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.

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...

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...

Percentages with Ratio Tables

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.

Cameron Setter

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