
Here is a puzzle: 36 cookies are shared between two classes in the ratio 4:5. What is the very first thing you would work out before you can share a single cookie?
Three tools solve ratio and proportion problems, and the real skill is picking the right one: sharing when a total is split by a ratio, the unitary method when you find what one is worth then multiply up, and scaling when everything grows by the same factor. Read the question first, decide which kind it is, then choose the tool. We will watch two worked on the ratio bars — look at how each one is cut up before anything is worked out.
Let's work this one together in two clear steps, and we will say out loud which method we are using before each step.
Step 1: A smoothie recipe for 3 people uses 5 strawberries. We want enough for 9 people. How many strawberries do we need?
Step 2: Now we take those strawberries we just worked out and share them between this smoothie and a second recipe in the ratio 2:3. How many strawberries go to each recipe?
In your maths copy, for each problem write the method you chose at the top (sharing, the unitary method, or scaling), then your working line by line. Box the final answer.
8 identical notebooks cost €12. How much do 5 notebooks cost?
Name the method first, then write the working step by step underneath. Box the final answer when you finish.
Today we crack a five-clue mystery. Each clue is a ratio, proportion or scaling problem, and every answer feeds straight into the next clue. The clues get harder as we go: clue 1 is a straight share, clue 5 needs two methods in one. Solve clue 1 to unlock clue 2.
We crack clue 1 together first so everyone sees how the chain works. Then pupils take turns at the board for clues 2 to 5. Before each clue, name the method out loud (sharing, unitary, or scaling).
€36 is shared between Ana and Ben in the ratio 5:7. How much money does Ana get?
Method: sharing. Add the parts: 5 + 7 = 12 parts. One part is €36 ÷ 12 = €3. Ana's share is 5 × €3 = €15.
Write €15 at the top of the chain. That number unlocks clue 2.
Ana spends her €15 on buns. 5 buns cost €2.50. How many buns does she get with €15?
Those buns would feed 6 people. How many buns are needed to feed 9 people at the same rate?
Share that new total of buns between girls and boys in the ratio 2:3. How many buns do the girls get?
The girls use their buns for a party. A tasting tray of 6 buns served 8 guests. First scale up to find how many times bigger their bun total is than 6, then use that factor to find how many guests they can feed. How many party guests?
Keep the running chain on the board: each answer unlocks the next clue. No numbers come from outside the chain.
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