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2011-02-01T00:00:01
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<p> </p>
<div style="text-align: center;"><mdo:image src="The%202%20red%20dice%20eazyDr.jpg"></mdo:image></div>
<div>Here are two dice.<br></br>
</div>
<div>If you add up the dots on the top you'll get $7$.<br></br>
</div>
<div>Find two dice to roll yourself. Add the numbers that are on the top.<br></br>
What other totals could you get if you roll the dice again?<br></br>
<br></br>
</div>
<div class="framework"><strong>Notes for adults</strong><br></br>
<br></br>
You will need two dice to play this game. The children can count the total number of spots on the dice or add them together using number facts they already know.<br></br>
Record the results and explore the different totals that you can get.<br></br>
Help them to find all the possible combinations.</div>
<div><br></br>
<br></br>
</div>
<div>
<pre>
Photograph acknowledgement.
http://imgisland.com/wallpapers/3D/red_dice.jpg
</pre></div>
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Joe Densley from Clutton Primary had this send for hom with the comments;<br></br>
<br></br>
Joe worked systematically to find all the possible combinations for throwing 2 dice. He identified the lowest possible score of 2 and the highest score of 12. At first he thought that 4 was the lowest score and was then able to correct himself.
<div style="text-align: center;"><mdo:image src="2dice.jpg"></mdo:image></div>
<div>Robert from St.Michael's Primary West Midlands sent in this very thorough solution;<br></br>
<br></br>
There are eleven possible solutions to 'Two Dice'.<br></br>
Let's say Dice One is 'A' and Dice Two is 'B'.<br></br>
<br></br>
They are as follows :<br></br>
<br></br>
$2$ (A=$1$ and B=$1$)<br></br>
$3$ (A=$1$ and B=$2$; A=$2$ and B=$1$)<br></br>
$4$ (A=$1$ and B=$3$; A=$2$ and B=$2$; A=$3$ and B=$1$)<br></br>
$5$ (A=$1$ and B=$4$; A=$2$ and B=$3$; A=$3$ and B=$2$; A=$4$ and B=$1$)<br></br>
$6$ (A=$1$ and B=$5$; A=$2$ and B=$4$; A=$3$ and B=$3$; A=$4$ and B=$2$; A=$5$ and B=$1$)<br></br>
<br></br>
$7$ (A=$1$ and B=$6$; A=$2$ and B=$5$; A=$3$ and B=$4$; A=$4$ and B=$3$; A=$5$ and B=$2$; A=$6$ and B=$1$)<br></br>
<br></br>
$8$ (A=$2$ and B=$6$; A=$3$ and B=$5$; A=$4$ and B=$4$; A=$5$ and B=$3$; A=$6$ and B=$2$)<br></br>
<br></br>
$9$ (A=$3$ and B=$6$; A=$4$ and B=$5$; A=$5$ and B=$4$; A=$6$ and B=$3$)<br></br>
$10$ (A=$4$ and B=$6$; A=$5$ and B=$5$; A=$6$ and B=$4$)<br></br>
$11$ (A=$5$ and B=$6$; A=$6$ and B=$5$)<br></br>
$12$ (A=$6$ and B=$6$)<br></br>
<br></br>
Two $1-6$ dice will not add up to any other number. This solution shows the<br></br>
amount of numbers possible to make. However there are 36 possible<br></br>
combinations of numbers to create the 11 possible answers.</div></mdoxml>
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<h2>Two Dice</h2>
<p> </p>
<div style="text-align: center;"><mdo:image src="The%202%20red%20dice%20eazyDr.jpg"></mdo:image><br></br>
<br></br>
Here are two dice.<br></br>
</div>
<div style="text-align: center;">If you add up the dots on the top you'd get $7$ !<br></br>
</div>
<div>Roll the dice. Add the numbers that are on the top.<br></br>
What other totals could you get if you roll the dice again?<br></br>
<br></br>
</div>
<div class="framework"><strong>Notes for adults</strong><br></br>
<br></br>
You will need two dice to play this game. The children can count the total number of spots on the dice or add them together using number facts they already know.<br></br>
Record the results and explore the different totals that you can get.<br></br>
Help them to find all the possible combinations.</div>
<div><br></br>
<br></br>
</div>
<div>
<pre>
Photograph acknowledgement.
