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<p>It's first grade stuff in the curriculum my kids did.</p>

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<p>Miranda</p>

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<p>Miranda</p>

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<p>Yes, first grade for our school, too. Fun that she's interested enough to figure it out!</p>

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<div class="quote-block">Originally Posted by <strong>Tjej</strong> <a href="/community/t/1350726/math-level-question#post_16949061"><img alt="View Post" class="inlineimg" src="/community/img/forum/go_quote.gif" style=""></a><br><br><p>I can not figure out what you are talking about. What does that rule mean? It sounds like 3 concepts to me - doubling and + 1s and -1s. I am sure I am missing something.</p>

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<p>Tjej</p>

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<br><br><p>You can figure out 8+7 quickly if you remember that 7+7 is 14. So you figure out (7+7)+1 or (8+8)-1. It's a commonly taught mental math technique.</p>

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</p>

<div class="quote-container"><span>Quote:</span>

<div class="quote-block">Originally Posted by <strong>Geofizz</strong> <a href="/community/t/1350726/math-level-question/0_100#post_16949063"><img alt="View Post" class="inlineimg" src="/community/img/forum/go_quote.gif" style=""></a><br><br><br><br><p>You can figure out 8+7 quickly if you remember that 7+7 is 14. So you figure out (7+7)+1 or (8+8)-1. It's a commonly taught mental math technique.</p>

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<div class="quote-block">Originally Posted by <strong>Tjej</strong> <a href="/community/t/1350726/math-level-question/0_50#post_16949640"><img alt="View Post" class="inlineimg" src="/community/img/forum/go_quote.gif" style=""></a><br><br><p>Ah, thank you. Yes. I think this newborn is sucking my brain out with the milk!</p>

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<p>They do that, you know. It takes at least 12 months for those cells that got sucked out to regenerate!<br>

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<p>I can see doubling is easier than tripling, quintupling, etc - but we're talking about addition, not multiplication here. </p>

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<p>Back to the addition - in binary form, I can see that adding 2 identical integers is preferable to adding 2 arbitrary ones (just add 0, it's like multiplying by 10 in decimal) - but why the preference for base-10? Why would one need a trick to add 2 single-digit integers anyway?</p>

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<p>They teach this at school? I'm a bit surprised, or shocked rather - this is nothing like what I think of as math, and is this really part of some formal curriculum?</p>

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<p>Edited for clarity.</p>

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<p>Have you worked with many elementary aged children in math? I think those that post in this forum based on their own personal experiences and their experiences with their own children sometimes lose sight of the path a lot of kids must travel to learn math. I did some mental math not dissimilar to this in class today, and it baffled my students. <em>My college students</em>.</p>

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<p>Teaching strategies like this seems like an excellent thing to be doing, and will serve as a bridge to multiplication for some, and a path towards memorizing math facts for others.</p>

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<p>Skills come to different kids in different ways. Some kids will struggle with learning to add 7+8 and get the answer right every time. Teaching them a lot of different strategies really helps. Not every kid will need every strategy, but many will make use of it. If you don't have single digit addition down, then moving into multi-digit addition, multiplication and division will become quite laborious. The Learning at School board used to have long impassioned conversations about the necessity to learn addition and multiplication facts. The fact of the matter is that the more of these micro steps you can make automatic, the more of the brain you can free up to focus on the higher level thinking skills.</p>

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<p>These lessons start on single digit addition, but I've noticed my kids both use mental math tricks like this on larger numbers. My daughter does her homework now without a calculator, and often in her head. She can fluidly move between addition and multiplication, picking whichever strategy is most efficient.</p>

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<p>I use strategies like this to calculate tips, figure my average running pace, and estimate a wide range of things in life.</p>

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<p>A lot of arithmetic is a bridge to higher level math for kids. Many would say that it's not necessary, but for many kids who require to go through the concrete stages before the abstract, these are pretty necessary.</p>

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<p>I'm not sure your point about different bases? Sure, you can add and subtract in base 2, but why? This is a topic my DD has seen in her middle-school "math circle", a program for kids who love math. It was hard for them.</p>

