Title Slide
Models of algebraic concepts
1
Y2
X
X2
Y
XY
PowerPoint Presentation
Developed by
Harvey Almarode
Modified by Carrie Newman
The Equation Mat
The Equation Mat consists of two Basic Mats
with an equal sign in between.
+
+
=
_
_
The Pieces
X
1
The rectangular yellow pieces will represent the
variable, or the number you don’t know yet.
The small green cubes will represent one whole.
If there are more than one, just count them up!
The whole point of algebra is to get that yellow variable
block all by itself on one side of the equal sign so you
can find out its value!
Anything in the top (white) part of
your equation math means that it is
positive, or that you are ADDING.
+
What does this say?!
If you said “x+2” you
were right!
_
Anything in the bottom (gray) part of your
equation math means that it is negative,
or that you are SUBTRACTING.
+
_
What does this say?!
If you said “x – 3”
you were right!
+
_
If you ever have something that matches on the top (positive)
and bottom (negative) of the mat, you will call it a “zero pair”.
These things will cancel each other out because they are equal
to ZERO!
Don’t believe me? I’ll prove it!
• Hold out your hand
• Add (+)2 green cubes to your hand.
• Now take away (-) 2 green cubes
from your hand
• You’re left with ZERO green cubes, aren’t
you?! That’s why we call it a zero pair!
• Just remember- you can only take away zero
pairs on the SAME SIDE OF THE EQUAL
SIGN!
+
X
1 1
1
1
+
=
1
1
1
1
1
1
1
1
1
1
1
1
_
What equation is modeled on the Equation Mat?
Answer:
X + 4 = 12
_
X
+
+
=
1
1
1
1
1
1 1 1
_
What equation is modeled on the Equation Mat?
Answer:
X-3 = 5
_
+
1
1
+
1
=
1
1
1
1
1
1
1
1
_
What equation is modeled on the Equation Mat?
Answer:
X+3 = 8
_
+
X
1
1
1
1
1
=
1
1
1
1
1
1
1
1
1
1
_
Add
Show
3the
X
to -the
each
3 =Zero
7sidePair
of the Equation Mat
Remove
Read
results
Answer:
X = 10
+
1
_
You can check your answers by replacing your yellow “x”
block with the number of green “1” cubes that you came up
with in your answer.
If you come up with the same amount of green cubes on each
side of the equal sign, your equation is balanced and your
answer is correct!
Let’s try some now!
+
+
X
1
1
1
1
=
1
1
1
1
1
_
Add
Set
25the
toXthe
each
– 2zero
3 pair
of sure
the equation
mat the variable in
Remove
Let’s
check
to=side
make
by replacing
Read
X =up
results
the original equation (X – 2 = 3) with our answer of 5
_
+
1 X1
1
1
1
+
1
1
1
=
1
1
_
_
Set
your
original
equation
variable
“X”
with say?
the
value
5 Great job!
5 –Replace
Now
2 =up
3!
what
Isthe
that
does
true?
yourThen
equation
your
value
of xyou
wasfound,
correct!
1 1 1
+
1
X
1
1
1
1
1
1
1
1
1
1
+
1
1
=
1
1
1
1
1
_
Check
Read
Let’s
your
try
your
results:
answer!
more
Xtogether!
Set
=side.
5up theSet
original
up X +equation.
4 = 9 on your mat
Subtract
from
each
Get
rid
of4one
your
zero
pairs
_
1 1 1
1
+
1 1 1 1
1 X
1
1
1
1
1
1
1
1
1
+
=
_
_
Now you have 9 = 9, is that true?! Your equation is balanced
Now replace your variable with your answer.
and your answer is correct!
Extension: Can you set up and solve these
problems on your mat?
Sam has some baseball cards and his mom brings him 5 more.
Now he has 7. How many did he begin with?
+
X
1
1
1
1 1
1
=
1
1
1
1
_
1
1
1
1
1
1
1
1
1
1
1
1
+
_
Let’s talk algorithms!
When we talk about using the standard algorithm, we mean that
we use numbers and operations to solve. It’s exactly what we’ve
been doing with our blocks, but we will use inverse operations
to solve.
For example…
Suzie had some apples and picked 3. Now she has 5 apples.
What does that look like?!
X+3=5
What
Addition!
do you
see?! of addition?!
Subtraction!
What operation
is the inverse
operation
2X +X3+=35= 25
- 3 -3
• So let’s subtract 3 from both sides to get the variable by
itself!
• Now get rid of your zero pairs
• +3 and -3 cancel and 5 – 3 = 2
Now to check, go back to your original equation…
… and replace the variable with your answer to check!
Let’s Practice!
X–2=3
Draw a Picture:
Show your steps:
Solution:
X–2=3
+2 +2
X=5
X=5
Check:
5–2=3
Write a word problem:
Carrie had some
balloons and 2 flew
away. Now she has 3.