The prompt connects the concepts of a ratio and an equation. Combining the two ratios into a three-part ratio (a:b:c = 8:12:15) acts as an intermediary step from which to derive the equation. Alternatively, it is possible to convert the two ratios into separate equations (3a = 2b and 5b = 4c) and then combine them into one equation. 

Students in year 10 (grade 9) classes have found the prompt intriguing. They have been enthusiastic to create more examples once they know how to show the conditional 'if-then' statement is true. 

In the question, notice, and wonder phase of the inquiry, students have responded to the prompt in the following ways:

• How do you work out if the equation is true?

• How do you get from the ratios to the equation?

• As a = 2 and b = 3 in the first ratio, 3a = 2b = 6.

• a and b are not necessarily 2 and 3. They could be 12 and 18, for example.

• The numbers in the ratios are consecutive. Should the numbers in the equation have the same difference?

• You can combine the ratios by making b = 12 and use equivalent ratios but then the equation would be 8a = 12b = 15c.

Explanation

Depending on students response to the prompt, the teacher might start the inquiry by explaining how to derive the equation from the ratios in the prompt. Alternatively, students might request an explanation by selecting the appropriate regulatory card.

In the slides, there are two ways to explain - firstly, by combining the ratios and, secondly, by converting the ratios in the prompt to equations. The second method is supported by the preparatory questions in the slides.