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Have I been scammed?

Unit pricing, best buys, call it what you will, this topic is great because it is relatable, practical and prompts rich conversation. This week I started a lesson with a lower ability Year 10 class with this image:


After some hesitations one student piped up:

"Do 80 divided by $5.39!" 

I wrote on the whiteboard 80/5.39 and the students told me confidently the answer was 14 cents. 

Me: "How do we know this is correct? Is there a way we can check?"

After some discussion we figured out we could multiply 80 by 14 cents which they told me was $11.20.

Me: "Are we happy with this?"

Students: "I guess."

Me: "So if you take this packet of lollies to the checkout and they charge you $11.20 you are ok with that?"

One Student: "You're gettting scammed!"

I was amazed. The students took quite some time thinking through how the shop keeper were cheating the customer. Eventually they were convinced that maybe the maths was wrong. It was decided to change the calculation to $5.39 divided by 80, which gave us 7 cents. When we checked by multiplying this by 80 we were happy when we got the correct cost of the packet of lollies. 

It was a really satisfying lesson to see unravel. I am certain that if I had commenced the lesson by displaying the formula 

Unit Price = price/number of units

then the same level of learning would not have occurred. The importance of having a reason to be confidence in your maths, to be able to check your working in another way, to be able to make sense of the situation in context, would have been lost had a formula been initially provided with no way to understand or check it's validity. 

It has shown the importance of witholding the 'answers' to everything, not correcting immediately students' errors but allowing them the time to realise them in their own way and in their own time. The depth of understanding and retention of knowledge is magnified using these techniques! 

I would love to hear from you, if you've had similar experiences.

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