8th Grade Pre-Algebra Curriculum Map

*Please Note: for the purposes of this curriculum map a week is not a calendar week. A week will be 5 school days regardless of the calendar week they fall into. This will allow the flow of the map to continue to exist in spite of unplanned absences and short school weeks. *
Teacher: Charles David Napier II
Grade: 8th
Content Area: 8th Grade Mathematics Pre-Algebra
Unit: 2012-2013
Week
Standard
Key Vocabulary
Learning Target
Resources
Assessment
1-4
8.EE.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. (For Ex., compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.
 
8.EE.6. Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y=mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
 
8.EE.7a Solve linear equations in one variable:
a. Give example of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equations of the form x = a, a= a, or a = b results (where a and b are different numbers).
 
8.EE.7b Solve linear equations in one variable:
b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.
 
Linear equation
Y-intercept
Slope-intercept form
 X-intercept
Similar figures Corresponding sides
Congruent
 Linear relationship Constant rate of change
Direct Variation
Slope
Distributive Property
Like Terms
 
I can graph proportional relationships.
 
I can compare two different proportional relationships represented in different ways.(For ex., compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.)

I can interpret the unit rate of proportional relationships as the slope of the graph.
 
I can identify characteristics of similar triangles.
 
I can find the slope of a line.
 
I can determine the y-intercept of a line.
 
I can analyze patterns for points on a line through the origin.
 
I can come up with an equation of the form y = mx for a line through the origin.
 
I can use similar triangle to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane.
 
I can solve linear equations with rational number coefficients.
 
I can solve equations whose solutions require expanding expressions using the distributive property and/ or collecting like terms.
 
Document Camera
Calculators
Promethean Board
Clicker Devices
Internet
Number lines
Scissors
Tape
Compass
Protractors
Algebra Scales
M3 Tiles
Integer Cards
Dice
Integer Robots
M3 Notebooks
Walk a thon cards
Geogebra
I-MAC computers
Rope
String
Styrofoam Cups
 
Formative may include:
Clicker Quizzes
Problem Sets
Thumbs up
Bell ringers
Modeling
Spot Checks
Exit Slips
In class questioning
Computer Printouts
Small Dry-erase board work
 
Summative Assessment will be at the end of week four. It will consist of approximately 20 multiple choice questions, 2 to 4 short answer questions, and an extended response.
 
 
5-10
8.NS.1:            Understand informally that every number has a decimal expansion; the rational numbers are those with decimal expansions that terminate in 0s or eventually repeat. Know that other numbers are called irrational.
8.NS.2:            Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2). For example, by truncating the decimal expansion of , show that   is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.
Work with radicals and integer
exponents.
 
Order of operations Evaluate
Properties
Negative number
Positive number Integers
Absolute value Opposites
Additive inverse, Terminating decimal
Repeating decimal Bar notation
Rational numbers Irrational numbers
Number line
Distributive property
Term
 
I can define and use in oral and or written language the vocabulary words.
 
I can show that the decimal expansion of rational numbers repeats eventually.
 
I can convert a decimal expansion which repeats eventually into a rational number.
 
I can show informally that every number has a decimal expansion.
 
I can approximate irrational numbers as rational numbers.
 
I can locate (approximately) irrational numbers on a number line.
 
I can estimate the value of expressions involving irrational numbers using rational approximations.( for ex: I can shorten the decimal Expansion of √2 is between 1 and 2, then between 1.4 and 1.5 and explain how to continue on to get better approximations.
 
I can compare the size of irrational numbers using rational approximations.
 
 
Document Camera
Calculators
Promethean Board
Clicker Devices
Internet
Number lines
Scissors
Tape
Compass
Protractors
Algebra Scales
M3 Tiles
Integer Cards
Dice
Integer Robots
M3 Notebooks
Walk a thon cards
Geogebra
I-MAC computers
 
Formative may include:
Clicker Quizzes
Problem Sets
Thumbs up
Bell ringers
Modeling
Spot Checks
Exit Slips
In class questioning
Computer Printouts
Small Dry-erase board work
 
Summative Assessment will be at the end of week 10. It will consist of approximately 20 multiple choice questions, 2 to 4 short answer questions, and an extended response.
 
11-13
8.EE.1: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 × 3–5 = 3–3 = 1/33 = 1/27.
 
8.EE.2: Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that the square root of 2 is irrational.   
 
Multiplicative inverse
Reciprocal
Exponent
Square
Cube
Square root
Cubic root
Radical
Scientific notation
Power of 10
Negative Exponents
I can explain the properties of integer exponents to generate equivalent numerical expressions. ( For ex
. x =  =  =
 
I can apply the properties of integer exponents to produce equivalent numerical expressions.
 
I can use square root and cube root symbols to represent solutions to equations of the form = p and = p, where p is a positive rational number.
 
I can evaluate square roots of small perfect squares.
 
I can evaluate cube roots of small perfect cubes.
 
I can know the square root of 2 is irrational by the decimal expansion
Document Camera
Calculators
Promethean Board
Clicker Devices
Internet
Number lines
Scissors
Tape
Compass
Protractors
Algebra Scales
M3 Tiles
Integer Cards
Dice
Integer Robots
M3 Notebooks
Walk a thon cards
Geogebra
I-MAC computers
Snap Cubes
 
Formative may include:
Clicker Quizzes
Problem Sets
Thumbs up
Bell ringers
Modeling
Spot Checks
Exit Slips
In class questioning
Computer Printouts
Small Dry-erase board work
 
Summative Assessment will be at the end of week 13. It will consist of approximately 20 multiple choice questions, 2 to 4 short answer questions, and an extended response.
 
