1. Interpreting Structure in Expressions Identifying Terms, Factors, and Coefficients
Lesson 1.1.1

2. Bellringer
At the beginning of the school year, Javier deposited $750 in an account that pays 3% of his initial deposit each year. He left the money in the bank for 5 years. Use this information to complete the problems that follow. Explain your answers.
How much interest did Javier earn in 5 years?
After 5 years, what is the total amount of money that Javier has?
Warm Up 5 minutes

3. Bellringer - debrief 5(0.03 • 750) = 112.50 112.50 + 750.00 = $862.50
At the beginning of the school year, Javier deposited $750 in an account that pays 3% of his initial deposit each year. He left the money in the bank for 5 years.
How much interest did Javier earn in 5 years?
The amount of interest Javier earned in 5 years is $
5(0.03 • 750) =
After 5 years, what is the total amount of money that Javier has?
The total amount of money that Javier has after 5 years is the sum of the simple interest and the initial deposit, or $
= $862.50
Warm Up 5 minutes
#1 Note:
I t is not necessary at this point for students to create and solve an equation to represent this situation, but it is important that the interest amount is calculated based on the initial deposit of $750. Look out for students who try to calculate compound interest. There are several methods to calculating interest; compound interest will be discussed later in the lesson. Focus the discussion on calculating 3% simple interest over five years.

4. Standard
MGSE.A.SSE.1b★ Given situations which utilize formulas or expressions with multiple terms and/or factors, interpret the meaning (in context) of individual terms or factors. Perform arithmetic operations on polynomials.

5. Learning Targets
I can interpret algebraic expressions that describe real-world scenarios.
I can perform the appropriate arithmetic operations on polynomials to simplify the expression.

6. Homework - debrief

7. Mini Lesson Introduction
Algebraic expressions, used to describe various situations, contain variables. It is important to understand how each term of an expression works and how changing the value of variables impacts the resulting quantity.
Notes 10 minutes

8. Mini Lesson Key Concepts
If a situation is described verbally, it is often necessary to first translate each expression into an algebraic expression. This will allow you to see mathematically how each term interacts with the other terms.
As variables change, it is important to understand that constants will always remain the same. The change in the variable will not change the value of a given constant.
Notes 10 minutes

9. Mini Lesson Key Concepts, continued
Similarly, changing the value of a constant will not change terms containing variables.
It is also important to follow the order of operations, as this will help guide your awareness and understanding of each term.

10. Click Here for Geogebra Example
Mini Lesson
Guided Practice
Example
To calculate the perimeter of an isosceles triangle, the expression 2s + b is used, where s represents the length of the two congruent sides and b represents the length of the base.
What effect, if any, does increasing the length of the congruent sides have on the expression?
Guided Practice 10 minutes

11. Mini Lesson
If the value of the congruent sides, s, is increased, the product of 2s will also increase. Which also means, if the value of s is decreased, the value of 2s will also decrease.

12. Mini Lesson Guided Practice Example
Click here for Geogebra Example
Mini Lesson
Guided Practice
Example
Money deposited in a bank account earns interest on the initial amount deposited as well as any interest earned as time passes. This compound interest can be described by the expression P(1 + r)n, where P represents the initial amount deposited, r represents the interest rate, and n represents the number of months that pass.
How does a change in each variable affect the value of the expression?
Notice the expression is made up of one term containing the factors P and (1 + r)n.
In other words, the change in P will multiply by the result of (1 + r)n.
(The base is the number that will be multiplied by itself.) This change in r will affect the value of the overall expression.

13. Mini Lesson
Changing the value of P does not change the value of the factor (1 + r)n, but it will change the value of the expression by a factor of P. Similarly, changing r changes the base of the exponent, but does not change the value of P. Changing n changes the number of times (1 + r) will be multiplied by itself, but does not change the value of P.
Notice the expression is made up of one term containing the factors P and (1 + r)n.
In other words, the change in P will multiply by the result of (1 + r)n.
(The base is the number that will be multiplied by itself.) This change in r will affect the value of the overall expression.

14. Work Session
Problem-Based Task 1.1.2: Searching for a Greater Savings Austin plans to open a savings account. The amount of money in a savings account can be found by using the equation s = p • (1 + r)t, where p is the principal, or the original amount deposited into the account; r is the rate of interest; and t is the amount of time. Austin is considering two savings accounts. He will deposit $1, as the principal into either account. In Account A, the interest rate will be per year for 5 years. In Account B, the interest rate will be 0.02 per year for 3 years. If he could, would it be wise for Austin to leave his money in the account that has less savings for an additional year? Explain your reasoning.
If needed, use the Scaffolded Questions to get students started.

15. Homework Practice 1.1.2 Interpreting Structure in Expressions
Choose 1 from #1-3
Choose 1 from #4-5
Choose 3 from #6-10
Intro HW 2 minutes

16. Closing
Share out:
Would it be wise for Austin to leave his money in the account that has less savings for an additional year?
Explain your reasoning.
3 minutes