to cut than halves (no folding trick!), so check the parts really are equal.
Your Turn
Draw a chocolate bar and split it into thirds. Shade 2/3. What fraction is unshaded? Check: 1/3.
Watch Out
Folding paper in half NEVER makes thirds. Three equal shares need careful measuring or a lucky guess!
Explanation
Five sharers? Cut into 5 equal parts — fifths. Each part is 1/5, three parts are 3/5, and 5/5 is the whole again. Your hand is a great fifths reminder: five fingers, each one a fifth of the set. Reading is the same as always: bottom = total equal parts, top = parts we're talking about.
Your Turn
Shade 4/5 of a bar. What fraction is left unshaded? Check: 1/5.
Watch Out
Don't confuse the WORD with the SIZE: 'fifth' sounds grand, but 1/5 is a smaller piece than 1/3.
Explanation
Line up the bars: 1/3 is clearly bigger than 1/5. Why? A cake shared between 3 people gives bigger slices than the same cake shared between 5. The rule from last lesson still holds: for one piece, a bigger bottom number means a SMALLER piece. So 1/2 > 1/3 > 1/4 > 1/5 > 1/8 — a staircase going down.
Your Turn
Put in order, biggest piece first: 1/5, 1/2, 1/3. Check: 1/2, 1/3, 1/5.
Watch Out
This rule is for comparing ONE piece each (top numbers both 1). Comparing 2/3 and 2/5? Same idea — thirds are bigger pieces, so 2/3 > 2/5.
Explanation
Fractions aren't just pizza pictures — they're numbers with homes on the number line, between 0 and 1. Count the thirds: 1/3, 2/3, then 3/3 lands exactly on 1. Count the fifths: 1/5, 2/5, 3/5, 4/5, 5/5 = 1. When the top matches the bottom, you've reached one whole.
Your Turn
On the fifths line, which fraction is closest to 1 (but not equal)? Check: 4/5.
Watch Out
The steps must be equal-sized on the line — just like the pieces in the bar.
Explanation
Thirds and fifths show up whenever 3 or 5 share: a chocolate bar between three friends (1/3 each), five teammates painting a wall (1/5 each). And the 'how much is left?' trick: drank 2/3 of your juice? The whole is 3/3, so 3/3 − 2/3 = 1/3 remains. The whole is always the fraction where top equals bottom.
Your Turn
You read 3/5 of a book. What fraction is left to read? Check: 2/5. Now the quiz and exercises!
Watch Out
To find what is left, subtract from the WHOLE (3/3 or 5/5) — not from 1/3 or some other piece.
Step 1: Introduction
Step 1 of 5
Cut into 3 equal parts 1/3 2/3 3 equal parts → each part is one THIRD (1/3). Two parts together make 2/3. All three make 3/3 = the whole. Thirds can't be made by folding in half — you need 3 fair shares.
Cut into 5 equal parts 1/5 3/5 5 equal parts → each is one FIFTH (1/5). Handy helper: you have 5 fingers — a hand is a ready-made fifths ruler! 3/5 means 3 parts out of 5. 5/5 = the whole.
1/3 vs 1/5 — which is bigger? 1/3 1/5 1/3 is BIGGER than 1/5 — see the bars! Sharing between 3 gives bigger pieces than sharing between 5. Rule: for ONE piece, the bigger the bottom number, the smaller the piece.
A fraction number line 01/32/31 01/52/53/54/51 Count up: 1/3, 2/3, 3/3 — and 3/3 lands exactly on 1! Fractions are numbers too — they live between 0 and 1 on the line.
Fair shares in the wild 🍫 a chocolate bar shared by 3 each gets 1/3 🎨 5 team members paint a wall each paints 1/5 "I drank 2/3 of my juice" — how much is left? 3/3 − 2/3 = 1/3 left. The whole is always top = bottom! Ready? Show what you know in the quiz and exercises!
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