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Process Versus the Reason Why

Process Versus the Reason Why. How Should I Teach This?. Sometimes it’s easier to explain the process to solving a problem as oppose to the reason why we solve it. We, as current and future mathematics teachers , must make a decision about which way to teach an idea or concept.

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Process Versus the Reason Why

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  1. Process Versus the Reason Why

  2. How Should I Teach This? Sometimes it’s easier to explain the process to solving a problem as oppose to the reason why we solve it. We, as current and future mathematics teachers , must make a decision about which way to teach an idea or concept. Integer Operations lends itself to making these decisions; specifically with regards to Subtraction and Division.

  3. A Formal Wayto Subtracting Integers Leave the minuend unchanged Change the subtraction sign to an addition sign Add the opposite of the subtrahend Example: -8 – 3 -8 + -3 The Answer is -11 PROCESS or the Reason Why??

  4. Keep Change Change Keep Change Change follows the same procedure as the formal way of subtracting fractions. The difference is the omission of the vocabulary. Example: 8 – (- 3) 8 + 3 The Answer is 11 PROCESS or the Reason Why??

  5. Chop Chop Chop Chop is a fun method of handling a subtraction problem with two negatives together. Example: -7 – (- 9) -7 ( 9) The Answer is 2. PROCESS or the Reason Why??

  6. I am positive I am positive positive

  7. I am negative I am negative negative

  8. I am not positive I am not positive negative

  9. I am not negative I am not negative positive

  10. Time to Practice Subtraction Using these Processes 10 – 4 = Keep Change Change 10 + (-4) =6 -10 – (-4) = The Formal Way -10 + (+4) = -6 15 – (-12) = Chop Chop 15 + (+12) = 27 3 – (+14) = I am not positive 3 – 14 = -11

  11. A Process for Division The Process for Division can be taught in many ways. It is not often, however, that you see a negative divided by a negative using mats and counters.

  12. Here is a Explanation from the Project Alpha Website using reverse multiplication, mats and counters. (-6) ÷ (-3) = (?) Rewrite as: ? • (-3) = (-6) How many groups of 3 negative tiles would you have to add/take away to get 6 negative tiles? You would have to add 2 groups of 3 negative tiles. ? = +2 Therefore, (-6) ÷ (-3) = (+2) — — — — — — — — http://www.erusd.k12.ca.us/ProjectAlphaWeb/index_files/NS/Using%20Integer%20Tiles%20-%20Multiply%20&%20Divide.pdf ALPHA, L. Ponciano, Rev. 10/2/2006

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