Download Handout #1

Name: __________________________
Algebra Tiles
Algebra tiles will help you visually see the concepts and principles used in Algebra.
Each small square tile represents the value of 1. The red (grey) side of the tile represents the value of -1
1. Use the small square tiles to represent each number below. Make a sketch of your model.
a. 7
c. 4 degrees below zero
b. -5
2. What number does each model represent?
a.
b.
d. 8 feet above sea level
One of the basic rules in algebra is “You can only add zero” to an equation or an expression. Look at this
visually with algebra tiles.
3. Write an equation for each diagram.
a.
b.
4. Draw two different models that represent zero.
a.
b.
In the previous two problems you saw and represented zero pairs. Using zero pairs you can model many
different values.
5. Remove (cross out) the zero pairs and determine the value of each integer modeled.
a.
b.
6. Using zero pairs (you must use both color tiles) model these integers.
a. 3
b. -3
We will use the value of x to represent the length of the larger tiles. Then we can name each of the
Algebra tiles using the area of each tile as follows:
x
This is the x2 tile because the area of the tile is x*x=x2
x
x
1
This is the x tile because the area of the tile is 1*x=x
1
1
This is the unit tile because the area of the tile is 1*1=1
We can use these tiles together to represent quadratic algebra expressions.
7. Use Algebra Tiles to represent the following polynomials
a. 5𝑥 + 2
b. 3𝑥 2 + 7𝑥
If you use the red side of the tile you can model negative values.
8. Write the polynomial represented by the following models.
a.
b.
Above we named the large length x and the small length 1. We can name the length other names if we
are representing different polynomials.
9. State what you would name the tiles and then represent the following polynomials:
a. 3𝑐 2 + 4𝑐𝑑 − 2𝑑2
Large Square ______________
Rectangle _________________
Small Square ______________
10. Use Algebra Tiles to model the following sums (Sketch your answer):
a. 5 + (−5) =
b. 4𝑥 2 + (−4𝑥 2 ) =
c. −3𝑥 + 3𝑥 =
11. Use Algebra Tiles to model the following sums (Sketch your answer):
a. 7 + 4 =
b. (−3) + (−5) =
c. (2𝑥 2 + 4𝑥) + (5𝑥 2 + 3𝑥) =
12. Use Algebra Tiles to model the following sums (Sketch your answer):
a. 5 + (−3) =
b. −7 + 9 =
c. 7𝑥 + (−9𝑥) =
d. (4𝑥 2 − 7𝑥 + 2) + (−5𝑥 2 + 4𝑥 + 5) + (3𝑥 2 − 4)
When you model subtraction you need to remove tiles. Therefore you will model the first quantity and
remove (take away) the second quantity. You need to pay attention to the signs of the numbers.
For instance:
𝟕 − 𝟒 is saying you have 7 objects and you are taking away 4 and is modeled by sketching 7 tiles and
removing 4 tiles.
There are 3 left that are not removed so the answer is 7 − 4 = 3
−𝟔 − (−𝟐) is saying you have negative 6 objects and you are taking away negative 2 and is modeled by
sketching -6 (red/grey) tiles and removing -2 (red/grey) tiles.
There are 4 (red/grey) tiles left so the answer is −6— (−2) = −4
In subtraction problems where the two integers have different signs you need to add zero pairs to figure
out the problems.
For example:
𝟓 − (−𝟑) is saying you have 5 objects and you are taking away negative 3 of them and is modeled by
using zero pairs.
We start with 5 unit squares
We need to add 3 zero pairs (because we are subtracting -3 and we
don’t have any -3 tiles to remove).
Now we are able to remove -3 tiles. The result is 8 positive tiles. Therefore 5 − (−3) = 8
−𝟒 − 𝟐 is saying you have negative 4 (red/grey) objects and you are taking away positive 2 of them and
is again modeled by zero pairs.
We start with -4 objects
We need to add 2 zero pairs because we are subtracting (+)2 objects and
we don’t have any positive objects to take away.
Now we have (+)2 objects to take away. The result is -6 tiles. Therefore the answer is −4 − 2 = −6
13. Use Algebra Tiles to model the following subtraction problems. Sketch your answer. Remember,
you may need to add zero pairs to determine your answers.
a. 7 − 4
b. −4 − (−5)
c. 5 − 7
d. −6 − 4
14. Now, let’s look at the similarity between addition and subtraction. As you are doing these
problems do each row together. Use Algebra Tiles to model each problem, and sketch your
answer. Again, you may need to add zero pairs to model the problem.
a. −4 − (−3)
b. −4 + 3
c. 7 − 9
d. 7 + (−9)
15. What rule do you notice about subtracting two integers compared to addition?
16. For the following problems, use your observation from 16. and rewrite the subtraction problems
as addition problems and then find the answer.
a. 8 − 12 =
b. 14 − (−7) =
c. −4𝑥 2 − 2𝑥 2 =
d. (4𝑥 2 − 7𝑥 + 2) − (−5𝑥 2 + 4𝑥 + 5) + (3𝑥 2 − 4) =