T

Halves, Quarters & Eighths

Maths · Y3 Fractions
Year 3
Lesson Guide
Explanation
A fraction is a fair share of one whole thing. Cut a pizza into 2 EXACTLY equal pieces and each piece is one half — written 1/2. But careful: if the two pieces aren't the same size, they are not halves — just two unfair pieces! Equal is the magic word for every fraction.
Your Turn
Fold a piece of paper into 2 equal parts. Open it up — each part is 1/2. Do the two parts match perfectly? They must!
Watch Out
Cutting into 2 pieces isn't enough — they must be EQUAL pieces to be halves.
Explanation
Fold your halves in half again: now the whole is cut into 4 equal pieces — quarters. One piece is 1/4. Three pieces together are 3/4. Read a fraction like this: the BOTTOM number says how many equal pieces the whole was cut into; the TOP number says how many of them we're talking about.
Your Turn
Shade 2/4 of a square (draw and cut it into 4 equal parts first). Notice: 2/4 covers the same as… 1/2!
Watch Out
The bottom number is NOT "how many are left" — it is the total number of equal pieces in the whole.
Explanation
One more fold and the whole is in 8 equal pieces — eighths. Notice the pattern: 2 pieces, 4 pieces, 8 pieces — each fold doubles the count. And here's the big surprise: the MORE pieces you cut, the SMALLER each piece gets. One eighth of a pizza is a skinny little slice; one half is a feast. Bigger bottom number = smaller piece!
Your Turn
Which is more pizza: 1/2 or 1/8? Draw both if unsure. Check: 1/2 — even though 8 is a bigger number than 2!
Watch Out
This trips everyone: 1/8 is NOT bigger than 1/2. The bottom number counts cuts, and more cuts make smaller pieces.
Explanation
Look at these three bars: 1/2, 2/4 and 4/8 all shade exactly the same amount! They're different NAMES for the same share — we call them equivalent fractions. It makes sense with the folding: 2 quarters snap together into a half, and 4 eighths do too. Same pizza, different slicing.
Your Turn
How many eighths make a quarter? Fold or draw to check. Check: 2/8 = 1/4.
Watch Out
Equivalent means same AMOUNT, not same number of pieces. 2/4 uses more pieces than 1/2 — but no more pizza!
Explanation
Halves, quarters and eighths live all around you: pizza slices are eighths, a sandwich cut both ways makes quarters, sharing an orange makes halves, and the clock says 'quarter past' when the minute hand is 1/4 of the way around. Once you see fractions as fair shares, you'll spot them everywhere. Quiz and exercise time!
Your Turn
At your next meal, find one half, one quarter or one eighth of something and name it out loud.
Watch Out
Always check shares are EQUAL before naming a fraction — a big slice and a small slice are not both 1/2!
Step 1: Introduction
Step 1 of 5
A fraction is a FAIR share 1/2 — a half NOT halves! Halves must be EXACTLY equal pieces. Two pieces that aren't the same size are just… two pieces.
Fold a half again → quarters 1/4 shaded 3/4 shaded 3 4 how many pieces pieces in the whole Bottom number = how many equal pieces the whole is cut into. Top number = how many pieces we are talking about.
Eight equal pieces = eighths 1/8 — one eighth 5/8 shaded Fold: whole → halves → quarters → eighths (2 → 4 → 8 pieces). More pieces means each piece is SMALLER: 1/8 is tiny compared to 1/2!
1/2 = 2/4 = 4/8 1/2 2/4 4/8 All three bars shade the SAME amount! Different names for the same share are called equivalent fractions.
Halves, quarters and eighths everywhere 🍕 a pizza cut into 8 slices each slice = 1/8 🍊 an orange split with a friend each share = 1/2 🥪 a sandwich cut both ways each triangle = 1/4 ⏰ "quarter past" on a clock 1/4 of the way round Spot a fraction at your next meal! Now the quiz and exercises.
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