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<p>But then I thought - hey, this actually can make things easier if the numbers are in their binary form and they can be arbitrarily large. For example, let's take 6 + 7, which is 110 + 111 in binary form. Doing long addition, one has to worry about carryover, this is prone to mistake for larger numbers.</p>

<p>Now, let's apply the trick above:</p>

<p>a. take the smaller of the 2 numbers</p>

<p>--- which 6 or 110</p>

<p>--- don't want to take the larger number, it's easier add 1 then subtract 1 later, in case of carryovers etc</p>

<p>b. double it</p>

<p>--- we have 12</p>

<p>--- but in the binary form, you just add a 0 because doubling in binary is like multiplying by 10 in base-10</p>

<p>--- so we have 1100</p>

<p>c. add 1</p>

<p>--- we get 13 in decimal</p>

<p>--- or in binary, 1100 + 1 = 1101</p>

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<p>I am all for learning the concrete first, you have to know your facts, mathematical or otherwise - but it's the over-complication and lack of generality that got me - the trick only works for single-digit numbers with very specific constraint.</p>

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<p>Though, at the end of the day, this is probably a matter of esthetics - I don't know, perhaps this can work for some ...</p>

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<div class="quote-container"><span>Quote:</span>

<div class="quote-block">Originally Posted by <strong>MamaMunchkin</strong> <a href="/community/t/1350726/math-level-question#post_16952741"><img alt="View Post" class="inlineimg" src="/community/img/forum/go_quote.gif" style=""></a><br><br><p>Yeah - I agree arithmetic is useful - that's not what bothers me. What surprise me is how the trick seems to complicate things. Why do you want to double anything when all you want is to add 2 single-digit numbers? The trick only works for a pair of very small numbers with certain pattern - why all the trouble?</p>

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<p>It does not seem to complicate it for the 5/6/7 yr olds in a regular 1st grade class.</p>

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<p>For most kids-- they find the higher integer math problems harder and result in finger count/numberline/etc the math problems past +/- 1,2 and for memorization, doubles are fairly quick for most kids due to the pattern. so if a kiddo knows 6+6.....but honestly may struggle with 6+7 or 5+6. They can easily +/- 1--- which for many kids this is easier than starting at 5and adding up 6, or finger counting, etc.</p>

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<p>The 1st grades here are also using the base ten to add/- higher numbers. If you know 15-10.....then you can easily find 15-9 by - 1. Same goes for 9+ 7 (you can easily figure it out if you know 10+7). </p>

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<p>The basic facts that have 6,7,8,9 seem to take longer to master. Using double +/- or base ten )=/- are great mental tools to help kids move past finger counting/number lines, etc.</p>

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<p>My kids DO use it for higher math since it is easy to use base tens with larger digits. They easily can mentally figure out what 500-432 is (they say it is 70 counting up by tens to 500 from 430 then add 2) or 40-21---- they know there are 20 between 20 and 40 then to add one, but they would not know how to 'borrow' to find the answer at this point.</p>

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<p>Their general education 1st grade class regularly does mental math like what is 18-9 +1 or what is 6+6-2 or what is two tens plus one or what is double 7 and take away 2. It is really fun to hear the kids do this and they love it!</p>

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<p>I could go on, but my point is that doubling/halving observations are extremely common in a small child's world. Far more so than, say, 5+6. As such, kids tend to naturally absorb these math facts without much if any overt memorization work. So when they're trying to answer addition problems that they don't have memorized, it is very natural for many of them to use those already-internalized doubles-facts as touchstones. My kids, like the OPs dd, all used this strategy very naturally. </p>

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<p>Whether this strategy, if explicitly taught, will be helpful for any particular child depends in large part on their learning style and on the way they conceptualize numerical values. But I still think it's very much worth teaching as a mental math strategy, even if it doesn't click with every last person. A similar approach can help with other mental math problems too. Consider the problem of 378 + 199. I would look at that and think to myself "Well, I know what 378 + 200 is, so it must be one less than that!" This is very much analogous to saying "I know what 8+8 is, so 8+7 must be one less than that."</p>

