Challenge Corner Project By: Akash Kunchum
Math • Math is awesome! • Math is very important. • Math is composed of over 20 subjects. • Math is sometimes easy & sometimes hard.
Patterns • A pattern is a form of math in which something is done to a certain number repeatedly. • A pattern asks you to find the number that adds to the end of the pattern. • An example of a pattern is: 2,4,6,8,10,_,_,_ • 2 is being added to each number. In this case, multiples of 2. • The dashes are asking a person to put in the next three numbers: 12,14,16. • Patterns can not only be composed of numbers but they can have shapes, letters,& even words! • Patterns can be also be multiplied, added, subtracted, etc.. • The answer to a pattern problem can be found by finding out what is being done to a number to get the next number. • Another example is this:2,6,3,9,6,18,15,_ • The rule…*3,-3. The rule can also be two things. • The answer is 45. if 18-3=15, then the next thing you should do is multiply by 3.
Variables • A variable is a letter or a shape used to take the place of an unknown number or word. • In a variable expression, you are trying to find the value of the variable. • An example would be 5x=50. • How do you get the answer? You have to do the opposite of what is done to the variable. In this case, multiplication. • So you would have to do division. This is like a balance scale. Whatever you do to one side has to be done to the other side to stay equal. • 5x/5 would be just x. 50/5 is 10. So x=10. • In a variable equation, the value of the variable is given & you are trying to find the answer. • Ex: 5+x8-4/2=?X=7 • Plug it in: 5+7*8-4/2. 7*8=56. 5+56-4/2. 4/2=2. 5+56-2. 5+56= 61. 61-2=59. 59 is the answer.
Exponents • Exponents are numbers that are minimized and put at the northeast tip of another number. • An example of an exponent is 2. An exponent equation is 22. • There are three ways to say that out loud. • 2 to the power of 2. • 2 to the 2nd power. • 2 squared. If the number’s exponent is 2, you can say squared. If it is 3, you can say cubed. • The answer is 4. How do you get it? Since the exponent is 2, the equation is 2*2. • Power of factors: Power of factors a.k.a. repeated multiplication is the number written over & over as much times as the exponent. • If the equation is 37. The power of factors would be 3*3*3*3*3*3*3. That is 3, 7 times. • Don’t be mistaken by 37. It is not 3*7. It is3*3=9*3=27*3=81*3=243*3=729*3= 2,187.
Order of Operations • Order of Operations is the order is the order in which to solve any equation. • Order of Operations goes by the rule PEMDAS. • P=Parentheses. E=Exponents. (M=Multiplication. D=Division). (A=Addition. S=Subtraction). • An equation: [3+5*(6-1)+62]/4. • Follow PEMDAS. • Parentheses first. There are also brackets. These are parentheses that tell you that there are more parentheses inside.6-1=5. (3+5*5+ 62)/4. • You are still in parentheses but we can’t do it until we solve the things inside that come next. Exponents come next. 62=6*6=36. (3+5*5+36)/4. • Still parentheses. Then comes multiplication & division as a pair. You can do either but you have to do the one that comes on the left first.5*5=25. (3+25+36)/4. • Again, parentheses. Addition & subtraction are like multiplication & division. 3+25= 28. (28+36)/4. • Finally, you can finish parentheses. 28+36=64. 64/4. • Now, you are done with P. You can move onto E. There is no E. Next comes M & D. There is no M but there is D. 64/4=16. • There is no A & S. You are done with the equation. The answer is 16. • Don’t forget that M & D are a pair & A & S are a pair. Do them from left to right.
Perimeter & Area • The perimeter of a shape is the total ft., in., etc. on the outside of the shape. • The area, always squared, is the total ft., in., etc. turned into squares on the inside of the shape. • There are formulas used to find the perimeter or area of shape. • Rectangle formulas: To find the perimeter, you use the formula P=2l+2w. This means the perimeter is 2 lengths plus 2 widths.To find the area of a rectangle, you use the formula A=l*w. This means the area is the length times the width. • Square formulas: To find the perimeter, you use the formula P=4s. This means the perimeter is 4 sides; 4 times any side. To find the area of a square, you use the formula A=s2. This means the area is any side multiplied by itself. • A rectangle example: L=7in., W=3in.. The perimeter is 20 in. because 7*2=14. 3*2=6. 14+6=20. The area is 21 in.2because 7*3=21. Remember, the area is always squared. • A square example: S=5ft.. The perimeter is 20 ft. because 5*4=20. The area is 25 ft.2 because 5*5(itself)=25.
Distance Formula • Distance formula is a method used to find either the distance traveled, rate of speed, or time spent using the formula D=rt. This is called dirt because if you put a line in between the equal sign, it looks like an I. • If you want to find the distance traveled, you would have to multiply the rate & time(given).Then, you would take the top number of the rate & use it as the distance label. • If you want to find the rate of speed, then you would have to divide the distance by the time. Then, you would take the labels for both & use it as one label: 6 ft./min.. • If you want to find the time spent, then you would have to divide the distance by the rate. Then, you would take the bottom number of the rate & use it as the time label. • An example: D=?, r= 7 ft./sec., t= 20 sec.. Find the distance: multiply. 7*20=140. Add the label: ft.. D=140ft.. • Another example: D=80 mi., r=?, t=5 hrs.. Find the rate: divide. 80/5=16. Add the label: mi./hr.. r=16 mi./hr.. • Final example: D=54 in., r=2 in./ms., t=?. Find the time: divide. 54/2=27. Add the label: ms.. t= 27 ms.. • Remember: distance: multiply, rate: divide, & time: divide. If you forget, plug it in. D=rt. D=7*20. 80=r*5. 54=2*t.
Algebraic Equations • An algebraic equation is an equation in which the answer is given and there is also a variable. • An example of an algebraic equation is 5x=20. You have to try to find out what the variable is. • The variable(x) is 4. To solve an algebraic equation, you have to do the opposite of what is done to the variable. This is like a balance scale, whatever you do to one side has to be done to the other to keep it balanced.The opposite of multiplication is division. 5x/5 is x. 20/5=4. So x=4. • The opposite of addition is subtraction. x+5=20. x+5-5=x. 20-5=15. x=15. • The opposite of subtraction is addition. x-5=20. x-5+5=x. 20+5=25. x=25. • The opposite of multiplication is division. x*5=20. x*5/5=x. 20/5=4. x=4. • The opposite of division is multiplication. x/5=20. x/5*5=x. 20*5= 100. x=100. • This works with addition & multiplication even if the variable is in the middle. 5+x= 20. 5+x-5=x. 20-5=15. x=15. 5*x=20. 5*x/5=x. 20/5=4. x=4 • But it doesn’t work with subtraction & division. 20-x=5. You can’t do the opposite. You have to do the same thing. 20-5=15. x=15. 20/x=5. Do division. 20/5=4. x=4.