In the 1st chapter which was the Number unit I learned basically a new way to learn at numbers. Such as a prime number; a number that can we times by 1 and itself, e.g. 7; 1×7, and a composite number; a whole number which has more than two factors, e.g. 10; 1×10, 2×5. Then I learned about the Applications of Prime Factors. The Applications of Prime Factors was mostly based around the Greatest Common Factor (GCF); the largest whole number that can divide into each number you are using, e.g. the GCF of 8, 16, and 20 would be 4. Then I learned about all the different kinds of numbers such as Natural Numbers: 1, 2, 3, etc. Whole Numbers: 0, 1, 2, 3, etc. Integers: -3, -2, -1, 0, 1, 2, 3, etc. Rational Numbers: Decimal numbers which repeat or terminate can be converted into fractions. Then I went on to learn about Radicals which is basically the Square Roots and the Cubed Roots. If 4×4=16 then the sqaure root of 16 would be 4. If 5x5x5=125 the cubed root of 125 is 5. Expanding onto squared and cubed roots we learned Entire Radicals and Mixed Radicals. For example an entire radical would be √80 because the number is entirely under the root symbol. 2√20 would be a mixed radical because there is a co-efficient before the square root sign.

In the 2nd chapter which was the Exponents unit I learned all about exponents, such as the Power; a number written in exponential form, it consists of a base and an exponent. Then I went to move on to Combining the Exponent Laws which was basically simplifying equations with powers. What does 4x to the power of 5 times 2x to the power of 3 equal, simplifying them to one equation. First you times 4x by 2x and get 8x then you subtract the power of 5 to the power of 3 because the equations are getting multiplied by each other. For knowing whether to add or subtract the powers you do what goes with what your originally doing with the equations. If you were to be multiplying the original equation I would think of the bedmas chart where it was b at the top with e under it, with d under e and m to the right of e and a under d and s under m so you would go directly across for m and a and d and s. So you would get division with subtraction and multiplication with addition. Knowing that now I would know if the original equation was multiplying I would add the powers but if the original equation was dividing I would subtract the powers.

In the 3rd chapter which was the Measurement chapter I learned about basically the measurement of items and converting and stuff like that. It started out as rounding numbers to a certain point such as the hundredth or the tenth. Knowing what each one was for the hundredth and tenth basically came as common sense to me just knowing how many digits those numbers already are. We then moved on to Referents in Measurement which was basically what referent you would have to use for different objects, such as what measurement referent would you use to measure a football field? A pace. This also came as common sense to me kind of just growing up with these things around me my whole life such as in soccer when the coach would tell me to move the cone 5 paces over I would know how far to move it. Next I moved on to learning conversions. This was kind of new to me because I would estimate how many centimeters are in an inch but I would never exactly know so doing this unit definitely helped me and will actually help me a lot moving on into my every day life.

In the 4th chapter which was the Trigonometry chapter I learned all about the triangle. This chapter was all based around SOH CAH TOA. The way I used to remember this was “Suck a toe”. I don’t know why but going into every homework assignment it sort of just clicked and even writing this Math 10 summary months later I still have it remembered. What SOH CAH TOA means is for SOH: Sine ratio = Opposite/Hypotenuse. So basically how that effects with SOH is the S stands for sine, the O stands for opposite, and the H stands for hypotenuse. For CAH it was Cosine ratio = Adjacent/Hypotenuse. For TOA it was Tangent ratio = Opposite/Adjacent. The Opposite, Hypotenuse, and Adjacent are the sides of the triangle. The Opposite side is the opposite to the angle θ. The Hypotenuse side is the longest side. The Adjacent side is adjacent to the angle θ.

I learned about the Polynomial Operations in the 5th chapter. It started off with polynomial terms. A polynomial with 1 term is a monomial, a polynomial with 2 terms is a binomial, a polynomial with 3 terms is a trinomial, a ploynomial with 4 or more terms is called a polynomial. When polynomials are in a single variable they are arranged in ascending order of the powers of the variable. The leading coefficient of a polynomial in a single variable is the coefficient of the term with highest power of the variable. Knowing these things I know when I had to simplify the polynomials I would put them in order by the power. Then I would do what the equation is asking me to do for example subtract 4x from 2x and i would be left with 2x. If the equation asked me to multiply I would know that if it was 4x times 2x the answer would be 8x squared. During this unit I would also have to always have bedmas in the back of my mind for some of the equations that I would have to solve.

