7431
/www/nrich/html/content/id/7431/
1
2011-02-01T00:00:01
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I have a pile of nine digit cards numbered $1$ to $9$.<br></br>
<br></br>
I take one of the cards. It is the $3$.<br></br>
<br></br>
Which card would you choose so you could make the largest possible
two-digit even number with the two cards?<br></br>
<br></br>
We put the cards back in the pile. This time, I choose the
$6$. Which card would you choose this time to make the largest
possible two-digit even number?<br></br>
<br></br>
Have a go at this with a partner. One of you chooses the
first digit from the set of cards. The second person then
chooses a card to make the largest possible two-digit even number.
You can then swap over.<br></br>
<br></br>
Try it several times so you are sure you have a good method. Talk
about your ideas with your partner so you agree together on a
'best' method.<br></br>
<br></br>
How would your strategy change if you had to make the largest
two-digit odd number?<br></br>
<br></br>
<p style="font-style: italic;">If you don't have a partner to work
with, you could use the interactivity below. The computer
selects one digit at random. You must then choose a
digit to make the largest possible two-digit even number or largest
possible two-digit odd number.</p>
<br></br>
<div style="background-color:#bfe8ff;padding:20px;padding-bottom:20px;width:550px;height:400px;position:relative;">
<div style="color:#000000;font-size:32px;font-family:helvetica,arial,sans-serif">Enter the biggest two-digit <select id="gamechoice" style="background-color:#ffbff7;color:#000000;font-size:32px;font-family:helvetica,arial,sans-serif"><option value="even">even</option><option value="odd">odd</option></select> number you can think of that uses the digit:</div>
<div id="Number" style="color:#000000;font-size:48px;font-family:helvetica,arial,sans-serif; text-align:center"> </div>
<input id="Answer" type="text" size="3" style="color:#000000;font-size:32px;font-family:helvetica,arial,sans-serif; height:36px;" onkeydown="if (event.keyCode !== 13) {blankout();} else {check();}" />
<input id="testButton" name="Test" type="button" value="Check" onClick="check()" style="color:#000000;font-size:28px;font-family:helvetica,arial,sans-serif; height:36px;" />
<br></br>
<div id="Feedback" style="color:#000000;font-size:32px;font-family:helvetica,arial,sans-serif"></div>
<br></br>
<input id="clickhere" name="clickhere" type="button" size="10" value="New digit" onClick="generate()" style="color:#000000;font-size:28px;font-family:helvetica,arial,sans-serif; height:38px; position:absolute; top:360px;"/>
</div>
<script src="liz-script.js" type="text/javascript"></script>
<br></br></mdoxml>
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<p class="editorial">Well done for giving clear solutions to this
problem. Many of you were able to explain a general strategy.
Tom and Jeevan from Devonshire Primary School said:</p>
If you are trying to make the largest even number using an odd
number you put the odd number in the tens column and in the units
column you put $8$.<br></br>
But if you're doing it with an even number then you put $9$ in the
tens column and then put the even number in the units column.<br></br>
<br></br>
<p class="editorial">Peter, Henry, Charlie, Lulu and Samuel at
Weald C of E Primary School assumed that you could also get a zero.
They went on to think about how you would make the smallest
even number:</p>
Largest Even<br></br>
1.If you get an odd number, put an eight in the units column.<br></br>
2.If you get an even number, put a nine in the tens column.<br></br>
3.If you get a zero, put a nine in the tens column.<br></br>
<br></br>
Smallest even<br></br>
1.If you get an odd number, add a zero in the units column.<br></br>
2.If you get an even number, add a one in the tens column<br></br>
3.If you get a zero, put a one in the tens column.<br></br>
<br></br>
<br></br>
<p class="editorial">Homeroom 7 at Kororoit Creek Primary School,
Australia looked at a strategy for making the largest odd number
too:</p>
<div>The largest two-digit odd number we could make is $97$. We
could not make $99$ because we only have one $9$.</div>
<div>If you pulled out an odd number first this should always go in
the 'ones' column. Unless you pull out a number $9$. The $9$ will
always go first because $97$ is the biggest number we can make.
