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 blog post showing this.

Using a ratio table links the multiplicative relationship of equivalent fractions to similar relationships with converting units, exchange rates and even speed. If students have a strong understanding of the multiplicative relationship in equivalent fractions they are able to simplify fractions easily. This also supports students understanding when simplifying and calculating with algebraic fractions at a higher level.

So the next time you are teaching students to find equivalent fractions use ratio tables... As well as prime factors.

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 st

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.

England v Wales: Who teaches Maths better?

England V Wales: Who teaches Maths better? Times are changing in Wales, there is a new Curriculum focus and in Maths there are 5 proficiencies that the government want to see. Here's my take as a new HOD crossing the border from England. The Welsh government have overhauled the curriculum and not just in Maths. They have identified key statements of what matters and laid out principles for progressing in each subject. Maths in every country is the same though surely.... Well yes... we still focus on Number, Algebra, Geometry and Statistics. But also no....in Wales it is mandatory to use their 5 proficiencies to progress students in Maths. This isn't an explicit thing in England. The 5 proficiencies are: conceptual understanding, fluency, logical thinking, strategic competence and communication with symbols Lots of big words. But if you dive deeper into the detail that the Welsh government provides on each of them it is no different to what the NCETM in England recommend with t

Cameron Setter

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