Prime Numbers and Factors

Image Source

Today we are going to use Erastothene’s Sieve to find the prime numbers up to 100. You will use the “Count By” app on the iPods or iPads or your netbook with the interactive 100 chart program. Color in the corresponding numbers on your paper 100 chart.

Prime numbers are numbers with exactly two factors – you can divide a prime number by one or itself, but no other number, to get a whole number. The number one only has one factor, so it is not a prime number. So, 2 and 3 are the first two prime numbers. 4 is not a prime number because it has three factors (1, 2 and 4). Circle the prime numbers on your paper chart and stick it firmly in your work book to refer to later.

Multo – a maths game for middle years

multo_cards

This fun game helps students to remember their times tables and understand what prime numbers are. Print out cards with each of the timestables from 0 x 0 to 9 x 9. Students draw up 4 x 4 grids and place 16 numbers from zero up to 81 in the boxes. The teacher calls out the timestable cards randomly, while students cross the answer the sum called off their grids. If they get four numbers in a line (column, row, diagonally) or four corners they call “MULTO“!

Which numbers should not be used in the grids and why? What numbers are most likely to be called and why?

The Fibonacci numbers

Golden Sunflower

Can you see a spiralling pattern in the image above? It is a similar kind of pattern you might see on pine cones, pineapples, the arrangement of leaves and the petals of flowers.

Can you continue this sequence? 0, 1, 1, 2, 3, 5, 8, 13, 18, 31, …………

If you count the numbers of tiny flowers and seeds in each sunflower head, starting in the centre and working your way out, you will find, more or less, this is the numerical pattern that is formed. Plants don’t know the Fibonacci series, so why do they grow this way? Well, it turns out that this is the most efficient way to pack many objects into a small space. Petals into a flower, seeds into a fruit, bracts into a cone and leaves onto a branch.

Another amazing thing about these numbers, is that when you study the ratio of one Fibonacci number to the next, you get closer and closer to one peculiar number, an irrational number, called “phi” or the “golden ratio”. Try these ratios (fractions) on your calculator:

1/1; 2/1; 3/2; 5/3; 8/5; 13/8; 21/13; 34/21; ………….

If you convert these to decimal numbers what happens? I’d love to read your answers in the comments section. If you are interested in finding out more about the beauty of maths in nature, check out this YouTube video, “Nature by Numbers”.

Read more at Science Ray “The Fibonacci Sequence in Nature – The Mystery of the Golden Ratio” and  at How Stuff Works “Fibonacci Numbers“.