Lesson Plan Revamp

EDUC 150 Section 113

Steven LaMaita

10/5/15

Lesson Plan Revamp TemplateGrade Level(s): 7-9Subject area: AlgebraFocus Topic: Quadratics/Completing the SquareURL for the original lesson plan: http://www.teach-nology.com/lessons/lsn_pln_view_lessons.php?action=view&cat_id=5&lsn_id=25047Technology resource that you are adding: Interactive White Board

Step 1Step 2Step 3

ItemOriginal LP OnlineModified to Fit TemplateImproved with New Technology

Learning Objective1) Students have a beginning understanding of completing the square. 2) Students will begin to be able to solve quadratic equations by completing the square. 3) Students will build on their knowledge of complex numbers as they complete the square and solve.By the end of this lesson, students will re-structure quadratic equations into the correct format and solve all basic quadratic equations using the Completing the Square technique 4 out of 5 times.Same from step 2

Materials Neededoverhead, overhead markers, transparencies, whiteboard, whiteboard markers, calculator White board Markers Worksheets/Practice Problems PencilsThis lesson no longer needs the white board or markers or the worksheet, only need a pencil and paper for students to copy the equations from the interactive white board.

The Hook5 minutes- Teacher reminds students about what they did in the previous lesson - Teacher gives students the definition of completing the square - Teacher tells students that completing is when you can't factor or find the square root easily.- This lesson will start with a combined refreshment of the previous factoring techniques mixed with learning how to identify equations to factor using completing the square. Students will sort different given equations into groups of equations that they know how to factor, and equations that they have not yet learned. After a complete list of the completing the square factorable equations have been made, a quick definition of completing the square will be introduced.

For reference, the form of a completing the square equation is when the variable terms on the left with the constant number on the right or with a non-perfect square factorable quadratic equation.The lesson will start with a combined refreshment of the previous factoring techniques by displaying a file on the interactive white board with all of the previously learned formulas in the class. We will highlight the ones learned most recently using the enhancing magnifying feature to focus on the ones about factoring. We will then open up the vortex program which will have previously been filled by the teacher with equations set up in factorable forms previous to the completing the square method and quadratic equations that are disguised or obviously in a newer form that are solved using the completing the square technique. Students will come up one at a time and place an equation into the correct category. This will lead with a new interest in these different equations, using the vortex to not only reinforce prior knowledge but to make it clear what these new quadratic equations look like. The vortex will also condense a new list of equations that will be used for the next step in the lesson.

With an interactive white board the teacher needs to go over with the class the responsible use for the white board. Only one student at a time, using only the correct materials for the board in the software with only their own information correlating t the subject. They may not use profanity, put up any personal information, or touch anything on the screen that is not theirs. The vortex program may be new and may be the teacher should complete the first two equations and show what happens when they are right and wrong.

For reference, the form of a completing the square equation is when the variable terms on the left with the constant number on the right or with a non-perfect square factorable quadratic equation.

Direct Instruction10-15 minutes-Teacher has students factor, then learn how to complete the square so that they can factor - Teacher shows students how to solve quadratic equations when solutions are real, complex,and when a is not 1 -Teacher shows students how to complete the square in vertex form At this point we are going to factor Students are not allowed to use quadratic formula for any of these examples, they either have not learned it yet or it will make the problem much more difficult. Show step by step in process below, how to do completing the square. Since this is factorable by grouping and perfect squares, this is an example that works to show that completing the square and perfect squares give us the same answer. First prove the 2AM rule, (squared(2), Add the middle, Multiply the third) to show that 8+2 = 10 and 8*2 = 16. So the factors are x=-8, and x=-2, from prior class knowledge. Now show the same thing by completing the square

-16 Formula for completing square is and then add that number to both sides since the leading factor () has no coefficient.

Now the left side of the equation is factorable by grouping. Due to the perfect square of 25.

Now routine algebra functions are done to find the factors.

This then leaves us with the final answer and explains the process of completing the square for a simple factor

Explain that by using the formula above, you will always make the left side a perfect square and it will always be factorable by grouping. After the vortex activity, the students will all sit down and regain focus back to the teacher. The teacher will then use the different magic pens to show a more animated presentation of the formula and process of completing the square. This can be done by writing out one problem, the example on the left in Step 2, showing how to do it difficultly in grouping methods, and then use the enhanced pen to shadow out the background and zoom in on the changes being made in the completing the square method. At this point, a basic introduction to the method will have occurred and the formula to solve these questions will be given.

