5722
/www/nrich/html/content/id/5722/
1
2011-02-01T00:00:01
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><br></br>
<mdo:image width="332" height="134" src="3Aliens.jpg" alt="3aliens"></mdo:image><mdo:image width="236" height="130" src="2Aliens.jpg" alt="2aliens"></mdo:image><br></br>
Well here are five Aliens, all from different planets. <br></br>
They all count using one "hand" except the last one who uses his
six tentacles. <br></br>
So let me introduce them:<br></br>
<br></br>
1st - Serious "Dubo" who counts in twos;<br></br>
2nd - The two headed "Threebee" who counts in threes;<br></br>
3rd - The laughing "Quort", who counts in fours;<br></br>
4th - The green-headed "Chindi" who (you guessed it) counts in
fives;<br></br>
Finally - The four-eyed "Senda" counting in sixes.<br></br>
<br></br>
They've come to Earth to learn about us and what we do!<br></br>
They visit a school and are interested in how many earth children
there are in each room.<br></br>
Dubo starts counting like this (up to what we would call seven and
record as "7"):<br></br>
<div style="text-align: center;"><mdo:image width="361" height="324" alt="Pic1" src="Picture%201.jpg"></mdo:image></div>
<br></br>
<div style="text-align: center;"></div>
<div style="text-align: center;"></div>
<div style="text-align: left;">Then the next two:</div>
<div style="text-align: left;"></div>
<div style="text-align: center;"></div>
<br></br>
<table border="0">
<tbody>
<tr>
<td>Threebee</td>
<td>and then Quort</td>
</tr>
<tr>
<td><mdo:image width="251" height="235" src="PictBase3.jpg" alt="Threebee"></mdo:image></td>
<td><mdo:image width="257" height="239" src="PicBase4.jpg" alt="Quort"></mdo:image></td>
</tr>
</tbody>
</table>
<br></br>
<br></br>
Then the last two aliens, Chindi and Senda, do their
counting:<br></br>
<div style="text-align: center;"><mdo:image width="243" height="232" alt="base5" src="PicBase5.jpg"></mdo:image><mdo:image width="238" height="244" alt="base6" src="PicBase6.jpg"></mdo:image></div>
<div style="text-align: center;"></div>
<div style="text-align: left;">When <span style="font-style: italic;">we</span> do our counting we have units, tens
and hundreds. Those hundreds are ten lots of ten.</div>
<div style="text-align: left;">Notice that when Chindi counts he
can only use 0, 1, 2, 3 and 4 whereas we use 0, 1, 2, 3, 4, 5, 6,
7, 8, 9.</div>
<div style="text-align: left;"></div>
<div style="text-align: left;"></div>
<div style="text-align: left;">The aliens go to a classroom and
count the children. We would count 30 - but they would record and
say that differently.</div>
<div style="text-align: left;">Here's how they record:</div>
<div style="text-align: left;">Dubo 11110; 1 (2 lots of 2 lots of 2
lots of 2), 1 (2 lots of 2 lots of 2), 1 (2 lots of 2), and 1 (lot
of 2)</div>
<div style="text-align: left;">Threebee 1010; 1 (3 lots of 3 lots
of 3), and 1 (lot of 3)</div>
<div style="text-align: left;">Quort 132; 1 (4 lots of 4), 3 ( lots
of 4), and 2</div>
<div style="text-align: left;">Chindi 110; 1 (5 lots of 5), and 1
(lot of 5)</div>
<div style="text-align: left;">Senda 50; 5 (lots of 6)</div>
<div style="text-align: left;"></div>
<div style="text-align: left;"></div>
<br></br>
<div>It would be a good idea to try to see how their counting goes
after (our) "7", what they'd say and how they'd record it.</div>
<br></br>
<div style="text-align: center;"><mdo:image width="371" height="65" alt="words2" src="Words2.jpg"></mdo:image></div>
<br></br>
<div style="text-align: center;"></div>
<div style="text-align: left;">When we humans try to look at what
the aliens had written we might put a mask over most of the digits,
all except the second from the right!</div>
<div style="text-align: left;"></div>
<div style="text-align: center;"><mdo:image width="208" height="37" src="Simple%20window.jpg" alt="simplewindow"></mdo:image></div>
<div style="text-align: left;">So when for example we try to look
at one of Quort's numbers (suppose 0 0 1 3 1) a mask is over it and
all we see is the 3.</div>
<div style="text-align: center;"><mdo:image width="210" height="112" src="egOfWindow.jpg" alt="Eg window"></mdo:image></div>
<div style="text-align: center;"></div>
<div style="text-align: left;"></div>
<br></br>
<div style="text-align: center;"><mdo:image width="327" height="61" alt="words1" src="words1.jpg"></mdo:image></div>
<div style="text-align: center;">Find numbers that the aliens used
to count the children in the classroom that look the same</div>
<div style="text-align: center;">to the humans looking at the
masks.</div>
<div style="text-align: left;"></div>
<div style="text-align: left;">For example, to start you off:</div>
<div style="text-align: left;"></div>
<div style="text-align: left;">When we look at Quort's 3 it looks
the same as Senda's 35, or Chindi's 33 etc.</div>
<div style="text-align: left;"></div>
So find one alien's number that would look the same to humans as
another alien's number.
