Math · Stage 5
Ratio and fraction problem sums with the bar model (units method)
A ratio like 2 : 3 is just a bar cut into equal units. Add the ratio numbers to get the TOTAL units, find what ONE unit is worth, then multiply to read off every quantity — the total fills ALL the units, a difference fills only the EXTRA ones.
✦ Math📘 Stage 5 · S5⏱ ~12 min🧒 Ages 9–10★ Free to start
I can solve ratio problem sums with the units method.
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Kavi Shares the Treasure 🪙
Two friends must split 40 gold coins in the ratio 2 : 3 🪙. "No guessing!" hoots Kavi. "A ratio is just a bar made of equal units. 2 + 3 = 5 units for 40 coins, so 1 unit = 40 ÷ 5 = 8. One friend gets 2 units = 16, the other 3 units = 24 — fair and square!"
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What your child will learn
1A ratio bar cut into equal unitsRead the ratio 2 : 3 as 2 units and 3 units — all the same size. Line them up and the bar has 2 + 3 = 5 equal units in all. If the whole bar is worth 40, then one unit = 40 ÷ 5 = 8. The 2 shaded units are the first share (that is also 2/5 of the whole — ratio and fraction are the same bar!).
2Draw the ratio as same-size unitsIn the ratio 2 : 3, the first quantity gets 2 units and the second gets 3 units — every unit the SAME size. Tap each card.
3Total, one part, or difference → then 1 unitAlways find the value of one unit first. The clue can give you the TOTAL (all the units), ONE PART (some of the units), or the DIFFERENCE (only the extra units). Tap each card.
4Total, one-part, or difference clue?
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A peek inside
Red and blue beads are in the ratio 2 : 3. There are 40 beads in all 🔵. How many of each colour?
units = 2 + 3 = 5 → 1 unit = 40 ÷ 5 = 8 → red = 2 units, blue = 3 units
Try this at home: Units: ratio 3 : 5, so the bar has __ equal units
Ready to play and learn?
Start the free interactive lesson, or print the handout for screen-free play.
Part of Math · Stage 5 · S5 on KAVI Academy — a secular, whole-child learning platform for ages 5–12.