Pressure and Density with 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.

📝 Weekly Report #21

The trainee teacher in our department has started to teach my Year 10 group this week. It has taken me back to when I was training and the struggles that I had and the feedback my mentor would give me. One thing I didn't consider back then was how the class teacher feels who I was taking over from. I know that as a trainee I was no where near being an amazing teacher but over time I have continually improved. So it has been a struggle for me to allow the trainee to teach my class thinking that there would be aspects that I know I could deliver much better. On the flip side of this it has been great to learn from him by watching him teach and being able to give small steps to improve for next time. The initial focus has been on general pedagogy, e.g. use of questioning, planning for misconceptions etc. It's made me reflect on my own teaching ensuring I don't just talk it, I walk the walk too! I've also enjoyed seeing the improvements he has been able to make lesson on l...

Equivalent Fractions with Ratio Tables

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...

Ratio Tables: Why you need to use them?

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...

Cameron Setter

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