This trick appears to be mathematical but perhaps it is not!

Can you change this square into two using only a pencil? You are not allowed to come anywhere near the screen (or whiteboard).

**The Trick**: Carefully use the blunt end of a pencil to push up the
lower eye lid of one eye and you will see double!

Each student is asked to think of a number between 2 and 9 inclusive (or ace, jack, queen or king). Whatever number they have chosen, there are four cards in their pack with that value. Students are asked to shuffle the pack while thinking about their cards.

Students are considered to have magical powers if two of their cards come
together in the pack (well there might be one card between them but for the
purposes of this exercise we will call that coming together).

Most students should find that this works for them ... so they have magic
powers ... or have they?

**The Trick:** In fact this is an example where the odds are weighted in
favour of a success ... can you estimate the probability from the results of
this activity?

- Multiply it by nine
- Add the digits of your answer together
- Subtract five
- If A=1, B=2, C=3 etc what letter is represented by the number you are thinking of now?
- Think of a country beginning with that letter
- Think of an animal beginning with the second letter of that country
- What is the colour of that animal?

*"There aren't many grey elephants living in Denmark are there?"*

Virtually everyone in the room will have thought of Denmark as their country
and as elephant as their animal. Is this magic?

Students can now investigate the probability of this happening. Having first
satisfied themselves that everyone will arrive at the letter D independently
of their starting number, how many countries are there starting with D?

How many animals beginning with E? Of all the animals beginning with E how
likely is a person to choose elephant? Perhaps a survey might answer this
question.

Students could now be asked to make up for themselves a similar trick (but
not using Elephants from Denmark). Try out the tricks on some other students
and teachers.

Finally a demonstration of tree diagrams can be used to explain the
probabilities of these tricks working.

**Update November 2014:** The 96% and 85% on the tree diagram above were made-up figures for illustrative purposes only. We have now conducted our own survey to see what those figures should be. You can see the results on the Predictive Survey Results page.]

You can amaze your students by pretending to add up a whole column of
three digit numbers in a couple of seconds.

Ask three students to write three digits each on a piece of paper as if they
are to be added and return the paper to you.

You write two more numbers below those. Choose your first number (which is
the fourth one in the problem) so that the first number and fourth numbers
add up to 999. Choose your next number so that it adds with the second
number to give 999.

283

234

549

716

__765__

Give a student the paper and ask them to add up the numbers on a
calculator. Then the student could return the paper to you. Look at it
briefly as if you are adding the numbers in your head and announce the
answer.

The answer will be 2000 plus the third number minus 2 which you could
compute very quickly once the student returns the paper.

This could be followed by a class discussion about how this trick works ...
students practise with friends.

The Teacher writes a number on a large piece of paper. The students can
see this going on but can't see which number it is. The paper is the put in
an envelope or a box and put in a safe place in view of the students.

The Teacher then asks a student to think of a very large number. This number
is written on the board in words.

"How many letters are in these words?" ... the answer is written underneath
in words...."How many letters are in these words?" ... and so on repeating
the process again and again till the list of numbers has reached the bottom
of the board. The envelope is then opened to reveal the number FOUR which
will be the last number written on the board.

F O U R

"What if we start with a different number?" ... another student
volunteers a different starting number which eventually generates four
again.

"Does this always happen?".. students try some of their own.

"Why does it always happen?"

"What about other languages?"

Students now do an investigation looking at the properties of the number
words in different languages. They can use foreign language dictionaries or
the internet as appropriate. They should produce a write up of their
findings for their folders.

many calculations have short cuts or tricks associated with them which enable students to perform the calculations quickly in their heads.

A list of such tricks can be found here.

Here are a couple of examples:

**Quick Square**

Did you know that there is a quick way of squaring a two digit number
which ends in 5?

Just multiply the first digit by that number plus one.... stick a 25
after your product and there's your answer .... simple ?

Example:

Q. What is 35 squared?

A. 3x4=12

.....now stick on the 25

...........the answer is 1225

Do you know why it works?

**Times Eleven**

The eleven times table has always been very easy to learn up to 9 x 11.
Here's a way of multiplying large numbers by 11 too:

Example:

Q. What is 324 x 11 ?

A. Write down the first digit ... 3

.......Add the first and second digits ... 3 + 2 = 5

.......Add the second and third digits .. 2 + 4 = 6

.......Write down the last digit ........... 4

The answer is 3564.

Try it yourself ... multiply 543 by 11

Do you know why it works?

Does it work for all three digit numbers?

A large house plan made from 9 pieces of carpet (each 3m by 3m) is set out in the middle of a large room as shown:

A student is dressed to look like the murderer(!) and stands on the
carpet piece marked "Hall".

