6606
/www/nrich/html/content/id/6606/
2
2011-02-01T00:00:01
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<p>This game follows on from <a href="http://nrich.maths.org/public/viewer.php?obj_id=6605&part=">Nice and Nasty</a><br></br>
Again, there are several games to choose from.<br></br>
<br></br>
Find a partner and a 1-6 dice, or preferably a 0-9 dice if you have one. The interactivity in <a href="http://nrich.maths.org/6717&part=">Dice and Spinners</a> can be used to simulate throwing different dice.<br></br>
<br></br>
Take turns to throw the dice and decide which of your cells to fill. This can be done in two ways:<br></br>
either fill in each cell as you throw the dice or collect all your numbers and then decide where to place them.<br></br>
</p>
<h4>Game 1</h4>
<br></br>
<p>Each of you draw an addition grid like this:<br></br>
<br></br>
<mdo:image alt="3 by 3 addition grid" height="167" src="DiceyOperationsGame1.png" width="172"></mdo:image><br></br>
<br></br>
Throw the dice nine times each until all the cells are full.</p>
<h4>Whoever has the sum closest to 1000 wins.</h4>
<br></br>
<p>There are two possible scoring systems:</p>
<ul>
<li>A point for a win. The first person to reach 10 wins the game.</li>
<li>Each player works out the difference between their result and 1000 after each round. They keep their running total. First to 5000 loses.</li>
</ul>
<p>You can vary the target to make it easier or more difficult.<br></br>
</p>
<h4>Game 2</h4>
<br></br>
<p>Each of you draw a subtraction grid like this:<br></br>
<br></br>
<mdo:image alt="4 by 2 subtraction grid" height="125" src="DiceyOperationsGame2.png" width="197"></mdo:image><br></br>
<br></br>
Throw the dice eight times each until all the cells are full.</p>
<h4>Whoever has the difference closest to 1000 wins.</h4>
<br></br>
<p>There are two possible scoring systems:</p>
<ul>
<li>A point for a win. The first person to reach 10 wins the game.</li>
<li>Each player works out the difference between their result and 1000 after each round. They keep their running total. First to 5000 loses.</li>
</ul>
<div>You can vary the target to make it easier or more difficult, perhaps including negative numbers as your target.</div>
<br></br>
<h4>Game 3</h4>
<br></br>
<div>Each of you draw a multiplication grid like this:</div>
<br></br>
<div><mdo:image alt="3 - 1 multiplication grid" height="125" src="DiceyOperationsGame3.png" width="173"></mdo:image></div>
<br></br>
<div>Throw the dice four times each until all the cells are full.</div>
<br></br>
<h4>Whoever has the product closest to 1000 wins.</h4>
<br></br>
<div>There are two possible scoring systems:</div>
<ul>
<li>A point for a win. The first person to reach 10 wins the game.</li>
<li>Each player works out the difference between their result and 1000 after each round. They keep their running total. First to 5000 loses.</li>
</ul>
<div>You can vary the target to make it easier or more difficult.</div>
<h4>Game 4</h4>
<br></br>
<div>Each of you draw a multiplication grid like this:</div>
<br></br>
<div><mdo:image alt="3 -2 multiplication grid" height="129" src="DiceyOperationsGame4.png" width="218"></mdo:image></div>
<br></br>
<p>Throw the dice five times each until all the cells are full.<br></br>
</p>
<h4>Whoever has the product closest to 10000 wins.</h4>
<br></br>
<div>There are two possible scoring systems:</div>
<ul>
<li>A point for a win. The first person to reach 10 wins the game.</li>
<li>Each player works out the difference between their result and 10000 after each round. They keep their running total. First to 10000 loses.</li>
</ul>
<div>You can vary the target to make it easier or more difficult.</div>
<br></br>
<div>You could introduce a decimal point. The decimal point could take up one of the cells so the dice would only need to be thrown four times by each player. You will need to decide on an appropriate target.</div>
<br></br>
<h4>Game 5</h4>
<br></br>
<div><mdo:image alt="4 -1 division grid" height="85" src="DiceyOperationsGame5.png" width="213"></mdo:image></div>
<br></br>
<div>Each of you draw a division grid like this:</div>
<br></br>
<div>Throw the dice five times each until all the cells are full.</div>
<br></br>
<h4>Whoever has the answer closest to 1000 wins.</h4>
<br></br>
<div>There are two possible scoring systems:</div>
<ul>
<li>A point for a win. The first person to reach 10 wins the game.</li>
<li>Each player works out the difference between their result and 1000 after each round. They keep their running total. First to 5000 loses.</li>
</ul>
<div>You can vary the target to make it easier or more difficult.</div>
<br></br>
<h4>Game 6</h4>
<br></br>
<div>Each of you draw a division grid like this:</div>
<br></br>