I learned how to Factor Polynomial Expressions in the 6th chapter which is basically expanding on the 5th chapter. This unit was basically revolved around factoring a polynomial by removing a common factor such as a monomial, binomial, and grouping, factoring a trinomial which is basically inspection and decomposition and factoring a difference of squares. When I first did this unit I remember thinking back to the 2nd chapter on Exponents and remember very similar things such as factoring. The only difference in factoring this time was that I did it all the time with polynomials now. I also remember when I was doing this unit I had to use a lot of brackets in order to find the equation that would be the answer to the question. Another way for me to look at this unit would basically be simplifying the equations into brackets.

In Chapter 7 I learned all about Relations and Functions. This unit was all about graphing which usually isn’t my favorite thing to do but in this unit I didn’t mind it. The general idea of this unit was having the x and y co-ordinate and having to then graph then onto a grid. At the beginning I found this easy but as the unit progressed it got much harder. One of the things I found difficult at first was knowing the independent variable and the dependent variable. Over time I learned it though and now find it as common sense. The dependent variable is a variable whose value depends on that of another. The independent variable is a variable whose variation does not depend on that of another. Near the end of the unit we went on to learn about relations and functions. A function is the relation between the input and output where the input is related exactly to one output. A relation is just a set of ordered pairs. It took me a little while to fully understand these 2 terms but over time it kind of just clicked in my head I didn’t have to do anything special, I guess just having the words always come up it eventually just became common knowledge to me.

In Chapter 8 I learned the Characteristics of Linear Relations. This unit started out with finding the length of the x-coordinates. For me the beginning part was extremely easy it was just basically subtracting what it told you to do. I remember that there are two special lines that both have slopes. A horizontal line which would have a slope of 0 and a vertical line which would have an undefined slope, obviously because the line goes straight up. The most important thing I learned through out this whole unit and probably the thing I most took away was to know all about perpendicular lines and parallel lines. Two lines with the same slope will be parallel and two lines with the opposite slope will be perpendicular. When I figured that out this unit became a lot easier for me and everything just started to click in.

In Chapter 9 I learned about the Equations of Linear Relations and the Equation of a Line in Slope Y-Intercept Form. The 3 different equations we learnt were Slope-Y Intercept Form, General Form, and Slope Point Form. Slope-Y Intercept Form was y=mx+b, General Form was Ax+By+C=0, and Slope Point Form was m(x-x1)=y-y1. The main concept of this chapter was knowing how to convert one form of equation to the other. Another important thing you had to know how to do would be knowing how to solve an equation with missing variable not filled in using your given clues such as co-ordinates and slopes. For Slope-Y Intercept Form you would have to know that the m in the equation stood for  the slope and the b stood for the y-intercept in y=mx+b. Another important thing you would have to know if how to determine slope which would be rise/run which I also remembered as y/x. This chapter also had a little bit of graphing so for that you would have to know which form to put it in and then how to draw it on the graph. You would want to have it in Slope-Y Intercept Form which is y=mx+b. You would start at where b is which is the y-intercept on the graph and place your point there and then go use the slope to see where you would put your next point.

In Chapter 10 where we learned the Systems of Linear Equations and Solving Systems of Linear Equations by Graphing is where I fully understood. This unit was basically just continuing on from Chapter 9 using the same equations. The most important thing I can tell you with this unit is to know how to substitute and eliminate while solving the equations. When you know how to do this it should be extremely easy for you to do this unit. Another important thing to know in this unit is to see how many solutions there are. If the equation’s value of m are identical but the values of b are different, there is no solution. If the values of m are different, there is one solution. If the values of m are identical and the values of b are identical, there are infinitely many solutions. For this unit you would have 2 equations and you would have to simplify them into one either using elimination or substitution to find out the values of x and y. To do elimination you would have to get either x or y to be equal to 0 and then solve but remember what you do to one side you have to do to the other. For using substitution you would sub in the value of whatever one of the equations was into the other equation so for example if the equations were y=x+3 and 3x+4y=1 then you would substitute y=x+3 into where y is in the other equation so your new equation would be 3x+4(x+3)=1.

This week we went over algebra tile models and how to draw them. On Friday near the end of the class I had my “Ah ha” moment realizing how to organize the algebra tiles in the drawing. I now know that the squared tiles go in the top left, the x tiles go in the top right and bottom left, and single tiles go in the bottom right. Also you figure out how to answer the question by drawing the tiles time sing them straight across from each other and drawing it so its in line with one another.