Interdisciplinary Unit Plan Algebra I Section [5 Lesson Plans, 1 Test (w/ key)] Jesse Steffen
Lesson Plan #1 Introduction Lesson: Introduction/7-1 Length: 45 min Age or Grade Level Intended: Algebra 1 Academic Standard(s): A1.5.1: Use a graph to estimate the solution of a pair of linear equations in two variables. Performance Objective(s): Given 6 problems that use a graph to estimate a solution, students will answer them with 80% accuracy. Assessment: 6 problems will be given out of the textbook as homework and will be handed in tomorrow. Advance Preparation by Teacher: Supplies: Duct tape, masking tape, blue tape, army men. Move the desks as far back as possible to make as much room as you can in the front. Use duct tape to tape a + on the floor. This will be the X and Y axis. Use masking tape to make a grid so it is essentially a graph on the floor. Put the blue lines representing rivers making the lines. Make one start at point (-3,-2) and have equation y=x+1. Have the other one start at (-2,-4) and have equation y=2x. Have a blanket covering everything above vertical line x=-1. Put a small army or army men on point (3,-4). Procedure: Introduction/Motivation: Tell the students that we will be incorporating war and its effects on development in algebra class as much as we can for this unit. Ask the students how they think math is used in war. Here are some things you can say if they don t: finding the right trajectory for a missile, figuring out how many soldiers you want fighting, figure out how many types of people you will need (tanks, foot soldiers, horse back in older days, etc), what is the best weapons to use for the environment, what path is the quickest to the enemy, etc. We will be using this grid to see an example of how math can be used in a battle. Step-by-Step Plan: 1. Explain to the students that back in the day where there were no cars or tanks and everyone got around on foot, horse, or boat, rivers were very high traffic areas. This would make the places where 2 rivers came together very important in times of war. This picture represents 2 rivers. Tell the students they have a map of the rivers but it ends before it shows the rivers meeting. Ask the students to hypothesize how they would figure out where they meet in this situation? (Bloom s Synthesis) (Gardner s Visual/Spatial) 2. If they say walk along or take a boat up the rivers, explain to them that that wouldn t work because if the enemy already has where the rivers come together they would easily be overpowered. If they don t get the answer, tell them that if they could make a grid on the map they have and find it out with algebra. 3. Once you have a grid you can find the equations to each of the rivers as if they were lines. The
easiest way to do this is slope intercept form. Ask one of the students to tell you the slope of one of the rivers. Write this answer on the board. (ANS: should be 2 or 1) (Bloom s Knowledge) 4. Once they do this ask another student how the first student got that answer. (Bloom s Comprehension) (Gardner s Verbal/Linguistic) 5. Ask another student what the y-intercept of the chosen line is. (ANS: 0 for the line with slope=2 and 1 for line with slope=1) 6. Pick another student and ask them what the equation is for the other river. Write this on the board as well. (ANS: again it should be y=2x or y=x+1[whatever wasn t previously picked]). (Bloom s Application) 7. Ask the students how they can find where they meet after knowing the equations of both of the rivers? (ANS: use the slope to extend both of the rivers until the cross.) 8. Sketch the graph quick on the board and continue the lines until they intersect. Ask one of the students what point it is that they intersect. (ANS: (1,2) ) (Gardner s Logical/Mathematical) 9. Ask the students if they were the leader of this small army (the army men), how would they find the equation of the line that gives them the shortest path to the intersection of the river. (ANS: draw a line from the army to the river intersection and one thru the y-axis. The you take the slope of that (-3/1) and the y-intercept (5) ) 10. Ask the students to use this information and find the equation with a partner. (ANS: y=-3x+5) (Gardner s Interpersonal) 11. Tell them to do 1-11 odds page 343. Closure: Tell them what they think the equations would look like if they never intersected. Would you be able to tell with just the equation or would you have to graph it? This is what we will be going over next class after we review the stuff we just went over today. Adaptations/Enrichment: Student with ADHD: Let them write the equations on the board when the other students answer and let them draw the graph. This way they have something to do rather than just try and sit still and listen. Student that is hearing impaired: Have a copy of the notes to give them after class so they can just watch our lips instead of taking notes. Also sit her as close to the front as possible. Student that is gifted and talented: Ask them to answer the question in step 7. This is the new material in this chapter, so most of the students won t know the answer. Ask them after how they know the lines will intersect there and not somewhere else (ANS: Because they are linear equations so they are in straight lines.) Student with autism: Have them sit in the front to minimize the distractions. Avoid putting posters and other things that might distract them in the front of the room. Give them a stress ball to squeeze during the lesson so they have something to do that keep them moving a little bit. Reflection: The 6 problems will let me know how much we need to review this material tomorrow. I am hoping they will answer these with 80% accuracy, but if they don t it isn t a big deal because I will go over it again tomorrow if I have to. Hopefully by walking through it step by step the students will understand it enough to do this homework assignment.
