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.
Problem
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Well here are five Aliens, all from different planets.
They all count using one "hand" except the last one who uses his six tentacles.
So let me introduce them:
1st  Serious "Dubo" who counts in twos;
2nd  The two headed "Threebee" who counts in threes;
3rd  The laughing "Quort", who counts in fours;
4th  The greenheaded "Chindi" who (you guessed it) counts in fives;
Finally  The foureyed "Senda" counting in sixes.
They've come to Earth to learn about us and what we do!
They visit a school and are interested in how many earth children there are in each room.
Dubo starts counting like this (up to what we would call seven and record as "7"):
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Then the next two:
Threebee  and then Quort 
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Then the last two aliens, Chindi and Senda, do their counting:
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When we do our counting we have units, tens
and hundreds. Those hundreds are ten lots of ten.
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.
The aliens go to a classroom and
count the children. We would count 30  but they would record and
say that differently.
Here's how they record:
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)
Threebee 1010; 1 (3 lots of 3 lots
of 3), and 1 (lot of 3)
Quort 132; 1 (4 lots of 4), 3 ( lots
of 4), and 2
Chindi 110; 1 (5 lots of 5), and 1
(lot of 5)
Senda 50; 5 (lots of 6)
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.
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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!
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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.
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Find numbers that the aliens used
to count the children in the classroom that look the same
to the humans looking at the
masks.
For example, to start you off:
When we look at Quort's 3 it looks
the same as Senda's 35, or Chindi's 33 etc.
So find one alien's number that would look the same to humans as
another alien's number.
Find all the pairs you can.
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).
Getting Started
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.
Th H T U
So saying 1234 as one Thousand two Hundred and Thirty Four could  more clumsily  be said as
one (ten lots of ten lots of ten) 2 (ten lots of ten) 3 (tens) and 4.
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.
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Student Solutions
There is a lot to explore in this challenge!
Have you tried writing out numbers above 7 for each alien?
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?
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.
Teachers  you might like to send a summary of your children's work.
Teachers' Resources
Here's a help for either checking or to set you thinking about further explorations.
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So, if we saw 1 in the unmasked window then these would be the possibilities:
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Plenty to explore here!
Pupils can explore all kinds of things around these five different counting methods.
You can arrange a whole period of time for being a Threebee. For example calculating and saying and recording all numbers in that style.
These different ways of counting are also known as "bases". We use base 10, and many things connected with electrical engineering use base 2.