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Our focus over the last week has been number patterns. We've been exploring our understanding of number sequences and have developed our knowledge of the stratergies we can use to find them.

You task is to go to the following sites (in order). Read the information then complete the activities. Make sure you do the quiz.

Once you've done this come back to this page and record you reflections on the discussion section of this page.
Use the sentence starters:
  • I learnt ...
  • I now understand ...
  • I want to find out more about ...


Common Number Patterns

Pascal's Triangles

Sequences

Fibonacci Sequence

BBC schools - number patterns

Toy Theater


Finally for an extra challenge go to the MathsFiles Excel . Read the instructions before carefully downloading the number sequence xl file. After opening up the file in excel make sure you allow the macros then work your way through. Beginning at the easy level of difficulty and only move on once you feel confidant. Again don't forget to record your reflections in the discussion section of this page, as a small group we can all learn from each other.

Further Information:
Remember some patterns are obvious, 2, 4, 6, 8 .... or 5, 10, 20, 40, 80 ...
In these sequences each new number can be expressed as the nth number of the sequence. In the first example, the nth number = 2n.
To find the 1st number, put n = 1 into the equation, to find the 3rd number, replace the n with 3:

3rd number = 2 × n or 2 × 3 = 6.

Number sequences are not just based around one of the four operations (+, -, ×, ÷) but can include a combination of operations including brackets, to power of and square root symbols.

For Example:
What if we want to find the 5th, 9th or even 20th number of this sequence 0, 3, 8, 15, 24?
To find the answer, we experiment by considering some possibilities for the nth number and seeing if they fit (this is Guess and Check):
n
=
1
2
3
4
5

=
1
4
9
16
25
n² - 2
=
0
3
8
15
24
The last is our sequence, so the nth number is found by is n² - 1.
There is no easy way of working out the nth term of a sequence, other than to try different possibilities (this is Guess and Check).