Lesson Plan #2 (Teaching a Skill) Lesson: 7-1 Continued: 1, 0, and Infinitely Solutions Length: 45 min Age or Grade Level Intended: Algebra 1 Academic Standard(s): A1.5.1: Use a graph to estimate the solution of a pair of linear equations in two variables. Performance Objective(s): Given 16 problems where students graph two lines and find their solutions from the textbook, students will answer them with 80% accuracy. Assessment: 16 problems from the textbook will be given as homework and will be handed in tomorrow. Advance Preparation by Teacher: Draw a coordinate plane on the board. Use a ruler to make lines straight and even. Make the whole thing like a grid, do not just put the x-axis, and y-axis with dash marks. Make sure the x-axis and y-axis are clearly marked. Draw in the line y=-2x+1 in blue. Procedure: Introduction/Motivation: Tell the students not to open their book yet. Ask the students what the river would look like if they never crossed. Once drawn on the coordinate plane, ask how many solutions it will have. Transition to the steps now where more questions are asked about 2 lines that never intersect. (Gardener's Visual/Spatial) Step-by-Step Plan: 1. Ask one of the students to come up and draw a line that does not ever intersect the blue line. Make the new line red. Once they are done, call up another student to draw another line that does not ever intersect the blue one. Make this line green. (Gardener's Bodily/Kinesthetics) 2. Ask the students how many lines can be draw in that do not ever intersect the blue line. (ANS: infinity) 3. Ask the students if the red line and the blue line will ever intersect. (ANS: no) (Gardener's Mathematical/Logical) (Bloom's Synthesis) 4. Tell them that lines that do not ever intersect are called parallel lines. 5. When 2 separate lines are parallel to the same line, those 2 lines themselves are also parallel. In other words, in our example, the red line and the green line are both parallel to the blue line, therefore the red line is parallel to the green line. We will go over why in just a minute. 6. Ask the students what they notice about what these lines all have in common. If they do not know, then write the equation of all the lines on top of each other to see if they can think of it after that. (ANS: The slopes are the same) 7. If you have not already, write the equations of the lines on the board. Show them that if the slope of the red line = the slope of the blue line, and if the slop of the green line=the slope of the blue line, then the slope of the red line = the slope of the green line. This is a small proof of step
5. 8. Ask the students to take what they know and say why you can have infinitely many lines that are parallel to the blue line. (ANS: The slopes will be the same but the y-intercept can be anything, therefore there are infinitely many lines.) 9. Ask the students, how many solutions were we getting for our lines yesterday? (ANS: 1) (Bloom's Knowledge) 10. Ask why we were only getting 1 solution. (ANS: because they intersected 1 time) (Bloom's Comprehension) 11. Ask them, knowing this, how many solutions will parallel lines have? (ANS: 0) (Bloom's Analysis) 12. Ask them if there is any other way to draw 2 straight lines that would have more than 1 solution. Tell them you want to find a line that intersects the blue line more than once. This problem is a little bit more difficult so they might not have the answer. As they answer tell them to come up and draw the line on the board. 13. If they do not get the answer draw it up for them. Draw a line right on top of the blue line. Ask the students how many times the line you drew in intersects the blue line. If they do not get the answer remind them the definition of the point where 2 lines intersect is where they have a point in common. If they still do not get it, ask how many points in common these 2 lines have. (ANS: infinite many points) 14. Ask them if there are any lines that will intersect at exactly 2 places. (ANS: No, if they intersected at exactly 2 places, that would mean one of the 2 lines is actually a curve.) 15. Tell them to open their books now and turn to page 342. At the bottom of the page there is a box that says, Summary. This box gives the 3 situations we went over and describes what the equations of the lines have in common. 16. Assign to them numbers 15-23, and 26-32 on page 344. The students can work in groups if they would like. (Gardener's Interpersonal) Closure: Tomorrow we will be learning how to find the solution of a line without looking at the graph. We will be given to 2 equations and finding where the lines will intersect if we graph them. Adaptations/Enrichment: Student with ADD: I will let this student get up to draw some of the lines on the board. This will get them up and moving so they do not have to sit still the whole time. I will also make sure I walk past their desk a couple times so they do not start talking to their neighbors and distracting others. Student with learning disabilities: I will copy the notes for the lesson and give it to him/her before class starts. By doing this they can fully focus on what I am lecture about and on my examples rather than trying to write down what I am saying. Student with Behavior Disorder: Encourage the student to work alone on their homework. Some students that have a behavior disorder work better in small groups. They are able to focus better and stay on task. Student with Autism: I will have a stress ball that I will let them hold during my lesson. This will give them a way to move around without tapping their desk or rocking which will distract others in my classroom.
