How To Do Or Not To Do Calculating And Presenting: Fill & Download for Free

There actually is a solution to your equation if we are creative.As pointed out by many of the other answers [math]y+2=y[/math] is equivalent to [math]2=0[/math]. This is clearly not true in most number systems. However, if we assume we are working in a special kind of number system called a modulo ring we may find an answer to this equation. In a modulo ring we use “clock arithmetic”, that is, numbers are arranged in a circle (like on a clock). On a clock face we add hours to find a new time: 3 + 2 = 5, 7 + 3 = 10, etc. A special thing happens when our answer exceeds the number of hours in this “modulo ring”: 11 + 2 = 1, 10 + 5 = 3, etc. Instead of increasing ever further, the numbers “wrap around” as we count. And on a clock the number 12 is equal to the number 0: [math]12=0[/math] and any value of [math]y[/math] would solve [math]y+12=y[/math].The equation you presented therefore is solvable in a ring with 2 elements {0, 1} - imagine a clock face with 0 at the top and 1 at the bottom. Since we only have 0 and 1 to calculate with the solutions to your equation are y = 0 and y = 1, or[math]0+2=0 [/math]because 2=0 in this ring, and[math]1+2=1 [/math]because 3 wraps back to 1 on this clock face.If you think of this clock arithmetic of 0 and 1 as a useless number system, you should consider that computers only use 0 and 1 to do calculations; and clock arithmetic allows them to do the kinds of calculations that we need them to do.A special kind of clock arithmetic that you perform regularly is when you add number: we say that 9 + 2 = 11. How did you get the digit 1 and 1 that make up 11? The second 1 is the result of clock arithmetic on numbers from 0 to 9. The first digit tells us how often we wrap around to get to that number. E.g., 37 + 8 = 45. You get the 5 by calculating 7+8 in clock arithmetic. The 3 updates to a 4 because we wrapped around once more.Even if this was not the main interest of your question, I hope you find it interesting.

As David Joyce said, what really matters in teaching math is doing the calculations “in real time”, writing them a bit at a time and explaining each step.Slide presentations are counterproductive, because they convey the impression that mathematics is “already there”, created by some expert, and all we need to do is passively read it. That’s not how math works.The students need to see that it’s possible to start with nothing - a blank board or piece of paper - and build up the ideas one at a time. They need to learn to do this themselves.It doesn’t really matter much one uses chalk on a blackboard, a marker on a whiteboard, or whatever. But there is a certain charm to using a stick of tiny fossilized seashells on a slab of slate, because it shows that we don’t need fancy technology to do mathematics. The Greeks, they say, preferred an iPad and stylus.

Have you ever noticed this on your Casio Scientific calculator ?The area above display encircled by red color reads S-V.P.A.M .S-V.P.A.M stands for Super Visual Perfect Algebraic method. Many scientific calculator models from Casio like fx-82MS, fx-90ES etc. come under S-V.P.A.M range.S-V.P.A.M indicates that the calculator supports direct algebraic input and processing. For example, if we want to calculate [math]2^3+3^3[/math] so we can directly input this in Casio’s S-V.P.A.M calculators unlike other simple calculators where you manually have to calculate [math]2^3[/math] and [math]3^3[/math] and then add them. Not only that, we can permanently store numbers or answers in variables A, B, M etc. provided and use the variables instead of writing the whole number. For e.g. if variable A stores [math]2^3[/math] and B stores [math]3^3[/math] then we can write [math]A×B[/math] in the calculator instead of [math]2^3×3^3[/math]. The answer will be same. These are the features of S-V.P.A.M models.Image source: My phone.Calculator model shown: fx-82MSEDIT: Asked in comments commonly, so writing it here.How to store numbers in calculator?I consider you are using fx-82MS.Consider you did a calculation, say [math]24.3/56[/math] .Now to store this answer in variable ‘A’ pressSHIFT + RCL(STO) + A SHIFT is present in the top left. Press that. Now RCL(STO) button is present in the left end just 3 buttons below shift vertically. Press this and then above RCL(STO) button you will find buttons like (-), degree, hyp etc. These buttons have inscribed A, B, C on upper side. Press any button which has those variables of your selection. The answer will be permanently store and will look like this.So, variable A has answer stored which you can use anytime and won’t have to calculate always. To get the value from a variable press “ALPHA” button which is next to “SHIFT” and the variable.For example: ALPHA + A and press equal to So it will give value in A. You can make any math operation on A now. Like to multiply the value in A by 2 you can write “2A” by pressing2+ALPHA+A+'='  where A is "(-)" button. to get the valueP.S. These values are permanently stored in the variables until you store “0” i.e, clear the data in them. So, definitely you can store your important password or mathematical/physical constant values for exams without letting anyone know :p .EDIT 2: Thanks Vinita Jagannathan and Audhithya S V (ஆதித்யா ஸ்ரீ வெ) for suggesting edit.EDIT 3: Arpit Mishra (ଅର୍ପିତ ମିଶ୍ର) shared a very good piece of information by which one can store upto 80 numbers in CASIO scientific calculator (each upto 10 Digits). So, I am adding it here.Assuming fx-82MS, just go to SD mode from mode button by pressing MODE+2 .Now start calculation and after getting the answer, press M+ (add to memory) each time after calculation and clear the display and continue doing calculation pressing M+ each time getting answer.In this way you can store upto 80 answers at a time and retrieve each of them pressing replay button up/down. This works even you put off the calculator.Note that this works only in SD mode. If you change mode, all data from stack will get cleared off.You can perform operations like sum of all numbers, sum of square of numbers or any statistical calculation by pressing SHIFT+1 or SHIFT+2 i.e, S-SUM/S-VAR button.Thanks Arpit Mishra (ଅର୍ପିତ ମିଶ୍ର) for this.