# Understanding and Application of Linear Equations

Understanding and Application of Linear Equations[1] [2]

Lesson Guide

Lesson Overview

The goal of these lessons is for students to be able to write expressions from word phases, write algebraic equations to represent real-world scenarios, and match linear expressions to word problems.  Often students are able to figure out the solutions to mathematical concepts taught in isolation, but are challenged when ask to explain what the answer means in the context of a word problem.  This lesson is designed to teach students the relevance of their mathematic answer.  Before introducing this lesson, think about some real world relevant examples where the algebraic equations would assist the students in their everyday lives.  Have these ready to address the issue of relevance in students’ lives.

Key Concepts

Understand the meaning of numbers in the context of the world and be able to apply that information in way that will make sense in real world scenarios.

Goals and Learning Objectives

• Create algebraic expressions
• Use equations to model situations
• Substitute values and evaluate algebraic expressions
• Be able to identify components of  linear expressions
• Be able to write and match linear expressions to word problems

Activate prior knowledge with this quick warm up. Quick review of what algebraic expressions are using Do Now 6.2.  Making sure to address misconceptions, especially for question 1, choices b, and c.   Problem 3 was created to start students thinking about relationships between the numbers, variables, and constant.

Foundational Practice, 5.2.  This activity is to help student make connections between numbers and variables.  Students can easily work through problems a – d, however for problem 1, supported may be needed.  It may need to be explained that when we do not know the value, we use a place holder called a variable – a letter that represents the missing and/or changing number.

Guided Notes – This activity will establish the foundation for writing expressions and modeling equations.  Have students read about Ben’s Family Farm on page 3, follow up with questions that to help student develop equations.

• How much does it cost for 1 person to enter the maze?
• How much does it cost for 6 people to enter the maze?
• How much would the farm collect if 10 people? 100 people?
• How can we show the amount of money collected for any number of people, (use “n” to represent any number of people) in an expression?

Explain the connection between n and the varying numbers of visitors.  Have students substitute numbers for n, to determine the total amount of sales for n people and make a table using that data.  In preparation for making a graph, introduce the relationship between independent and dependent values.  Questions to ask:

• What changes to make the sales amount increase or decrease?
• Does the ticket price make the sales amount change? If so, how?
• Does the number of tickets sold make the sales amount change? If so, how?

Explain that since the number of tickets effect amount of money collected, it is the independent variable; the amount of money collected is dependent on how many tickets are sold. Explain that the independent variable goes on the x-axis, and the dependent variable is on the y-axis.

Students will create a graph using their data tables, noting that the n values are plotted on the x-axis and the corresponding amount of sales is plotted on the y-axis.

Monitor the students’ progress.  Once finished, students should discuss what they notice about their graphs and what that says about the total sales of the Corn Maze.

Students practice skills using sheet 5.2 Extra Practice.  As you monitor their progress, especially note answers for problems 1, 3 and 6.  Look for whether or not students are placing the numbers and variables in the correct spot.  Question 1, do they see this as a division problem? Question 3, did student mistakenly use subtraction in their equation? Question 6, how do students respond to the fraction bar?

• Questions to ask struggling students:
• What does the variable represent?
• What does the number represent?
• What operation happens between the number and variable?
• If we substituted a value for the variable, how would we find out answer?
• If student answer these questions correctly, they can go to page 6.  Questions for students working on page 6:
• How does your expression represent the number of dimes Ella has?
• What is an efficient way to calculate the amount of money Ella has?
• In part e, how can you figure out the number of dimes Ella has?

Discussion regarding the term algebraic expression.  What comes to mind when you hear algebraic expression? What are the components of an algebraic expression?  Use AlgebraicExpressions_intro document to have students match expressions with statements.  Discuss what each variable means in the context of the statement.  This exercise is a preview of future expectations.  Note that the same numbers and values are used in all examples.

Gallery Walk and Discussion, students match expressions with statements.  This activity is about misconceptions, in all of the statements the sample numbers and variable will be used.

Activity

1. Six statements on poster paper will be placed around the room.
2. Each group member will have 6 sticky notes, students will be given 6 algebraic expressions and must write each expression on a separate sticky note.
3. Students will rotate around the room placing expression they think best match the statement onto the statement sheet.
4. Students will be given 1 – 2 minutes before rotating to the next statement. (time may be adjusted as necessary)
5. Once rotations are complete we will discuss their choices.  This will probably create some discourse because 15, 10 and x are used for all expressions.
6. Students defend their answers and the correct answer for each statement will be explained in depth, specifically the why the incorrect statements are wrong.

https://betterlesson.com/lesson/resource/2521010/algebraic-expressions_teacherversion-docx

Students will practice writing an algebraic expression to represent a word problem using algebraicexpressions_writing.  Ask students to work alone for several minutes before checking with a neighbor.  Once students have completed the worksheet, we will review, correct, then address any remaining questions/concerns.

Lesson will be complete using the formative assessment algebraicexpressions_exitticket.com.