Download M316K - Foundations of Arithmetic Exam 2, Spring 2009 and more Exams Data Analysis & Statistical Methods in PDF only on Docsity! M316K – Foundations of Arithmetic Spring 2009 Exam 2 – Version P You have 50 minutes to take this exam. No books, notes, calculators, or other electronic devices are allowed. Please write everything you want me to grade in your blue book; you will be allowed to take these questions with you when you are done. On the front of your blue book, please indicate which five questions you want graded. If you don’t choose which questions I should grade, then I will choose for you at random. Also, please sign the upper right corner of your blue book; by your signature, you affirm the following Honor Pledge: “I pledge that I will neither give nor receive any unauthorized help on this exam. I will not use any books, notes, calculators, or other electronic devices while taking this exam. I will not attempt to look at any other student’s paper, nor will I engage in behavior that will put me at risk of accidentally seeing another student’s paper. I will stop working immediately when time is called.” ♠ ♠ ♠ PART A: Reading. Please answer one of the following questions. Keep in mind that your goal is to demonstrate that you have read the material and understood the important points, so don’t spend time trying to craft an exquisitely written essay. There is no length limit for this question, but you should easily be able to fit your response on one page. A1. On page 178 of the text, Bassarear says that “although multiplication can be seen as repeated addition, if that is all you see multiplication as, then your students can achieve only limited understanding.” Give two different, brief arguments supporting this statement. (You can use examples, problems, classroom situations – whatever you deem appropriate.) A2. Suppose your friendly (but demanding) instructor asks you to find all of the prime numbers less than 200. Assuming you had plenty of time (and paper), how would you perform this task without checking two hundred numbers one-by-one to determine whether each one is prime? Describe a reliable, step-by- step method you can use to find all of the prime numbers less than 200. Try to include enough detail to convince me that you could carry out this method if you had time to do it (one way to do this is to show the first few steps of the process). PART B: Explorations. Please answer two of the following questions. Do not mix-and-match parts of different questions; if you choose to answer a question, you are expected to answer all parts of that question. B1. Consider the subtraction problem 357 − 169. Show how to perform this operation using the standard algorithm, and then model the operation using base-ten blocks. (Don’t worry about drawing the blocks in full detail; just make sure your picture shows what you’re thinking.) Show how the steps in the standard algorithm correspond to things that we see or do when we use the manipulatives. (For full credit, show at least two correspondences.) B2. For each of the following calculations, explain why the answer given is not reasonable. (a) 583 + 742 = 1225 (b) 4281− 3785 = 504 (c) 84× 67 = 5028 (d) 4368÷ 62 = 704 1
