2351 /www/nrich/html/content/id/2351/ 1 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <p>You may know that opposite faces of a dice add up to $7$, but did you know that there are two different types of dice?<br></br> Here are two dice, a right-handed one and a left-handed one:</p> <p style="text-align: center;"><mdo:image align="top" alt="right-handed and left-handed dice" bgcolor="" height="226" src="image_01.gif" width="456"></mdo:image></p> <p>Decide whether the dice below are right-handed or left-handed:</p> <p style="text-align: center;"><mdo:image align="top" alt="die with 5 on top face, 1 on near face, 3 on right face. Die with 3 on top face, 2 on near face and 6 on fight face" bgcolor="" height="201" src="image_02.gif" width="463"></mdo:image></p> <p> </p> <p>Now try these - they are more difficult.</p> <p> </p> <p style="text-align: center;"><mdo:image align="top" alt="Die with 6 on top face, 5 on near face and 3 on right face. Die with five on top face, 6 on near face and 3 on right face" bgcolor="" height="196" src="image_03.gif" width="459"></mdo:image></p> <p class="editorial">This problem is taken from the book "Mathematical Activities from Poland" published by <a href="http://www.atm.org.uk/">ATM</a>.</p> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <p class="editorial">Many of you sent in correct answers to this problem, but not all were as well explained as these. Wilson from Beecroft Primary School wrote to say:</p> <p>To work out the whether the dice are right- or left-handed, I pictured the dice in my head and then I matched them up with the pictures.</p> <p class="editorial">Philip from Woodfall Junior School also took this approach and says:</p> <p class="standard">You can mentally rotate each die (finding the missing numbers by using the knowledge that opposite faces add up to seven) so that this happens, and then you can see if the die is right-handed, with the two at the front, or left-handed, with the three at the front.</p> <p class="editorial">April from Springfield Junior School explains exactly what she visualised:</p> <p>1. Right-handed die<br></br> Roll it backwards so the $5$ is at the back and the $1$ is on the top. The front face will be $2$ because $5+2=7$. $3$ will still be on the right.</p> <p>2. Right-handed die<br></br> Roll it to the right so the $6$ is on the bottom. That means $1$ is on the top because $6+1=7$. $3$ is on the right and $2$ stays at the front.</p> <p>3. Right-handed die<br></br> Roll it backwards $2$ times so the $5$ is at the back and the 6 is on the bottom. The top is $1$ because $6+1=7$, and the front is $2$ because $5+2=7$. $3$ stays on the right.</p> <p>4. Left-handed die<br></br> Roll it forwards so the $6$ is on the bottom. The top is $1$ because $6+1=7$. The $5$ moves from the top to the front. Turn it left so the five moves to the left hand side and the $3$ moves to the front. The right hand side is $2$ because $5+2=7$.</p> <p class="editorial">This is a great step-by-step way of approaching the problem, April. Well done.</p> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <h3><span style="font-weight: bold;">Why do this problem?</span></h3> <div><a href="http://nrich.maths.org/2351&amp;part=">This problem</a> encourages children to explore dice in more detail.  Even though they may use them frequently, they may not have thought about a dice's properties before.  They will be challenged to visualise the dice but making nets of cubes might also be helpful. </div> <br></br> <br></br> <h3>Key questions</h3> <div>What do opposite sides of the dice add to?</div> <div>Can you imagine turning the dice so that you can compare it with the pictures of the right-handed and left-handed dice more easily?</div> <div>If the $1$ is at the top of the dice and the $2$ facing you, where is the $3$ on the right-handed dice/left-handed dice?</div> <div>Have a look at the dice in our classroom, are they left-handed or right-handed?</div> <br></br> <h3>Possible support</h3> <div>If learners are having trouble with the visualisation and you don't have left-handed and right-handed dice, they could stick spots onto cubes to help.   Alternatively, print off <a href="/content/id/2351/printable.doc">this downloadable word document</a> which has a net of a right-hand dice on the first page and a net of a left-handed dice on the second.</div> <br></br> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <p>If you are having trouble with the visualisation and you don't have left-handed and right-handed dice, you could stick spots onto cubes to help.</p> <p>Alternatively, print off this <a href="/content/id/2351/printable.doc">downloadable word document</a> which has a net of a right-hand dice on the first page and a net of a left-handed dice on the second.</p> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> <p> First dice - right-handed </p> <p> Second dice - right-handed </p> <p> Third dice - right-handed </p> <p> Fourth dice - left-handed </p> </mdoxml> 2 4 0 1 0 0 0 Which of these dice are right-handed and which are left-handed? Using, Applying and Reasoning about Mathematics Visualising Mathematics Tools Dice