e.g. $97$, $79$, $59$, $39$, $19$.</div>
<div>If you pull out an even number first it should always go in
the 'tens' columns, otherwise your two-digit number will not be
odd. You should still always choose the number $9$ as your second
card to make the largest number possible. e.g. $89$, $69$, $49$,
$29$. </div>
<br></br>
<p class="editorial">Well done too to Robert from West Hoathly and
Sophie from Greenacre who also sent very full responses.</p>
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<h2>Largest Even</h2>
<br></br>
I have a pile of nine digit cards numbered $1$ to $9$.<br></br>
<br></br>
I take one of the cards. It is the $3$.<br></br>
<br></br>
Which card would you choose so you could make the largest possible two-digit even number with the two cards?<br></br>
<br></br>
We put the cards back in the pile. This time, I choose the $6$. Which card would you choose this time to make the largest possible two-digit even number?<br></br>
<br></br>
Have a go at this with a partner. One of you chooses the first digit from the set of cards. The second person then chooses a card to make the largest possible two-digit even number. You can then swap over.<br></br>
<br></br>
Try it several times so you are sure you have a good method. Talk about your ideas with your partner so you agree together on a 'best' method.<br></br>
<br></br>
How would your strategy change if you had to make the largest two-digit odd number?<br></br>
<br></br>
<p style="font-style: italic;">If you don't have a partner to work with, you could use the interactivity below. The computer selects one digit at random. You must then choose a digit to make the largest possible two-digit even number or largest possible two-digit odd number.</p>
<br></br>
<div style="background-color:#bfe8ff;padding:20px;padding-bottom:20px;width:550px;height:400px;position:relative;">
<div style="color:#000000;font-size:32px;font-family:helvetica,arial,sans-serif">Enter the biggest two-digit <select id="gamechoice" style="background-color:#ffbff7;color:#000000;font-size:32px;font-family:helvetica,arial,sans-serif">
<option value="even">even</option>
<option value="odd">odd</option>
</select> number you can think of that uses the digit:</div>
<div id="Number" style="color:#000000;font-size:48px;font-family:helvetica,arial,sans-serif; text-align:center"> </div>
<input id="Answer" onkeydown="if (event.keyCode !== 13) {blankout();} else {check();}" size="3" style="color:#000000;font-size:32px;font-family:helvetica,arial,sans-serif; height:36px;" type="text"></input> <input id="testButton" name="Test" onclick="check()" style="color:#000000;font-size:28px;font-family:helvetica,arial,sans-serif; height:36px;" type="button" value="Check"></input><br></br>
<div id="Feedback" style="color:#000000;font-size:32px;font-family:helvetica,arial,sans-serif"> </div>
<br></br>
<input id="clickhere" name="clickhere" onclick="generate()" size="10" style="color:#000000;font-size:28px;font-family:helvetica,arial,sans-serif; height:38px; position:absolute; top:360px;" type="button" value="New digit"></input></div>
<script src="liz-script.js" type="text/javascript">
</script></div>
<br></br>
<h3><span style="font-weight: bold;">Why do this problem?</span></h3>
<div>The idea of <a href="http://nrich.maths.org/7431&part=">this problem</a> is to encourage children to work together to develop a method of finding a solution which will always work and perhaps one that is the most efficient or quickest. This challenge will also help to reinforce understanding of odd and even numbers.</div>
<br></br>
<h3>Possible approach</h3>
<div>You could introduce the challenge by inviting one child to choose a card from the digit cards $1$ to $9$, perhaps without looking so it is a random choice. You could then ask another child to choose a card, again without looking. What is the largest two-digit even number that can be made from the two cards? You could try this a few times so that the children have a chance
to explain when it is impossible to make an even number.</div>
<div> </div>
<div>Then tweak the task. This time, the second person to choose can decide which digit they would like in order to make the largest possible two-digit number. You could suggest that in fact a pair of children chooses the card so that they have a chance to talk to each other about the best choice. You could invite others to comment on their choice. (You could use the
interactivity at this point instead.)</div>
<div> </div>
<div>Ask pairs to have a go at the challenge for themselves with a set of digit cards per pair. Explain that you'd like them to come up with a method that will always work so they can identify the best card to choose as quickly as possible. </div>
<div> </div>
<div>After a suitable length of time, bring the whole group together and share their strategies. You could test out a few of them and perhaps a consensus can be reached about the 'best' method to use. (This may not be possible but having the discussion is valuable. In this case 'best' might be quickest but perhaps the children may want to clarify that for themselves.)</div>
<div> </div>
<div>How would they change their method if the task was to make the highest two-digit odd number?</div>
<br></br>
<h3>Key questions</h3>
<div>What do you know about even numbers?</div>
<div>What do you know about the units digit of even numbers?</div>
<div>Where could the digit on that first card go - in the units or tens? Why?</div>
<div>How can we make a large number?</div>
<div>How do we know that's the biggest even number we can make?</div>
<br></br>
<h3>Possible extension</h3>
<div>Challenge children to extend the strategy for three-digit numbers. They could pick two numbers out of the pack of digit cards at random, then try to make the largest possible three-digit even number by selecting one of the remaining cards as well. Another possibility would be to aim for multiples of $5$ rather than even numbers. Some learners might want to investigate what
happens if $0$ is included as well.</div>
<br></br>
<h3>Possible support</h3>
<div>Some children might benefit from having equipment to help them check whether a number is even, for example multilink cubes or counters that can be put in pairs.</div>
<br></br>
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<mdoxml version="1.0">What do you know about even numbers? <br></br>
What do you know about the units digit of even numbers? <br></br>
Where could the digit on the first card go - in the units or tens?
Why? <br></br>
How can you make a large number? <br></br>
How do you know that's the biggest even number you can make?<br></br></mdoxml>
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<mdoxml version="1.0">i<a href="/content/id/7431/icon.png">co</a>n<br></br></mdoxml>
5
3
1
0
0
0
0
Largest Even
How would you create the largest possible two-digit even number
from the digit I've given you and one of your choice?
Numbers and the Number System
Odd and even numbers
Numbers and the Number System
Comparing and Ordering numbers
Numbers and the Number System
Place value
Admin
Lower primary mapping document