Take-Home Final Exam Math

EDEL 3394 Math EC-6 – Take-Home Final Exam (60 Points) Part I: Teaching Scenarios (20 Points) Name:__Michelle Castillo______________________________________ For each section below, you will choose one scenario. Each section’s scenario is worth 10 points and you must answer each question in full sentences. Your responses must fully address the scenario and answer all parts of the question. Your response must be coherent and appropriate to the scenario. I am not grading grammar, spelling, etc. Your responses will be assessed for their clarity, accuracy, and applicability to the situation. Section 1 Fraction Teaching Scenarios Choose one of the following scenarios and type your answer below. Scenario 1 Imagine that you are teaching a group of sixth graders to solve the following problem: A rope 43 3 8 meters long is cut into pieces which are each 5 3 meters long. How many such pieces can we get out of the rope? 1. Describe how you would approach this problem with your students in a way that builds on their prior mathematical knowledge and/or skills related to the division of whole numbers. 2. Suppose your answer is A B C where A, B, and C are whole numbers so that 0 < B < C and C ≠ 0. How would you explain to students what the A means and what the B C means? Scenario 2 Imagine that one of your sixth graders missed your lesson on fraction division. He studies the textbook and attempts the homework on his own. The next day he comes and tells you, “The book says 17 8 ÷ 5 9 = 17 8 x 9 5 but I do not understand why.” How would you respond to this student and help him understand the process? Answer (in your first sentence, please indicate what scenario you chose): In this section, I chose scenario two. The first thing that I would mention to the student is the equals sign in the middle. The equal sign is defining that the equation 17 8 divided by 5 9 is equal to 17 8 × 9 5 . Although, I would tell the student that we are going to check if that equation is true. First let’s start off with the division. 17 8 ÷ 5 9 equals to 3 33 40 . Multiplying the first fraction by the reciprocal (inverse) of the second fraction is the same as dividing two fractions. To get the answer you are going to flip the numerator and denominator and change the operation to multiplication to get the reciprocal of the second fraction. The equation then becomes 17 8 x 9 5 . In order to multiply fractions, you are going to multiply the numerators first, then multiply the denominators. So, seventeen times nine equals one hundred fifty-three and eight times five equals forty 17 x 9 8 x 5 = 153 40 . The fraction 153 40 can not be reduced. This fraction is considered an improper fraction, so you are going to convert it into a mixed number by dividing the numerator one hundred fifty-three by the denominator forty. After dividing this fraction, your answer should be 3 33 40 . Now, let’s multiply the second equation which is 17 8 x 9 5 . You are going to multiply the numerators which is seventeen times nine which equals to one hundred fifty-three and multiply the denominators, eight times five which equals to forty, 153 40 . You are going to convert it again to a mixed number

by dividing one hundred fifty-three by forty because this is an improper fraction. Your answer should be 3 33 40 . Now, look at both answers, are both answers the same or different? Correct, they are the same so then this equation would be correct because 17 8 ÷ 5 9 and 17 8 x 9 5 both equal to the same answer which is 3 33 40 . Section 2: Choose one of the following scenarios and type your answer below. Scenario 1: Working with Families A student in your class has been doing very well with multiplying 1 and 2-digit numbers. However, when you begin with three-digit numbers, he begins to struggle. Although it may be due to the size of the numbers since there are more opportunities for errors, the student knew how to do all of the steps with two-digit numbers, so it is probably not due to regrouping issues. You ask him to show you how he is solving the problems and he shows you a “trick” that his dad taught him. You explain why we avoid tricks and get him back on the right track, but a few days later, the same thing happens. As you talk to the student, you find out the child’s father is encouraging his son to use the trick because the “new” way is stupid. What would you tell the student? How would you address this situation with the family to ensure you can all be on the same page. Scenario 2: Frustrated Student Mrs. Winn is monitoring her students during independent seatwork. She observes Justin getting frustrated with one of the math problems he is working on. Justin slams his pencil down, which causes Mrs. Winn to go over to him immediately. She asks Justin why he slammed his pencil down and if she can help him. He responds, “I am never going to understand this. My mom and dad said they were not good at math, and I hate working on this stuff.” Mrs. Winn says, “I went over this on the board multiple times and you gave the thumbs up that you know what we were doing, so you need to calm down and look at the book because everything is there.” If this was your classroom, what could you have done differently to prevent this situation? What is wrong with Mrs. Winn’s response and how would you have responded to Justin if it happened even after you took steps to prevent it? Scenario 3: Advice from a Veteran Teacher You have been teaching skip counting and 10 more/10 less for two days more than the district’s pacing guide suggests. Although the school plans for each unit lasting 1-2 days more than the guide, you know that students will not have the concepts mastered for another 2-3 days. You talk to a veteran teacher about what you should do and he/she responds, “Don’t worry about it. Just go to the next unit because you have to be ready for STAAR and even if they don’t get it, they can catch up later. Besides, that stuff is easy. If they are struggling now, they are never going to get math, so don’t hold back the good students just to help the ones who are behind.” What would you do in this situation? How would you respond to the teacher and his/her statement? Who else would you reach out to and how would you ask them to help you? Answer (in your first sentence, please indicate which scenario you chose): In this section, I chose scenario two. If this were my classroom, I would have comforted the student by saying that it is okay to not get some math equations on their first try. Everybody usually has trouble on some math equations, take a deep breath slowly Justin and relax. I would tell the child to come meet me in the banana table and I am willing to help him with the problem he is having trouble on. I would not let Justin leave the banana table until he has fully understood what the assignment is about by him asking questions if necessary. The wrong thing about Mrs. Winn’s response is thinking that the students reading the book will get them to understand the concept. Sometimes students learn on a one-to-one basis instead of just reading from a book. If Justin continues to have trouble with the assignment and the one-to-one session in the banana table, I will provide physical objects and use these physical objects to illustrate the problems he is having trouble on for the student to understand the concept better. I would tell him that it is okay to not understand everything all at once