Reflection: The questions I ask during the lesson will let me know if I need to go into more depth or if they are keeping up with my pace. When I get the assessment back I will be able to see what I have to go over again before I move on to the next section. The next section heavily relies on this section so I have to make sure everyone is comfortable with this section before I move on.
Lesson Plan #3 (Another Content) Lesson: 7.2 Solving Systems Using Substitution Length: 45 min Age or Grade Level Intended: Algebra 1 Academic Standard(s): A1.2.2: Solve equations and formulas for a specified variable. 5.6.8: Use simple sentences (Dr. Vincent Stone is my dentist.) and compound sentences (His assistant cleans my teeth, and Dr. Stone checks for cavities.) in writing. Performance Objective(s): Given 12 problems that students have to solve for x and y, students will answer them with 80% accuracy. Also the students will write a story that include this mathematical strategy and will use simple and compound sentences. Students will include at least 5 compound sentences. Assessment: 12 problems will be given out of the textbook as homework and will be handed in tomorrow and a story will be given to hand in in 2 days. It will be graded out of 6 points, 1 point for each simple sentence (up to 3) and 1 point for each compound sentence (up to 3). Advance Preparation by Teacher: Supplies: masking tape, duct tape, and blue tape. Create the same grid you did in the first lesson. Do not mark the rivers in yet though. We will be solving the equation with substitution and then the students will lay the rivers down. Procedure: Introduction/Motivation: In our first lesson we talked about rivers meeting and how important that is to battles. We can find where 2 rivers met by using the slope and making a graph. After doing this you can visually see where the 2 rivers intersect. Well what if the people did not have time to make a graph and plot both of the rivers? In this lesson we will be learning how to find where 2 lines intersect by using substitution. At the end of the lesson we will be practicing writing simple sentences and compound sentence by writing a story where math is used to solve a problem. (Bloom's Synthesis) Step-by-Step Plan: 1. Write down 2 equations on the board: y=2x-3 and y=x-1. Tell the students that these are the equations for our rivers. Briefly explain how war has developed rivers because rivers were once the best way to transport lots of people. So the rivers would develop because trading posts would develop and towns would form since they were high traffic areas. 2. We are now going to use these equations to find where the rivers meet. We will then graph them to check our answer. 3. They call it substitution because we are substituting one equation in for the other. We know y=x-1, so we can replace the y in the first equation with x-1. You can pick either equation to do
this, they will both give you the same answer. 4. So now we have the equation x-1=2x-3. We only have one unknown so we can solve for x to get the answer. Ask what we should do first to solve for x. (ANS: Subtract x, subtract 2x, add 3, or add 1 to each side are all answers for this.) Ask another student what to do next. (ANS: this would depend on the first step.) Once they solve for x you will get x=2. 5. Now we take x=2 and substitute that back into one of our first equations. Again it can be either one. Ask the right half of the room to solve for y for the first equation and have the second half solve for the second equation. This will show then that they will get the same answer and show them they can use either equation. The answer will be y=1. 6. This gives us the ordered pair (2,1). This is the intersection point of our 2 rivers (lines). Have the students check to see if this is correct by having a few volunteers to graph the 2 lines on the floor using the blue tape and seeing where they cross. Have them do this on their own and walk around the room to see how everyone is doing. This is an example of how your story could start. (Bloom's Analysis)(Gardner's Mathematical/Logical) 7. Now tell them that the way they can check their answer is by plugging x=2 and y=1 to one of the equation. Tell the students to do this and ask then to explain how they can tell if they have the right ordered pair. (ANS: The equation will make a true statement, in this case 1=1. If it was 2=1 it would be wrong because 2 does not equal 1) (Bloom's Comprehension) 8. Tell the students to open their texts and turn to page 348. The example we just did is like example one in this section. 