A to Z Math Project BY: AUSTIN WAHL

A is for Algebra Tiles  Algebra Tiles are used to represent variables and constants. Also The tiles help you visualize algebraic expressions and equations. The large square represents x2, rectangle represents x, and the small square represents ones Algebra Tiles are very useful in Unit Three, Polynomials because they give you an easier way to answer the algebraic equation.

B is for Binomial  A Binomial is an expression that is a sum or difference of two terms. The term is a combination of numbers and variables. For a Binomial to be true it must have two terms, and if the variables are the same the exponents must be different. Also exponents must be whole positive integers, not negative or a fraction. A Binomial is from unit three, Polynomials.

C is for Common Denominator  A common denominator is when two or more fractions have the same denominator. You can only add and subtract fractions if they have a common denominator. To make a common denominator you must multiply the top and the bottom of a fraction by the same amount. Making a common denominator was very common in many units of grade 9 math, therefore understanding the concept is key.

D is for Division Law  In unit 2 I learned how to divide exponents and to do that we used the division law. In the division law you either subtract the exponents or divide the bases. The base is the whole number like 4 and the exponent is the small number above the base. When dividing exponents with the same base all you do is subtract the exponents. Then multiply the base by the exponent. When dividing the exponents with different bases and exponents, you calculate each exponent then divide.

E is for Enlargement  In unit 7 I learned that an enlargement is the change in size of the object without changing the shape. To make an enlargement you find the scale factor and multiply each point on the shape by the scale factor. To find the scale factor you divide the scale diagram (enlargement) by the original shape. For example, In this picture the scale factor is 3 because PQ is 2cm and PR is 3cm. In the enlargement PQ is 6cm and PR is 9. 3 times 2 is 6, 3 times 3 is 9.

F is for Fraction from “BFSD”  When you solve an equation you use Best friends share dessert aka Brackets, Fraction, sort, Divide. If an equation doesn’t have any fractions you skip this step, but if it does your goal is to rid rid of the fractions. To do this you have to make everything a fraction, even the whole numbers. Then you find a common denominator between all of the fractions. After that you multiply the numerator by the common denominator. Finally you divide the numerator by its denominator and then you get your whole number which brings you to the dividing step of this equation.

G is for Graphing Graphing is a diagram of values usually shown as lines or bars. There are many different kinds of ways to graph data but the graphs I used most in grade 9 was a line graph and a quadrant graph. In a line graph the x-axis represents the variable and the y-axis has a scale and indicates the measurement. In a quadrant graph there are four quadrants numbered 1-4 and in the quadrants there can be shaped being reflected or coordinates from an equation.

H is for Hypotenuse  A hypotenuse is the longest side of the right triangle and opposite of the right angle. A hypotenuse is also known as c^2 because it is the length of the right triangle that is trying to be solved from a^2+b^2=c^2( Pythagorean Theorem). For example, if one of the other sides has a length of 3 (when squared, 9) and the other has a length of 4 (when squared, 16), then their squares add up to 25. The length of the hypotenuse is the square root of 25, which is 5.

I is for Isosceles Triangle  An isosceles triangle has two equal sides and has two equal angles. I learned that isosceles triangles are even found in circles. To make this triangle in a circle you draw a chord and then draw your two radius lines connecting to both sides of the chord. Also the right isosceles triangle is found in a circle which means the Pythagorean theorem can come in place if the hypotenuse is missing its length.

J is for “Just Do It”  They saying, “just do it” is a helpful and easy way to teach you how to multiply fractions. What it is trying to say is that whatever equation you have to answer you simply do the math without any steps. For example, if you have two fractions being multiplied you multiply the numerators together and then the denominators together. Then you will find your answer.

K is for Kilometres (km)  Kilometres is a measurement that is commonly used on shapes. The most important part of having Km or any measurement in a question is to add the measurement to your answer one you are finished a question.

L is for Line of reflection  In unit 4, symmetry and surface area I learned that a line of reflection lies directly in the middle between the figure and its image. Also each point on the reflected image is the same distance away from the line of reflection. To determine the line of reflection you measure each point to the line and then measure the same distance on the other side and draw a dot on each new point. Once that is done all you do is connect the dots together and then you will have a line of reflection.

M is for Multiplication Law  Multiplication law is the exact opposite of division law, instead of subtracting the exponents you add them. If the bases are the same you simply add the exponents to find the answer. If the bases and the exponents are different you calculate each exponent then multiply.

