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Eva's Eggs and Fickle Fractions

Friday 1st May 2020

This is the Transum Newsletter for the month of May 2020 and I will begin by reminiscing.

When I was 10 years old if I had been asked to name some famous mathematicians I would probably have said Pythagoras and Johnny Ball. The former obviously for his proclamations about right-angled triangles but for me, the name Johnny Ball was very familiar. He was a regular fixture on children's television in the late 1970s and throughout the 1980s presenting programmes about maths. Though he's now in his eighties he's as jolly as ever and still super enthusiastic about mathematics.

His daughter, Zoe Ball, presents the breakfast show on the UK's BBC Radio 2 and Johnny was a guest on her show recently presenting the following puzzle.

Eva keeps chickens and one day was taking a basket of eggs to market.

Along comes David who buys half of her eggs plus half an egg. Following that Clara buys half of her remaining eggs plus half an egg. Next she meets Betty who buys half of her remaining eggs plus half an egg. Finally Alan buys half of her remaining eggs plus half an egg at which point she is completely sold out.

How many eggs did Eva take to market?

The answer is at the end of this newsletter. Johnny’s telling of this puzzle story is included in this month’s Transum podcast which can be found on Spotify, Stitcher or Apple Podcasts.

While you think about that I'll ask you how you are. Have you been keeping yourself busy and happy this last month? I have been super-busy not only teaching online but also getting engrossed in programming projects for the website. Here are some of the recent creations:

New Maths Learning Resource New Maths Learning Resource

Fickle Fractions is a new activity I created in one day in response to a request from a teacher working at home, teaching her class online as well as supporting her own two children. This activity requires pupils to compare pairs of fractions in order to make their way through the maze to find the door with a trophy hidden behind. There are five levels so I’m sure one of those might be suitable for your pupils.

Threes and Fives is a dominoes game that I remember playing many years ago with my family at home. The score is calculated as the sum of the number of three and fives that divide exactly into the numbers on the ends of the domino line added together. It is a drag and drop activity for two players or two teams of players and works well via a video link shared screen.

Visualise Percentages has been created for the Shine and Write collection. Initially designed to be projected onto a whiteboard in front of a class while the teacher holds an interactive discussion about strategies for thinking about percentages in mental calculations.

New Maths Learning Resource New Maths Learning Resource

Also during this last month I have made help videos for:

Each of them is intended to be a reminder of a concept the viewer will have hopefully already covered at school and will help the viewer do the associated online exercise. I am trying out different formats for these videos and I am still not sure whether the viewer will, as research suggests, benefit from seeing me in the video!

I hope the videos will be of use to you particularly at this difficult time when we are all involved in remote learning.

A mathematical Style Guide has been started and I hope I remember to update it. It's really for my own benefit trying to achieve consistency in the text throughout the website. I have just added a weekly reminder to my calendar to add one new item to the Style Guide each week.

A new level 6 has been added to the Averages exercise to include grouped data.

Many more worked solutions to exam-style questions have been uploaded.

I have been doing some one-to-one tuition via video link during these difficult times and I would like to report one teaching situation that actually worked better remotely than it would have been if we had been in the same room. Measuring angles with a protractor! Normally it is difficult for the teacher to see in detail what is going on when the pupil is hunched over their work. The online version enables zooming in and I could see in such clear detail exactly what the student was doing. I was so impressed I tweeted the following:

Thanks for all the feedback I receive. It is so nice to receive your emails with suggestions, questions and compliments. Because of time differences these emails often arrive during the night but it is nice to have them waiting for me when I get up. Thanks.

Finally the answer to this month's puzzle: I figured it out by working backwards from the end of the story.

Alan’s purchase was for half of her remaining eggs plus half an egg and this left Eva with nothing. So half of her eggs were equal to half of an egg. She had one egg left before meeting Alan.

Betty’s purchase must have been two eggs as Eva would have had three eggs before meeting her.

Clara’s purchase must have been four eggs as Eva would have had seven eggs before meeting her.

David’s purchase must have been eight eggs as Eva would have had fifteen eggs before meeting him.

So the answer is 15. Note the number patterns generated by this sequence of events.

That's all for now,

John

PS. When do Maths teachers watch prime-time TV?

Any time between 1:01 and 11:53.


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