9. Now lets take a look at example #2. In this example we start with 2 equations that are not solved for y. So the first step will be solving these for y. Ask the students what equation they would solve for y. You can solve either of them for y, but one of them is much easier. (ANS: the second one is easier because there is no coefficient in front of the y variable). Let the students solve this equation for y. Let them work on this on their own and when everyone is done, ask one of them what they got. (ANS: y=6x-7) 10. Once you have this equation solved for y, you sub it into the first equation. Let the students finish this problem on their own to see if they understand. They have the book as guidance but ask them to not use the book to see what they know. They are not getting graded on this so there is no real reason to look off the book. (Bloom's Application)(Gardner's Intrapersonal) 11. Example 3 in the book is the same as the ones we have done, but we have to get the equation out of the story problem. So we will go through the first part of finding the equations and leave the rest for the students to do if they want. 12. Read the problem out loud and have them follow along. Point out that they labeled the number of buses as b, and m the number of minivans. In the paragraph it said they had 8 drivers total. This means that if you add the number of bus drivers and the number of minivan drivers have to add up to 8. So the equation will be b+m=8. 13. It also stated that there at 193 people total. The buses seat 51 people and the minivans seat 8. So each bus holds 51 people and each van holds 8. So if you have 2 buses and 3 minivans, you would have 102 people in buses and 24 people in minivans making 126 people total. Knowing this what would we do to make and equation that adds up to 193 people. (ANS: 51b+8m=193) 14. Once you know this they can solve for m or b and then sub it into the other equation to solve for m and b. 15. In math we have a lot of problems that are story problems. The problem we just went over was a story problem. To be able to solve these types of problems you have to be familiar with how they are set up. There are 2 ways of writing a sentence. It can be a simple sentence like, I lost my homework. or a compound sentence like, I lost my homework, and was late for class. 16. What is the difference between a compound sentence and a simple sentence? (ANS: A compound sentence joins to ideas that could be 2 separate sentence, often using a comma.)
17. How many compound sentences does the story problem in example 3 have. (ANS: 3) 18. Write a short story about an army getting ready to go into battle that uses math in some way. This can be 1 paragraph or 2 pages, whichever you want. It does not matter what time period its in. Be sure to include at least 3 compound sentences and 3 simple sentences. (Gardner's Verbal/Linguistic) 19. Assign 1-4, 5-15 odds, 18, and 24. Tell them that if they work quietly they can work in groups. (Gardner's Interpersonal) Closure: Tomorrow we will be learning a new way of solving equations called elimination. Once you know these three ways you can pick what you like best or analyze the equations and decide which method will be quickest and easiest. Adaptations/Enrichment: Student with ADHD: Let them be one of the students that stands up and graphs the lines on the floor. This will get them up and moving. Student with a Learning Disability: I will copy my notes and give it to them before class. This way they do not have to multitask and takes notes as they try to learn what I am teaching. Student with Behavior Disorder: Encourage the student to work alone on their homework. Some students that have a behavior disorder work better in small groups. They are able to focus better and stay on task. Student with Mild Mental Retardation: Meet with one of the higher level students before class and tell them to work on their assignment with the exceptional learner. Then the higher level student can explain it to them if they have trouble. Reflection: I ask a lot of questions as I go through the lesson so I will be able to tell if they are understanding my lesson. When I give them a problem to work on by themselves in the middle of my lesson I will walk around to see if they are getting it really well or if any of them are still struggling. Lastly the homework I assigned will be handed in tomorrow and graded before I give my next lesson, so I will be able to go over some problem areas if needed before I start the next lesson.