A step by step process seen to the left in step 2 will be completed on the interactive white board using the pen features to give the students the information necessary to succeed at this new method of factoring. Different color coding and using the blank/white cover up features on the interactive white board will help this process go by smoother and hopefully keep the students engaged and organized. The entire step by step process and presentation will be recorded on the interactive white board so that it can be referred to later by students when studying, if they need extra help, or if they are absent.

Guided Practice 10-30 minutesexample 1: (x^2)-12x+36=9 (solve and check) example 2a: (x^2)+20x+_ (cts) 2b: (x^2)+7x+_ example 3a: (x^2)+4x+1=0 (solve using cts) 3b: (x^2)+6x+12=0 example 4: 2(x^2)=-7x+1(a is not 1) example 5: y=(x^2)+5x+2 (vertex form)After giving the first example, the formula, and the style in which this method should be set up, students will start practicing. Because math, algebra especially, is easier said than done, after one clear easy example, it is better to send the students off to discover on their own the other tricks to Completing the Square.

Students will enter in groups of 3-4 depending on class size and each be given 2 problems to work on. One will be an easier example and the second will be a challenge problem including a coefficient in front of the leading factor. Estimating about 5-7 groups, after 5-10 minutes of working on these 2 problems, which after mastery of skill should take under 1 minute each, the students will regroup as a whole class and begin observing the board again.

While the students are working on the problems, the teacher should walk the room and see how each group is doing, but not correcting small mistakes. Big errors or lost students should be assisted by giving them the first step of using the formula, or dividing out the coefficient in the challenge problem.

After the 5-10 minutes are up, 2 representatives from each group will come up to the board and write down the process for their problems. The teacher will then ask the students of the whole class if they are correct, why they are correct, or what errors they may have run into. A lot of the problems that go with completing the square have little nuances that can be caught in this step of peer review, which the whole class can discover together.

After each group has presented their solutions, they should have a clear understanding of the material. The same activity will occur but instead of giving the students a worksheet, the different groups will be assigned two different problems from the vortex group in the completing the square section. The teacher will assign the problems to each group respectively so that they each get one simple example to test their understanding of the content, and then a more difficult problem that is not as obvious which may involve applying prior knowledge (an important skill in math courses) or a different way of thinking that as a group the different sets of students may be able to collectively solve.

Once the groups finish their first problem, the groups will go up to the teachers computer and use the interactive white board software to record their step by step process for their problem. There will never be more than one group up at a time and when the students are not entering their solution to the simple problem on the computer they will be working on the challenge problem with guided assistance from the teacher walking the classroom group to group. Since the simple problems only take upwards to 1 minute to complete, this will be a great time frame to make sure all students get their first problem recorded on the computer and have enough time to give a good shot at solving the challenging problem with the teacher reaching each group at least once.

The students will then play their recording and present their solution to the class. This is a great interactive whole class participation activity, because if the students recognize something they see may be a mistake they can call out Stop and explain what the error may be. This is a good reflecting period to either catch typical mistakes in the process that students make or to present a correct logical step by step process to these examples instead of just the teacher throwing information at the student.

The teacher will then always step in and explain the mistake and the common errors.

After each group has presented their solutions, they should have a clear understanding of the material.

Assessment5 minutes-Teacher asks students clarifying questions throughout the lecture. -Teacher tries to get students active in their learningTo complete the lesson, the teacher should put one more challenge problem on the board, and let the students work individually to try and set it up or solve it. The teacher will not assist them, but just take note of who has grasped it, and if the class still needs work on this or if they have a clear understanding. The challenge problem will be the basis of beginning of the next class to see how students did as well as with assigned homework.

Students who do not finish this problem in class will add it to their homework.

The challenge problem will be:

With a fraction as a solution. The last conclusion and assessment is the same from part 2 but just with writing the homework equation on the interactive board.

