7006
/www/nrich/html/content/id/7006/
1
2011-02-01T00:00:01
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<mdoxml version="1.0"><br></br>
<div style="text-align: center;"><mdo:image width="325" height="170" alt="pic of spinners" src="pic%20of%20spinners.jpg"></mdo:image></div>
<br></br>
<br></br>
For this activity I've chosen first of all to use a $1$ to $6$ and
a $0$ to $9$ spinner.<br></br>
The $1$ to $6$ we will use to give us the "tens" figure and the
other one for the "units" (or "ones").<br></br>
<br></br>
<div style="text-align: center;"><mdo:image width="433" height="254" src="2%20spinners.jpg" alt="2 spinners"></mdo:image></div>
<div>You will need two
spinners like those above and two cards which each have six boxes
drawn on them. You can download and print <a href="/content/id/7006/OurNumbers.pdf">these</a>, or you could use
our <a href="http://nrich.maths.org/6963&part=">interactive
spinners</a>. You will also need twelve counters.</div>
<br></br>
<div>A person with one card
chooses the special types of numbers that they will collect. The
other person chooses some other special types of numbers to
collect.</div>
<br></br>
<div style="text-align: left;">For example, Sara chooses numbers you can
share equally among $3$ ( eg. $3, 9, 21, 39 ... $).</div>
<div style="text-align: left;">Nala chooses even numbers (eg. $4, 10,
20, 44 ... $).</div>
<div style="text-align: left;">Each of them spins a spinner and then
when it rests they read out the number (tens and units).</div>
<div style="text-align: left;">Suppose it's a $21$ then Sara places a
counter in one of the boxes on her card. If it is a $10$ then Nala
gets a counter for her card. If it's a $30$ then both of them get a
counter.</div>
<br></br>
<div style="text-align: left;">So you can do something similar.</div>
<div style="text-align: left;">When you've tried it a few times decide
what's best to choose so that you fill all the boxes on both cards
as quickly as you can.</div>
<br></br>
<div style="text-align: left;">Think about other spinners - there are
some <a href="/content/id/7006/extra%20spinners.pdf">here</a>. Or
of course you can design your own.</div>
<br></br>
<div style="text-align: left;">Are there good choices of spinners that
work really well?</div>
<br></br></mdoxml>
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<mdoxml version="1.0"><br></br>
<span class="editorial">Jacob and James from Fishergate Primary
School played this game using our interactive
spinners.</span><br></br>
<br></br>
Using spinners $1-6$ and $0-9$ we tried to see who would win if one
was even and one was odd. The odds won as we got these
numbers.<br></br>
<table border="1">
<tbody>
<tr>
<td style="text-align: center; font-weight: bold;">Numbers</td>
</tr>
<tr>
<td style="text-align: center;">25</td>
</tr>
<tr>
<td style="text-align: center;">32</td>
</tr>
<tr>
<td style="text-align: center;">29</td>
</tr>
<tr>
<td style="text-align: center;">35</td>
</tr>
<tr>
<td style="text-align: center;">54</td>
</tr>
<tr>
<td style="text-align: center;">52</td>
</tr>
<tr>
<td style="text-align: center;">55</td>
</tr>
<tr>
<td style="text-align: center;">22</td>
</tr>
<tr>
<td style="text-align: center;">35</td>
</tr>
<tr>
<td style="text-align: center;">51</td>
</tr>
<tr>
<td style="text-align: center;">11</td>
</tr>
</tbody>
</table>
<br></br>
Then we found out the $3$ times table beat the $5$ times
table.<br></br>
<br></br>
<table border="1">
<tbody>
<tr>
<td style="text-align: center; font-weight: bold;">Numbers</td>
</tr>
<tr>
<td style="text-align: center;">29</td>
</tr>
<tr>
<td style="text-align: center;">51</td>
</tr>
<tr>
<td style="text-align: center;">22</td>
</tr>
<tr>
<td style="text-align: center;">36</td>
</tr>
<tr>
<td style="text-align: center;">26</td>
</tr>
<tr>
<td style="text-align: center;">51</td>
</tr>
<tr>
<td style="text-align: center;">11</td>
</tr>
<tr>
<td style="text-align: center;">54</td>
</tr>
<tr>
<td style="text-align: center;">23</td>
</tr>
<tr>
<td style="text-align: center;">26</td>
</tr>
<tr>
<td style="text-align: center;">37</td>
</tr>
<tr>
<td style="text-align: center;">10</td>
</tr>
<tr>
<td style="text-align: center;">69</td>
</tr>
<tr>
<td style="text-align: center;">24</td>
</tr>
</tbody>
</table>
<br></br>
<span class="editorial">Someone else wrote in to tell us that they
found that broad sets work well if you have to get one but narrower
sets work better if you want to get them all. Jacob and James then
tried different spinners.</span><br></br>
<br></br>
<mdo:image height="163" width="309" src="our%20numbers%202.jpg" alt="spinner"></mdo:image><br></br>
We did numbers more than $20$ and numbers less than $20$. Numbers
more than $20$ won because there are four tens on the left spinner
that would work but there are only two tens that would work for
less than $20$.<br></br>
<br></br>
<table border="1">
<tbody>
<tr>
<td style="text-align: center; font-weight: bold;">Numbers</td>
</tr>
<tr>
<td style="text-align: center;">37</td>
</tr>
<tr>
<td style="text-align: center;">24</td>
</tr>
<tr>
<td style="text-align: center;">38</td>
</tr>
<tr>
<td style="text-align: center;">14</td>
</tr>
<tr>
<td style="text-align: center;">14</td>
</tr>
<tr>
<td style="text-align: center;">28</td>
