Math · Stage 6
Mixture and concentration problems
Concentration is the solute (the stuff dissolved) compared to the whole solution — solute ÷ solution. Find it, work backwards to the solute or the water, and track how mixing, diluting or boiling changes it.
✦ Math📘 Stage 6 · S6⏱ ~15 min🧒 Ages 10–12★ Free to start
I can solve mixture and concentration problems.
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Kavi's Squash Stand 🥤
Kavi mixes orange squash at her stall. “Two spoons of syrup in a small glass tastes strong 💪 — the same two spoons in a big glass tastes weak 💧,” she hoots. “How strong a drink is depends on the syrup compared to the whole glass — that is its concentration: solute ÷ solution.”
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What your child will learn
1Concentration is a part of the wholeA solution is a solute (the stuff that dissolves — syrup, sugar, salt) mixed into a solvent (usually water). Concentration compares the solute to the whole solution. This drink is 1 part syrup in 5 parts of drink = 1/5 = 20%. Tap the parts to see the fraction.
2Concentration = solute ÷ solutionDivide the solute by the whole solution, then times 100 for a percentage. The whole solution is the solute PLUS the solvent — the common trap is dividing by just the water. If you know the concentration you can turn the formula around to find the solute or the solution.
3Add water down, boil water upThe solute does not change when you add plain water or boil water off — only the whole solution changes. Here a drink starts with 20 g of syrup in 100 g (20%). Add 100 g of water and the glass doubles to 200 g, so the syrup is now spread thinner.
4Mixing: add the solutes, add the solutionsTap each card. Pour together 100 g of 30% salt water and 200 g of 15% salt water. One way just averages the percentages — that only works for equal amounts. The right way adds the real grams.
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A peek inside
A glass holds 30 g of syrup dissolved in a 120 g drink. What is the concentration?
concentration = solute ÷ solution × 100% = 30 ÷ 120 × 100%
Try this at home: Concentration: 40 g of sugar in a 160 g syrup → __
Ready to play and learn?
Start the free interactive lesson, or print the handout for screen-free play.
Part of Math · Stage 6 · S6 on KAVI Academy — a secular, whole-child learning platform for ages 5–12.