# 8th Grade Pre-Algebra

• Final Exam Topics to study
Chapters on the Pre-Algebra Final:

Digits Topic 2 (1-7)
2-1: Representing Proportional Relationships
2-2: Linear Equations: y = mx
2-3: The Slope of a Line
2-4: Unit Rates and Slope
2-5: The y-intercept of a Line
2-6: Linear Equations: y = mx + b
2-7: Distinguishing Between Proportional and Non-Proportional Situations
Digits Topic 3 (1-4)
3-1: Recognizing a Function
3-2: Representing a Function
3-3: Linear Functions
3-4: Nonlinear Functions
Digits Topic 4 (1-2)
4-1: The Pythagorean Theorem
4-2: Finding the Unknown Leg Lengths
Digits Topic 5 (1-2)
5-1: Surface Area of Prisms (and Lateral Area of Prisms)
5-2: Surface Area of Cylinders (and Lateral Area of Cylinders)
Digits Topic 6 (1-2)
6.1: Writing and Solving Two-Step Equations
6.2: Writing and Solving Equations with Variables on Both Sides
Digits Topic 7 (1-2)
7.1: Angles, Lines and Transversals
7.2: Reasoning and Parallel Lines
Digits Topic 9 (1-2)
9.1: Translations
9.2: Reflections

Topic 2

• Ways to show proportional relationships:
• Tables: a table shows a proportional relationship when one quantity is a constant multiple of the other quantity.
• Graphs: a graph shows points with a proportional relationship if a line that passes through the origin can be drawn through the points.
• For each point, the y-coordinate is a constant multiple of the x-coordinate.
• Equations: in the form y=mx represent proportional relationships.
• m is the constant of proportionality • k used to represent the constant of proportionality
• y = kx is the same as the equation in the form y=mx

• Linear Equation: if the graph of all of its solutions is a line; has a constant rate of change
• Direct Variation: a relationship that you can represent with an equation in the form y = kx, where k ≠ 0. The ratio of the 2 variables x and y is constant.
• Constant of Proportionality: is a proportional relationship; coefficient k
• Constant speed equation d = rt (d varies directly with t)

• Rate: ratio that describes how one quantity changes as the other quantity changes
• Unit Rate: same as slope

Topic 3
• Equations with 2 variables:
• Relation: any set of ordered pairs
• Function: rule for taking each input value and producing exactly one output value (x does not repeat)
• Linear Function: function where the graph forms a straight line (function & straight line)
• Constant Rate of Change – same change in y over change in x (slope)
• Proportional Function: (linear function and point of origin) function where :
• 1) the graph forms a straight line
• 2) the line crosses through the point of origin
•  Nonlinear Function: function where the graph does not form a straight line
•  Not a Constant Rate of Change – change in y over change in x varies

• Ways to represent functions:
• Ordered Pairs: set of ordered pairs identifies specific values that satisfy the function
• (x,y) where input values are x-coordinates and output values are y-coordinates
• Tables: table identifies specific values that satisfy the function
• Graphs: graph gives a visual picture of the function
• For each point, the y-coordinate is a constant multiple of the x-coordinate.
• Rules or Equations: function is a rule for taking each input value and producing exactly one output value
• Mapping Diagrams: describes relationship by linking the input values to the corresponding output values using arrows.
• Slope-Intercept Form: y = mx + b
• slope (m): change in y over change in x; refers to the steepness of a line
• The larger the number, the steeper the slope
• y-intercept (b): y-value at which the graph (line) crosses the y-axis
• x: input
• y: output
• undefined slope: vertical line
• zero slope: horizontal line

Topic 4
• Pythagorean Theorem: in any RIGHT triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
• • Legs: the 2 shortest sides
• Hypotenuse: longest side, opposite the right angle