<div><mdo:image alt="4 -2 division grid" height="85" src="DiceyOperationsGame6.png" width="254"></mdo:image></div>
<br></br>
<div>Throw the dice six times each until all the cells are full.</div>
<br></br>
<h4>Whoever has the answer closest to 100 wins.</h4>
<br></br>
<div>There are two possible scoring systems:</div>
<ul>
<li>A point for a win. The first person to reach 10 wins the game.</li>
<li>Each player works out the difference between their result and 100 after each round. They keep their running total. First to 500 loses.</li>
</ul>
<p>You can vary the target to make it easier or more difficult.<br></br>
</p>
<h3><span class="editorial" style="font-style: italic;">You may like to make use of this</span> <a href="/content/id/6606/Dicey_Operations.pdf" style="font-style: italic;"><span class="editorial" style="text-decoration: underline;">Operations grids / Scoring sheet</span></a></h3>
<br></br>
<p><a href="http://nrich.maths.org/7209&part=">Click here for a poster of this problem</a>.<br></br>
<br></br>
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<h3>Why play these games?</h3>
These games are thought provoking and very engaging. They encourage
discussion of place value, mental calculations and estimation,
alongside valuable strategic mathematical thinking.<br></br>
<h3>Resource Downloads</h3>
<div><a href="/content/id/6606/Dicey%20Operation%20-%20Instructions%20Sheet.pdf">
Instruction sheet</a></div>
<div><a href="/content/id/6606/Dicey%20Operations%20-%20Operation%20Grids.pdf">
</a><a href="/content/id/6606/Dicey_Operations.pdf">Operations
grids / Scoring sheet</a></div>
<br></br>
<h3>Possible approach</h3>
<div>These games follow on from <a href="http://nrich.maths.org/public/viewer.php?obj_id=6605&part=">
Nice and Nasty</a></div>
<div>They can be played with 1-6 die but ideally would be played
with a decahedral 0-9 dice or a spinner (an interactive 10-sided
spinner is available <a href="http://nrich.maths.org/6717&part=">here</a>).</div>
<br></br>
<div>Draw three copies of the addition grid on the board and ask
for three pairs of volunteers to work at the front. Give each pair
a dice. Explain that they are each trying to get as close to 1000
as possible and have to decide where to place each number after
each throw of their dice.</div>
<br></br>
<div>When the game is over confirm who has won and briefly compare
strategies.</div>
<br></br>
<div>Working in teams of two, set the students off on playing Game
1. Depending on your aims for the lesson, offer the simple or more
complicated scoring system. Downloadable grid sheets are available
<a href="/content/id/6606/Dicey_Operations.pdf">here</a>.</div>
<br></br>
<div>When appropriate, move onto the other games, clarifying the
targets and scoring system for each. Encourage students to vary the
targets.</div>
<br></br>
<div>Encourage students to justify their strategies to their
partners. </div>
<div></div><br></br>
<h3>Key questions</h3>
<div>Why are some cells more significant than others?<br></br>
How do you decide which targets are appropriate?</div>
What are effective strategies for placing the numbers?<br></br>
<h3>Possible extension</h3>
You may wish to move students on to <a href="http://nrich.maths.org/public/viewer.php?obj_id=6499&part=">
Countdown</a> and <a href="http://nrich.maths.org/public/viewer.php?obj_id=6564&part=">
Countdown</a> <a href="http://nrich.maths.org/public/viewer.php?obj_id=6606&part=">
</a> <a href="http://nrich.maths.org/public/viewer.php?obj_id=6564&part=">
Fractions</a><br></br>
<br></br>
<h3>Possible support</h3>
<div>Simplify the calculations by using fewer cells in each
game.</div>
<br></br>
<div>Perhaps provide students with number cards that they can move
around the grid to consider different options.</div>
<br></br>
<div>Pupils who find estimation difficult could use calculators to
check their estimates.</div>
<br></br>
<div>Choose the easiest scoring system or allow calculators for
scoring the more difficult version.</div>
<br></br>
<div>Allow pairs of students to play against other pairs, so that
they can support each other.</div>
<br></br>
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Dicey Operations
Who said that adding, subtracting, multiplying and dividing
couldn't be fun?
Using, Applying and Reasoning about Mathematics
Games
Numbers and the Number System
Place value
Numbers and the Number System
Comparing and Ordering numbers
Calculations and Numerical Methods
Estimating and approximating
Calculations and Numerical Methods
Mental addition & subtraction
Calculations and Numerical Methods
Mental multiplication & division
Secondary Mapping Document
Place value, ordering and rounding LS
Secondary Mapping Document
Number operations and calculation methods