## psychic mathemagics!

I love introducing algebra this way. I like to add a bit of theater with the Birthday Magic Trick. You can either ask a class to perform the calculations in their head, by calculator or use the flow chart document which is linked at the bottom of this page.

The trick works by taking the number that they have calculated and adding 110, this should give the day and month of birth. For example, my final result pictured on the right is 6970, and 6970+110=7080. My birthday is 7/08 (7th of August).

I usually then proceed with the psychics maths cards (also linked below.) These are much simpler versions of the birthday trick, resulting in the same answer every time. I get pupils to test out these with decimals, fractions and negative numbers to try and disprove the trick by counter example. For strong groups, you can then launch straight into proving this with algebra. For weaker groups, I use a trick that my PGCE tutor taught me: try it with a million. Pupils are used to saying "half of 2 million is 1 million." So, it is not a giant leap to pretend to be lazy and write one million as 1m - then half of 2m is 1m or m. Then "one million and 10" becomes 1m + 10, etc.

The psychic cards below are organised from easy (red) to difficult (green) and an extension (purple) which is using two digit numbers. Here the challenge is to get pupils to write 10a+b instead of ab for a two digit number. This task leads into this fairly well. If you have some really high flyers in your class, they can be asked to prove the birthday problem algebraically.

The real benefit of these activities is the questioning and inquiry that can come from an apparently simple task. It also differentiates very easily.

The trick works by taking the number that they have calculated and adding 110, this should give the day and month of birth. For example, my final result pictured on the right is 6970, and 6970+110=7080. My birthday is 7/08 (7th of August).

I usually then proceed with the psychics maths cards (also linked below.) These are much simpler versions of the birthday trick, resulting in the same answer every time. I get pupils to test out these with decimals, fractions and negative numbers to try and disprove the trick by counter example. For strong groups, you can then launch straight into proving this with algebra. For weaker groups, I use a trick that my PGCE tutor taught me: try it with a million. Pupils are used to saying "half of 2 million is 1 million." So, it is not a giant leap to pretend to be lazy and write one million as 1m - then half of 2m is 1m or m. Then "one million and 10" becomes 1m + 10, etc.

The psychic cards below are organised from easy (red) to difficult (green) and an extension (purple) which is using two digit numbers. Here the challenge is to get pupils to write 10a+b instead of ab for a two digit number. This task leads into this fairly well. If you have some really high flyers in your class, they can be asked to prove the birthday problem algebraically.

The real benefit of these activities is the questioning and inquiry that can come from an apparently simple task. It also differentiates very easily.

birthday_trick.docx | |

File Size: | 55 kb |

File Type: | docx |

psychic_cards.pdf | |

File Size: | 281 kb |

File Type: |