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.

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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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