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<p>Miranda</p>

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<div class="quote-container"><span>Quote:</span>

<div class="quote-block">Originally Posted by <strong>moominmamma</strong> <a href="/community/t/1350726/math-level-question#post_16953280"><img alt="View Post" class="inlineimg" src="/community/img/forum/go_quote.gif" style=""></a><br>

Consider the problem of 378 + 199. I would look at that and think to myself "Well, I know what 378 + 200 is, so it must be one less than that!" This is very much analogous to saying "I know what 8+8 is, so 8+7 must be one less than that."

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<p>Miranda</p>

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<p>yes, and part of math education is learning to THINK in different ways. It's like exercises to help the brain become more flexible.</p>

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<p>So much of success in life is about being able to think in a variety of ways.</p>

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<p>About the over-complication:</p>

<p>Addition of integers seems like a concept that a child can easily intuit. You have some stuff, add/subtract some, then you have more/fewer - math gives you the tool to say how many more/fewer. While the notion of division by 2 and doubling seems more complex - it involves the ability to discern some pattern, or matching pattern. Of course - who am I to judge what is simpler or not. If one assumes the notion of addition to be more elementary - then why obfuscate the intuition and simplicity with tricks?</p>

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<p>About the lack of generality:</p>

<p>The trick given doesn't seem to lead to more general concepts or ideas in mathematics. It applies to a very special case, which is how to add 2 integers that differ by 1. In my mind, math is not about special cases. Its power comes from how ideas can be applied in so many different cases - its power comes from its generality.</p>

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<p>It seems that the trick approach might lead to the impression that math has lots of tricks which are unrelated, with no bigger picture or more fundamental ideas behind them. This approach doesn't seem to teach what's beautiful about math - just my personal preference <span><img alt="smile.gif" id="user_yui_3_4_1_2_1334889679210_164" src="http://files.mothering.com/images/smilies/smile.gif"></span></p>

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<p>Originally Posted by <strong>MamaMunchkin</strong> <a href="/community/t/1350726/math-level-question#post_16953416"><img alt="View Post" class="inlineimg" src="/community/img/forum/go_quote.gif" style=""></a></p>

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<p>The trick given doesn't seem to lead to more general concepts or ideas in mathematics. It applies to a very special case, which is how to add 2 integers that differ by 1. In my mind, math is not about special cases. Its power comes from how ideas can be applied in so many different cases - its power comes from its generality.</p>

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<p>It seems that the trick approach might lead to the impression that math has lots of tricks which are unrelated, with no bigger picture or more fundamental ideas behind them. This approach doesn't seem to teach what's beautiful about math - just my personal preference <span><img alt="smile.gif" id="user_yui_3_4_1_2_1334889679210_164" src="http://files.mothering.com/images/smilies/smile.gif"></span></p>

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<p>I totally disagree. It isn't a trick.</p>

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<p>It's teaching that 7+8 is the same as 7+7+1 OR 8+8-1.</p>

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<p>That's not about doing tricks. That's teaching how numbers work.</p>

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<p>Learning to manipulate numbers is at least as important as the facts, if not more so.</p>

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<div class="quote-container"><span>Quote:</span>

<div class="quote-block">Originally Posted by <strong>Linda on the move</strong> <a href="/community/t/1350726/math-level-question#post_16953360"><img alt="View Post" class="inlineimg" src="/community/img/forum/go_quote.gif" style=""></a><br><br><p> </p>

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<p>yes, and part of math education is learning to THINK in different ways. It's like exercises to help the brain become more flexible.</p>

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<p>So much of success in life is about being able to think in a variety of ways.</p>

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<p>It's not the trick per se. Of course you can do any shortcuts - even professional mathematicians do that. But math is not about shortcuts - it's a lot more than that.</p>

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<p>Edited: don't want to change the subject ... sorry ...</p>

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