Reflection

Rationale for Technology IntegrationBy adding the interactive white board into this original lesson plan, it will enhance learning, creating a deeper root and understanding of the material being taught, as well as being more efficient in time and organization for both the students and the teacher. By using the white board the teacher can get all different types of learners involved and participating in class in various different ways. This technology gets the students out of their seats and using the white board to not only display and prove their own understanding of the material, but also teach the class by association as they watch the student present their understanding. The technology itself really helps visual, interactive, and immersive learners all at the same time. With the different color coding, blank cover ups, and calm animations used throughout a presentation it will help the visual learner better see the formula in action. For the interactive learner who needs to be more hands on, they get to actually go up to the board, complete a problem or an activity and do it by themselves to prove they understand the process. And for immersive learners who like the whole process of a teacher feeding them information, it still maintains a small feeling of that with the teacher using the board in a more organized way to present the information and having it written on the board. Therefore, the interactive white board clearly meets the needs of all students by creating different styles of teaching to appeal to all types of learners. The interactive white board also simply contains a multitude of different functions to help students with learning for math and especially with calculation lessons like this one. The features like the animations, the charts with the sealed boxes, the magic featuring pen, and the recording feature all work wonderfully for step-by-step procedural math tactics like completing the square. The interactive white board can be used to its full potential by having students each make their own small presentation and it does not require them to speak in front of the class if they choose not to which sometimes frightens students and shies them away from learning. By recording their own presentation on the computer they can just add comments and prove that they understand or they can talk as much as they want to give further explanation to their process. This lesson also puts the teacher in a really good role because they get to oversee and fix bigger glaring mistakes while letting the simple mistakes go and watch them flesh out how to avoid these simple errors later. This applies to all of the 21st century skills we have been discussing in class including collaboration, critical thinking, applying previous knowledge, and discovering the tricks to the problems by doing instead of watching. Overall, my newer lesson is a big improvement to the original plan. The lesson plan from the internet was only helpful to really give the examples that might be used in the vortex and in the presentations. Other than that there is no real useful material to help the students actual undedtsand and retain this knowledge. The learning objective is packed with a tough topic, and to achieve this goal students need a more constructive form of learning. By placing them in groups, perhaps assigned to pair different type of learners or students on different skill levels, the students can actually apply what they have seen already and what they know to actually make a discovery. This discovery can then be applied to all of the different completing the square problems, while gaining experience from other class members. The presentation portion allows students to prove in a different way than just looking at problems over and over again and trying to solve them, to prove not only to the teacher and class but to themselves that they understand the material. By adding the interactive white board the students are able to keep these presentation and the original lesson from the teacher and always refer back to exactly how it was presented if they need to study or to test their understanding. The vortex in the beginning is also a more fun and interactive to grab the students and keep them interested in the material from the very beginning. It gets the students out of their seats in a new environment where they will be forced to wake up and be attentive to what is going on which will hopefully carry them over the period of direct instruction so they fully grasp the material. In conclusion, I strongly feel that this lesson is a big improvement to not only the original, but my own lesson without technology because it helps students really do the learning themselves and using the teacher as another resource rather than their sole dependency.

Responsible Use of Technology

With an interactive white board this far into an algebra course, it could be safe to assume that the students have a basic understanding of how it may work, but in the event the white board is new or the students have never seen it before, there are tons of different rules and checks that a teacher must apply to the classroom to make sure it is used responsibly. Since the technology is used from the get-go, the teaching of how to use the technology will be used immediately. First, by using the vortex, the teacher will clearly demonstrate how it works by dragging either with their finger or the assigned pen the equation to its respective category. The teacher can show a correct and a wrong answer to show the full features of the vortex program. The teacher will also then show the different features that can be used in the students presentation during their own direct instruction proving the first simple equation and the base formula. This will introduce the different pens and the functions, including the recording feature that the students can use in their own presentation. While the students come up to record, the teacher can of course answer any questions they may have to enhance their presentation. This gives a good basis of functions the white board has and will allow success in the students work. With this privilege to go up to the computer as a group and use the software an the interactive white board comes with a lot of responsibility. The students will be told directly that absolutely no profanity or anything they may find funny may be written on their slide. There should only be material that is directly presentable and involving the idea of completing the square. There is no need for any names to be written on their slides so no bullying can occur in any way and no form of privacy will be invaded. They do not have to give any form of personal information so they do not have to worry about any of their personal information being presented. There are several other rules that go along with using the software and the smart board. If the students are using the computer to make their slide, they must stay in only the opened software that correlates with the interactive white board. No other tabs, no internet browser or any other programs should be opened because it may contain something inappropriate, personal, or off-topic. They also have to stay on their slide only. It should not take more than one slide to make their presentation so there is no reason to check out another groups work. This will eliminate the risk of deleting others work or copying something that has already been done. There should also be no other features used than those presented by the teacher in their first small lesson. This can tackle the issue of disrupting fonts and crazy animations, it must remain respectful. The students can only use the given materials to write on the board, whether it is the assigned pen or eraser tool or their fingers. If they use their own fingers they must be sure to clean them so it does not make the board disgusting. Also make sure that when they are writing using a pen that it is in fact the right pen and not another dry-erase or permanent marker. Lastly, the students must understand that only one person should be using the board or the software at a time. Not to be mistaken that only one student should be accessing the board the whole time, but that when presenting only one should be using it to avoid damage or miscommunication. Since the teacher is exhibiting in the opening and their direct instruction appropriate behavior, and after they set these rules, there should be no excuse for a student to not understand what is going on or to break these rules. If any student misuses the technology they will be asked to sit down and just diligently work on their assignment instead of aiding their group on the board.