12 12 12

The 12th December 2012 12.12.12Wow – what a day!

We wont see this for another 100 years – the 12th of December 2012 – 12.12.12

We’ve been spoilt! For the last twelve years we’ve had a special day every year, from 01.01.01 ’till today 12.12.12  and many other interesting dates in between like 10.11.12 but they’re going to get much more rare from here on in.

But its not all doom and gloom! We don’t have to wait until 01.01.(21)01 for the next interesting date.

In less than a year we’ll be enjoying 11.12.13

The second of February 2022 gives us 2.2.22, the third of March 2033: 3.3.33 and so on.

And, as long as you’re not American (they write the month before the date) we can look forward to:

1.2.34

in a little over 21 years time!

But enough of the future, enjoy today 12/12/12

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A Christmas Puzzle

A Christmas Puzzle

On the first day of Christmas my true love gave to me …

You all know the song, Five Gold Rings, Four Calling Birds, Three French Hens, Two Turtle Doves and a Partridge in a Pear Tree etc.

But what I want to know is, in total, how many gifts did my true love give me over the twelve days of Christmas?

Answers on a postcard … (or in the comments section!)

Two Turtle Doves
Two Turtle Doves

Thinking Caps on and Merry Christmas!

(pictures courtesy of dots and spots)

Spoiler alert: If you want to see the solution, click here, but why not try and solve the problem yourself first.

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Percentages of …

 

10% Sales Tag - find 10% of an amount

To find a percentage of any amount, start by finding 10%

Finding 10% is easy – just divide the amount by 10

So, to find 10% of 120, all you do is 120 ÷ 10 = 12

So,

10% of 120 = 12

30% of

If we need to find 30% of an amount, we still start by finding 10% (remember: to find 10%, just divide the amount by 10).

To go from 10% to 30% we just multiply by 3.

Example:

Find 30% of 80

Answer:

First, find 10% of 80:

10% of 80 = 80 ÷ 10 = 8

30% = 10% x 3, so

30% 0f 80 = 8 x 3 = 24.

 

 

Find 5% of an amount

Finding 5% of an amount is not much harder.

Again start by finding 10%.

5% is just half of 10%, so when you’ve found 10%, just halve it (divide by 2) to get 5%.

Example

Find 5% of 260

Answer

10% of 260 = 260 ÷ 10 = 26

5% = 10% ÷ 2

so 5% = 26 ÷ 2 = 13

65% Sales Tag

And now we can put that all together in a “tough” (only joking!) example!

Example

Find 65% of 180

Answer

First (as ever!) find 10%:

10% of 180 = 180 ÷ 10 = 18

so

60% of 180 = 10% x 6 = 18 x 6 = 108

Now find 5%

5% of 180 = 10% ÷ 2 = 18 ÷ 2 = 9

… and …

65% = 60% + 5%

=  108 + 9 = 117

So,

65% 0f 180 = 117

Easy!

Remember:

To find a percentage of any amount start by finding 10%

To find 10% of an amount, simply divide by 10

If you want to find out more about percentages, and how to swap between fractions, decimals and percentages, then you may want to read this.

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BODMAS

BODMASBODMAS – one of my favourite topics to teach.

2 + 3 x 4

Does it equal 20 or does it equal 14?

We can’t have two answers to one question – that would cause all sorts of confusion!

So, back in the day, mathematicians got together and agreed to BODMAS – the order in which we do operations.

The B is for brackets – we do them first.

The O is the confusing one, it stands for “Order” which means squared, or cubed or to the power 7 etc: 52 is an example of an order, and means 5 squared, or 5×5 = 25.  Some people use the term Indices instead of Order and so talk of BIDMAS, not BODMAS, but it all means the same.

As we’re talking maths, you’ve probably guessed that the other letters stand for

D – Division

M – Multiply

A – Addition

S – Subtraction

So, going back to our question from above:

2 + 3 x 4

there are no brackets, orders or divisions, so the first thing we do is multiply

2 + 3 x 4 becomes …

2 + 12

So the correct answer is 14.

Remember – BODMAS tells us the order in which we do a sum.

If you want to practice BODMAS  you can find some questions on this worksheet.

Or you could print out and try this BODMAS puzzle.

Or you could try the interactive version of the same puzzle

Here are two great videos that help explain BODMAS.

Boys, in particular, seem to like this one:

 

… and a little warning, the tune from this one could end up being in your head all day long:

So now you know all about BODMAS, here’s a little puzzle for you to try. Can you arrange all of the digits  from 1 to 9 in each of empty boxes below? You can only use each number once. Remember the rules of BODMAS!

 

*** UPDATE The puzzle below is now available on pdf for you to download and print: BODMAS Worksheet and also as a ‘draggable’ puzzle for PC, iPad, Whiteboard or whatever: interactive draggable BODMAS puzzle ***
BODMAS puzzle

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Numbers!

The Number 5

Visualising Numbers

We all see numbers differently, but I recently stumbled upon a great website for visualising numbers:

http://www.datapointed.net/visualizations/math/factorization/animated-diagrams/

All non-prime numbers are made up of prime numbers – this is often called prime factorisation, in maths lessons we ask pupils to …

“… write [some number] as the product of its prime numbers in index form”

This great website starts at the number 1, and works its way up through the integers, in an animated dance.

The number five is shown above, this is how it shows the number 18:

Number 18 - 2 x 3 x 3can you see how its displayed?

Its shows 3 lots of 2, 3 times.  Or 2 x 3 x 3 (which just happens to equal 18)

And the dance goes on and on and on …

Here’s a pic of the number 1,395 or 31 x 5 x 3 x 3:

1395 or 31 x 5 x 3 x 3It’s really quite beautiful to watch and very, very clever in the way that it breaks each number down into its prime factors.

Don’t take my word for it, visit Dance, Factors, Dance now.

Cool.

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