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When learning how to write 3-part ratios students need to understand how ratios can be made equivalent. The start of the lesson reminds students by asking which of six ratios is the odd one out. This is presented to the class as they come into the lesson.

A few students immediately go the ½ : 1.5 : 1 as the odd one out as the other five ratios involve integers. I encourage the class to consider any equivalence between the 6 ratios in order to find the odd one out. After a few minutes I ask students to show me, on their whiteboards, one of the ratios that is not the odd one out along with any working out that explains why. Across the class each of the five equivalent ratios are represented. All the class use the ratio 1 : 3 : 2 to show why the other is equivalent.

The aim of the lesson is to write and use a fully simplified 3-part ratio from two connected 2-part ratios. However, the connection between the two 2-part ratios is not always obvious. To make this connection easier to identify we begin with the ratios presented within a table. This video shows how I use tables to establish the link between two 2-part ratios.

If more practice is needed, I use the interactive Excel file to provide additional questions for students to work through on their whiteboards. After a couple more examples the class are ready to work independently through the slide below.

In the final part of the lesson I pose the problem below to the class.

About 8 to 10 minutes later I ask students to show me their working on mini-whiteboards. All students write the correct 3-part ratio and about a half of the class have correctly calculated one share to be worth 20 books. However, a common misconception is to write either the biography or travel books as 60 shares.

We discuss that the travel section has three more shares than the fiction section which equates to 60 books. The value of one share is therefore 20 books. With this information all students were able to find the correct total number of books.

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## Doug1943 says:

An excellent explanation and lesson, especially the part about typical student mistakes.

This ought to be Required Reading over the summer for all maths teachers!

## mrmath_admin says:

Thanks for the comment Doug1943. It was interesting looking at the student’s whiteboards as we worked through the examples. The key to solving the more complicated problems was understanding the difference between how the shares are split and the value of a share.