Level 3 · Ages 11–13
Read it again any time, including while you work through the exercises.
Three notebooks cost 6 euros. How much do seven notebooks cost? If every notebook has the same price, you can answer with confidence: this is a proportional situation. When one quantity doubles, the other doubles; when it triples, the other triples.
The secret of proportionality is multiplication. You move from one row of the table to the other by always multiplying by the same number, called the coefficient of proportionality. Here, price = number of notebooks × 2, because one notebook costs 2 euros. This price for a single item is called the unit method, and it is often the safest approach.
Careful, not everything is proportional! Your height is not proportional to your age: you will not be 4 times taller at 40 than at 10. Before calculating, always ask yourself: does doubling one really double the other?
Also beware of the addition trap. If 3 photos cost 9 euros, 5 photos do not cost 9 + 2 = 11 euros. You do not add the difference: you reason with multiplications. One photo costs 3 euros, so 5 photos cost 15 euros.
In this lesson you will learn to spot proportionality, complete tables and pick the fastest method: unit method, coefficient, or adding and multiplying columns.
3 identical notebooks cost 6 €. How much do 7 notebooks cost?
6 ÷ 3 = 2
I go to the unit: if 3 notebooks cost 6 €, then 1 notebook costs 2 €.
2 × 7 = 14
I multiply the price of one notebook by 7 to get the price of 7 notebooks.
Result: 7 notebooks cost 14 €.
In a proportional table, 2 corresponds to 10. What does 6 correspond to?
10 ÷ 2 = 5
I look for the coefficient of proportionality: what do I multiply 2 by to get 10? By 5.
6 × 5 = 30
I apply the same coefficient to 6: every number in the first row is multiplied by 5.
Result: 6 corresponds to 30.