Lesson Plan #4 Lesson: Solving Systems Using Elimination (7-3) Length: 45 min Age or Grade Level Intended: Algebra 1 Academic Standard(s): A1.5.4: Understand and use the addition or subtraction method to solve a pair of linear equations in two variables. (Core Standard) Performance Objective(s): Given 12 problems that use the addition and subtraction method, students will answer them with 80% accuracy. Assessment: 10 problems from the textbook will be given as homework and will be handed in tomorrow. Advance Preparation by Teacher: No advanced preparation is needed. Procedure: Introduction/Motivation: On the first day of class we talked about when we have 2 rivers and how we can find where they meet by using a graph. Yesterday we talked about how to find where they meet by using substitution. We are going to further out development and learn a new was to find where they would meet, however we will not be having a war. Just like societies develop over time, so does math. Counting dates back to 30,000 BC. The earliest forms come from India, Egypt, Mesopotamia, and China. Algebra itself came from Mesopotamia about 3800 years ago. This was so primitive that they did not have negative numbers or fractions. If you were to get in a time machine and go back to that day, you would be considered a genius for sure. It is hard to say where the methods we have been using the last few days to solve systems of equations came from and what time period. The important thing is that we have it now and we are going to use it today. :) Step-by-Step Plan: 1. The method we are going to be learning today is called elimination. This would be used when you have an equation that if you would solve for a variable, you would get fractions which would be hard to deal with using substitution. For example, if you have the equations 5x-7y=- 18 and 3x+7y=34, solving for x and y gets messy. If you solve the first for x and y you get x=(7/5)y-18/5 and y=(5/7)x+18/7. In the second equation you get x=(-7/3)y+34/3 and y=(- 3/7)x+34/7. 2. We will solve this equation by using elimination now and you will see it is much easier. Elimination is when you add 2 equations together to eliminate one of the variables. You can subtract to, but I find it easier to add. The biggest key to doing this is staying organized. If there is an equation that obviously has bigger numbers then you will want to put that one on top. So we set up the equation like this:
5x-7y=-34 Now add them together 5x-7y=-34 3x+7y= 18 + 3x+7y= 18 When you add the 7's cancel 5x-7y=-34 + 3x+7y= 18 8x+0y=-16 Now we have the equation 8x=-16, so x=-2. (Gardener's Visual/Spatial) 3. Once we have what one variable is equal to, we simply sub it into either of our equations and solve for the other one. Half the class solve for the first equation and half solve for the second on their owns. (ANS: 1 st ] -10-7y=-34, 10+7y=34, 7y=24, y=24/7; 2 nd ] -6+7y=18, 7y=24, y=24/7) 4. This equation does have a fraction at the end, however, we do not have to plug that fraction back into the equation at all, so its not that bad. Do you think this method was easier for this problem than the last one? (Bloom's Analysis) 5. The second part in the lesson is elimination when you do not have the same coefficient in both equations. What do you think we would do if we have the equations 7x+15y=32 and x-3y=20? (ANS: You multiply the whole second equation by -7.) (Bloom's Evaluation) 6. So -7(x-3y=20) -7x+21y=-140. Now we can use the elimination method that we just went over to solve for x and y. have them solve this on their own and compare answers when they are done. (ANS: y=-3, x=11or (11,3)) (Gardener's Intrapersonal)(Bloom's Application) 7. Tell the students that got y=3 and x=11 to stand up. (Gardener's Bodily/Kinesthetic) 8. Pick one of the students that is standing to solve it on the board for the other students to see and check. 9. Make sure they know that when they solve for 1 variable and then sub it back in, any equation will work, even the very first one before it was multiplied by -7. 10. Now ask the students how they think they would do one of these problems if there is no way of multiplying one equation to match a coefficient in the other one. For example, what would they do with the equations. 3x-10y=-25 and 4x+40y=20? (ANS: You have to multiply both of the equations by something, namely the first by 4 or -4 and the second by3 or -3 depends on the first.) (Bloom's Analysis) 11. Ask the students to solve this equation on their own and compare answers. (ANS: x=-5, y=1) 12. Again, have the students that got it right stand up and have one of them do it on the board. 13. Lastly before you let them go on their own, make sure they know that to check their answers you do it the same way we did it yesterday. You plug the x and the y variables we found into the equations and see if we get the left side to equal the right side. 14. Assign 1-25 Odds, skip 15. Let them work in groups if they would like to as long as they stay quiet. (Gardener's Interpersonal) Closure: This is the last method we will learn to solve a system of equations. This is very important to any math. I used these methods in every math class I had in college. Next year in Algebra 2 you will learn how to do this with 3 equations and 3 unknowns. Adaptations/Enrichment: Student with ADHD: I will have this student do one of the problems on the board to give him/her a chance to move around. If he/she does not get it right, I will still have them do it on the board and have the class help him/her work through it.
