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A Few
Favorites and Why

These are free to download
and use.

**1. Numatzee**

I created some
new challenges in the wonderful game called
Yahtzee. The new version has number patterns and
collections and is played with six 0-9 dice. The
players still have three throws each but can opt
to use all 6 dice or just 5. The explanation of
the pattern is important. I usually add the rule
that die numbers can be joined, so, for example a
2 and a 3 can be joined to make 32.

Here is the template
to print and copy for individual or teams to play.
I like groups of 4 and two teams of two. This
causes collaboration.

2. Triangular
Numbers

These numbers are
very important because they link to so many different
problems and open up a myriad of different formulae and
interpretations.

Here is the file.
Do not think this is simple and can be done quickly or
skipped.

The new ASSESSMENTS expect connections between strands
and this is a powerful resource to support this journey.

Sum of n Natural or Counting Numbers 1+2+3+4+5+... n =
n(n+1)/2

This formula can be established by looking at the
pattern

1

1+2

1+2+3

1+2+3+4 etc which is reinforced through out teh resource
in different contexts.

Depending on where we use the /2 in the formula n(n+1)/2
we get two different views...

1. Sum = middle number x number of numbers = (n+1)/2 x n

A useful insight here is that the middle number of an
ordered set of data is the median. So a formula to find
the middle number is (n+1)/2. [Why add 1?]

2. Sum = n x (n+1) and then divide by 2. So this
means take the last number and then multiply it by next
one and then half this product.

For example the Sum of the first 9 Natural number is 9 x
10 all divided by 2 = 45.

3. This is also how Gauss worked out the sum of the
first 100 numbers with a small difference. He
wrote the same series in reverse order and added.

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