Download Instructor's Notes on Place Value and Whole Number Arithmetic and more Study notes Mathematics in PDF only on Docsity! Chapter 3 Notes for Instructors Content The third chapter of Long and DeTemple discusses place value and algorithms for whole number arithmetic. I tested students on the material from the first four sections. I spent one class discussing material from 3.5. I think this is a fun topic. This discussion was pretty relaxed so I only included one question from 3.5 on the exam. I did not have time to cover the material in section 3.6. Moreover, it is difficult to cover the calculator sections because we do not require that the students use a specific type of calculator. Notes and Suggestions Notes on Section 3.1:Numeration Systems Past and Present • In section 3.1, Long and DeTemple introduce some of the numeration systems that have been used throughout history. At first glance, it may appear that this section is extraneous and unnecessary, but I have found that this section really does provide a foundation for the positional system. It also introduces the concept of borrowing in subtraction and making exchanges with addition. • I tested students over the ideas from section 3.1, but I did not require that they memorize the notation from section 3.1 because I do not think the systems themselves are the point of section 3.1. • Manipulatives: Several types of manipulatives are discussed at the end of section 3.1. My personal favorites are the the classroom abacus and the base ten blocks. We do not have a classroom abacus, though you can improvise with some colored block and a sheet of paper. We do have a set of base ten blocks. The also mention UnifixTMcubes. I do not believe that we have any of these, but we do have multilink cubes which could be used in a similar mannar. • An Activity Note: I have provided you with a worksheet that I had my students do in class. I did not lecture on section 3.1. I found that it was better to have them work through the ideas of this section in small groups. Of course, I was willing to answer questions, but they should be able to figure out a lot of the ideas from the reading. I brought the Unifix block to class for the last quesiton on the worksheet. I doubt the designer of these blocks intended them for this purpose, but they did help the students. Notes on Section 3.2:Nondecimal Positional Systems • In section 3.2, students study the concept of place value in nondecimal system. Nor- mally students find the nondecimal positional systems frustrating. It is not uncommon to hear comments along the lines of “I will never teach this stuff to my students” and “Who would ever use this stuff?” With regards to the latter comment, you can 1