<div style="text-align: left;"></div>
<div style="text-align: left;"></div>
<br></br>
<div>Find all the pairs you can.</div>
<br></br>
<div style="text-align: left;"></div>
<div style="text-align: left;"></div>
Some of you might like to go on to say what those numbers would
have been if humans had been counting, for example Senda's 35 which
humans would have counted as 23 (three 6's and a 5 makes 23).
<div style="text-align: left;"></div>
<br></br>
<br></br></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><br></br>
There is a lot to explore in this challenge!<br></br>
Have you tried writing out numbers above 7 for each alien?<br></br>
Can you find numbers that the aliens used to count the children in
the classroom that look the same to the humans looking at the
masks?<br></br>
Do let us know what you discover.Please don't worry that your
solution is not "complete" - we'd like to hear about anything you
have tried. <br></br>
Teachers - you might like to send a summary of your children's
work.<br></br></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><div class="embed">
<h2>Alien Counting</h2>
<br></br>
<mdo:image alt="3aliens" height="134" src="3Aliens.jpg" width="332"></mdo:image><mdo:image alt="2aliens" height="130" src="2Aliens.jpg" width="236"></mdo:image><br></br>
Well here are five Aliens, all from different planets.<br></br>
They all count using one "hand" except the last one who uses his six tentacles.<br></br>
So let me introduce them:<br></br>
<br></br>
1st - Serious "Dubo" who counts in twos;<br></br>
2nd - The two headed "Threebee" who counts in threes;<br></br>
3rd - The laughing "Quort", who counts in fours;<br></br>
4th - The green-headed "Chindi" who (you guessed it) counts in fives;<br></br>
Finally - The four-eyed "Senda" counting in sixes.<br></br>
<br></br>
They've come to Earth to learn about us and what we do!<br></br>
They visit a school and are interested in how many earth children there are in each room.<br></br>
Dubo starts counting like this (up to what we would call seven and record as "7"):<br></br>
<div style="text-align: center;"><mdo:image alt="Pic1" height="324" src="Picture%201.jpg" width="361"></mdo:image></div>
<br></br>
<div style="text-align: center;"> </div>
<div style="text-align: center;"> </div>
<div style="text-align: left;">Then the next two:</div>
<div style="text-align: left;"> </div>
<div style="text-align: center;"> </div>
<br></br>
<table style="" border="">
<tbody>
<tr>
<td>Threebee</td>
<td>and then Quort</td>
</tr>
<tr>
<td><mdo:image alt="Threebee" height="235" src="PictBase3.jpg" width="251"></mdo:image></td>
<td><mdo:image alt="Quort" height="239" src="PicBase4.jpg" width="257"></mdo:image></td>
</tr>
</tbody>
</table>
<br></br>
<br></br>
Then the last two aliens, Chindi and Senda, do their counting:<br></br>
<div style="text-align: center;"><mdo:image alt="base5" height="232" src="PicBase5.jpg" width="243"></mdo:image><mdo:image alt="base6" height="244" src="PicBase6.jpg" width="238"></mdo:image></div>
<div style="text-align: center;"> </div>
<div style="text-align: left;">When <span style="font-style: italic;">we</span> do our counting we have units, tens and hundreds. Those hundreds are ten lots of ten.</div>
<div style="text-align: left;">Notice that when Chindi counts he can only use 0, 1, 2, 3 and 4 whereas we use 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.</div>
<div style="text-align: left;"> </div>
<div style="text-align: left;"> </div>
<div style="text-align: left;">The aliens go to a classroom and count the children. We would count 30 - but they would record and say that differently.</div>
<div style="text-align: left;">Here's how they record:</div>
<div style="text-align: left;">Dubo 11110; 1 (2 lots of 2 lots of 2 lots of 2), 1 (2 lots of 2 lots of 2), 1 (2 lots of 2), and 1 (lot of 2)</div>
<div style="text-align: left;">Threebee 1010; 1 (3 lots of 3 lots of 3), and 1 (lot of 3)</div>
<div style="text-align: left;">Quort 132; 1 (4 lots of 4), 3 ( lots of 4), and 2</div>
<div style="text-align: left;">Chindi 110; 1 (5 lots of 5), and 1 (lot of 5)</div>
<div style="text-align: left;">Senda 50; 5 (lots of 6)</div>
<div style="text-align: left;"> </div>
<div style="text-align: left;"> </div>
<br></br>
