Friday 27 February 2015

Smarties - Part I

There is talk in the news about Smarties boxes changing size to better reflect portion size. The new 45 g box has three compartments, each representing one portion size of 15 g. So if you have three children you only need to buy one box of Smarties which they can easily share! How many Smarties would they each get? What if you have four children? How many Smarties should they each expect to get if they share a 75 g box?

There also exists a GIANT holiday box of Smarties that weighs in at 430 g. 
What questions come to mind?
How many Smarties? How much would that cost?

Let's tackle the second question first. What do we need to know? The cost per gram or the cost per Smartie. Collect some data!

They should get something similar to this:

Graphing cost vs. mass, we get:

Drawing a line of best fit would allow students to determine a model relating cost and mass. Students then need to think about what the slope or rate of change of this line represents.

The slope would give them the cost per gram. My equation was cost = 0.0215(mass) so for a box weighing in at 430 g should cost approximately $9.25. 

Alternatively you could look at the cost per Smartie. We need to know the number of Smarties in each different size box. 

Students can count the number of Smarties in each size box and then determine the cost per Smartie with a graph or a table:

Hopefully students make the connection that the cost per Smartie is the slope of the graph.

My equation was cost = 0.0226(number of Smarties). We can use that equation to determine the approximate number of Smarties you would get for $9.25. A little linear equation solving yields 409 Smarties. Now I have to wait until December to verify my work!

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