Assignment Instructions for Students
Step One - Distributing Positive and Negative Integers
Let's begin! First of all, you can use algebraic distribution to solve equations with both positive and negative integers.
Now, please note distribution is different when using positive versus negative integers. Let's take a look:
- 2(3a + 2) = 6a + 4
- -2(3a + 2) = -6a - 4
See the difference? In the second example, you literally distribute the negative to both numbers in the parentheses.
Now you try.
- Note - The answers and explanations are at the bottom of the assignment. Try to solve all problems the first time without using a calculator.
Problem #1
-3(a - 3) = ?
Step Two - Fractional and Negative Exponents
A fractional exponent is one such as a1/2, which is really just another way of writing ''the square root of a''. On the other hand, a1/3 is really just another way of writing ''the cube root of a''.
A negative exponent is one such as a-1/2, which is really just another way of writing 1/a1/2 or ''1 divided by the square root of a''.
Can you solve this problem?
Problem #2
a-1/5 = ?
Step Three - Polynomials
Distributing a term over polynomials is similar to what we just did in Step One of this assignment. For instance:
2a(a2 + 3a - 5) = 2a3 + 6a2 - 10a
It's your turn again.
Problem #3
3a(a3 - 2a2 + 4a - 1) = ?
Step Four - FOIL
Let's talk about a cool little ''trick'', which is actually a reliable math rule, you will need to use as you improve your algebra skills.
The important acronym you need to memorize is FOIL, which stands for First, Outer, Inner, Last, when performing certain math operations. For instance, let's solve:
- (a + 3) (2a + 2) = ?
- 2a2 + 2a + 6a+ 6 =
- 2a2 + 8a + 6
That wasn't too bad, was it? To review what we just did:
- First - multiply a times 2a to get 2a2
- Outer - multiply a times 2 to get 2a
- Inner - multiply 3 times 2a to get 6a
- Last - multiply 3 times 2 to get 6
Then we simply combined like terms to get the final answer. Now you solve one.
Problem #4
(b - 2) (3b + 8) = ?
Optional
Have an online contest between fellow students to see who can solve one dozen algebra equations the quickest.
Deliverable
Part A
Prepare your own worksheet in which you show all your work on these problems, and then apply the answers to a similar real-world scenario, such as preparing recipes in the kitchen and having to double or halve the ingredients. On the other hand, as a mechanical engineer, you would utilize your polynomials to design your new favorite thrilling roller coaster.
For another illustration, if you were a zoologist you might use your aforementioned a-1/5 exponent to measure your pet bat's wingspan. Furthermore, NASA astronauts often use algebra to determine how much breathable air is contained in spacesuits.
Part B
To demonstrate your knowledge of how to perform algebraic distributions, you could:
- Create a podcast or video explaining the concepts to other persons
- Design a poster containing relevant information from this assignment, including polynomials, fractional along with negative exponents, as well as positive and negative integers
Create in your mind's eye an algebra board game you can play with your family and schoolmates.
Answers
Problem #1
-3(a - 3) = -3a + 9
In this case, remember a negative number times a negative number equals a positive number.
Problem #2
a-1/5 = 1/a1/5 or ''1 divided by the fifth root of a''
Problem #3
- 3a(a3 - 2a2 + 4a - 1) =
- 3a4 - 6a3 + 12a2 - 3a
Be sure not to make any careless sign errors during your calculations.
Problem #4
- (b - 2) (3b + 8) = ?
- 3b2 + 8b - 6b - 16 =
- 3b2 + 2b - 16
Assignment Rubric
| Requirements |
0-5 points |
| Define above three key terms |
|
| Show how to distribute positive and negative integers |
|
| Solve fractional and negative exponents |
|
| Distribute a polynomial |
|
| Explain FOIL |
|
| Give a presentation to an adult |
|
| Total: |
/30 |
