This is based on multiplication modulo 6. Down the left and across the top put the numbers 1 to 6 (or 1 to 5 and 0) and multiply mod 6. Which colour for each number?
1 Comment
Pascal's Triangle in arithmetic modulo 4.
1 = green, 2 = brown, 3 = yellow, 4 = red. Year 7 (grade 6) students and up quickly get the idea of modular (clock) arithmetic, and can have fun colouring Pascal's Triangle to any modulus. Interesting patterns always emerge. It would make a good school Christmas Competition. This painted in watercolours, Paul Jackson Feb 2019 Wales scored 38 points in this game against Italy. A converted try is worth 7 points, a try 5 points and a penalty (or drop goal) 3 points. All prime numbers! List the possible ways Wales scored their points.
In fact, there's an interesting investigation here if you start from the lowest score and list the possible ways of scoring it. What is the lowest rugby score that can be scored in 2 ways? 3 ways? and so in. There are some surprising results. What is so special about 38 points? There are 3 ways of scoring in rugby - a try, a conversion or a penalty. The result of this game was Wales Women 15 Italy Women 22. Given that Wales scored 2 tries, one conversion and one penalty, and Italy scored 4 tries and a conversion, form two simultaneous equations in 3 unknowns. The number of points for each way of scoring must be a positive integer. Find the possible scoring systems (there is more than one!).
This would be a good trial and error problem for younger students, link to intersection of planes for older kids. A nice little problem from an Aussie Rules Footy game.
I was hoping Essendon might score once more to make the equations more difficult to solve! As it is, it’s a nice intro to simultaneous equations. The score was: St Kilda 16, 13 (109) Essendon 9,9 (63). There are two ways of scoring. St Kilda scored 16 of one and 13 of the other for a total of 109 points. Form two simultaneous equations to find how many points each scoring type earns. Other games (Rugby Union, Rugby League and ??) have more than one scoring situation, so easy to adapt. Extension: Had St Kilda scored a few more times, what score would have failed to give a unique solution? |
Author -
|