N is for Number Line  A number line is a line that shows negative numbers on the left and positives on the right. This year I learned that a number line can be used to compare many numbers, decimals, and fractions. I found that using a number line was the best way to represent fractions because it was easier to tell what fractions are bigger or smaller. Number lines aren’t only in whole numbers, they can be in decimals, fractions, square roots, mixed fractions, and variables. This year I found that I used number line most when showing fractions or decimals from least t greatest.

O is for Oblique Lines  An oblique line is a line that isn’t horizontal or vertical, it is on an angle. Also these lines are neither parallel or perpendicular. This year I worked with oblique line in unit 5 linear relations.

P is for Pythagorean Theorem  The Pythagorean theorem is an equation, a^2+b^2=c^2 that an only be solved on a right triangle. C^2 aka the hypotenuse is the line directly across from the right angle of the triangle. To find the length of the hypotenuse after doing a^2+b^2 you add the two lengths together and then find the square root of that number.

Q is for Quadrant  A quadrant is when the graph is divided up into four quadrants. Each quadrant is the same size and is divided up by an x-axis and a y-axis. They are usually numbered in Roman Numerals from 1-4. This year I learned how to draw a shape being mirrored in each quadrant form the coordinates provided. In this example the shape is being reflected in quadrant 1 and 2

R is for Reduction  In unit 7 I learned that a reduction is when the sale diagram is smaller than the original shape. For example, if a shape has been reduced by a half then the scale factor is ½. Usually reductions are drawn out on 1cm grid paper so it is easier to measure out the size and change of the reduction. In this example of a reduction the scale factor is 1/3 because if you divide 3 by each length on the original image it equals the lengths on the scale diagram.

S is for Sort from “BFSD”  Sort is step 3 from BFSD on solving linear equations. The goal in this step is to get the variable in the equation to be alone on its side by creating zero pairs. Zero pairs are when you add or subtract certain amounts to make the equation have the same equivalency. The most important thing I learned about this step is what you do on one side you have to do to the other, even if that means going to negatives.

T is for Tangent Line  A tangent line is a straight line that touches only one point on a circle. In the unit circle geometry I leaned that tangent lines are perpendicular to the radius at the point of tangency. It is a very useful property when the radius that connects to the point of tangency is part of a right angle because the Pythagorean thereon apply to right triangles. The point of tangency is when the tangent line intersects with the circle.

U is for Unlike Terms  In Algebra equations unlike terms are when the terms do not have the same coefficients raised to the same powers. For example this equation has unlike terms 11m 3 n 3 - nm + 9m 2 - 4m 2 n 2 because We observe that the four terms of the polynomial have different variables raised to different power. The numerical coefficients are also different. So, the polynomials is made up of four unlike or dissimilar terms.

V is for Variable  A variable is a symbol for a number that you do not know yet. The symbol usually is represented by the letter x or y. A variable can be on its own or beside a whole number, making it a coefficient. If the variable is beside the whole number that means it is a multiplication question. (ex) 4x is 4 times x. The main goal in an equation when there is a variable is to find the value of x or y.

W is for Whole Number  A whole number is a number without fractions, decimals, or negatives. A whole number is every number on the right side of the number line not including zero. Whole numbers are in almost every question in math, therefore it is important to know how to work with them.

X is for X- axis  An x-axis is the line on the graph that runs horizontally (left-right) through zero. The x-axis is used a reference line so you can measure from it. The x- axis can be used to compare things on a graph, measure coordinates, find data on a line graph, and you can draw shapes being reflected. This year I found that I used the x-axis most when placing coordinates from a t- chart on a graph.

Y is for Y- Axis  A y- axis is the line on the graph that runs vertically (up and down) through zero. The y-axis is used a reference line so you can measure from it. The y- axis can be used to compare things on a graph, measure coordinates, find data on a line graph, and you can draw shapes being reflected. This year I found that I used the y-axis most when placing coordinates from a t-chart on a graph.

Z is for Zero Pairs  Zero pairs are when you add or subtract certain amounts to make the equation have the same equivalency. A zero pair will always feature the positive and negative form of the same number. For example, +3 and -3 would be considered a zero pair because the sum when they are added together is zero. The main purpose of a zero pair is to simplify the process of addition and subtraction in complex equations featuring multiple numbers and variables. This year I used zero pairs many times solving linear equations because the variable needed to be isolated.