Topic 5
• Area of polygons (2-Dimensional shapes)
• Area of a square: • Area of a rectangle: • Area of a parallelogram: • Area of a triangle: • Area of a circle: • Lateral Area: the area of the side faces
• L.A. = ph
• p – the perimeter of the base
• h – the height of the prism

• Surface Area: the Lateral Area plus the area of the 2 bases
• S.A. = L.A. + 2B
• L.A. – lateral area
• B – area of the base

Topic 6
• Solving multi-step equations: isolate the variable
1. Combine like terms – use properties
1. Distributive Property
2. Commutative Property
3. Associative Property
2. Inverse Operations – addition and subtraction first
3. Inverse Operations – multiplication and division second
4. Write variable equal to value
5. Check

Topic 7
• Transversal: line that intersects two or more lines at different points.
• Corresponding angles: lie on the same side of a transversal and in corresponding positions.
• Alternate interior angles: lie within a pair of lines and on opposite sides of a transversal.
• Alternate exterior angles: lie outside a pair of lines and on opposite sides of a transversal.
• Be able to identify and find angle measurements for corresponding angles, alternate interior angles and alternate exterior angles.
• Determine if angles are corresponding, alternate interior or alternate exterior based on the angle measurements.
Topic 9
• Transformation: change in the position, shape or size of a figure.
• Rigid Motion: transformation that changes only the position of the figure.
• Image: result of a transformation of a figure. Identify points of an image with prime notation.
• Translation: (slide) rigid motion that moves every point of a figure the same distance and in the same direction.
• Reflection: (flip) rigid motion that flips a figure over a line
• Line of reflection: line that a figure reflects over.
• Be able to graph translations and determine the ordered pairs for the images.
• Be able to graph reflections across the y-axis and x-axis and determine the ordered pairs for the images.
• Be able to determine if an object was translated, reflected or rotated. ACCESS GUIDE FOR MATHEMATICS

• eBackpack (app or website): provides access to assignments sent by teacher and allows students to turn in assignments.
• Website: stmatts.ebackpack.com
• Calendar Bar at the top – show all assignments that were assigned through eBackpack for the week (it will not show assignments sent home on paper)
• Classes and Groups – access to all documents and assignments that have been sent to your child through eBackpack for each class
• My Files – where your child is able to save all of the assignments they complete and documents they create
• Calendar – shows all assignments for the month
• Assignments – will show you all assignments your child has been assigned
• Red – past due
• Yellow – due soon
• Green – due in the future
• Will also specify whether or not the assignment has been turned in
• Graded Work – allows access to anything your child turned in that has been graded and returned to them through eBackpack

• Pearson Realize (website): provides access to the math program being used for 6th – 8th grade
• Website: pearsonrealize.com
• Select Math Book:
• UNITS (labeled with letters) -
• TOPICS (labeled with numbers) – similar to chapters
• LESSONS - (labeled with the topic number and the lesson number)
• Topic Opener: provides a brief intro to the lesson/topic
• Launch: provides an intro activity to the lesson
• Key Concepts: provides definitions for the lesson
• Part 1-3: provide videos, tutorials and steps for the concepts covered in the lesson
• Close and Check: provides a thought provoker or reflection for the lesson

Virtual Nerd (app or website): provides videos with step by step procedures for solving math concepts
• Website: virtualnerd.com
• To use:
• Choose course:  Pre-Algebra or Grades 6-8 Math
• Choose a topic or search for a topic

• Khan Academy (app or website): provides videos with step by step procedures for solving math concepts
• To use:
• If you use the website – an account will need to be created
• If you use the app on your child’s iPad – access is automatic
• Select a topic or search for a topic

• Purple Math (website): provides step by step procedures for solving math concepts with explanations for solving
• Website: purplemath.com
• To use:
• Select index of lessons to find a topic or use the search bar at the top to search for a topic

• Mrs. Smith’s Website: smcssa.org/mrssmith
• You will find Quick Links to the following websites on my website:
• eBackpack
• Pearson Realize
• Mathletics
• Virtual Nerd