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Email me 6 free activities →Evaluating Algebraic Expressions Lesson Plan
Overview
Ever planned a birthday party for a friend or family member?
By learning how to evaluate algebraic expressions, you can more easily create and stick to a budget as you plan the party.
Use this artistic, real-life lesson plan to teach your students about evaluating algebraic expressions. Students will learn material with artistic guided notes, check for understanding, practice with doodle math and a maze, and conclude with the real-life application of evaluating algebraic expressions for budgeting a birthday party.
- Type: Lesson Plans
- Duration: 2 Hours
- Topic: Expressions
- Standards: CCSS 6.EE.A.2.c, CCSS 6.EE.A.2, CCSS 6.EE.A.1
- Grades: 7th Grade, 6th Grade
Learning Objectives
After this lesson, students will be able to:
Evaluate algebraic expressions using the order of operations (PEMDAS)
Describe how to algebraic expressions to real-life situations, such as budgeting for a party
Note: This lesson only contains positive numbers only. Students do not need to know negative integer rules for this lesson. See the extensions for harder problems with both positive and negative integers.
Prerequisites
Before this lesson, students should be familiar with:
Identifying parts of expressions (see my lesson plan for this)
Order of operations (PEMDAS)
Exponents
Materials
Pencils
Colored pencils or markers
Evaluating Algebraic Expressions Guided Notes
Key Vocabulary
Algebraic expression
Substitution
PEMDAS
Variable
Coefficient
Constant
Order of operations
Procedure
Introduction
As a hook, ask students why evaluating algebraic expressions is important in budgeting for a party. Refer to the last page of the guided notes as well as the FAQs below for ideas.
Use the guided notes to introduce the topic of evaluating algebraic expressions using PEMDAS. Use it also to explain the concept of substitution. Walk through the key points of the topic of the guided notes to teach. Refer to the FAQ below for a walk-through on this, as well as ideas on how to respond to common student questions.
Check for Understanding. Have students practice the expressions on the guided notes page. Call on students to talk through their answers. Based on student responses, reteach concepts that students need extra help with.
Practice
Have students practice evaluating algebraic expressions using the Doodle Math activity. In this activity, students will evaluate various expressions using substitution and color the corresponding sections of a picture according to a key.
Walk around to answer student questions and provide assistance as needed.
Fast finishers can dive into the maze activity for extra practice. You can assign it as homework for the remainder of the class.
Real-Life Application
Bring the class back together, and introduce the concept of budgeting for a birthday party. Discuss the costs associated with throwing a party, such as invitations, decorations, food, and entertainment. Refer to the FAQ for more ideas on how to teach it!
Extensions
Additional Self-Checking Digital Practice (Pixel Art Google Sheets)
If you’re looking for digital practice for evaluating algebraic expressions, try my Pixel Art activities in Google Sheets. Every answer is automatically checked, and correct answers unlock parts of a mystery picture. It’s incredibly fun, and a powerful tool for differentiation. For expressions with positive and negative integers, there’s Halloween and Christmas/Winter versions perfect for additional practice. For version with positive integers only, check out this spring/St. Patrick’s Day pixel art activity.
Real-Life Application Project
As a culminating activity, have students plan a birthday party on a budget. Provide them with a budget and a list of necessary items such as decorations, food, and entertainment. Students will need to use their knowledge of evaluating algebraic expressions to determine the cost of each item and ensure that they stay within budget. They can then present their party plan to the class and discuss how they used algebraic expressions to make decisions.
FAQs
Algebraic expressions are mathematical statements that involve variables, constants, and arithmetic operations such as addition, subtraction, multiplication, and division. They are used to represent real-world situations and can be manipulated and simplified using algebraic rules and properties.
The parts of an expression include terms, coefficients, variables, and constants.
A term is a single numerical or algebraic expression separated by addition or subtraction operators within an overall expression. For example, in the expression 3x + 2y - 5, 3x, 2y, and -5 are all individual terms.
A coefficient is the numerical factor that is multiplied by a variable in an algebraic expression. For example, in the expression 3x + 2y - 5, the coefficient of x is 3, and the coefficient of y is 2.
