On our family holiday this year, the children came face to face with amusement arcades. Never having seen anything like it before, they were enamoured and very enthusiastic to spend our money in order to win more back. Needless to say we did not allow them. Until, that is, the last day. It was pouring with rain and we thought we might be able to teach them a lesson by allowing them the experience. So, we gave them each a pound, changed it into 2 penny pieces and let them at it. At the end of approximately half an hour, whilst some money had been won along the way, all three older children ended up with not a penny to their name. However, along the way, they had ‘won’ two tacky plastic rings each. They were chuffed! This was the time for some homeschool living maths of the probability persuasion.

#### Arcades

At the time, we had made it clear that amusement arcades were not the best way to spend their money. Now I was asking them why. The children genuinely felt surprised by the question. They felt they had got a bargain. Six rings for three pounds. So, I started probing them about the rings. Were they of good quality and therefore would they last? How much did they think they would pay for them in a shop and what type of shop and/or aisle did they think they would find rings like that?

It was, as always, fascinating to see them think through what I was asking. They had seen similar rings, sold in a pack of 20, in a discount store down the party favour aisle, selling for Â£1. Light bulbs began glowing! They could buy 20 for Â£1 or lose three pounds and gain 6 rings. This was a good starting point for some homeschool living maths all about probability and the game of chance.

#### Game of Chance

I asked them to think about who ran the arcades and why. Thomas immediately answered to make money. All the children suddenly started looking at the whole experience from a different perspective. I asked whether they thought the owners of the arcade knew they would make money or was it just luck. Nudging them in the right direction I asked what the costs would be of running a place – they came up with rental of the premises, electricity and staff. I added rental of the machines. Thomas realised that in order to run it as a business they needed to turn a profit. They were horrified when I told them that the machines were fixed so that, although there would be some winners, there were more losers. And the probability of winning was smaller than the probability of losing.

#### Probability

Together we looked into what the actual word probability meant. Charlotte thought it might mean that something was probable. Thomas asked if the probability of something was a measurement of how probable it was. Bingo, we had our starting point!

As you know, I want to be teaching their maths using things they have made or are using in their history studies (the mainstay of our home school). Whilst we were making the Viking Runes I had thought how perfect they were for a probability lesson. First, I wanted them to just play with them, sorting them into their letter groups and then separating them into marked and unmarked (I had kept some unmarked for the purpose):

I asked if a stone would be more likely to be marked or unmarked. They answered correctly, saying marked because there were more marked than unmarked. I reiterated what they had just said inserting the word ‘probable’ in the place of ‘likely’. Lillie jumped up and said it was probability!

Eureka!

The children played with the runes. They asked each other whether it was more probable that so and so letter was chosen until I was sure each understood that the higher the number present, the higher the probability of it being chosen. This ended our first lesson.

I did a total of three lessons on probability, because the girls had never encountered it before.

#### Homeschool Living Maths: Probability and Equations

#### Lesson One

The next day I gave them a bag of runes and asked them to follow the instructions I had typed out on the sheet (click on picture below to enlarge it). This lesson was about applying everything from the day before and making some predictions based on this knowledge. Afterwards, they tested their predictions and finally to come up with a simple formula that expressed what they had learnt. It was fascinating to watch.

Lillie, who struggles so much to understand mathematical concepts, really grasped this lesson and I encouraged her to come up with the equation without the other’s help. She managed it completely on her own! I can’t believe the difference seeing maths is making to her. Thomas and Charlotte are getting a lot out of it but Lil is just developing in leaps and bounds. It is SO worth the extra work (which by the way is quite considerable!).

The equation L10 came up with, and the others agreed with was:

*The probability of an S Rune being picked was equal to the number of S runes divided by the total number of runes*

I taught them to put it into vaguely (!) mathematical terms:

* P(S Runes)= No. of S Runes/ Total no. of Runes*

#### Lesson Two

In the next lesson I gave them 25 runes. I had chosen 5 different letters and there were different amounts of each letter. I had them do the following activities (click to enlarge):

They found the work sheet very easy, which was heartening but the last question ** really **stumped Lillie.

**Why did I teach her maths? **

She understands the need to know about money and stuff but struggled to come up with any feasible reason why anyone would need to go through the pain of being taught maths. Oh dear, I really have failed her! In the end she conceded that using the equation was quicker than working it out manually and therefore there might be some point to it all! I’m hoping that the more we do this type of maths and the less we do worksheet type maths, the more she’ll embrace and enjoy her maths and * see the purpose to it*.