Need Assistance Lesson

Lesson Plan: Direct Instruction

 

Title: Solving One Step Equations Using Addition

 

Overview:

In this lesson, students will learn the concepts behind solving for an unknown quantity in an equation.  Students will learn that variables are used to represent unknown quantities in equations.  They will also learn the steps involved in solving a one step equation (in the form of x + 3 = 7), and understand the concept of an equation as a scale that must always remain in balance.  In addition to meeting these content objectives, students will also be expected to use higher order thinking skills in writing short explanations of the reasoning they used to arrive at their answers.  This lesson is important because it helps to develop the logical thinking skills needed to successfully explain mathematical reasoning.  These skills will be important in more advanced mathematics, as well as the study of other academic subjects.  This lesson also allows students to continue developing their understanding of how letters are used to represent numbers in mathematics—an important foundation for algebraic thinking.  By developing these algebraic skills at the middle school level, students will be able to make a smooth transition to high school mathematics.

Grade Level and Subject Area:

· 6th Grade

· Math

 

Materials Needed:

· Pencils and paper for notes and guided practice problems

· Whiteboard and dry erase markers

· “One Step Equations” worksheet for each student

· Test for each student

Time Required: 50 Minutes

Curriculum Integration/Connections:

Writing – For several problems, students will be asked to provide a written explanation of the reasoning and mathematical processes they used to arrive at their answers. 

Accommodations of Diverse Learners:

· Visually impaired students – Students with visual impairments will be seated near the whiteboard and given materials with larger print.

· Gifted students – Students who work at a faster pace will be given the option of working on more advanced problems during independent practice. 

· ELL students – Students who are not yet fluent in English will be allowed to work in a small group with a volunteer away from distractions. 

· Math IEP Students - Students who have difficulty in math will be allowed to work with a volunteer away from distractions.  They will also be given materials with problems that are appropriate for their ability levels.

Content Objectives:

· Students will learn the meaning of the term “variable.”

· Students will learn the steps involved in solving for an unknown quantity.

· Students will be able to solve one step equations using addition.

· Students will be able to verify their answers.

· Students will be able to explain the equation solving process in writing.

Objectives:

Math

Grade Level:  6

 

Core Content: 6.2. Mathematical expressions and equations  (Operations, Algebra)

 

Performance Expectation: 6.2.E Solve one-step equations and verify solutions.

 

Writing

Grade Level:   6

 

 

EALR:  2. The student writes in a variety of forms for different audiences and purposes.

 

 

Component:   2.2. Writes for different purposes.

 

 

Anticipatory Set:

I will begin the lesson by talking about balance. 

      I will ask the students: “What does it mean to balance?”  I will then allow time for student answers and write them on the board.  I will be looking for students to acknowledge the idea that it takes an equal distribution of weight on both sides.  I will reinforce this idea by saying, “So, you could say that balance is about something being equal on both sides or having an equal distribution of weight.”

      Next, I will draw a basic scale on the board.  In the middle of the scale, I will make an equal sign, so that the top of the scale looks like this:  _________ = __________.  (There would be a basic vertical line down beneath the equal sign).

      I will say, “Here is my scale.  If I have 5 pounds on one side of the scale, what do I need to have on the other side of the scale for this scale to be balanced?”  (I will allow a student to answer and write it on the board) “Good, so if I have 5 pounds on one side of the scale and I have 5 pounds on the other side of the scale, then my scale will balance.”

Next, I will introduce the term “variable.”

      On one side of the scale, I will write “60 tons” and on the other side I will write the letter x.  I will ask, “In order for my scale to balance now, what does x need to be?”  (I will then allow student answers). “Good, so in this problem, x = 60 tons.”  I will write this out on the board.

      I will explain that in Algebra, whenever we have an unknown quantity, we use something called a variable: “Instead of using a blank for the unknown number, we are going to use a variable whenever we have a missing quantity. In the problem that we just did,  x was the variable used the represent the quantity that we were looking for.”

       On the board, I will write:   “VARIABLE- a letter representing an unknown quantity,” and explain that many times, they will see x as the variable, but the variable could also be any other letter.

      To reinforce the idea of balance, we will visit the following website and complete a problem using the interactive moving balance scale model.

o    http://nlvm.usu.edu/en/nav/category_g_3_t_2.html

Modeling:

I will explain that equations are just like the scale.  Both sides of a scale need to be equal to balance, and both sides of an equation need to be equal to balance.

· I will write the first example on the board and explain the steps of the procedure used to solve the equation:

. I will write on the board: x + 7 = 15

. “First, we want to have the variable all by itself.  To do this, we need to reverse what was done to x in the equation.  Because the problem adds 7 to x,  I will subtract 7.  Remember that we need to keep the equation balanced.  What I do on one side of equation, I must do on the other side.  So, I have +7 –7 which = 0, and I have 15 – 7 = 8.  The answer to my problem is x = 8.”

                                               On Board:   x  + 7 = 15

                                                                        -7     -7

                                                                   x        =  8

o   “To check your answer, plug it back into the original equation.  For this problem, we would replace the x with 8.”

o   On Board: 8 + 7 = 15

o   “Because this is correct, we know that our answer is correct.”

I will model a second example with the variable and the constant in the reverse order, explaining that the procedure is the same:

· “To get the variable by itself, we need to subtract 12 from both sides.”

o   Write on the board:

  12 + x = 18

                   - 12        - 12

                            x  =  6

Students will be required to write explanations of the steps they used to solve problems.  I will model this by writing on the board:

o   Because 12 was added to x on the left side of the equation, I subtracted 12 on the left side.  To keep the equation in balance, I also subtracted 12 from 18 on the right side.  This gave me a value of 6 for x.

Guided Practice:

I will begin the first guided practice problem by saying, “Let’s do one more together.  Someone talk me through it as I write on the board.”      

o   Write on the Board:

                                       x + 122 = 295 

I will select a student volunteer to walk me through the steps, and write them out on the board:

                                     x + 122 = 295

                                           -122   -122

                                      x           = 173. 

I will have another volunteer explain the steps that we used, and write them on the board:

o   I subtracted 122 from the left side of the equation because 122 was added to x on the left side.  To keep the equation balanced, I also subtracted 122 from 295 on the right side.  This gave me a value of 173 for x. 

I will answer students’ questions and move on to the worksheet.

Independent Practice:

The students will be instructed to begin working on the problems from the worksheet on their own. 

Checking for Understanding/Questions:

Throughout the lesson, students will be encouraged to ask questions.  I will also randomly select students to answer questions at certain points during the lesson to make sure that the class understands what I am teaching them.  While the students are working on the independent practice worksheets, I will walk around the room asking them to explain their answers to the problems they are working on. 

Closure:

At the end of the lesson, I will ask the students several questions:

o   What is a variable?

o   Why did we use subtraction to solve these equations?

o   Why do we need to do the same thing to both sides of an equation?

o   How do we check our answers?

Assessment Strategy:

Informal: I will check for understanding by asking students questions throughout the lesson.  I will also walk around the room and check students’ work during independent practice. 

Formal: Students will complete the problems on the test.  This test will be formally graded using the attached rubric.