Lesson 1 (90 minutes)

Solving Algebraic Equations Using Inverse Operations

Addition and Subtraction

 

(1-8 Pre-Algebra -PA) Solving Equations Using Inverse Operations

(1-11 Mathematics Connections - MC) Solving Equations Using Addition and Subtraction

 

 

Lesson Objective:

            Students will be able to use inverse operations to solve equations. Students will also be able to solve problems using equations using addition and subtraction.

 

 

Time (minutes) and Description:

2-3                   Attendance

10-15               Introduction Section 1-8 (PA) Inverse operations. Then the teacher will hand out 1-8 practice sheet (attached).

20-23               The students will be working on 1-8 practice sheet.

15-18               Teacher will ask for any problems on 1-8 Practice sheet and help students solve the problems on the overhead projector. The teacher will collect the entire classes 1-8 practice sheet (to be graded). The teacher will go through with the checking your understanding section of the PA book page 43 (copy at end of this lesson). The teacher should only go over the highlighted ones.

10-15               Teacher will do demonstration in front of class with a balance.

10-15               The teacher will introduce section 1-11 (MC) Solving Equations Using Addition and Subtraction. The teacher will give examples of one-step equations using addition and subtraction to solve them. The teacher will give Practice Worksheet 1-11 for the students to work on in class (attached). If they do not finish the work sheet they will have to take it home for homework (1-11 is do the next day beginning of period).

23-1                 Before time is up the teacher will ask the class if there are any problems which they might need help with, if there are the teacher will then do a few on the overhead.

 

 

 

 

 

 

 

 

 

 

What the Teacher Will Do:

      Inverse operations: (PA section 1-8)

            Introduction:

                        The teacher will start off with asking the students to define "inverse".

                        Then the teacher will go right into the following definition and examples of using inverse operations in equations.

 

            Definition - inverse operations undo each other. For example, to "undo" addition one would subtract. The same way division and multiplication "undo" each other.

                        9 +21 = 21 ®  9 = 21 - 12      or         12 = 21 - 9

 

                        9 + n = 18 ®   9 = 18 - n         or         n = 18 - 9

 

            Guided practice examples - the teacher should do this along with the students.

                        3 + 9 = 12 ®   3  = 12 - 9                   or         9 = 12 - 3

                        16 - 12  = 14 ® 16  = 4 + 12              or         -12 = 4 - 16

                        13t = 39 ® t = 39 ¸13                                    or         t =3

                        k ¸ 13 = 7 ® k = 7 ´ 13                     or         k = 91

 

      The teacher will now ask for any questions on inverse operations. If no, hand out 1-8 practice sheet. If yes, the teacher will clear up the students questions then hand out the 1-8 practice sheet.

 

      While the students are working on the 1-8 practice sheet, the teacher will have to walk around the room and make sure all students are on task and answer any questions they might. While doing the above the teacher will need to get set up for the Balance Demonstration.

      Before the teacher starts the balance demonstration, ask the class if they have any questions on 1-8 practice. If no, collect 1-8 practice to be graded and go on with the balance demonstration. If yes, the teacher will do a few problems that the class has on the overhead projector and then collect 1-8 practice to be graded and go on with the balance demonstration.

 

(Balance Demonstration)

 

            The teacher will have to set up the balance on a flat and level surface. The teacher will now attach an equal sign to the middle of the balance. The teacher will be using this to show if you do something to one side of the balance or equal sign it must be done to the other side. The teacher will do a few examples of addition, subtraction, multiplication and division to each side of the equal sign with using the weights or pennies. For example, if I add 3 ounces/pennies on the right side, what would one have to do to the left side for this to balance? The teacher must remember that "wait time" is crucial here. The teacher should state that this is what one needs to do to an equation one must do the same thing on both sides of the equal sign. What ever you add, subtract, multiply or divide to one side of the equal sign you must do the same thing on the other side of the equal sign. This will keep the equation in balance.

            Introduction: 1-11 (MC) Solving Equations Using Addition and Subtraction:

 

                        The teacher should refer back to and summarize the balance demonstration and the inverse operation practice sheet. Then the teacher will go right into the following examples of solving equations using addition and subtraction remembering the balance demonstration and the inverse operation practice. State the fact that one wants to get the value of the variable. Tell the students you want the variable = to something or something = to the variable.

·        If a number has been added to the variable, then you need to subtract.

·        If a number has been subtracted from a variable, then you need to add.

            Method of solving an equation using addition or subtraction:

1.      Identify the variable.

2.      Add or subtract the same number on each side of the equation to get the variable by itself.

3.      Check the solution by replacing the variable in the original equation.

            Subtraction:

            Solve:   x - 7  = 12                    Check:               n - 7 = 12

                   x - 7 + 7 = 12 + 7                                     19 - 7 = 12

                   x             = 19                                                 12 = 12

 

            Addition:

            Solve:      k + 0.5  = 0.9            Check:                k + 0.5 = 0.9

                   k + 0.5 - 0.5 = 0.9 - 0.5                            0.4 + 0.5 = 0.9

                   k                   = 0.4                                             0.9 = 0.9

 

            Guided practice examples - the teacher should do as many examples as needed for students to gain the knowledge needed for the 1-11 practice sheet.

                        b + 9 = 12        ®        b + 9 - 9  = 12 - 9        ®        b = 3

                        16 + k  = 21     ®        16+ k -16  = 21 - 16    ®        k = 5

                        x - 4 = 11         ®        x - 4 + 4  = 11 + 4       ®        x = 15

                        -7 + h  = 30     ®        -7+ h +7  = 30 +7        ®        h = 37

 

      The teacher will ask for any questions on solving an equation using addition or subtraction. If no, hand out 1-11 practice sheet. If yes, the teacher will clear up the students questions then hand out the 1-11 practice sheet. The teacher must remind the students to think about the balance demonstration and the guided practice examples. If the students don't get this done in class they must do it as homework. This practice sheet is due the next day.

 

 

 

      Five or six minutes before time is up in the period the teacher will ask the class if there are any problems which they might need help with, if there are the teacher will then do a few on the overhead.

What The Students Will Do:

Each student is required to participate in class. Class participation during the guided practice, lectures and balance demonstration, students will have the opportunity to receive 1 point. The one point is given to each and every student that stays focused and participates during class. In this such class at Hobart High School, it will be more reasonable to take a point off a student's participation grade for that day if he or she doesn't participate.

 

1-8 Practice sheet

The student is required to do this assignment in class. Students will receive a score out of a possible 25 points where the two story problems count as 2 points each. For the story problems, one point will be given if the equation is set up correctly and another point for the correct answer. This assignment will count towards the student's homework grade. (x / 25) Where "x" is the number of points the student received on this assignment.

1-11 Practice sheet

If there is any time left the students could work on the 1-11 practice assignment. If the student is unable to complete this assignment in class he or she is required to do it as homework and turn it in the following class. Students will receive a score out of a possible 30 where the four story problems count as 2 points each. One point will be given if the equation is set up correctly and another point for the correct answer. This assignment will count towards the student's homework grade. (x / 30) Where "x" is the number of points the student received on this assignment.

 

 

Special items:

            The teacher will need a balance, one that big enough so that the entire class can see it. The teacher will also need two sets of weights for the balance or just get 20 pennies. The teacher will also have to make and cut out an equal sign so it can be attached to the middle of the balance.

 

Assessment:

 

            Two assignments will be graded under homework 1-8 and 1-11 practice sheets. The student's participation grade, a one (1) or zero (0) will be given for this day.