<div>It would be a good idea to try to see how their counting goes after (our) "7", what they'd say and how they'd record it.</div>
<br></br>
<div style="text-align: center;"><mdo:image alt="words2" height="65" src="Words2.jpg" width="371"></mdo:image></div>
<br></br>
<div style="text-align: center;"> </div>
<div style="text-align: left;">When we humans try to look at what the aliens had written we might put a mask over most of the digits, all except the second from the right!</div>
<div style="text-align: left;"> </div>
<div style="text-align: center;"><mdo:image alt="simplewindow" height="37" src="Simple%20window.jpg" width="208"></mdo:image></div>
<div style="text-align: left;">So when for example we try to look at one of Quort's numbers (suppose 0 0 1 3 1) a mask is over it and all we see is the 3.</div>
<div style="text-align: center;"><mdo:image alt="Eg window" height="112" src="egOfWindow.jpg" width="210"></mdo:image></div>
<div style="text-align: center;"> </div>
<div style="text-align: left;"> </div>
<br></br>
<div style="text-align: center;"><mdo:image alt="words1" height="61" src="words1.jpg" width="327"></mdo:image></div>
<div style="text-align: center;">Find numbers that the aliens used to count the children in the classroom that look the same</div>
<div style="text-align: center;">to the humans looking at the masks.</div>
<div style="text-align: left;"> </div>
<div style="text-align: left;">For example, to start you off:</div>
<div style="text-align: left;"> </div>
<div style="text-align: left;">When we look at Quort's 3 it looks the same as Senda's 35, or Chindi's 33 etc.</div>
<div style="text-align: left;"> </div>
So find one alien's number that would look the same to humans as another alien's number.
<div style="text-align: left;"> </div>
<div style="text-align: left;"> </div>
<br></br>
<div>Find all the pairs you can.</div>
<br></br>
<div style="text-align: left;"> </div>
<div style="text-align: left;"> </div>
Some of you might like to go on to say what those numbers would have been if humans had been counting, for example Senda's 35 which humans would have counted as 23 (three 6's and a 5 makes 23).
<div style="text-align: left;"> </div>
<br></br>
</div>
<br></br>
Here's a help for either checking or to set you thinking about further explorations.<br></br>
<mdo:image alt="upTo30" height="358" src="bases%3E30.jpg" width="578"></mdo:image><br></br>
<br></br>
So, if we saw 1 in the unmasked window then these would be the possibilities:<br></br>
<div style="text-align: center;"><mdo:image alt="solutions" height="228" src="solutions%204%201.jpg" width="202"></mdo:image></div>
<div style="text-align: left;">Plenty to explore here!</div>
<br></br>
Pupils can explore all kinds of things around these five different counting methods.<br></br>
You can arrange a whole period of time for being a Threebee. For example calculating and saying and recording all numbers in that style.<br></br>
These different ways of counting are also known as "bases". We use base 10, and many things connected with electrical engineering use base 2.<br></br></mdoxml>
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<mdoxml version="1.0"><br></br>
It's useful to recall that we humans use 10 as our source for
counting and our columns for writing are Units, Tens, Hundreds,
Thousands etc.<br></br>
<div style="text-align: center;">Th H T U</div>
<br></br>
So saying 1234 as one Thousand two Hundred and Thirty Four could -
more clumsily - be said as<br></br>
one (ten lots of ten lots of ten) 2 (ten lots of ten) 3 (tens) and
4.<br></br>
Looking at this practically here we have a heap of red dots and you
see how they would be grouped to be counted, firstly in human 10's
and then in Senda 6's.<br></br>
<div style="text-align: center;"><mdo:image width="531" height="423" src="Counting2.jpg" alt="Counting"></mdo:image></div>
<div style="text-align: center;"></div>
<div style="text-align: center;"></div>
<br></br></mdoxml>
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Alien Counting
Investigate the different ways these aliens count in this
challenge. You could start by thinking about how each of them would
write our number 7.
Numbers and the Number System
Counting
Using, Applying and Reasoning about Mathematics
Investigations
Numbers and the Number System
Place value
Numbers and the Number System
Number bases