Skip to main content

Speed, Distance, Time with Ratio Tables



How would you answer the question above? How would you teach students to answer it?

What I used to do

When introducing Speed, I previously used a formula triangle much like the one below. Explained what S, D and T stand for. Completed a few examples on the board before setting some questions for students to complete themselves.


As I wander around the room, I notice lots of students have done 72 x 20 (this is incorrect). I pause the class and go through this particular question showing students that minutes and hours are different and how they should have done 72 x 1/3 = 24 miles.

Very quickly, I have hands up. Students haven't fully understood what to do.

Where did 1/3 come from Sir? - Not understanding converting time

Why is it multiply when they are next to each other? What does it mean with the D on top of S? - remembering how to use the triangle effectively

Where does the S go? - forgetting the formula

Teaching using a formula triangle is ineffective. Students aren't being given a deeper understanding of the underlying relationship between distance and time. Having to remember the triangle and how to use it increases cognitive load. Students refer back to the triangle for easier questions where an understanding of the relationship would be much simpler.

What I do now

The learning will start with a focus on the units themselves. Converting time, distance and speed units and understanding the different ways of writing these quantities. After this students are ready to look at the relationship between distance and time. We start with simpler examples and build up as we go but the whole way through it is using a clearly labelled ratio table. 

Taking the question above it would look something like the diagram below. We are able to look at the relationship between time and distance vertically (blue) and horizontally (red) to support in answering the question. Whichever relationship we choose, we will still get to the correct answer of 24. 


Example 2:




Using a ratio table gives students an understanding of the multiplicative relationship between distance and time. The ratio table allows links to be made with other topics that also have a multiplicative relationship such as Pressure, Density, Proportion etc. 

So…the next time you are teaching Speed, use a ratio table!!




Popular posts from this blog

Literacy in Maths

I'm a Maths teacher, I teach numbers. Why is Literacy so important for me? Well….here's why: "Literacy is fundamental for success in school and later life. Students who cannot read, write and communicate effectively are highly unlikely to access the challenging academic curriculum in secondary school and are more likely to have poor educational outcomes across all subjects." (Link 3)  Unfortunately there are a lot of Maths teachers who believe (wrongly) that literacy is a thing that the English department do. They see it as a tick box for observations. Rather than being an essential component of students being able to learn maths.  -  So what does it look like in Maths? Answer the question: Blindle 4x + 6 Are you able to do it?  This is the challenge a lot of students face in Mathematics. Subject specific vocabulary can seem really confusing to a lot of students. Understanding what a keyword is asking of students is often the hardest part of a question and can hold s...

πŸ“ Weekly Report #33

This week I listened to a really good podcast episode from Greg McKeown called Where am I wrong? In it he talks about a really effective method to have deeper discussions on what is important.  Write down/say the 3-5 issues/priorities you think there are as well as the cost/consequence of them. Then just simply ask where am I wrong? It starts the conversation off with the other person talking and getting their points across. You can then get that shared understanding about what needs to be done and why.  It got me thinking about other areas this could be useful for e.g. dealing with conflicts, leading departments/teams, pitching a new initiative. I am going to start doing this in some of these scenarios as I think we can have more productive conversations from it.  Have a listen to the episode here .  πŸ”Š Listen: Alan Stein Jr on the Modern Wisdom podcast discussing high performance and overcoming stress. He talks about thinking like an athlete with your work and impr...

πŸ“ Weekly Report #9

πŸ‘¨β€πŸ« Teaching : Have done a lot of thinking this week about the tasks I set students. Mark McCourt put a wonderful tweet out listing the different parts of a learning sequence for students. See tweet here . It nicely puts into words some of the ideas I was thinking about myself. I then also listened to Craig Barton's podcast with Tom Francombe and they spoke about giving students tasks that distract their attention but have them practicing the skill taught in the lesson. From this I have been writing tasks and noticing other tweets with exercises on that distract student thinking. So for the next half term one of my focus points is on creating and regularly using these distraction tasks in lesson.  πŸ”Š Listen : Walter Isaacson on the Knowledge project discussing Creativity. He talks about how some of the most creative people of all time, Davinci etc, immersed themselves in learning as much as they could and then linking things together. So tying the art knowledge to his engineering...