![]() If there are four 25's in 100 there are twelve 25's in 300) 3. Use knowledge about factors of 100 to understand the structure of multiples of 100 (ex. There are twenty 5's in 100 and five 20's in 100) 2. Develop familiarity with factors of 100 and their relationships to 100 (ex. Translated into specifics, the following are major goals in the third-grade unit on "landmark" numbers: 1. This means considerable work with multiplication and division as students answer questions such as, "how many 40's are there in 400? In 800? In 520?" To understand "landmark numbers", focus student work on taking apart and putting together 100 and multiples of 100, using 100's to build other numbers, and how numbers such as 20, 25 and 50 are related to 100 and multiples of 100. These are referents from which we build our knowledge about the number system. Deep understanding begins with understanding "anchor points" or "landmark numbers" such as 100, 200, 500, and 1000. Many students will not know that 342 is between 300 and 350, and cannot tell you easily how far 342 is from 400 or 1000. That is, they don't know that 342 is ten less than 352, ten more than 332, or a hundred more than 242. They can tell you that the number 342 is composed of "3 hundreds, 4 tens, and 2 ones" but they cannot make much used of what they recite and really don't have an understanding of the number's magnitude or relationship to other numbers. Third graders' knowledge of numbers in the hundreds are often not deep. Finding one's way around the number system and understanding its intricacies is an essential goal of elementary school mathematics. They are not able to apply their knowledge, because they have little idea about what these numbers mean. ![]() These same students may be correctly adding, subtracting, and multiplying with such numbers because they have learned memorized procedures. For example, if an athlete scores 5.73, is her performance better or worse than that of someone who scores 5.8? Many students believe that 5.73 is the better score, because 73 is bigger than 8. ![]() Traditionally, students have learned to calculate with fractions and decimals in the elementary grades without necessarily understanding how fractions and decimal numbers represent quantities less than 1. Their calculations are based on sound knowledge of the number system, and they typically have good strategies for estimating and for double-checking for accuracy. ![]() I know 60 and 60 is 120, then I subtract the 5 that I added on, and I get 115." People who use these methods can mentally figure this problem quickly and efficiently. Here's another example: Suppose we ask you to add 58 and 57 in your head, Some people will try to use the traditional "carrying" algorithm, but people with good number sense are more likely to do it another way: "Well, 50 and 50, that's 100, and 8 and 7 is 15, so it's 115." Others with good number sense might think: "Both numbers are close to 60. Rather, I immediately "see" that if I needed 1 cup of flour, I would need 1/2 cup more, but I need 1/4 cup more than 1, so in fact I need 1/2 cup and 1/4 cup, or 3/4 cup. Consider a practical example: I have 1/2 cup of flour and need 1 1/4 coups of flour how much more flour do I need? If I have a good sense of these familiar fractions, their magnitudes, and their relationships to each other and to 1, I would be unlikely to use the traditional subtraction algorithm, (1 1/4 - 1/2) which requires finding common denominators, transforming the mixed number into an improper fraction, then subtracting. To have "sense" about number means to understand how numerical quantities are constructed and how they relate to each other. Current research suggests that the math curriculum in the elementary school must contain a balance of study in at least four areas: number, statistics or data analysis, geometry, and what we call mathematics of change. They can find common denominators to add two fractions, such as 5/6 and 4/5, but don't know just by looking that the sum will be a little less than 2. For example, students can add up three given prices, but can't choose three items from a menu that total less than $4.00. Math 103 Lecture 3 The results of a traditional Math Education: students' weakness in number sense, estimation, and reasoning. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |