This is a card game I made up where you do basic mental calculations and race your opponent ( 2-4 players). Using Ace -10 cards only. Rules: 7 cards are placed face up for each player and two in the middle. The player who gets rid of their cards first wins. You can put a card in the middle (on top of either pile) when one of your cards is an answer to an expression using the two cards in the middle. eg. if 6 and 2 are in the middle possible cards that can be played are 8 (6+2) or 4 (6-2) or 3 (6 divided by 2) or 2 (6×2) – 12 is the answer but we use the last digit only. Each player has to say the expression as they put the card down. eg 6 twos are 12 – placing the 2. or 6 minus/take/sub 2 is 4. all players play on until no cards can be played. Then the dealer deals each player a card then put one on one of the two middle piles. Players then race to place cards until someone gets rid of all their cards! (4 players start with 6 cards)
We played a few games of this and made up our own versions:
Instead of a race we played in turn – competitively or collaboratively
This activity comes from the great website mathsisfun.com.
Have you ever coloured in a pattern and wondered how many colours you need to use?
There is only one rule
Two sections that share a common edge cannot be colored the same!
Having a common corner is OK, just not an edge.
Let’s start with a simple pattern like a group of nine squares:
What is the minimum colours you need to colour the pattern of nine squares?
A Little More Complicated
How about this one?
How many colours do you need this time?
Even More Complicated
Let’s try another:
How many colours do you need this time?
Nine? Eight? Seven? Six? Five? Four?
Maps
Things get more interesting if we want to colour a map.
Here is a map of Africa, showing six countries and how they border on each other:
Try colouring in the map and see what is the fewest number of colours you need.
Extension
Can you draw a map with 3 countries such that every country has exactly two neighbours, and then colour it.
Can you draw a map with 4 countries such that every country has exactly two neighbours, and then colour it.
Can you draw a map with 6 countries such that every country has exactly four neighbours, and then colour it.
Can you draw a map with 12 countries such that every country has exactly five neighbours, and then colour it.
Further Reading
The proof of the four colour theorem was famously tricky, and comes from graph theory, where mathematicians investigate an equivalent problem of colouring vertices of a network so that no edge has endpoints the same colour. The original four-colour proof was attempted byAlfred Kempe in 1879, but unfortunately Percy John Heawood found an error 11 years later. However his work was not useless, as Percy was able to prove the five-colour theorem (that one can colour a map with no two adjacent regions the sample colour using at most 5 colours) based on Kempe’s work. The four colour theorem was finally proved in 1976 by Kenneth Appel, Wolfgang Haken, and John Koch using a computer to check it. This was the first major theorem to be proved using a computer. They checked around 1500 configurations using about 1200 hours of computer time. Some people were sceptical about a proof using a computer but independent verification soon convinced everyone that the four colour theorem had finally been proved.
We played a simplified version of Cribbage, and looked at some of the interesting maths behind it.
Rules
Game for up to 8 players. Each person is dealt six cards. Players choose four cards to keep. Then one card is turned up in the centre of the table and counts as part of each player’s hand. Ace is considered the low card, and king high. The scoring is as follows:
Fifteens. Each card is assigned a value. Ace through 10 are the face value of the card, and jack, queen and king have value 10. Each combination that totals fifteen is awarded 2 points.
Pairs. Each pair of cards, ace through king, is awarded 2 points.
Runs. Each run of three or more cards is awarded the number of points equal to the length of the run – a run of three is worth 3 points, a run of four, 4 points, and a run of five, 5 points. In this instance runs are not counted in multiple ways. For example, A ,2, 3, 4, 5 is not counted as one run of five, two runs of four and three runs of three, but only as a single run of five.
The person with the highest score after four rounds is the winner.
Example hand (scores 16 points)
Questions to think about:
What do you think is the minimum and maximum scores possible?
Can you find the maximum hand?
Are there any impossible numbers inbetween?
Are some points totals more common than others? How could we know for sure?
See this page for some of the answers to these questions.
