Following on from our last numeric lesson; now that we know our numbers better, now we can start using them.
Mathematical motivation
Whilst trying to get through our lockdown homeschooling, maths was always a struggle. I sympathise with Matilda here. I didn’t enjoy maths at school, it can be a very dry subject when not handled carefully.
So how do you inject some fun into maths? Mix it with your favorite things! Matilda loves her Hatchimal toys so this provided me with an opportunity. If you’re not familiar with Hatchimals, they’re a bit like a campaign to sell extreme genetic engineering to girls; providing a range of cute chimeriod creatures. Regardless of your views on genetic interference, this was my way in!
SI units
We make measurements all of the time. We measure time, distance, weight, light levels, battery charge, all kinds of things. But whenever you measure something real, you record it with something made up, as we saw when we considered leap years. Pounds, stones, ounces, grams, tonnes; they’re all ways (or units) of measuring weight and they’ve all been made up by people.
In science, we try to avoid confusion by picking one unit for everyone to use. It’s something called the International System of Units. The units that have been picked are called SI units. It’s very useful, but it’s not always fun.
Colourful units
The masters of fun units are journalists. They seem to have their own standard units, ‘SJ units’ if you will. How many times have you heard things referred as in the size of football pitches, the weight of double-decker buses, or taller than the Empire State Building? There is nothing wrong with this if it allows you to communicate effectively, and I am looking to communicate.
You can use anything as a unit for anything else, provided that you know how to do it. So we are going to weigh Matilda in Hatchimals.
Doing this is not an exact exercise, especially when you consider that not all Hatchimals weight the same amount. So the first thing that we need to do is to make them all the same weight.
Becoming Average
Clearly we can’t change the weight of the Hatchimals, but we can take an average. An average is a way to give one amount for lots of different things in a group. That amount may not be right for any single thing in the group, but it will be the amount closest to all of the others.
It’s hard to show with weight, so here’s an example with height.
You can see that everyone has changed height and they are now all the same height, somewhere in the middle. This average value (also known as a mean) becomes our new unit; the Hatchimal.
Our Unit
I got Matilda to weight all of the Hatchimals that she could find on the kitchen scales and we made a note of them all. It always best to use as many measurements as you can when working out an average. More normal values will keep things stable in case a really weird number crops up.
In order to work out our average, I added up all of those weights. If you’re in a rush, you can chuck all of your hatchimals on the scales at once and just look at what the weight is. I then took the total and divided it by the number of Hatchimals that we weighed (this isn’t a test, you can use a calculator. I’m trying to keep this fun). We got an average of 4 grams. This is our Hatchimal unit: 4 grams = 1 Hatchimal.
Using your unit
For the next stage we needed to weigh Matilda. We did this on the bathroom scales. This gave us a weight in kilograms. Our Hatchimals were weighed in grams, so we need to convert it. ‘This is easy. A ‘Kilo’ means one thousand so 1 kilogram (kg) contains 1000 grams (g). So if we multiple those 10kg by the 1,000g grams that they each contain, then we end up with 10,000g. If you done the last lesson you’ll know that a comma and 3 zeros means one thousand anyway, so that’s all that we’ve added to our 10. We now have a lot of zeros, and it’s precisely why we use kilograms. It keeps things simple for the types of weight you are working with.
The final stage is to divide Matilda’s weight (in grams) by the average Hatchimal weight. We ended up with a figure of just under 3000 Hatchimals, or 3 kiloHatchimals.
The Hatchimal unit may not be all that useful, but we had fun making and using it. What is useful is knowing how to do something like this. Matilda can’t do this by herself yet and that doesn’t matter. What matters is that we used numbers and maths to have fun.
Let the fun continue…
Just to add, you don’t need to use grams and kilograms as I have done. Provided that you can convert between your larger weights and your smaller ones, you can use whichever units you like. Since you will be correcting them into your own custom unit anyway, you will get the same answer regardless.
Matilda's Lab 