A teacher (acting as Sherlock Holmes) explains that the murderer will be
tracked down in the house and arrested. Sherlock is blindfolded.

A second student throws the dice and states the number on the dice out loud.
The murderer walks through that many doors on the plan of the house.

Sherlock says "I know the murderer is not in the kitchen (or name of other
room) , so will someone please take away the kitchen"

A third student takes away the piece of carpet labelled "kitchen". the
murder from now on cannot step on the area which was once the kitchen.

The process is repeated a number of times until Sherlock can say "I know
that the murderer is in the ........... (name of room), you are under
arrest.

"How does the trick work?"

Well if the murderer starts in the hall, four rooms are one door away
(study, bathroom, dining room and conservatory). We shall call these rooms
odd rooms.

The other rooms are two doors away. We'll call these rooms even rooms.

If the number on the dice is even, Sherlock knows that the murderer must
have walked into an even room so can ask for one of the odd rooms to be
removed.

The process continues. Sherlock uses the principles that:

Odd + odd = even

Even + even = even

Even + odd = odd

Odd + even = odd

... to keep track of the rooms the murderer can't be in. By process of
elimination the correct room can be found (In practice Sherlock must reserve
the right not to remove a room in certain cases)

This could be followed by whole group discussion about how the trick was
performed (using student's own theories and words.

Students in pairs try to perform the trick using the a diagram and a counter
to represent the murderer.

Acting as Sherlock requires a great mental effort keeping track of the
rooms.

A number of items can be memorised in order by associating each item with
a place on a familiar journey.

For example 20 geometric shapes could be visualised at various places on the
journey from bed to school each morning. The shapes could be visualised at
places such as the bathroom, kitchen bus stop etc.

Students challenge each other to memorise the order and names of 20 shapes
such as pyramid, sphere, octagon etc.

One technique for remembering a list of items in order is by associating each item with an item from the following children's rhyme:

One is bun

Two is shoe

Three is tree

Four is door

Five is hive

Six is sticks

Seven is heaven

Eight is gate

Nine is line

Ten is pen etc.

This activity could start by collecting from the students a list of ten
popular video films. Students are then asked to conjure up in their minds a
crazy image of the item from the list above involved in the action of the
film.

Eg if the fifth film is The Sound of Music; a student might picture Julie
Andrews being chased over the Austrian Mountains by a swarm of angry bees.

Working in pairs students could practice this technique by memorising ten
items from a shopping list

Many mind reading tricks involve a "plant" in the audience secretly giving information to the mind reader. The way this information is given often involves mathematical codes or systems.

Nine objects are arranged in a 3 by 3 grid formation

While the magician isn't looking, the students are asked to choose an
object an concentrate on it. The magician can quickly identify the chosen
object by feeling the thought vibrations coming from it ... well not really.
One of the students has previously been asked to act as the "plant" giving
the magician a secret sign. Students are asked to work out some secret signs
which could correctly identify one of the nine objects.

One system could be that the plant and the magician agree to define each
object in terms of its row and column (like a matrix). The plant uses the
position of their head to indicate the row and arms to indicate the column.

Students are encouraged to invent similar (more complex) illusions.

(alternatively this trick could be performed using nine buckets placed
upside down on the floor with an item being put under one while the magician
isn't looking.)

"**Black Magic**" is a well known old party trick
in which a person apparently mind reads to find an object previously
selected by an audience. An accomplice helps by pointing to various objects
asking "is this it?". The mind reader always says no till after the
accomplice has pointed to a black object; the next object to be pointed out
will be the chosen object.

Students could devise similar mind reading tricks using number codes of
other systems.

One person thinks of a number 1 - 20. They are asked which cards contain their number. The magician can work out the number by adding up the top left numbers on each of the selected cards.

How does it work? The numbers in the top left of each card are powers of two and any number can be expressed as a combination of powers of two. this can be shown to be the basis of the binary system.

This trick could be described by a teacher without showing the students a set of cards. Students challenged to make their own set of cards and extend for numbers greater than 20 (the trick works better the more numbers there are on each card). Students should practice performing this trick on each other using their own set of cards

Here's a more detailed Interactive version

The Online Psychic

Wouldn't it be impressive if you could instantly write down a 4x4 magic
square giving any total that a friend suggests. It can be done ... there's a
trick to it!

First you have to memorise the basic 4x4 magic square which gives a total of
34. (Memorising this could lead to some interesting multisensory work!)

14 | 1 | 12 | 7 |

11 | 8 | 13 | 2 |

5 | 10 | 3 | 16 |

4 | 15 | 6 | 9 |

Let's suppose your friend chooses the number 57. Firstly subtract 33 from
this giving 24.

