##### Ratio problems

Just a load of interesting (ish) ratio problems to work though.

I used bar modelling. I am increasingly into bar modelling for KS3, although I’m still not massively convinced when it comes to negatives.

I call these ‘reverse’ ratio problems. I don’t know if that’s the correct terminology.

I have been watching a lot of Queer Eye recently.

I like bar modelling for questions like this.

Also

Some questions adapted from Don Steward and White Rose Maths Hub’s Barvember 2017.

No posts for two weeks now. I’m on holiday. When I get back, Pythagoras and Trig!

##### Sharing in a ratio

Something I’ve wanted to get around to completing for a while. I love ratio and I’ve got into doing a little bit of bar modelling. There’s some LOVELY questions in the White Rose Barvember stuff.

This lesson has an example problem pair and some mini-whiteboard work. When I taught this lesson, the mini-whiteboard stuff really, really worked on getting students on the same page and up to speed.

I put quite a lot of thought into this set of questions, too.

I think I’ve done a good job with question 2 in particular, there.

Also there’s some worded questions.

Question 5 might be my favorite question of all the questions I have ever written. There’s just something lovely and crunchy about it.

Obviously this lesson includes the plenary check as well and also a problem solving question.

Friday’s resource is the last one for a while. It’s the Easter break. If I’m writing maths on a beach in Laos, my wife will murder me. On a personal note, I’ve managed to have a blog ready every Monday, Wednesday and Friday this half term. Pat on the back for me, there. I hope to have the same schedule next term.

##### New Resource : Simplifying ratio timed questions

Like the old ten quick questions, but with three levels of difficulty.

Level one (first three questions) : Prime divisor

Level two (second three questions) : Compound divisor

Level three (third three questions) : 1 : n

Level four (last question) : Units

Tempted to extend it to do 12 questions. That last question feels odd on it’s own.

Also the PDF generation is weird. Think you have to click go for it not to be a blank page. And allow cookies.

I messed up the question generation code so had to go back in and manually edit hundreds of answers 🙁

Sometimes if you mess around with changing the id and sid parts of the url you might see stuff I’ve been working on but not blogged about yet. (Try 8,1 8,2 for instance )

##### New resource : Equivalent and Simplifying ratio lesson

It’s like my ProjectALesson stuff but I’ve taken A LOT of explanation out. I’ve also got some stuff you need to print out. I’m not sure making them ‘pick up and go’ was that helpful.

It takes a lot of inspiration from variationtheory.com. It’s my new favourite website. It’s ACE.

I also took a lot of inspiration from Jo Morgan’s MathsConf session . She was talking about covering stuff in depth, and not missing an opportunity to go into negatives and fractions.

I made what is probably my favourite exercise of all time based on this. My colleague Mike helped me write the questions (Hi Mike!) and some of them are superb, although they might be a bit much/challenging. As an aside, sitting with my colleague and writing some questions was a great use of our time. Mike came up with some questions that I wouldn’t have. I love the misconception of $2^3 : 2^2$ being the same as 2 : 3. Mike came up with that. It also made us discuss stuff really deeply. If you’ve got some gained time, write some questions with a colleague.

See what you think. As always, the discussion is the fun bit.

EDIT : I’ve uploaded this ‘Pixel Picture’ as word file on TES here. It makes the formatting a little nicer.

##### Vary and twist: Simplifying ratio

This one was hard. I spent ages rearranging questions and looking at what should be added. Specifically, I had a massive dilemma when it came to introducing fractions. I was trying to point out the ways in which simplifying fractions and simplifying ratio were similar, but I’m not sure that I haven’t just led students down the wrong path thinking they’re equivalent. For instance 5 : 6 is 5/11 and 6/11, not 5/6. Hmmmm.

The variations I used for section A.

1. An example where you can use a prime divisor
2. The opposite way around. What happens to our answer. Order is important!
3. Half one side. 8 : 5 becomes 4 : 5
4. One that’s already as simple as possible. Time for some questioning? How do you know you can’t simplify it?
5. It’s not just reducing the numbers down. Here you have to multiply up. Deals with what simple is. I have changed this from the picture to make only one number vary from the previous question.
6. Needs a non prime divisor. This isn’t really a variation, though. It has nothing really to do with the previous questions!
7. Again, double one side
8. Double both. Our answer does not double!
9. Adding a third part of the ratio. Changes the answer significantly.
10. Doubling two parts here. Our parts don’t double in our answer!

If you amend this and it works better, please let me know!