</tr>
<tr>
<td style="text-align: center;">11</td>
</tr>
<tr>
<td style="text-align: center;">30</td>
</tr>
<tr>
<td style="text-align: center;">23</td>
</tr>
</tbody>
</table>
<br></br>
<br></br>
<br></br></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><div class="embed">
<h2>Our Numbers</h2>
<br></br>
<div style="text-align: center;"><mdo:image alt="pic of spinners" height="170" src="pic%20of%20spinners.jpg" width="325"></mdo:image></div>
<br></br>
<br></br>
For this activity I've chosen first of all to use a $1$ to $6$ and a $0$ to $9$ spinner.<br></br>
The $1$ to $6$ we will use to give us the "tens" figure and the other one for the "units" (or "ones").<br></br>
<br></br>
<div style="text-align: center;"><mdo:image alt="2 spinners" height="254" src="2%20spinners.jpg" width="433"></mdo:image></div>
<div>You will need two spinners like those above and two cards which each have six boxes drawn on them. You can download and print <a href="/content/id/7006/OurNumbers.pdf">these</a>, or you could use our <a href="http://nrich.maths.org/6963&part=">interactive spinners</a>. You will also need twelve counters.</div>
<br></br>
<div>A person with one card chooses the special types of numbers that they will collect. The other person chooses some other special types of numbers to collect.</div>
<br></br>
<div style="text-align: left;">For example, Sara chooses numbers you can share equally among $3$ ( eg. $3, 9, 21, 39 ... $).</div>
<div style="text-align: left;">Nala chooses even numbers (eg. $4, 10, 20, 44 ... $).</div>
<div style="text-align: left;">Each of them spins a spinner and then when it rests they read out the number (tens and units).</div>
<div style="text-align: left;">Suppose it's a $21$ then Sara places a counter in one of the boxes on her card. If it is a $10$ then Nala gets a counter for her card. If it's a $30$ then both of them get a counter.</div>
<br></br>
<div style="text-align: left;">So you can do something similar.</div>
<div style="text-align: left;">When you've tried it a few times decide what's best to choose so that you fill all the boxes on both cards as quickly as you can.</div>
<br></br>
<div style="text-align: left;">Think about other spinners - there are some <a href="/content/id/7006/extra%20spinners.pdf">here</a>. Or of course you can design your own.</div>
<br></br>
<div style="text-align: left;">Are there good choices of spinners that work really well?</div>
</div>
<br></br>
<h3><span style="font-weight: bold;">Why do this problem?</span></h3>
<div>This <a href="http://nrich.maths.org/7006&part=">problem</a> gives pupils the opportunity to use all their number knowledge and expand their number awareness. There is a chance to experience an element of scientific exploration as they choose the properties of the two groups and test to see what happens.</div>
<br></br>
<h3>Possible approach</h3>
<div>Have two spinners ready to generate the tens and units figures, and then with the class decide on two different groups (sets) of numbers to look out for. (You could make your own spinners or use our <a href="http://nrich.maths.org/6963&part=">interactive versions</a>.) When a number is generated this gives an opportunity for discussion about which group the number belongs to - if
any.</div>
<br></br>
<div>When this introduction has been repeated a number of times with different sets being chosen, discuss with the pupils about what affects the choices of sets so as to get six of each set in as few spins as possible. Give them chance to try out their own combinations in pairs.</div>
<br></br>
<div>Allow time for the whole group to come together to talk about the combinations they tried and to report on their findings. This might also be a good time for children to pose further questions which they would like to investigate.</div>
<br></br>
<h3>Key questions</h3>
<div>Tell me about the group you've chosen.</div>
<div>Can you say something about why you made this choice.</div>
<div>How do you decide whether the spinners' number belongs to your choice?</div>
<br></br>
<h3>Possible extension</h3>
<div>Some children could make hundreds, tens and units spinners.</div>
<div>For a further challenge, learners could design some different spinners - what about ones that contain just some of the numbers twice? How does this affect the children's choice of numbers?</div>
<br></br>
<h3>Possible support</h3>
<div>The children may need some adult support to physically spin the spinners. Some may need help in remembering how to check whether the number belongs to their group.</div>
<br></br>
<br></br></mdoxml>
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<mdoxml version="1.0">What could you try first?<br></br>
How will you know whether the spinners' number fits in your
set?<br></br></mdoxml>
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Our Numbers
These spinners will give you the tens and unit digits of a number. Can you choose sets of numbers to collect so that you spin six numbers belonging to your sets in as few spins as possible?
Using, Applying and Reasoning about Mathematics
Making and testing hypotheses
Numbers and the Number System
Properties of numbers
Numbers and the Number System
Place value
Admin
Lower primary mapping document