Now replace the numbers 1, 2, 3 and 4 in the basic square with 24, 25, 26
and 27 in that order.

You now have a magic square with 57 as the sum of each column, each row,
each diagonal and each 2 by 2 square within the larger square.

Why does this work? Look at the positions of the numbers 1 - 4. How are they
significant?

Try some of the other areas of the Transum Maths website:

- Starter of the Day
- Shine+Write
- Fun Maths
- Maths News
- Random Names
- Maths on YouTube
- Laptops in Lessons
- Class Admin
- National Curriculum

Comment recorded on the 2 May 'Starter of the Day' page by Angela Lowry, :

"I think these are great! So useful and handy, the children love them.

Could we have some on angles too please?"

Comment recorded on the 7 December 'Starter of the Day' page by Cathryn Aldridge, Pells Primary:

"I use Starter of the Day as a registration and warm-up activity for my Year 6 class. The range of questioning provided is excellent as are some of the images.

I rate this site as a 5!"

Comment recorded on the 12 July 'Starter of the Day' page by Miss J Key, Farlingaye High School, Suffolk:

"Thanks very much for this one. We developed it into a whole lesson and I borrowed some hats from the drama department to add to the fun!"

Comment recorded on the 19 October 'Starter of the Day' page by E Pollard, Huddersfield:

"I used this with my bottom set in year 9. To engage them I used their name and favorite football team (or pop group) instead of the school name. For homework, I asked each student to find a definition for the key words they had been given (once they had fun trying to guess the answer) and they presented their findings to the rest of the class the following day. They felt really special because the key words came from their own personal information."

Comment recorded on the 17 November 'Starter of the Day' page by Amy Thay, Coventry:

"Thank you so much for your wonderful site. I have so much material to use in class and inspire me to try something a little different more often. I am going to show my maths department your website and encourage them to use it too. How lovely that you have compiled such a great resource to help teachers and pupils.

Thanks again"

Comment recorded on the 26 March 'Starter of the Day' page by Julie Reakes, The English College, Dubai:

"It's great to have a starter that's timed and focuses the attention of everyone fully. I told them in advance I would do 10 then record their percentages."

Comment recorded on the 17 June 'Starter of the Day' page by Mr Hall, Light Hall School, Solihull:

"Dear Transum,

I love you website I use it every maths lesson I have with every year group! I don't know were I would turn to with out you!"

Comment recorded on the 3 October 'Starter of the Day' page by Mrs Johnstone, 7Je:

"I think this is a brilliant website as all the students enjoy doing the puzzles and it is a brilliant way to start a lesson."

Comment recorded on the 1 February 'Starter of the Day' page by Terry Shaw, Beaulieu Convent School:

"Really good site. Lots of good ideas for starters. Use it most of the time in KS3."

Comment recorded on the 5 April 'Starter of the Day' page by Mr Stoner, St George's College of Technology:

"This resource has made a great deal of difference to the standard of starters for all of our lessons. Thank you for being so creative and imaginative."

Comment recorded on the 9 October 'Starter of the Day' page by Mr Jones, Wales:

"I think that having a starter of the day helps improve maths in general. My pupils say they love them!!!"

Comment recorded on the 19 November 'Starter of the Day' page by Lesley Sewell, Ysgol Aberconwy, Wales:

"A Maths colleague introduced me to your web site and I love to use it. The questions are so varied I can use them with all of my classes, I even let year 13 have a go at some of them. I like being able to access the whole month so I can use favourites with classes I see at different times of the week. Thanks."

Comment recorded on the 25 June 'Starter of the Day' page by Inger.kisby@herts and essex.herts.sch.uk, :

"We all love your starters. It is so good to have such a collection. We use them for all age groups and abilities. Have particularly enjoyed KIM's game, as we have not used that for Mathematics before. Keep up the good work and thank you very much

Best wishes from Inger Kisby"

Comment recorded on the 2 April 'Starter of the Day' page by Mrs Wilshaw, Dunsten Collage,Essex:

"This website was brilliant. My class and I really enjoy doing the activites."

Comment recorded on the 14 September 'Starter of the Day' page by Trish Bailey, Kingstone School:

"This is a great memory aid which could be used for formulae or key facts etc - in any subject area. The PICTURE is such an aid to remembering where each number or group of numbers is - my pupils love it!

Thanks"

"This has saved me a lot of time over my summer holidays - thank you."

D. Boyce, Rohwell

Monday, August 26, 2013

"Thank you and blessings."

Sadhana Bhat, Mpsmkbh@gmail.com

Saturday, October 19, 2013

Do you have any thoughts about the mathemagic above? Do you know any mathemagical tricks that we could share with the world on this page? Click on the link below to submit your ideas.

Click here to enter your comments.