Unit 1: Algebraic Expressions & Evaluation

VA SOL Standards A.EO.1, A.EO.3a-b

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Day 1: Translating Verbal to Algebraic Expressions

Warm-Up

A movie ticket costs $12. If you buy tickets for a group of friends, how could you write a mathematical phrase to represent the total cost?

Total Cost = 12(where x is the number of friends)

Key Vocabulary

A variable is a letter used to represent annumber.
A coefficient is the numberby a variable.
A term is a number, a variable, or theof a number and variable(s).
An algebraic expression contains one or more, numbers, and operations.

Translating Phrases

Certain words and phrases indicate specific mathematical operations. The order is very important, especially for subtraction and division!

Example (I Do):

  • "The sum of a number and 5" translates to n + 5.
  • "The product of 3 and a number" translates to 3n.
  • "7 less than a number" translates to x - 7. (The 'than' flips the order!)
  • "The quotient of a number and 10" translates to n/10.

Your Turn 1:

Translate "12 decreased by a number x":
Translate "the sum of 6 and the product of 2 and y":

Your Turn 2:

Translate "a number cubed":
Translate "9 less than the quotient of 6 and a number":

Cool-Down (Exit Problem)

A high school is hosting a canned food drive. The freshman class collected 's' cans. The junior class collected 50 more than the freshmen. Write an expression for the total cans collected by both classes.

Total Cans =

Day 1 Reflection

What was the most important concept you learned today? What concept is still confusing, or what questions do you have?

My Extra Notes for Day 1

Day 2: Evaluating Expressions

Warm-Up

If a pizza costs \$15 and you have a coupon for \$3 off, how much would you pay?

dollars.

Key Vocabulary

To evaluate an expression means to find its single.
To do this, you first substitute, which means toa variable with its given value.

Order of Operations

After substituting, you must simplify the expression using the correct Order of Operations to get the right answer.

  • P - Parentheses & other (like | |, √ ).
  • E - (powers and roots).
  • MD - Multiplication & Division (from ).
  • AS - Addition & Subtraction (from ).

Evaluating Expressions in Practice

Example (I Do): Evaluate $3x^2 - 5y$ when $x=2$ and $y=4$.

  1. Substitute: $3(2)^2 - 5(4)$
  2. Exponents: $3(4) - 5(4)$
  3. Multiply: $12 - 20$
  4. Subtract: $-8$

Your Turn 1: Evaluate $5a + |b - c|$ when $a=3$, $b=2$, and $c=10$.

Remember that absolute value bars act like grouping symbols (parentheses).

The value is.

Your Turn 2: Evaluate $\sqrt{a^2 + b^2}$ when $a=3$ and $b=4$.

The square root symbol also acts like a grouping symbol. Simplify everything inside it first.

The value is.

Cool-Down

The formula for the area of a trapezoid is $\frac{1}{2}h(b_1 + b_2)$. Find the area if the height $h$ is 6 cm, base $b_1$ is 10 cm, and base $b_2$ is 8 cm.

Area =cm².

Day 2 Reflection

What was the most important concept you learned today? What concept is still confusing, or what questions do you have?

My Extra Notes for Day 2

Day 3: Laws of Exponents

Warm-Up

What is a shorter way to write $2 \times 2 \times 2 \times 2$?

Key Vocabulary

In the expression $x^a$, $x$ is the base and $a$ is the exponent.

The exponent tells you how many times to multiply theby itself.

