By Alan Sultan
What wisdom of arithmetic do secondary college math lecturers have to facilitate figuring out, competency, and curiosity in arithmetic for all in their scholars? This specified textual content and source bridges the distance among the math realized in collage and the maths taught in secondary faculties. Written in a casual, transparent, and interactive learner-centered type, it's designed to assist pre-service and in-service lecturers achieve the deep mathematical perception they should interact their scholars in studying arithmetic in a multifaceted method that's fascinating, developmental, hooked up, deep, comprehensible, and infrequently, spectacular and enjoyable. positive factors comprise release questions at the start of every part, scholar studying possibilities, Questions from the study room, and highlighted subject matters all through to help readers in changing into lecturers who've nice "MATH-N-SIGHT": M a number of Approaches/Representations A functions to actual lifestyles T expertise H background N Nature of arithmetic: Reasoning and facts S fixing difficulties I Interlinking thoughts: Connections G Grade degrees H Honing of Mathematical talents T standard blunders this article is aligned with the lately published universal middle kingdom criteria, and is splendid for a capstone arithmetic path in a secondary arithmetic certification application. it's also applicable for any tools or arithmetic direction for pre- or in-service secondary arithmetic lecturers, and is a priceless source for school room lecturers.
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Additional info for The Mathematics that Every Secondary School Math Teacher Needs to Know
4 Show that, for any integer k, (2k + 1)2 − (2k − 1)2 is divisible by 8. Solution. If we square the expressions in parentheses and simplify, we get (2k + 1)2 − (2k − 1)2 = (4k2 + 4k + 1) − (4k2 − 4k + 1) = 8k. Clearly, this result is divisible by 8. 5 A man buys apples at 3 cents a piece and oranges at 6 cents a piece, and hands the salesperson a 5 dollar bill. 12. Did he receive the right change? Solution. At first glance, this problem seems impossible to answer, but it can be answered. If the man bought x apples and y oranges (both positive integers), his cost would be 3x + 6y cents.
We hope that you guessed 2n−1 . Now go through the process one last time for 6 points. Be sure to check your answers by drawing a picture. Did you get 25 regions? Well, if you did, then you didn’t draw the picture correctly. For, when n = 6, we get 31 regions as a maximum and that is not 2n−1 since 26−1 = 32. Our pattern broke down. These examples are just a few of many similar examples, and are meant to show us the danger of accepting or making statements without proof. Let us give one final example.
Ask a particular student to think of the price of an item he recently bought that cost more than 10 dollars. Ask that student to write this price in large numbers on an index card. Then while you turn your back to the class and cover your eyes, ask that student to show the price written on the card to the class without your seeing it. Then ask the class to do the following computations: Write down the price without the decimal. ) Take the first two digits of the number (in this case 16) and add the next consecutive number (in this case 17).
The Mathematics that Every Secondary School Math Teacher Needs to Know by Alan Sultan