Student with Learning Disabilities: I will give them a copy of my notes before class so they can pay attention and not have to keep up with writing the notes down. After the lecture is over I will meet with him/her and make sure they understand everything fully. If they do not I can go over a problem or two that is due for homework to give them some extra guided practice. Student that is Gifted and Talented: I will have this student show the class how to do the last example where you have to multiply both equations by something. They should pick up on how to do this after doing the example before this one. They will be able to put it into words the other students understand, making it easier for them to learn while challenging this student. Student that is Hearing Impaired: I will give this person a copy of my notes before the lecture so they can follow along and watch my lips so they know what I am saying. I will also make a conscious effort to face the student more and not talk while I am facing the board. Reflection: I will be able to walk around the room during the problems that I have them do on their own during the lesson. This will let me see how well the students are understanding it. I also have the homework assignment that will be graded before the lesson tomorrow. If there is one that a lot of the students had a problem with I will be able to walk them through it so they understand it before we move on. Sources: Allen, D. (1997, January 22). A General View of Mathematics Before 1000 b.c.. Retrieved from http://www.math.tamu.edu/~dallen/history/1000bc/1000bc.html Wadzicki, M. (2004, January 19). Early History of Algebra: A Sketch. Retrieved from http://math.berkeley.edu/~wodzicki/113/histintr.pdf
Lesson Plan #5 Lesson: C.O.D: War Culminating Activity- Game Lesson plan by: Alina BigJohny, Karla Conrad, Brian Kunze, Jesse Steffen Length: 20 min for rules, then 25 min for the review games per class. Age or Grade Level Intended: Algebra 1 Academic Standard(s): A1.5.2: Use a graph to find the solution set of a pair of linear inequalities in two variables. A1.5.3: Understand and use the substitution method to solve a pair of linear equations in two variables. A1.5.4: Understand and use the addition or subtraction method to solve a pair of linear equations in two variables. Performance Objective(s): Given 12 problems covering solving by graphing, substitution, and eliminations, students will answer them with 80% accuracy. Assessment: 12 problems from the text book will be given as homework to help them study for the test on Monday. Advance Preparation by Teacher: Have score sheet to hand out to the teams. Procedure: Introduction/Motivation: Today we are going to play a game among the entire grade; the questions in each class will be a review of what you have learned during this C.O.D: WAR unit and will also help you review for your assessment on Monday. The top ten teams will receive extra points towards their homeroom s amount for penny wars. At the end of this game, we will announce the penny war winners! For this competition, you will need to be in groups of five. You will get points by correctly answering questions in each of your content areas: English, World Geography, Algebra and Pre-Algebra. (Since we have two math classes within our interdisciplinary team, we are treating them as two different content areas.) - Students break into groups of five. (Gardner: Interpersonal) o Come up with a creative team name. - Pass out score sheets. o These will be used to record points earned in each class. Teachers will sign each students sheet in order to keep accurate and fair records. - Go over rules. Write on board. (Gardner: Visual-Spatial) o No cheating. Keep answers to yourself. o If you take advantage of this game, teachers can take away points. o Ties will be broken by rock-paper-scissors during the ending presentation. Once teams have done this explain that they will now be rotating into the class rooms and you will have review in each class. If your group answers the questions right then they will get points. Since there are 4 classes we will be rotating 4 times.
