How to Write 3 Part Ratios - Mr-Mathematics.com (2024)

January 19, 2022

Differentiated Learning Objectives

• All students should be able to simplify a 3-part ratio using the highest common factor.
• Most students should be able to combine two 2-part ratios into a 3-part ratio.
• Some students should be able to share amounts between a 3-part ratio

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Students need to understand their equivalences when learning how to write 3-part ratios. Therefore, the start of the lesson reminds students by asking which of six ratios is the odd one out. Then, I present the first slide as students enter the classroom.

Writing Equivalent Ratios

A few students immediately go the ½ : 1.5 : 1 as the odd one out as the other five ratios involve integers. I encourage them to consider any equivalence between the 6 ratios. After a few minutes, I ask students to identify at least one of the ratios that are not the odd one out, along with any working out that explains why.

How to Write 3 Part Ratios

The lesson aims 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. Therefore, we begin with the ratios presented within a table as shown in the image to the right.

Thisvideoshows how I use tables to link the two 2-part ratios.

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

Applying 3-Part Ratios

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

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

We discuss that travel books have three more shares than fiction, which equals 60. The value of one share is, therefore, 20 books. All students could find the correct total number of books with this information.

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