Cameron Setter

What if I said you could teach your students one thing and they could answer everything to do with Percentages? Don't believe me? Let me show you: Finding a percentage of an amount Q: Find 20% of 925 Increasing/Decreasing by a percentage Q: Decrease 45 by 16% Expressing as a percentage Q: A cereal bar weighs 24g. The cereal bar contains 3.6g of protein. Work out what percentage of the cereal bar is protein Percentage Change Q: Rebecca bought a dress for £80.  She later sold it for £116. Find the percentage profit. Reverse Percentages Q: A car increases in value by 35% to £2500. What was its original price? Ratio tables can be used for it all. There is obviously going to need to be some further teaching about what an increase/decrease is, how to work out the multiplier etc, but it is a great tool we should all be using more often You may have worked out by now that I like using Ratio tables. 

Pressure and Density (like Speed) is not taught very well! Pressure and Density have a proportional relationship that can be modelled effectively using a Ratio table, just like Speed. Below are some examples: Density Q: A cylinder has a mass of 270g. It has a density of 3g/cm^3. Find the volume of the cylinder Pressure  Q: An object is placed on the ground and exerts a force of 3000N on an area of 4m². Work out its pressure on the ground. Ratio tables become more effective when combining compound measure . It can help give students a frame for their workings. My class were able to answer questions similar to this with no mention of a triangle or even a formula! Compound Measures are a great example of an area of Maths that is often taught at a surface level using formula triangles. For students to gain a greater understanding of the relationships between mass-volume, distance-time and force-area use a ratio table. 

The following is a slide taken from NCETM Checkpoints. I was happy with the fraction pair on the right but the left stumped me! Then I had that 'aha' moment!  What I used to do I never used to teach equivalent fractions like the one on the left to my classes. I would just use arrows to multiply both numerator and denominator to find an equivalent fraction, very similar to the fractions on the right.  The issue with this though is, like me, students don't necessarily see all of the multiplicative relationships between the fractions as well as within the fraction. They are missing that key knowledge to support them answering the first pair of fractions.   What I do now Ratio tables allow students to see those multiplicative links. By doing this it makes questions like the checkpoints task much easier for students to do.  Disclaimer: this isn't the only way I teach equivalent fractions. I also show students how prime factors can also help us. There will be a future...

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 ...

Only 36% of students were able to answer the question on the right. Whereas 75% of students were able to correctly answer the problem on the left. (7) Why? What's the big difference?  Students are more likely to relate values between objects (left question) than within an object (right question). (7) A similar issue comes up in the questions below. 91% getting the bottom question correct, relating 11 people to 33 people. Whereas only 51% answered the top question correctly.  Students often struggle to see all of the multiplicative links between and within values. One of the misconceptions my own students had with the right 'L' question was that the answer was 45. They had added 13cm because 8 + 13 = 21 on the base of the 'L'. "Young children tend to see multiplication additively" Dietmar Kuchemann   DfE suggests teaching multiplication as repeated addition, with arrays, in Yr2. Yr3 scaling is introduced but after that isn't mentioned again. It is as...