http://imgisland.com/wallpapers/3D/red_dice.jpg
</pre></div>
</div>
<br></br>
<h3><span style="font-weight: bold;">Why do this problem?</span></h3>
<div>This <a href="http://nrich.maths.org/public/viewer.php?obj_id=150&part=">activity</a> provides a valuable experience for younger pupils to explore some simple additions while finding all possibilities.</div>
<h3><br></br>
What children need to know to play this game</h3>
The children need to be able to roll two dice and identify their score.<br></br>
<br></br>
<h3>Possible approach</h3>
<div>Using a dice with dots on, encourage discussion as to what numbers are represented by the faces of the dice before introducing the challenge itself.</div>
<br></br>
<div>You could support the children to collect their totals on the board. Ask them how they should be arranged and see if they can suggest a systematic way of recording their results. For example, they might start with all the totals that use a $1$. In this way, you can ask the class to talk about the patterns they notice and this will help to reveal any combinations that are missing.</div>
<br></br>
<h3>Key questions</h3>
These questions have been phrased in ways that will help you to identify the children's prior knowledge about both the number concepts involved and the strategies and mathematical thinking needed to solve the problem.
<div>Can you make a bigger/smaller total?</div>
<div>What is the highest total you could make?<br></br>
What is the lowest total you could make?<br></br>
If one dice shows $6$, what could the other dice be showing?</div>
<div>How will you know when you've found all the totals?</div>
<br></br>
<h3>Possible extension</h3>
<div>You could make use of more dice and/or dice with different numbers of faces. Alternatively, consider finding the difference between the two numbers or the product of the two numbers.</div>
<br></br>
<h3>Possible support</h3>
<div>Children who struggle with addition may count the dots to help them but encourage them to articulate the number sentence once they have done so. This will help them to build the visualisations of the numbers as dotty dice patterns which will support their learning of number bonds.</div>
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If one dice shows $6$, what could the other dice be showing?<br></br>
What totals would they give?<br></br>
What could the other dice be if one is a $5$? A $4$?<br></br>
How do you know you've found all the totals?<br></br></mdoxml>
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<mdoxml version="1.0"><div style="text-align: left;">These are all the possible combinations;</div>
<div style="text-align: center;"><mdo:image alt="pic1" height="91" src="Picture%201.jpg" width="339"></mdo:image></div>
<div style="text-align: left;">so the totals available are 2 through to 12.</div>
<div style="text-align: left;"> </div>
<br></br>
<br></br>
<br></br>
pics at: http://illustrator.tutfactory.com/wp-content/uploads/2009/08/271.jpg<br></br>
http://www.shindigz.com/images/itm_img/S04010.jpg<br></br>
http://t3.gstatic.com/images?q=tbn:ANd9GcR9LrtfJXzgv28uYgZxL3VRlvPwvF1bQnCIfbBI94uKAQ-WjgFxsN4ftxxu<br></br>
<br></br>
Solution pre 2012<br></br>
From Debra from Singapore:<br></br>
<br></br>
My solution is: Every number from 2-12 is possible. But there can be different combinations. Like if the total was 4, there would be two combinations: 3+1 and 2+2. If the total was 5, there would be: 2+3 and 4+1.<br></br>
<br></br>
A question to think about next ... Which total are you most likely to get when you roll two dice?</mdoxml>
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Two Dice
Find all the numbers that can be made by adding the dots on two dice.
Calculations and Numerical Methods
Addition & subtraction
Mathematics Tools
Dice
Decision Mathematics and Combinatorics
Combinations
Using, Applying and Reasoning about Mathematics
Working systematically
Admin
Lower primary mapping document