ALEX | Alabama Learning Exchange

Equations and Solutions

You may save this lesson plan to your hard drive as an html file by selecting "File", then "Save As" from your browser's pull down menu. The file name extension must be .html.

This lesson provided by:

Author:	Morgan Boyd
Organization:	Retirement

General Lesson Information

Lesson Plan ID:	35677
Title:	Equations and Solutions
Overview/Annotation:	This lesson will use the substitution property to determine solutions to equations and inequalities. The students will be given a replacement set of values. The student will check the values to determine if the result is true or false. The values that are true will be the solution. The student will graph the inequality solutions on the number line. This lesson results from the ALEX Resource Gap Project.

Associated Standards and Objectives

Content Standard(s):

Mathematics
MA2019 (2019)
Grade: 6

18. Determine whether a value is a solution to an equation or inequality by using substitution to conclude whether a given value makes the equation or inequality true.

Unpacked Content

Evidence Of Student Attainment:

Students:
Given situations that have been modeled with equations or inequalities:

Substitute given specified values for the variables and the evaluate expressions.
Determine if the resulting numerical sentence is true when the specified values are substituted for the variables.
Explain with mathematical reasoning why a specified value is or is not a solution to a given equation or inequality.

Teacher Vocabulary:

Substitution
Equation
Inequality

Knowledge:

Students know:

Conventions of order of operations.
The solution is the value of the variable that will make the equation or inequality true.
That using various processes to identify the value(s) that when substituted for the variable will make the equation true.

Skills:

Students are able to:

Substitute specific values into algebraic equation or inequality and accurately perform operations of addition, subtraction, multiplication, division and exponentiation using order of operation.

Understanding:

Students understand that:

Solving an equation or inequality means finding the value or values (if any) that make the mathematical sentence true.
The solution to an inequality is often a range of values rather than a specific value.

Diverse Learning Needs:

Essential Skills:

Learning Objectives:
M.6.18.1: Define exponent, numerical expression, algebraic expression, variable, base, power, square of a number, and cube of a number.
M.6.18.2: Compute a numerical expression with exponents, with or without a calculator.
M.6.18.3: Restate exponential numbers as repeated multiplication.
M.6.18.4: Choose the correct value to replace each variable in the expression (Substitution).
M.6.18.5: Calculate the multiplication of single or multi-digit whole numbers, with or without a calculator.

Prior Knowledge Skills:

Use comparison symbols.
Examples: >, =, or < .
Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits using >, =, and < symbols to record the results of comparisons.
Comparison symbols.
Examples: >, =, and < .
Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits using >, =, and < symbols to record the results of comparisons.
Compare two fractions with the same numerator or the same denominator by reasoning about their size.
Recognize that comparisons are valid only when the two fractions refer to the same whole.
Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
Convert fractions to decimals.
Compare two decimals to tenths.
Compare whole numbers.
Identify comparison symbols.
Examples: >, <, and = .

Alabama Alternate Achievement Standards

AAS Standard:
M.AAS.6.19 Match equations and inequalities to real-world situations.

Local/National Standards:

Primary Learning Objective(s):

Using the replacement set, the student will be able to determine the solution to a given equation.

The student will be able to graph the solution to an inequality.

Additional Learning Objective(s):

Preparation Information

Total Duration:	31 to 60 Minutes
Materials and Resources:	Notebook Pencil Calculator Ruler Textbook (will use for additional examples, if needed) https://www.youtube.com/watch?v=ArbMdAMYd_s https://www.youtube.com/watch?v=nif2PKA9bXA http://www.commoncoresheets.com/Algebra.php (Worksheet from the first box "Using Substitution to Solve Problems" and third box "Expressing Inequalities on a Numberline"--make copies for all students) Same website fourth box "Writing Inequalities from a Numberline" for the accelerated students (make appropriate amount of copies) Bell Ringer Substitution 6th Grade (located in the attachments) Exit Slip Substitution 6th Grade (located in the attachments--make copies for all students)
Technology Resources Needed:	Interactive Whiteboard Calculator
Background/Preparation:	Teacher: The teacher will need to preview the videos to assess good stopping points for students to ask questions. The teacher will need to select a worksheet from the first, third, and fourth boxes on the website http://www.commoncoresheets.com/Algebra.php and make copies for the students. Student: The student will need to know the following terms: replacement set, solution, and substitution. The student will need to be able to use the order of operations adequately.

Procedures/Activities:

Before:

The teacher will have the bell ringer (in attachments) on the interactive whiteboard. The students will answer the questions in their notebooks. The teacher will ask selected students to answer the problems. The teacher will do an informal assessment to see if the students are ready to continue. The teacher will write on the interactive whiteboard, “Replacement Set and Solution.” The teacher will discuss the meanings of these terms. The replacement set will be the numbers used to test the equation. A true result when substituting the number for the variable means that the number is a solution. A false result when substituting the number for the variable means that the number is a not solution.

During:

The teacher will start the video https://www.youtube.com/watch?v=ArbMdAMYd_s. The teacher will stop the video and solicit questions from the students. As the teacher stops and continues the video, the teacher will make informal assessments.
The teacher can use more examples from the class's textbook as needed.
The teacher will assign students into groups of four. The teacher will hand out the worksheet from common core sheets first box, "Using Substitution to Solve Problems." The teacher will monitor the students and use differentiated instruction. The teacher will allow students to answer the problems on the interactive whiteboard. The teacher will do an informal assessment.
The teacher will start the video https://www.youtube.com/watch?v=nif2PKA9bXA. The teacher will stop the video and solicit questions from the students. As the teacher stops and continues the video, the teacher will make informal assessments.
The teacher can use more examples from the class's textbook as needed.
The teacher will assign students into groups of four. The teacher will hand out the worksheet from common core sheets third box, "Expressing Inequalities on a Numberline." The teacher will monitor the students and use differentiated instruction. The teacher will allow students to answer the problems on the interactive whiteboard. The teacher will do an informal assessment.

After:

The teacher will hand out the exit slip Substitution 6^th Grade from the attachments. The students will answer and turn in as they leave the classroom. The teacher will grade the exit slip for a formal assessment.

Assessment

Assessment Strategies

Informal:

The teacher will do informal assessments during the videos.

The teacher will do informal assessments during group work on independent practice and adjust instruction as needed.

Formal:

The teacher will use the exit slip, "Substitution 6th Grade", as the formal assessment to make sure the standard is mastered.

Acceleration:	The teacher will make copies of the worksheet from the fourth box "Writing Inequalities from a Numberline" on the website http://www.commoncoresheets.com/Algebra.php. Students will be challenged to write an inequality to express the number line.
Intervention:	The teacher will assign students to groups with a peer tutor. The teacher will use differentiated instruction as needed with students by monitoring their work. The teacher will do one-on-one instruction if needed.

View the Special Education resources for instructional guidance in providing modifications and adaptations for students with significant cognitive disabilities who qualify for the Alabama Alternate Assessment.

ALEX Lesson Plan

Equations and Solutions