A variable is a symbol that represents a quantity that can change or vary. For example, in the expression 3x + 2y - 5, x and y are variables that can be replaced with specific numbers to produce a value for the expression.
A constant in an expression is a fixed numerical value that does not change. It is not multiplied by a variable, and it does not have any variables added or subtracted from it. For example, in the expression 3x + 2y - 5, -5 is a constant.
PEMDAS is an acronym that stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. It is used to determine the order of operations when evaluating algebraic expressions. Parentheses and exponents are evaluated first, followed by multiplication and division (which are evaluated in order from left to right), and finally addition and subtraction (also evaluated in order from left to right).
Here's an example of evaluating an algebraic expression using PEMDAS:
Evaluate 3 + 4 x 5 - 2 ÷ 6
First, we evaluate anything inside parentheses, but there are none in this expression.
Next, we evaluate exponents, but there are none in this expression.
Then, we evaluate multiplication and division from left to right. 4 x 5 = 20, and 2 ÷ 6 = 1/3. So the expression becomes: 3 + 20 - 1/3.
Finally, we evaluate addition and subtraction from left to right. 3 + 20 = 23, and 23 - 1/3 = 22 and 2/3.
Therefore, 3 + 4 x 5 - 2 ÷ 6 = 22 and 2/3.
If your students need a more visual example, here’s a Khan Academy video that I like:
Substitution involves replacing variables with known values to simplify an algebraic expression. For example, in the expression 5x + 3, if we substitute x = 4, the expression becomes 5(4) + 3 = 23.
There are several alternative methods for evaluating algebraic expressions, such as:
Substitution: Substitute a value for each variable in the expression and then simplify the resulting arithmetic expression.
Factoring: Factor the expression and then cancel out common factors.
Graphing: Graph the expression and then find the value of the expression at a specific point.
When evaluating algebraic expressions, there are some common mistakes that people tend to make. These include:
Forgetting to apply the order of operations (PEMDAS)
Forgetting to evaluate exponents
Applying the wrong operation (such as addition instead of multiplication)
Not paying attention to signs and parentheses
Misunderstanding the concept of negative numbers
Algebraic expressions are highly applicable in various fields, here are some specific examples:
Finance: Algebraic expressions can be used to calculate costs, revenue, and profit in a business. For example, a business owner can use algebraic expressions to determine the cost of producing goods or services, the revenue from sales, and the profit margin.
Engineering: Engineers use algebraic expressions to design and analyze structures such as bridges and skyscrapers. For instance, they can use algebraic expressions to calculate the load capacity of a bridge and ensure its stability.
Physics: Algebraic expressions are commonly used in physics to model and solve problems related to motion, energy, and forces. For example, algebraic expressions can be used to calculate the velocity of an object, the amount of work done on an object, and the force exerted on an object.
Computer Science: Computer scientists use algebraic expressions to write algorithms and perform various computations. For instance, they can use algebraic expressions to calculate the running time of an algorithm or to represent data structures such as arrays and matrices.
Statistics: Algebraic expressions are used in statistics to analyze data and make predictions. For example, algebraic expressions can be used to calculate the mean, median, and mode of a set of data, as well as to calculate probabilities and make predictions based on statistical models.
Evaluating algebraic expressions can be a useful tool when budgeting for a party. By using variables to represent the costs of different items, and then evaluating the expression, students can determine the total cost of the party and ensure that it remains within a certain budget.
For example, if the cost of decorations is represented by the variable "d", the cost of food by "f", and the cost of entertainment by "e", the total cost of the party can be represented by the expression "d + f + e".
By substituting in the actual costs of each item, students can evaluate the expression and determine whether the total cost is within their budget.
Here are some key points to keep in mind when using algebraic expressions to budget for a party:
Identify the various costs associated with hosting a party, such as decorations, food, and entertainment
Use variables to represent each of these costs in an algebraic expression
Substitute in the actual costs of each item to evaluate the expression and determine the total cost of the party
Compare the total cost to your budget to ensure that it stays within your desired range
Overall, evaluating algebraic expressions can be a practical and engaging way to teach students about budgeting and financial literacy.