Enriching
Mathematics at
Center School
In the classroom
And in Math Olympiads
With the implementation
of the Common Core
Standards
critical thinking and collaboration
with others are stressed.
Finding multiple strategies to
solve problems is
important at all levels,
and is an invaluable life skill as
students move forward
toward college and career.
Now here’s an
example of what
we do at
What’s another way we
collaborate and develop critical
thinking skills?
We play math games.
Are you ready to be amazed?
.
It’s time for
some
Math Magic
How about another game?
Ready,
Set,
Let’s go.
Pick a number
(1 – 10)
x
Multiply by 2
2x
Add 8
2x  8
Divide by 2
2x  8
2
Subtract the
original number
2x  8
x
2
Find your answer on the charts
Pick a country which starts with the corresponding letter
Pick an animal which starts with the next letter
Skip a letter and pick a color that start with the next letter
1
A
6
F
2
B
7
G
3
C
8
H
4
D
9
I
5
E
10
J
Who has
“Grey Elephants
in Denmark”?
How it Works
We think you probably have a gray elephant from Denmark.
What’s the trick:



The first half of this magical problem is an arithmetic trick. You
will (it is certain) map a letter to the number 4 to get “D”).
From there we are not certain where you will go, but having a
gray elephant from Denmark is quite probable!
You could have selected another country that starts with “D”
such as the Dominican Republic or Dominica or Djibouti…but it
is not probable.
You also could have selected another animal that starts with “E”
such as an elk or an ermine…but that’s not probable either.
Function Machine
Input
x
Result
2x  8
f ( x) 
x
2
?
Input
x
1
2
3
4
x
Function
2( x )  8
 ( x)
2
4
2(1)  8
 (1)
2
2( 2)  8
 ( 2)
2
2(3)  8
 (3)
2
2( 4)  8
 ( 4)
2
2( x )  8
 ( x)
2
Result
y
4
4
4
4
4
2( x )  8
 ( x)  4
2
What will we
investigate
next?
2x  8
x4
2
Future investigations ?
1. Why does this work?
2. Is the domain really limited to 1 - 10?
3. Find another equation which has
infinite solutions?
4. Play .