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

Part II: Error Analysis (40 Points) For each section below, choose one error analysis case (20 points each). Your responses must fully address the case, be coherent, and be appropriate to the case. Each response will be scored according to the following: scoring/marking of student work (5 points); identifying and analyzing the error patterns (10 points); devising two strategies for helping students overcome their error patterns (5 Points). When scoring, mark each incorrect digit in the answer, instead of marking the entire answer incorrect. Include your answer at the end of the sections, indicating which case you chose in the first sentence Section 1 Case 1: Javier, Age: 12, 7 th Grade Mrs. Moreno, a seventh-grade math teacher, is concerned about Javier’s performance. Because Javier has done well in her class up to this point, she believes that he has strong foundational mathematics skills. However, since beginning the lessons on multiplying decimals, Javier has performed poorly on his independent classroom assignments. Mrs. Moreno has asked you to conduct an error analysis on Javier’s assignment. For this case, please complete the following: Score his paper, identify what error he is making, the type of error it is (factual, procedural, or conceptual), and explain two (2) ways you would help Javier fix his error. Case 2: Madison, Age 8, 2 nd Grade

Madison is a bright and energetic third-grader with a math learning disability. Her class just finished a chapter about money. Madison’s individualized education program (IEP) suggests using concrete objects to help her more easily grasp concepts. Therefore, Ms. Brooks used play money and was pleased with Madison’s performance. In an attempt to build on this success, Ms. Brooks used concrete objects (cardboard clocks with moveable hands) to teach telling time. The class is now halfway through the chapter, but Madison seems to be struggling with this concept. Consequently, Ms. Brooks has asked you to conduct an error analysis of her work below. For this case, please score Madison’s paper, identify the error she is making, the type of error it is (factual, procedural, or conceptual), and explain two (2) ways you would help her fix the error. Section 2 Case 3: Elias, Age 7, 2 nd Grade

Case 4: Shayla, Age 10, 5 th Grade Shayla just moved to a new school district and h er new class is learning how to add and subtract fractions with unlike denominators . Shayla’s teacher, Mr . Holden, is concerned because Shayla is performing poorly . Before he can provide instruction to target Shayla’s skill deficits or conceptual misunderstandings, he needs to determine why she is having difficulty . For this reason, he has asked you to conduct an error analysis of her work below. For this case, please score Shayla’s work, identify the error she is making, the type of error it is (factual, procedural, or conceptual), and explain two (2) ways you would help her fix the error.

Section 1 Answer: Type answers here, beginning with which scenario/case you chose. In section one, I chose case one which was Javier, age twelve in the seventh grade. For this assignment, I would score his paper a grade of 8% since he only did get one answer correct out of twelve questions. The type of error is conceptual. The error that is he is making is placing the decimal in the wrong place once he solves the answer. One way that I can help Javier fix this error is multiplying both numbers without focusing on the decimals till the very end. For example, in the first question it is .78 times 9.6, Javier will multiply both numbers as regular numbers as 78 and 96. The answer he should get is 7488. Once he gets the answer, he will then count how many spaces each number must get to its decimal. For example, the number .78 has two spaces since there are two numbers after the decimal point. In the number 9.6, it has one space since there is only one number after the decimal point. Once he counts the total amount of spaces, which is three in total, he is going to count from left to right three numbers in his answer. When he reaches the third number, he is going to place the decimal right before the third number. This would give him the exact place on where to place the decimal which would be 7.488. Another way that I can fix Javier’s error is reteaching on simple multiplying decimals that the decimals from one number line up with the other number such as 3.4 times 5.6. This will give Javier more practice on how to place the decimals on the right space for the answer, by counting how many spaces each number is after the decimal which would be two. Section 2 Response: Type answers here, beginning with which scenario/case you chose. In section two, I chose case three which was Elias, age seven in the second grade. For this assignment, I would score his paper a 60% since he did get six questions right out of ten questions. The type of error is procedural. The type of error he is making is not carrying the number when he adds the first column of the two-digit addition. For example, in the first question it is 18+22. In the assignment, it is 18 at the top and 22 at the bottom. 8 plus 2 is 10. So, in this case, you would carry the number 1 on top of the other 1 and leave the 0 at the bottom. Then add 1 plus 1 plus 2 which would equal to three. The answer would be 40 not 310. The reason why he got 310 was because he did not carry the number 1 when he was supposed to. One way I would help him fix this error would be an open number line. This number line will help him how to add double digits. For example, he is given a problem that is 37+48. He will create three number lines to come up with the right answer. He will add the tens (30 + 40) and then the ones (7 + 8), starting with number line one. The number line begins at 30 (the tens from the first number) and continues to 70 after adding the four tens from the second number. He'll then add 7 by 8 to obtain 15, which he'll add by 70 to reach 85. He'll leave 37 as is on number line two and add the four tens from the second number. The 8 ones will be broken down into 3 + 5 and the 3 ones will be put together to make 80. He will then add the last five. He'll choose three of the eight ones from the second number in number line three to make a ten out of the number 37 (37+3=40). Then he will jump the last four tens to get to 80. Lastly, he will add the remaining 5 ones. The answer to this equation would be 85. Another way I could help him fix this error would be vertical addition in another way. Say the equation is 89+34. 89 is in the top and 34 is in the bottom. You are going to add the right side first which is 9+4. 9+4 equals to 13 but instead of carrying the 1 on the top, you are going to write both numbers below as how it is. Then, on the answer 13, put an X below the 3 and add 8+3. 8+3 equals to 11 so he will put the 11 next to the X. After, he will add those numbers without having to carrying any number which will equal to 123.