The Ten Circle Counter
This is not actually a game.
It is an online tool to help you become familiar
with an excellent subtraction strategy.
It puts the process into pictorial form.
Just press "Start"
This tool will visually explain one of the shorthand methods
for easy addition and subtraction.
Use the mouse to click the yellow (top) + arrow three times
After 3 clicks we have counted to 3.
If you do 12 clicks
you will fill the inner circle
then jump to the next outer ring
and land on the 12:
the green circle
tells you what number you are on.
The top red arrow
will undo the count
taking you back one at a time
Calculate 23 - 4 = 19
Begin by clicking the top yellow arrow
until you reach 23.
If you accidently overshoot
click the top red arrow to go back to 23.
Click the lower (shaded) minus button
to start subtracting from 23:
(a) We began at 23
(b) After one back-click we arrive at 22
(the shaded area is one step backwards)
(c) The sum was 23 - 1 and the last digits of that are just 3 - 1
(d) No surprise here. The working is just 3 - 1 = 2 for the last digit.
Repeat that process for two more back-clicks.
This takes us from 23 back to 20:
Not much happening here either.
We can see we have made 3 shaded steps back from 23
to arrive at 20.
The calculation on the right just shows 23 - 03 = 20
by virtue of subtracting 3 - 3 to 0.
Now things start to get a bit more interesting!
Click the lower red shaded negative button again.
Now we have gone backwards 4 steps from 23 to 19:
Let's see if we can interpret what this is all about!
The explanation is given below:
(a) we started on 23
(b) we went backwards 4 steps (the shaded area)
(c) we arrived at 19
(a) The units digit is worked out as 3 - 4 coming somehow to 9
(b) Astoundingly we see "3 - 4" is equal to "3 + 6" which admittedly is 9.
But how can we explain why we can do that?
(a) We need to explain that 3 - 4 is the same as 3 + 6 inside the 10-circle
(b) we start at 3 in the 10 circle because we began at 23.
(c) The green inside arrow counts FORWARDS 6 steps.
(d) it arrives at 9
Hence the 3 + 6 = 9
but how do we know which number to pick?
There are two paths around any circle.
A forward path (adding) and a backward path (subtracting)
This shows that starting from 3 and counting back 4
is the same in the 10-circle as
starting from 3 and counting forward 6:
3 - 4 = 3 + 6 = 9
This always works
and 4 and 6 are complements in 10-circle.
That is, they both add together
to make 10.
So we can be sure for example that
23 - 8 = 15
8 and 2 are complements (add to 10)
3 - 8 = 3 + 2
which comes to 5.
We get the
of the answer.
The first digit
we can guess.
ADDITION WORKS IN A SIMILAR WAY:
18 + 3 = 21
Start by counting to 18
then add another 3 using the shaded "+" arrow:
Here's the explanation:
(a) The last digits of 18 + 3 are just 8 + 3
(b) Somehow we need to show this is the same as 8 - 7 (which is 1)
(notice that 7 and 3 add to 10)
(c) We started at 18
(d) We added on 3 (the shaded portion)
(e) We arrived at 21
(f) The green arrow moves BACKWARDS 7 STEPS
from 8 to 1 inside the 10-circle.
Instead of adding 3
we took away 7
7 and 3 make 10
This is a perfectly general
way to get the last digit of the answer
when an addition goes
9 and 1
8 and 2
7 and 3
6 and 4
5 and 5
0 and 10
To subtract below zero:
ADD the complement.
Guess it's in the 20's
36 - 9 = 2 (6 + 1) = 27
To ADD over 9
SUBTRACT the complement.
32 + 9
Guess it's in the 40's
32 + 9 = 4 (2 - 1) = 21
Click to count up or count down
Once you have arrived at a starting number
click either of these to ADD or SUBTRACT from it
Reset back to zero
SPEED UP = UP ARROW
SLOW DOWN = DOWN ARROW
JUMP ROADBlOCKS = SPACEBAR
Just jump over the road blocks.
The same ones will come around again.
CHANGE MUSIC = ENTER
SUPER CHARGER GAME
Game too slow for you?
You can vamp it up by left clicking the top line
(the red arrow is pointing to it)