Step-by-Step Plan: (the following is the review I will give each class, so it is only 20 minutes long, but I will be giving the review to 4 different groups.) Have the students do each of these problems on their own, and then when they are done, check with their group and figure out the right answer. Walk around the room while they are working to make sure all the students are doing what they are supposed to be doing. This is NOT a race so take your time and help out your team mates. (Gardener's Intrapersonal) 1. Write the equations y=2x-3 and y=x-1 on the board and have the students graph the equations to solve. This is the first point they are able to receive in this class. Have the whole group stand up when they have found their final answer. (ANS: (2,1)) (Gardener's Bodily/Kinesthetic) 2. Have one of the students that got it right draw the graphs on the board. (Bloom's Application) 3. Have someone else in that group explain how they solved for the problem. (Bloom's Comprehension) 4. Now write the equations y=-5x-25 and y=-5x +33 and ask the students to solve. This time have them raise their hands when they are do not. This should not take to long. This is the second point. (ANS: no solutions, the slopes are both -5, therefore the lines are parallel and never intersect) 5. Once all the teams are standing ask one of the groups to tell the class the answer and make them state why it has no solution. (Bloom's Knowledge) 6. Now put the equations y=-4x+8 and y=x+7. Have the students solve this by using substitution. When they are doing and have their final answer have then all sit on the floor. This will be the third point. (ANS: (0.2, 7.2)) 7. Ask if anyone has any questions on that problem. If someone does, have the team that got done first do the problem on the board. 8. Tell them you are going to write 2 more equations on the board, but you have to write what you think the answer will be on a separate sheet of paper. Whatever team has the closest hypothesis will get a point regardless of if they were wrong or right once they solved it. (Bloom's Synthesis) 9. Write the equations 5x-6y=-32 and 3x+6y and have them hypothesize the answer. Go around and pick up their guesses as they work on this problem. Have them all touch their nose when their group is done. (ANS: (2,7)) 10. Again ask if anyone is confused on this problem. If they are have the quickest team demonstrate this on the board. 11. Assign pg 343: 1-7 odd; pg 350: 1-7 odds; and pg 356: 1, 3, 9, 11. This assignment is not due but should be completed to help study for the test. Make sure you tell them that if they study their old homework and do the knew homework they will do fine on the test. Closure: During the penny wars and the little competition we had today you should see how war can help the development of a country. Just in class with the competition you guys were more into it and trying harder. When a country is at war they try to invent the newest stuff that can help them win the war. This trickles down to helping us get what we want. For example, say the army invents an ear bud to put in your ear that is voice commanded and you can use it to call other troops in times of need. Next thing you know, the newest cell phones will be ones that is just and ear bud in your ear. Adaptations/Enrichment: Student with Autism: I will make sure he/she knows ahead of time that the day will be a bit out of the
ordinary and we will not be doing the usual routine. I will make a time line for him/her so they know what to expect. I will also give them a choice whether they want to participate or not. If they do not want to I will have them work on the homework assignment I assigned in the resource room. Student with a Learning Disability: I will meet with this student and another higher level student to talk to them about being in the same group. This way the higher level student can help out the learning disabled student in every class. Student that is Gifted: I will put this student in a group with a lower level student. I will make sure he/she knows to explain to the lower level student how to do problems that they are struggling with. This will help the lower level student understand and it will help the gifted student study for the test. Student with ADHD: I have put a lot of places in this activity to move around. That will allow this person to be able to move and not be forced to sit still all day. Since the movement is built into the lesson they will not be disrupting class. Reflection: This will show me how well the students know what we have gone over so far. If a couple of them are struggling hopefully the rest of their team will explain it. If not, hopefully they will ask for help when you give them the option. The assignment is a couple problems from each lesson we did. We will go over this Monday right before the test to see if there are any last questions.
