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Evaluating Algebraic Expressions Guided Notes & Doodles | Order of Operations
$4.25
Overview
- Standards: CCSS 6.EE.A.1, CCSS 6.EE.A.2, CCSS 6.EE.A.2.c
- Unit: 6th Grade → Unit 5: Algebraic Expressions
- Grade: 6th Grade
Get the Lesson Materials
Evaluating Algebraic Expressions Guided Notes & Doodles | Order of Operations
$4.25
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
An algebraic expression is a set of mathematical operations and variables represented using symbols, numbers, and operators. It can be used to represent a wide range of mathematical relationships and formulas.
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.
In an algebraic expression, a variable, coefficient, and constant are all important components. Here is a breakdown of the difference between them:
- Variable: a symbol that represents an unknown value or quantity in an expression.
- Coefficient: the numerical factor that is multiplied by a variable in an expression.
- Constant: a fixed number or value in an expression that does not change.
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:
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
Evaluating algebraic expressions can be useful in a variety of real-life situations. Here are some examples:
- Calculating the total cost of an order with a discount or tax applied
- Determining the amount of money saved over time with compounded interest rates
- Figuring out the distance and time necessary to travel a certain speed
By understanding how to evaluate algebraic expressions, students can apply these skills to everyday situations and make more informed decisions.
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.
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.