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.