Unit 1: Algebraic Expressions & Evaluation

Unit 1 Resources & Lessons

VA SOL Standards: A.EO.1, A.EO.3a-b. Use the buttons below to access unit-wide resources or jump to a specific lesson.

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Daily Lesson Slides

Day 1: Translating Expressions

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Day 2: Evaluating Expressions

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Day 3: Laws of Exponents

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Day 4: Simplifying Expressions

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Exponents Extra Practice Worksheet

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Exponents Extra Practice Worksheet #2

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Exponents Step-by-Step Guide

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Simplifying Expressions Practice Worksheet

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Simplifying Step-byStep Guide

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Unit 1 Mixed Review Worksheet

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Unit 1 Study Guide

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Unit 1 Study Guide 2

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Day 1: Translating Words into Math

Objective: To translate verbal phrases into algebraic expressions and understand key vocabulary.

Notes

An algebraic expression is a mathematical phrase containing numbers, variables, and operations. It does not have an equal sign.

A Variable is a letter, like $x,$ used to represent an unknown . .

A Coefficient is the number being multiplied by a . .

Keywords tell us which operation to use.
"Sum," "more than," and "increased by" all mean addition.
"Difference," "less than," and "decreased by" mean subtraction.
"Product" and "of" mean multiplication.
"Quotient" means division.

Watch out for "turnaround" words like than and from. They reverse the order of the terms. For example, "10 less than a number" is written as $x - 10,$ not $10 - x.$

Examples

I Do: Multi-Step Translation

Translate: "The product of 4 and the sum of a number and 2."

First, identify the main operation. "Product" means we are multiplying.
What are we multiplying? We are multiplying "4" and "the sum of a number and 2."
"The sum of a number and 2" needs to be grouped together. We write this as $(n+2).$
Now, combine the parts: $4 \cdot (n+2),$ which simplifies to $4(n+2).$

We Do: Translating with a Turnaround Word

Translate: "5 less than twice a number."

1. "Twice a number" can be written as . .

2. The phrase "less than" means we subtract FROM the first part. It's a word. word.

3. So, the final expression is . .

You Do: Practice Problems

Translate: "The quotient of a number squared and 7."

A movie ticket costs \$12. Write an expression for the cost of 't' tickets.

Day 2: Evaluating Expressions

Objective: To evaluate algebraic expressions by substituting values and using the order of operations.

Notes - Part 1: Substitution

To evaluate an expression means to find its final numerical value. The first step is to substitute.

Substitution is replacing the variables (letters) in an expression with their given . .

A good habit is to always use parentheses ( ) when you substitute. This helps avoid mistakes, especially with negative numbers later on!

Notes - Part 2: Order of Operations

After you substitute, you must simplify the expression in the correct order. We call this the Order of Operations. A common acronym to remember the order is GEMDAS.

G : First, solve anything inside ( ), [ ], or | |.
E : Second, calculate any powers like $3^2.$
M/D : Third, multiply or divide from left to right.
A/S : Finally, add or subtract from left to right.

Examples

I Do: A Basic Evaluation

Evaluate $x + y$
when $x=5$ and $y=8.$

Substitute: Replace the $x$ with 5 and the $y$ with 8.
The expression becomes $5 + 8.$

Simplify: There is only one operation: addition.

Calculate: $5 + 8 = 13.$
The final answer is 13.

We Do: Using Multiplication

Evaluate $4a + b$
when $a=3$ and $b=6.$

1. Substitute the numbers for the letters. The expression becomes $4(3) + ?$ . .

2. Look at GEMDAS. We need to do multiplication before addition. So, first calculate $4(3),$ which is . .

3. Now the expression is $12 + 6.$ The final answer is . .

You Do: Practice Problems

Evaluate $10 - 2m$
when $m=3.$

Evaluate $c^2 + 5$
when $c=4.$
(Remember to do the exponent first!)

Day 3: Working with Exponents

Objective: To simplify expressions using the basic laws of exponents.

Notes - Part 1: What is an Exponent?

An exponent is a shortcut for repeated multiplication.
For example, $x^4$ is the same as $x \cdot x \cdot x \cdot x.$

In the term $x^a,$ the $x$ is called the , ,

and the $a$ is called the . .

Notes - Part 2: The Product Rule (Multiplying)

Rule: When you multiply terms with the same base, you ADD the exponents.

Why?
Look at $x^2 \cdot x^3.$
This is just $(x \cdot x) \cdot (x \cdot x \cdot x).$
If you count them up, there are 5 x's being multiplied, so the answer is $x^5.$
It's a shortcut to just do $x^{2+3} = x^5.$

Notes - Part 3: The Quotient Rule (Dividing)

Rule: When you divide terms with the same base, you SUBTRACT the exponents.

Why?
Look at $\frac{x^5}{x^2}.$
This is $\frac{x \cdot x \cdot x \cdot x \cdot x}{x \cdot x}.$ You can cancel out two x's from the top and bottom, leaving you with $x \cdot x \cdot x,$ which is $x^3.$
The shortcut is $x^{5-2} = x^3.$

Examples

I Do: Product Rule

Simplify: $a^4 \cdot a^6$

The terms have the same base, which is 'a'.
Since we are multiplying, we add the exponents.
$a^{4+6} = a^{10}.$ The final answer is $a^{10}.$

We Do: Quotient Rule

Simplify: $\frac{y^8}{y^3}$

1. The terms have the same base, which is 'y'. Since we are dividing, we the exponents. the exponents.

2. We calculate $8 - 3,$ which is
. .

3. The final answer is . .

You Do: Practice Problems

Simplify: $m^2 \cdot m^5$

Simplify: $\frac{c^{12}}{c^4}$

Challenge: Simplify $(2x^3)(5x^4).$
(Hint: Multiply the numbers first, then use the product rule on the variables)

Day 4: Simplifying Expressions

Objective: To simplify algebraic expressions by combining like terms and using the distributive property.

Notes - Part 1: Like Terms

Like Terms are terms that have the exact same variables with the exact same exponents. The numbers in front (coefficients) can be different.

Think of it like sorting fruit: You can add apples to other apples, but you can't add apples to bananas. In the same way, you can add $3x$ and $5x,$ but you can't add $3x$ and $5y.$

To combine like terms, you add or subtract the , ,

and you keep the variable part the . .

Notes - Part 2: The Distributive Property

The Distributive Property is used to get rid of parentheses. You "distribute" or multiply the term on the outside of the parentheses to every term on the inside.

Rule: $a(b+c) = ab + ac.$ Be very careful when you distribute a negative number, as it will change the signs of the terms inside!

Examples

I Do: Combining Like Terms

Simplify: $7x + 2 + 3x + 5$

Identify Like Terms: The terms $7x$ and $3x$ are like terms. The numbers $2$ and $5$ are also like terms.
Combine the x-terms: $7x + 3x = 10x.$
Combine the numbers: $2 + 5 = 7.$
Write the final answer: $10x + 7.$

We Do: Using the Distributive Property

Simplify: $4(x - 3)$

1. We need to distribute the 4 to both terms inside the parentheses. First, multiply $4 \cdot x,$ which gives us . .

2. Next, multiply $4 \cdot (-3),$ which gives us . .

3. The final simplified expression is . .

You Do: Practice Problems

Simplify: $10y + 8 - 3y - 2$

Simplify: $-5(a+2)$

Challenge: $2(3x-1) + 4x$
(Hint: Distribute first, then combine like terms)

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