What is Number Sense and How Can You Improve It?Date: 08/29/2007 at 11:55:56 From: Sarah Subject: What does the term "number sense" refer to What does the term "number sense" refer to on standardized math tests? The other categories are: Patterns, algebraic thinking, data analysis/prediction, measurement, geometric concepts. Our daughter scores pretty highly in all categories except "number sense"--in which her score is average. Date: 08/29/2007 at 14:39:40 From: Doctor Ian Subject: Re: What does the term Hi Sarah, You can think of "number sense" as being short for "common sense regarding numbers". For example, it's knowing that if I multiply 5.8 by 6.9, I shouldn't get an answer greater than 100, or less than 1. (Note that either of those could happen if I'm using a calculator, and type in one or both of the numbers incorrectly.) It's knowing things like: 1/2 is greater than 1/3, 2/5 is greater than 2/7, 2.6 is greater than 2.59, and so on. Or that 2/5 and 4/10 and 0.4 all refer to the same number. Does this help? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ Date: 08/29/2007 at 14:46:41 From: Sarah Subject: What does the term "number sense" refer to Thanks, this does help! Any suggestions on helping someone improve their "math sense"? If it really is like common sense, I don't know if you can teach that. Date: 08/29/2007 at 15:58:58 From: Doctor Ian Subject: Re: What does the term Hi Sarah, The way you develop common sense about anything is through experience. A concept that is closely related to number sense is estimation. A good habit to get into is always predicting what kind of answer you're going to get, using estimation. For example, if I'm going to multiply 75 by 259, I might think: that's on the order of 100 times 200, or 20,000. So if I get something a lot different than that, I have a problem. (The actual result is 19,425.) A second thing you can do to develop number sense is to get in the habit of always looking for simpler ways to do calculations, often by changing representations. For example, suppose I need to do this division: _____ 0.02 ) 44.8 One way to approach this is to scale both numbers by the same amount, to get _____ 2 ) 4480 Now I have a much simpler problem. I could also arrive at it this way: _____ 44.8 0.02 ) 44.8 = ---- 0.02 448/10 = ------- 2/100 448 100 = --- * --- 10 2 448 100 = --- * --- 2 10 A good measure of your number sense is probably the number of different ways that you can think of to do any particular calculation. A nice way to motivate this is to look for ways to do calculations in your head. Here are a few more examples: 1) 20 * 17 = (10 * 2) * 17 = 10 * (2 * 17) = 10 * 34 = 340 2) 243 - 87 = 246 - 90 <- Add 3 to each term = 256 - 100 <- Add 10 to each term = 156 _____ 3) 52 ) 2340 _____ = 104 ) 4680 <- Double each of them _____ = about 100 ) 4600 <- Make each a little smaller to get nicer numbers = about 46 (Real answer is 45) I hope this helps. Write back if you'd like to talk more about this, or anything else. - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ Date: 08/29/2007 at 19:54:06 From: Sarah Subject: Thank you (What does the term "number sense" refer to) Thanks so much! This makes "sense"! I really appreciate you taking the time to answer my questions in such depth and breadth. This is a super web site!! Gratefully, Sarah |
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