Dotty Six

7337 /www/nrich/html/content/id/7337/ 1 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">Watch this video to see the game being played. Can you work out the rules? <div style="text-align: center;"> </div> <div style="text-align: center;"> </div> <video controls="controls" height="300" src="Dotty.mp4" style="padding-left: 144px;" tabindex="0" width="400"></video> You need a partner, a $1$-$6$ dice and a grid like this; <mdo:image src="grid%20of%209.jpg"></mdo:image> Take turns to throw the dice and draw that number of dots in one of the boxes on the grid. Put all of your dots in one of the boxes. You can't split them up and you can't have more than six dots in a box. When a box is full, you could put a tick in the corner like this: <mdo:image src="filled%20in%20dotty%206.jpg"></mdo:image> Keep going until there are three ticks in a row or column or diagonal. The winner is the person who puts the last tick. Now, can you change the game to make your own version? <a href="http://nrich.maths.org/8002">Click here for a poster of this problem</a>.</mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">We had a number of solutions sent in from Bomere Heath School, namely, Holly, Annalise, Noah and Guy, Chris, Alex and Eddi, Sam and Kyle A number of them said , we played dotty six and once we had got the hang of it we mooved on to dotty ten. Noah and Guy wrote; in dotty six you have two get three sixes in a row to win the game . We played dotty 10 also and found that it was much easier . To win dooty ten you need a lot of luck and to use strategy. Dotty ten is were you have $9$ squares and roll a dice and try and fill three boxes in a row full of sixes. We also heard that; Alex won three times and Eddi won one game. Keir and James from St. Andrew's School in Glasgow wrote in to say; We found the best place to start was in the middle because you can go in any direction and that gives you more chances to win. It was easier to fill in boxes if you chose wisely and block your opponent so they stand less of a chance of winning. Lucy from North Molton Primary  School in England had a good idea; I have made a new version of Dotty six. First instead of one dice, you use two $1-6$ dice each and have a square of six by six. Also what is different both of the people roll at the same time and pick a square each, the squares will hold twelve dots unlike the other one that only held six. You win when your colour dots go in an L shape, in a line or diagonally. Once a box is full put an X in the corner! You also can’t split up your numbers. Thank you for those wise words Keir and James and Lucy's new idea. </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><div class="embed"> <h2>Dotty Six</h2> You need a partner, a $1$-$6$ dice and a grid like this; <mdo:image src="grid%20of%209.jpg"></mdo:image> Take turns to throw the dice and draw that number of dots in one of the boxes on the grid. Put all of your dots in one of the boxes. You can't split them up and you can't have more than six dots in a box. When a box is full, you could put a tick in the corner like this: <mdo:image src="filled%20in%20dotty%206.jpg"></mdo:image> Keep going until there are three ticks in a row or column or diagonal. The winner is the person who puts the last tick. Now, can you change the game to make your own version? </div> <h3>Why play this game?</h3> <a href="http://nrich.maths.org/7337&part=">The game</a> as introduced is intended for KS1 children who are just beginning to become confident with small numbers. However there are many variations, some suggested below, that make it suitable for older children. As with many of the NRICH games, consolidation of basic number facts is combined with an element of strategic thinking. <h3>Possible approach</h3> With very small children you may wish to play the game with a small group first before encouraging them to play in pairs. If you have access to a projector and screen, you may wish to use <a href="/content/id/7337/Dotty6.ppt">the powerpoint animation</a> with older children. If that is not possible, choose a child or another adult to play the game with you somewhere where everyone can see what's going on. The children watch in silence, having been prompted to watch closely to see if they can work out what the rules of the game are. You may need to show the animation more than once. You can find some Dotty Six grids here as a <a href="/content/id/7337/Dotty%20six%20grids%207337.doc">Word</a> or a <a href="/content/id/7337/Dotty%20six%20grids%207337.pdf">PDF</a> file for recording the results of the game. Take suggestions about what the rules may be, perhaps recording them centrally once everyone has agreed. They are: <ul> <li>take turns to throw the dice and put the dots into a box</li> <li>you can put your dots anywhere but you can't have more than six dots in any one box</li> <li>you have to put all your dots in one box</li> <li>you win if you finish the line, row or diagonal of complete boxes</li> <li>if you can't go you miss a turn.</li> </ul> When everyone has played a few times, you can change the game: <ul> <li>by making the total different ($10$, $12$, $15$, $20$)</li> <li>by giving different dice (with only even numbers, only odds, dice to $10$ etc)</li> <li>by making the grid bigger ($4$ by $4$)</li> </ul> <h3>Key questions</h3> Where will you put your dots? Why? How do you know where to put your dots? How many more do you need to win? <h3>Possible support</h3> Small children can use multilink or counters, or Numicon, on a large grid (available as a <a href="/content/id/7337/DottySixLargeGrid.docx">Word document</a> or <a href="/content/id/7337/DottySixLargeGrid.pdf">pdf</a>), rather than recording with dots on a small one. They could begin with six counters in each box and take away the number thrown on the dice. <h3>Possible extension</h3> This is a great game for children to use their creativity and to work at a level at which they feel comfortable. The sophistication of their recording will change with their confidence. Provide a range of dice including blank ones. They could: <ul> <li>change the total in each box </li> <li>make the winner the first to complete a whole row that adds to a certain total (e.g. $20$)</li> <li>change the shape of the grid (triangles rather than squares perhaps)</li> <li>use a different sort of number - fractions, decimals, percentages ...</li> <li>change the rules completely.</li> </ul> <div>Encourage them to write the rules out for someone else to follow. Perhaps they could submit them to NRICH!</div> <div> </div> <div>You can follow Dotty Six on YouTube <a href="http://www.youtube.com/watch?v=c5v_loMvaLY">here</a>.</div> </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">Children at Hythehill Primary sent in some strategies for winning the game: If there were two sixes in a row, put your dots out of the row. Start in the centre box. The person that goes first should put the dots in a corner. Helen and Molly from Moorfield said: We think that when you play Dotty Six that you play it with two different coloured pencils and have one each so that you don't get confused. Many of you sent in your suggestions for changing the rules of the Dotty Six game. Here is a selection of those we received: Play to $12$ dots in each box, instead of $6$, still with one dice. This means that one person cannot win a box in one go. It also makes the game longer. Joe and Caitlin from St Michael's Players have a dice each. They roll at the same time. The person with the highest score on the dice places their dots on the grid. If both players throw the same, the person with the highest score last round places again. Play to $10$ in a box. The game is longer and harder - it's more competitive. Charlie and Kai from St Michael's Start by putting a random number of dots (from $0$ to $5$) in each box. Then play as before. This makes the game shorter, but you have to throw an exact number more often. Seb and Alex from St Michael's Play with two dice. You can use the scores to calculate a total using addition, subtraction, multiplication and division. $12$ wins a box, but you can place more and then subtract. This is a much more complex version. Sam and April from St Michael's Play as before but a line can only be won by winning all three boxes (as in noughts and crosses). This makes the game feel fairer, but can result in a draw. Molly and Asher from St Michael's Use a $4$ x $4$ grid and win by winning the fourth box in a line. This makes the game longer. Adding a rule to win a box by getting to $7$ makes it slightly harder still. Charlotte and Tiger-Lily from St Michael's Each player will have two boxes, one with the number one in the corner and the other with the number two in. You will also need two dice. In turn, each player rolls both dice and can add, subtract, multiply or divide to make a total. Put this in your first box. Roll both dice again and use add, subtract, multiply or divide to make another total. Put this in your second box. Then the other player has a go. The aim is to get a total of ten in your first box and twenty in your second box. You can add or subtract your numbers to your total in the box. The winner is the first person to get ten in their first box and twenty in their second box. April from St Michael's To make the game harder we also think that you should roll two die and $18$ to be the maximum number of dots in a square or have a $16$ square grid. Helen and Molly from Moorfield There isn't really a solution to this activity however we are going to share with you some of the ways that it could be adapted. You could make the grid bigger and use a bigger numbered die or play with more people. Harry and Jack from Moorfield Another variation of the game could be that each person is not allowed to draw dots on the same row as the person before them. The player who is stuck and cannot do their turn loses! Karnan from Stag Lane Juniors We tried lots of variations on the rules 1.You must split the dots into two boxes (this means if you roll $1$ you must miss a turn). 2. Different sized grids eg $4$x$4$, $5$x$5$, $6$x$6$ 3. Different totals for the box eg $7$, $9$, $15$ Children at Hythehill Primary These all sound very good suggestions. Well done!</mdoxml> 2 3 1 1 0 0 0 Dotty Six Dotty Six is a simple dice game that you can adapt in many ways. Admin Upper primary mapping document Admin Lower primary mapping document Numbers and the Number System Counting Numbers and the Number System Representing numbers Calculations and Numerical Methods Addition & subtraction Numbers and the Number System Reading and writing numbers Information and Communications Technology Video