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# Proportional problem 5: Bookshop

Martha buys 4 books for £11. In this bookshop, all books are the same price.

Billy buys 9 books from the same shop. How much do they cost in total?

## Activity 17 Reflecting

Timing: Allow 5 minutes

Look at the learner’s incorrect response below.

How can you explain the thinking behind this approach?

BooksPrice
4£11
8£22
9£23

### Discussion

This learner has used an incomplete application of the building-up method. They have attempted to use a building-up method, by doubling the original amount to get the price for 8 books and then they have made a mistake in the final step.

In the left-hand column, the learner doubled the number of books and then added a quarter of the original number of books. On the right-hand side, this has been translated to ‘double the price and add 1’.

As the teacher, unpicking this mistake means you can see that there is some understanding to build upon.

Bookshop

BooksPrice
4£11
8£22
1£2.75
9£24.75

Adding the extra step into the working could help to avoid the mistake made above.