Saturday, 12 March 2016

Smarties Ratios

What can five packs of Smarties help us to learn about ratios?

There really is nothing like chocolate to get kids instantly engaged in learning.

Each group was given a Smarties pack and before opening we had two prediction questions.  When sharing, we each explained our reasonings:

Some of our theories:

- I've investigated the colours in Skittles and I find there is no ratio pattern with them so I predict it will be the same with Smarties.

- I think the people counting the Smarties and putting them in packets don't really care that much.

- I think the machines that put the Smarties in the packets are programmed to count the exact amount so people don't feel ripped off.

- I think it is based on the mass rather than the number. I read the pack said 38 grams, so I think the machine weighs 38 grams of Smarties rather than counting them. 

Are there any clues on the packets that might help us?

We found what we thought was our answer:

17 Smarties! 

None of us mentioned how it is 1 portion.  We just all assumed it meant there were 17 Smarties in each packet.

We would come back to this later.

We then thought of the next prediction question, wrote and shared our theories:

There wasn't really a difference of opinion with the colour ratios. Most of us felt the machine or person doesn't worry about the colours.

So, is it possible for a pack to be completely red Smarties?

- It is possible, but unlikely.

I see.....

It was finally time for us to open the packs and find out how our theories stood.

- Wait!!!  There are more than 17 Smarties!

- Ours too!

- We have over 30!

- So do we!!!

Why is that?  Let's look at what the pack is telling us.

- Oh! It says '1 portion is 17 Smarties'.

- What does portion mean? 

- Why doesn't it just say how many Smarties are in the pack?

If 1 portion is 17 Smarties, how many portions do we have in a pack?

We then counted the number of Smarties in each pack and recorded together:

Each pack had exactly 33 Smarties. 

I then stepped in to help them understand portions by asking them to look at the nutrition guide on the pack:

When people want to control the amount of sugar or fat in their diet, they read the nutrition ingredients.  

How much sugar does it say is in this pack?

- 14% sugar

- 12 . 5 grams sugar

So, if you ate all the Smarties in the pack, how much sugar would you be eating?

- 12 . 5 grams

Have another think.  Are we sure?

- Hmmmmm.......

- Oh! It's 12.5 grams PER PORTION! Not the whole pack.

Exactly.  So how much sugar would you consume?

- About 25 grams.

- They are trying to trick us!

- That's not very fair!

- It's like they are trying to lie to us.

- Why are companies allowed to do this? Shouldn't the law be you show the amount per packet?

We just learnt something interesting about the morality of companies.  Why ARE companies allowed to deliberately deceive consumers?

How many ratios can we create with our pack of Smarties?

We had about 10 minutes to think about this in our groups.  Every now and then, we would stop and share the number of ratios each group had created and we also toured around to see the strategies each group were using:

We liked this more logical and patterning approach:

Numbering the amount of each colour:

A creative idea of using different coloured textas to represent the colours for the ratios:

Combining the ratios of two colours to form larger ratios:

A sequential, patterning and more logical approach:

Each group then created a ratio word problem for the rest of us to solve.

We had 4 word problems and ten minutes to try solve them as a group. To add some zest to this, I added a twist. The groups who show great group work skills will be able to collect 1 Smartie each from groups not showing these skills.

'Be a smartie for a Smartie!' was our catch phrase.

° Based on your pack’s ratio, how many red Smarties would there be with 100 Smarties?

° If there are 6 red Smarties in one pack, how many red Smarties are there in 1 756 370 Smarties?

° In a pack, there are 81 Smarties with a ratio of x : y : 14 : 9 : 12 : 13 :15.  X and y are equivalent. What is x and y?

° If 17 Smarties is one portion, how many Smarties are in 12 portions?

° Based on your pack's colour ratios, how many Smarties need to be made for you to get 100 blue Smarties?

Students shared strategies they tried to use to solve the problems. Strategies that did not work out were also being encouraged to share. Maths shouldn't be seen as a right / wrong line of thinking. There is great merit in creating unsuccessful strategies as they can help us to understand why other strategies are successful.

Finally, it was time to divide up the Smarties and enjoy each of those delicious bits of chocolate that had been plaguing our minds for the past 50 minutes or so.

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