Name: Chapter 7 Test Directions: Answer each question and put a box around your answer. Be sure to show your work because partial credit can be given. This test is out of 25 points. The amount of points for each question is indicated in the parenthesis. 1) Solve these 2 equations by graphing. y=-(1/3)x +1 and y=(1/3)x -3 (3 points) 2) Solve these 2 equations by graphing. y=(3/4)x-2 and y=(3/4)x +6 (2 points) 3) Solve these 2 equations by graphing. 3x+4y=12 and 2x+4y=8 (3 points) 4) Solve these 2 equations by graphing. y=2x+4 and y=2x+4 (2 points)
5) Solve these 2 equations using substitution. y=x-2 and 2x+2y=4 (4) 6) Solve these 2 equations using substitution. 3x-6y=30 and y=-6x+34 (4) 7) Solve these 2 equations using elimination. 2x+5y=17 and 6x-5y=-9 (2) 8) Solve these 2 equations using elimination. 3x+2y=-9 and -10x+5y=-5 (5)
Name: Chapter 7 Test (ANSWER KEY) Directions: Answer each question and put a box around your answer. Be sure to show your work because partial credit can be given. This test is out of 25 points. The amount of points for each question is indicated in the parenthesis. 1) Solve these 2 equations by graphing. y=-(1/3)x +1 and y=(1/3)x -3 (3 points) ANSWER: (6, -1) 2) Solve these 2 equations by graphing. y=(3/4)x-2 and y=(3/4)x +6 (2 points) ANSWER: No solution, same slope, parallel lines. 3) Solve these 2 equations by graphing. 3x+4y=12 and 2x+4y=8 (3 points) ANSWER: (4,0) 4) Solve these 2 equations by graphing. y=2x+4 and y=2x+4 (2 points) ANSWER: infinitely many solutions
5) Solve these 2 equations using substitution. y=x-2 and 2x+2y=4 (4) ANSWER: (2,0) 6) Solve these 2 equations using substitution. 3x-6y=30 and y=-6x+34 (4) ANSWER: (6,-2) 7) Solve these 2 equations using elimination. 2x+5y=17 and 6x-5y=-9 (2) ANSWER: (1,3) 8) Solve these 2 equations using elimination. 3x+2y=-9 and -10x+5y=-5 (5) ANSWER: (-1, -3)
References: In lesson plane #4 I used two resources. Allen, D. (1997, January 22). A General View of Mathematics Before 1000 b.c.. Retrieved from http://www.math.tamu.edu/~dallen/history/1000bc/1000bc.html Wadzicki, M. (2004, January 19). Early History of Algebra: A Sketch. Retrieved from http://math.berkeley.edu/~wodzicki/113/histintr.pdf
Reflection Over Team Teaching I think team teaching could be beneficial in many different ways if it is done right. All the teachers working together and knowing what the students are learning in other classes is a great way to connect lessons. I think team teaching would work best if the theme was a lot more vague and was easy to apply to every content. The middle school I observed at had some team teaching but they did not even have a them. There were a few instances that the teacher referred to another class and what the students were learning in there but that was about it. The teams were almost more for the teachers than the students. If they had a problem with a student they all had that student at some point so they worked together to deal with it. I think team teaching is greatly beneficial for the students as well as the teachers when it is done correctly. I did not like the way we did the team teaching in our class. Every time I wrote a lesson plan I felt like I spent most of my time trying to find ways to tie it into our theme. I could have gotten the lesson done much quicker if I were able to use my own attention grabber and build off that, rather than think of one that went with the theme. If the theme would have been more vague it also would have been easier to tie into my lessons. It could be because it is hard to relate a specific kind of math to something that does not usually relate to math. I feel like our team did not really operate like the text book example because we were not in the actual settings of a class room. It is hard to guess how students will react in certain situations. It is also hard to imagine yourself in a classroom when you have never been an actual teacher in a classroom. We were going to plan a field trip for one of our lessons but then thought about parents and parent approval slips and all the work that we did not think about before. If we would be teachers we would know what all that includes and would be able to plan accordingly. After our field trip idea we decided to have a scavenger hunt throughout the school. We started planning and were just getting ready to start writing things down when we thought about 4 teachers supervising 120 kids in the halls. This was the last thing
to enter our minds, but I feel like it would be the first thing that my cooperating teacher would think about. There really is no way to fix this problem, but that is why we did not work like the text book example. In our team I was the one that had money to print things off. This means I was the one that had to get everyone's information together and copy and paste it all onto one document and print it. This seems easy but with the whole group being very busy, I was getting things from different people at different times. We all helped a lot with brain storming different things to do for our culminating activity. We would start with an idea and all build on it until it was the idea we wanted. Our group worked really well together and everyone did their fair share of the work. I feel like our group would have worked really well together in an actual school setting. When all is said and done, I definitely learned a lot about team teaching. If I would have been hired into a school and told to team teach I would not have known what they were talking about had it not been for this class. Its not my favorite way to teach but at least now I can teach like that if they want me to. I will also be able to pitch in suggestions if I am working in a team. I know what kind of themes work best for math teachers and which ones require a lot of work. Team teaching with the right teachers can be an excellent way to help the students learn more.