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Without question, the concept of negative numbers is the hardest concept for kids to grasp. From the time they are first introduced all the way up to getting their first credit card, negative numbers remain a mystery. Take, for instance, the problem…
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3(x – 5) – 2(x – 7)
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This problem is filled with subtraction, but when we go to simplify it with the distributive property, we treat the “subtract 5″, the “ subtract 2″, and the “subtract 7″ as “negative 5″, “negative 2″ and “negative 7″. Wait, subtraction is an action and negative is an adjective! How can it be that the negative sign can morph from one part of speech to another? And this says nothing for the confusion between the rules for multiplication and addition involving negatives.
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So how does the ZeroSum Ruler work? They say that “a picture says a thousand words.” This video doesn’t actually say anything as its set to a remix of the best part of a Beck song, but if a picture can say a thousand words, than the many pictures that comprise this video must say at least a couple hundred thousand words… Enjoy!
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I am excited to bring to you this free version of the ZeroSum Ruler’s eBook! In this book, you will find pictures and explanations of how the ZeroSum Ruler is different yet more intuitive in its way of teaching integer addition and subtraction. if you like what you read, there is a version of the eBook on CurrClick that includes a ZeroSum Ruler, practice problems, and some more fun pictures. Enjoy! (click the picture below to be directed to your free download!)
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If you need convincing to download this eBook for free (??), you should go to the GRADUATE THESIS tab (up there) to read how the ZeroSum Ruler decreased student error by 62%!
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Shana, this is AMAZING! What a super great idea! NICE JOB!!
Thank you! I hope it catches on!
Shana,
I thought I’d try and post this note on your blog. Good luck with your ruler. I am excited for you and proud of you.
Hi Shana,
I just read a bunch of your posts. I love how you helped that student get through his algebra 2 and graduate! Powerful stuff.
I think your zero sum ruler idea would be mroe powerful if you explained why a bit more. Mainly at this point:
>Step 1: the student identifies which of the two integers being summed is farther from zero and marks down that integer’s sign.
Why do they mark down that sign? But also, I think it would be helpful to explain why the ruler works. (I’d say adding a positive and a negative is like subtracting, so you’re finding a distance.)
Thank you for your suggestions. I’m always looking for ways to improve what I’m doing. Maybe I should put together another video that explains WHY, which is the most important aspect behind the ruler being able to work. Thank you for taking the time to let me know! And the look on his and his family’s faces was priceless. Even though it was painful to get through that online couse, I would do it again! He was also an easy student to work with, which is 90% of it
[...] How the ZeroSum Ruler works [...]
Thank you for TWO ZeroSum rulers when I ordered just one! That was actually very helpful to my student (I tutor one 7th grade student). I am able to follow along with him on my own ruler as he works his way through problems. Great tool. I am looking forward to seeing more from you!