

Playing Fantastic
Four is sure to sharpen skills in basic math and in forming equations.
Players must use four randomly selected numbers to create an equation
that equals a fifth number. This game gives people a chance to practice
different mathematical operations—and to practice writing equations
correctly.
Preparation and Materials
For each group of two to five players you will
need:

One deck of cards 

A timer or clock 

A pencil and
scratch paper for each player 

Photocopies of
the blackline masters 
Make
one copy per pair of players of:
Playing
Fantastic Four with Cards.
Introducing the Game
We suggest that you
introduce this game by showing the group how to play it. Deal out four
cards, then a fifth, and ask the group if they can make an equation that
uses some or all of the four cards to equal the number on the fifth.
Give people a few
minutes to work on their own, writing down possibilities that they come
up with. Then ask what people’s equations are. Write the equations
down for everyone to see.
Try to show examples
of equations using two numbers (worth 4 points), equations using three
numbers (worth 9 points), and equations using all four numbers (worth
a whopping 16 points).
Don’t worry if you can’t find an equation that uses all four
numbers. Sometimes, it just isn’t possible!
A Word About Equations
Addition, subtraction,
multiplication, and division are all acceptable operations to include
in equations. Depending on how advanced your players are, you may want
to allow other operations, such as square roots, exponentials, factorials,
and so on.
An equation can yield
different answers, depending on the order in which you do the operations.
(See Where’s the Math?) That’s why
it’s important for players to use parentheses when writing equations.
When doing the mathematical operations in an equation, one always does
the operations that are in parentheses first. People should use parentheses
to make it clear which operations to do first.
Playing the Game
Once players understand
the rules, they can play independently in groups of two to five. Alternatively,
you can have an entire class or large group play together. The leader
deals out the cards and keeps track of time. Once time is up, players
calculate their own scores. Ask who has the highest score, then check
her or his equations together. Or have players swap papers and check each
other’s equations. You might want to remind everyone that a player
gets 7 points for finding someone else’s mistake!
Some
Helpful Strategies 
Are people having
trouble finding an equation that works? It may help to focus on
finding combinations that lead to 1’s or zeros.
Get Rid of Numbers by Making Zero
Suppose you
get stuck trying to use 3, 4, 7, and 7 in an equation that equals
4. You can get rid of unwanted numbers by creating a zero, like
this:
Notice how nicely the first term disappears. Dividing anything into
zero gives you zero. You may have to remind people that you can
divide into zero, but you can’t divide by zero. So you
can’t have:
because zero
can never be on the bottom of a fraction (in the denominator).
Making a 1
Suppose you’re
trying to use 3, 4, 7, and 7 in an equation that equals 7. You could
get rid of unwanted numbers by turning them into a "1,"
like this:

Where's
the Math ?

When doing the
calculations in an equation, it’s important to do them in the
right order. Here are two calculations that look very similar:
(1+2) x 3 =
1 + (2 x 3) =
The numbers and the operations are the same—but the answer
you get depends on which operation you do first.
Whenever you
make a calculation, you do whatever operation is in parentheses
first. So the answer to the first calculation is:
(1+2) x 3 = 3 x 3 = 9
And the answer to the second calculation is:
1 + (2 x 3) = 1 + 6 = 7
Very different answers!
Be sure that people in your group understand this and use parentheses
to identify the order in
which they want the operations done.
Using
parentheses is just one way to define the order of operations. Mathematicians
have a set of rules about the order in which operations are done.
Here are those rules:

First,
do whatever is inside parentheses. 

If there
are any exponents, do those next. 

Then, do
all the multiplication and division, starting at the lefthand
side of the equation and working through the operations in the
order in which they appear. 

Finally,
do the addition and subtraction. Once again, start at the lefthand
side of the equation and do the operations in the order they
appear. 

To remember
the order of operations, people can memorize the sentence: "Please
Excuse My Dear Aunt Sally." Take the first letter of each
word in order, and it tells you what to do:
Please P
Parentheses
Excuse E Exponents
My Dear M D Multiply and Divide
Aunt Sally A S Add and Subtract 

Guiding
the Game
Go to Playing
Fantastic Four with Cards
Go
to Playing Fantastic Four with the Computer
