Equivalent Ratio Hunt

Practice equivalent ratios with this challenging puzzle

There are lots of ways to express a given ratio and it is an important bit of mathematics to recognise when any of those ways are equivalent. Recognising this relies on a sound understanding of multiples, factors and proportion. To do this activity you will use a bank of numbers you are given to form lots equivalent ratios. The ultimate puzzle involves using all of the 40 numbers (only once) you are given to make 10 equivalent ratios.


You just need the following Ratio Hunt activity Sheet to have a go at this task


This is a really simple task in clear parts

Part 1 - Equivalence

  • Teachers may want to have a discussion about equivalent ratios or decide to let students help each other with this.
  • Hand out the activity sheet and let students start with the first side finding different equivalent ratios.
  • REMEMBER - For each question, students must not use a number any more often than it appears in the table.
  • Since there are multiple answers, teachers and students might want to discuss checking mechanisms. This is an excellent opportunity for peer assessment.

Part 2 - The Challenge

  • Students must use each of the 40 numbers and only once to create 10 pairs of equivalent ratios.
  • There are spaces for three attempts, but students may need some rough paper.
  • Again - checking mechanisms and peer assessment may be appropriate.

Teacher Notes

  • Teachers will have to decide about when they find this activity appropriate. As is often the case, there are a number of options.  Students will need some prior knowledge/experience of ratios, but it might not be necessary to do a formal lesson beforehand.
  • If students are working in groups then then the reasoning they do with each other is often the very best bit of the task. As such, the class become self-sufficient and don't need the teacher to do a formal definition of an equivalent ratios.
  • The limited choice of numbers introduces another layer of thinking. Having used the more 'obvious' numbers they will have to experiment with different multiples.
  • A pair of equivalent ratios can easily be found, BUT, that does not mean they fit in the final ten. The numbers need to be used carefully.
  • This task was made from the starting point of a given solution, but there are other solutions. For a side project, it was interesting to explore the question - 'If you start with 10 pairs of equivalent ratios - how easily can the numbers involved be re-arranged to create another set of 10 pairs?'
  • Since there are multiple solutions, students and teachers will need to give some thought as to how to check. There are many ways to do this and they all only add to the activity (e.g. using a calculator to divide the first number by the second - equivalent ratios will yield the same result). There is great potential for peer assessment here.
  • The nature of the task demands much speculation, reasoning and working with multiples factors and different equivalencies. It is essentially a medium for practicing a skill, but in doing so students are prompted to engage in many of the thinking and reasoning skills that we hold so dear.

Good luck!

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