Product of Powers Rule

To multiply powers with the same base, youthe exponents. x^a \cdot x^b = x^{a+b}

Example (I Do): $y^5 \cdot y^3 = y^{5+3} = y^8$

Your Turn 1: Simplify $a^7 \cdot a^2$

Your Turn 2: Simplify $2x^4 \cdot 5x^3$

Quotient of Powers Rule

To divide powers with the same base, youthe exponents. \frac{x^a}{x^b} = x^{a-b}

Example (I Do): $\frac{m^{10}}{m^2} = m^{10-2} = m^8$

Your Turn 1: Simplify $\frac{z^{12}}{z^5}$

Your Turn 2: Simplify $\frac{12b^7}{4b^3}$

Power of a Power Rule

To raise a power to another power, youthe exponents. (x^a)^b = x^{ab}

Example (I Do): $(c^4)^5 = c^{4 \cdot 5} = c^{20}$

Your Turn 1: Simplify $(b^6)^3$

Your Turn 2: Simplify $(2x^3)^4$ (Hint: Distribute the exponent to the coefficient too!)

Zero and Negative Exponents

Any non-zero number raised to the zero power is equal to. x^0 = 1
A negative exponent means to take theof the base. x^{-a} = \frac{1}{x^a}

Example (I Do): $5^0 = 1$ and $y^{-3} = \frac{1}{y^3}$

Your Turn 1: Simplify $100^0$

Your Turn 2: Simplify $4^{-2}$

Cool-Down

Simplify the expression completely: $(3a^2b^5)^2$

Day 3 Reflection

What was the most important concept you learned today? What concept is still confusing, or what questions do you have?

My Extra Notes for Day 3

Day 4: Simplifying Multivariable Expressions

Warm-Up

If you have 3 apples and your friend gives you 2 more apples, how many apples do you have?

. Can you add 3 apples and 2 oranges?.

Key Vocabulary

Like Terms are terms that have the exact same raised to the exact same .
A Constant is a term with no.

To simplify expressions, you combine like terms by adding or subtracting their coefficients.

Combining Like Terms

Example (I Do): Simplify $5x + 2y - 3x + 7y$

  1. Identify like terms: $5x$ and $-3x$; $2y$ and $7y$.
  2. Combine x-terms: $5x - 3x = 2x$
  3. Combine y-terms: $2y + 7y = 9y$
  4. Final Answer: $2x + 9y$

Your Turn 1: Simplify $7a + 3b + 3a - 2b$

Your Turn 2: Simplify $4x^2 + 8x - 2x^2 - 3x$

The Distributive Property

The Distributive Property allows you to a term across parentheses. a(b+c) = ab + ac

Example (I Do): Simplify $5(2x + 3)$

$5 \cdot 2x + 5 \cdot 3 = 10x + 15$

Your Turn 1: Simplify $-4(x - 6)$

Your Turn 2: Simplify $3(7a + 2b)$

Putting It All Together

Often, you must use the distributive property first, and then combine any like terms.

Example (I Do): Simplify $4(x-2) + 3x$

  1. Distribute: $4x - 8 + 3x$
  2. Combine like terms: $7x - 8$

Your Turn 1: Simplify $5(2n + 1) + 2(n - 3)$

Your Turn 2: Simplify $10x - (4x + 8)$

Hint: Distribute the negative sign!

Cool-Down

The perimeter of a triangle is the sum of its sides. Find the perimeter of a triangle with sides of length $2x+3$, $5x-1$, and $x+4$.

Perimeter =

Day 4 Reflection

What was the most important concept you learned today? What concept is still confusing, or what questions do you have?

My Extra Notes for Day 4

Unit 1 Quiz

Test your knowledge. You have 3 attempts.

Attempt 1 of 3

1. Which expression represents "5 less than the product of 3 and a number x"?

2. Evaluate the expression $2a^2 - 4b$ when $a=3$ and $b=2$.

3. What is the value of $|x - y| + \sqrt{z}$ when $x=5$, $y=10$, and $z=16$?

4. Simplify the expression $x^4 \cdot x^6$.

5. Simplify the expression $\frac{y^8}{y^4}$.

6. Simplify the expression $(a^5)^3$.

7. Simplify the expression $(2x^2)^3$.

8. Simplify the expression $5x + 3y + 2x - y$.

9. Simplify the expression $8x^2 - 3x^2 + 6x - 4x$.

10. A rectangle has a length of $3x+2$ and a width of 5. What is the expression for its perimeter?