*John Hamilton*Show bio

John has tutored algebra and SAT Prep and has a B.A. degree with a major in psychology and a minor in mathematics from Christopher Newport University.

Instructor:
*John Hamilton*
Show bio

John has tutored algebra and SAT Prep and has a B.A. degree with a major in psychology and a minor in mathematics from Christopher Newport University.

This end-of-year math homeschool assignment covers some fundamental Algebra I concepts, including basic arithmetic, square roots, absolute values, and matrices. The review assignment is designed to assist the 9th grade Algebra student.
Updated: 03/03/2021

**Arithmetic**. **Square roots**. **Absolute value**. **Matrices**. These are commonly known as the four food groups, and . . . never mind, those are my notes for a nutrition lesson. These are commonly known as four Algebra I concepts which will help you when you move on to more advanced mathematical concepts.

In addition to what is mentioned above, this synoptic assignment will cover matrices and order of operations.

By the end of this assignment, your student(s) will have completed four steps, solved five problems, and delivered two presentations.

Note - The answers are available at the bottom of the page.

- For an additional extensive course of related math topics, please visit our High School Algebra I: Homeschool Curriculum.

**Absolute value:**the size or magnitude of a number disregarding the sign**Arithmetic:**a branch of math which deals with manipulating numbers via four methodologies**Matrices:**rectangular arrays of numbers used to perform math operations

- Internet access
- Paper
- Pencil

- One day to complete this Algebra I material
- Two weeks to design two appropriate presentations

Before we move on to our review of more advanced Algebra I concepts, it is always helpful to complete a review of some of our basic arithmetic concepts.

First, do you remember the four arithmetic operations, which are **addition**, **subtraction**, **multiplication**, and **division**?

Second, the **commutative property** states the following:

3 + 1 = 1 + 3

Third, the **associative property** states the following:

(5 + 9) + 2 = 5 + (9 + 2)

Fourth, the **identity property** states the following:

8 + 0 = 8

One other fact we should note is that subtraction is considered the opposite, or the inverse, of addition, and division is considered the opposite, or the inverse, of multiplication.

A **number line** is utilized to visually represent real numbers. Our number system is a **base-ten system**, as opposed to say the **base-two system** used by computers.

By the way, don't forget it is crucial you follow your **order of operations**, or in order:

- Parentheses
- Exponents
- All multiplication and division from left to right
- All addition and subtraction from left to right

Hmmm! If we only had some sort of memory trick to help us with this rule. I think I'll invent one right now, and call it **PEMDAS**, or something similar.

PEMDAS = Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction

Let's work a problem.

Use PEMDAS to solve:

8 + (19 - 7 * 2) - 3 * 5

To simplify **square roots**, it is nice to turn to our product rule, which is:

- âˆš(
*ab*) = âˆš(*a*) * âˆš(*b*)

or

- (
*a**b*)1/2 =*a*1/2 **b*1/2

This reads as "the square root of quantity *a* times *b* equals the square root of *a* times the square root of *b*."

By the way, for this formula *a* and *b* are not negative numbers.

Simplify:

âˆš150

Now let's review the concept of **absolute value**, which is pretty straightforward. For example:

Find the absolute values of 5 and -5:

Find the absolute value of:

Next, let's recap the concept of **matrices**, which are grids of given numbers that we divide into rows and columns. We then place the numbers in brackets for the purpose of calculations.

Add the following two matrices:

At this point, please choose two of the following presentations:

- Create questions for a math quiz show based on one of your favorite game shows. Try doing an internet search for free game templates to set up your own game to play with others (suggested search terms: free Jeopardy template).
- Design a synoptic poster that contains the year-end information in this lesson, and use this poster to answer a series of questions related to the math material.
- Go ahead and ''be the teacher'' and walk through what you learned throughout this school year in your own TED Talk or YouTube video.
- Write thoughtful questions to assess understanding of these Algebra I concepts and processes.

Use PEMDAS to solve:

8 + (19 - 7 * 2) - 3 * 5 =

Remember, start with your parentheses, and first do your multiplication:

8 + (19 - 14) - 3 * 5 =

8 + 5 - 3 * 5 =

8 + 5 - 15 =

13 - 15 = -2

âˆš150 =

Can you find a perfect square in 150? Remember, the first ten perfect squares are 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100. It looks like 25 will work for us today.

âˆš(25 * 6) =

âˆš25 * âˆš6 =

5 * âˆš6

Your final answer reads as ''five times the square root of six'', which we often shorten to ''five square root of six.''

Check your answer:

âˆš150 = 12.25

5 * âˆš6 = 5 * 2.45 = 12.25

They match!

Find the absolute values of 5 and -5:

| 5 | = 5

| -5 | = 5

Do you see how the answer to both is five? Why? Absolute value cares about size, also known as magnitude, or distance, as opposed to caring about the sign of a number.

Find the absolute value of:

3 | 2 - 7 | =

3 | -5 | =

3 * 5 = 15

Add together the following two matrices:

Relax. Deep breaths. Focus.

First of all, please note both matrices are two rows by three columns, or 2 x 3 matrices, so we can simply add up the contents of the same location in each matrix. You can only add or subtract matrices if they are exactly the same size.

Let's start in the top left spot. We have an 8 in the first matrix and a 2 in the second matrix, so 8 + 2 = 10. Let's build a new third matrix with a 10 in the top left spot. Then we just repeat the process 5 more times for the other spots.

Now we rewrite our new matrix as:

See, that wasn't too horrible, was it?

Requirements | 0-5 points |
---|---|

Problem #1 is solved correctly | |

Problem #2 is solved correctly | |

Problem #3 is solved correctly | |

Problem #4 is solved correctly | |

Problem #5 is solved correctly | |

Deliverable #1 is clear and concise | |

Deliverable #2 is clear and concise | |

Total: |
/35 points |

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