14-15
8.EE.3: Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 × 108 and the population of the world as 7 × 109, and determine that the world population is more than 20 times larger.
 
8.EE.4:   Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.
Scientific notation
Base
Standard form
Powers f 10
I can express umbers as a single digit times an integer power of 10.
 
I can use scientific notation to estimate very large and/or very small quantities.
 
I can perform operations using numbers expressed in scientific notations.
 
I can use scientific notation to express very large and very small quantities.
 
I can compare quantities to express how much larger one is compared to the other.
 
I can interpret scientific notation that has been generated by technology.
 
I can choose appropriate units of measure when using scientific notation.
 
Document Camera
Calculators
Promethean Board
Clicker Devices
Internet
Number lines
Scissors
Tape
Compass
Protractors
Algebra Scales
M3 Tiles
Integer Cards
Dice
Integer Robots
M3 Notebooks
Walk a thon cards
Geogebra
I-MAC computers
Snap Cubes
Formative may include:
Clicker Quizzes
Problem Sets
Thumbs up
Bell ringers
Modeling
Spot Checks
Exit Slips
In class questioning
Computer Printouts
Small Dry-erase board work
 
Summative Assessment will be at the end of week 15. It will consist of approximately 20 multiple choice questions, 2 to 4 short answer questions, and an extended response.
 
16-21
8.F.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. Function notation is not required in 8th grade.
 
8.F.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.
 
8.F.3 Interpret the equation y=mx+b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A=s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4), and (3,9), which are not on a straight line.
 
8.F.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x,y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of a situation it models, and in terms of its graph or a table of values.
 
8.F.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
 
 
 
Independent variable Dependent variable
Vertical line test Function notation
Slope Intercept form
I can identify cases in which a system of two equations in two unknowns has no solution
Identify cases in which a system of two equations in two unknowns has an infinite number of solutions.
Solve a system of two equations (linear) in two unknowns algebraically.
Solve simple cases of systems of two linear equations in two variables by inspection.
 
I can estimate the point(s) of intersection for a system of two equations in two unknowns by graphing the equations.
 
I can identify functions algebraically including slope and y intercept.
 
I can Identify functions using graphs.
 
I can Identify functions using tables.
 
I can Identify functions using verbal descriptions.
 
I can compare and Contrast 2 functions with different representations.
 
I can draw conclusions based on different representations of functions.
 
I can recognize that a linear function is graphed as a straight line.
 
I can recognize the equation y=mx+b is the equation of a function whose graph is a straight line where m is the slope and b is the y-intercept.
Provide examples of nonlinear functions using multiple representations.
 
I can compare the characteristics of linear and nonlinear functions using various representations.
 
I can recognize that slope is determined by the constant rate of change.
 
I can recognize that the y-intercept is the initial value where x=0.
 
I can determine the rate of change from two (x,y) values, a verbal description, values in a table, or graph.
 
I can determine the initial value from two (x,y) values, a verbal description, values in a table, or graph.

I can construct a function to model a linear relationship between two quantities.
Relate the rate of change and initial value to real world quantities in a linear function in terms of the situation modeled and in terms of its graph or a table of values.
 
I can analyze a graph and describe the functional relationship between two quantities using the qualities of the graph.
 
I can sketch a graph given a verbal description of its qualitative features.
 
I can interpret the relationship between x and y values by analyzing a graph.
 
Document Camera
Calculators
Promethean Board
Clicker Devices
Internet
Number lines
Scissors
Tape
Compass
Protractors
Algebra Scales
M3 Tiles
Integer Cards
Dice
Integer Robots
M3 Notebooks
Walk a thon cards
Geogebra
I-MAC computers
Snap Cubes
Formative may include:
Clicker Quizzes
Problem Sets
Thumbs up
Bell ringers
Modeling
Spot Checks
Exit Slips
In class questioning
Computer Printouts
Small Dry-erase board work
 
Summative Assessment will be at the end of week 21. It will consist of approximately 20 multiple choice questions, 2 to 4 short answer questions, and an extended response.
 
22-23
8.EE.8a Analyze and solve pairs of simultaneous linear equations:
a. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.
 
8.EE.8b Analyze and solve pairs of simultaneous linear equations:
b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.
 
8.EE.8c Analyze and solve pairs of simultaneous linear equations:
c. Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.
Parent function Linear function Linear equation
Y-intercept
Slope-intercept Form
X-intercept
I can solve linear equations with rational number coefficients.
 
I can solve equations whose solutions require expanding expressions using the distributive property and/ or collecting like terms.
 
I can identify the solution(s) to a system of two linear equations in two variables as the point(s) of intersection of their graphs.
 
I can describe the point(s) of intersection between two lines as points that satisfy both equations simultaneously.
 
I can define “inspection”.
Identify cases in which a system of two equations in two unknowns has no solution.
 
I can identify cases in which a system of two equations in two unknowns has an infinite number of solutions.
 
I can solve a system of two equations (linear) in two unknowns algebraically.
 
I can solve simple cases of systems of two linear equations in two variables by inspection.
 
I can estimate the point(s) of intersection for a system of two equations in two unknowns by graphing the equations.
 
 
 
 
I can define “inspection”.
 
I can identify cases in which a system of two equations in two unknowns has no solution
 
I can identify cases in which a system of two equations in two unknowns has an infinite number of solutions.
 
I can solve a system of two equations (linear) in two unknowns algebraically.
I can solve simple cases of systems of two linear equations in two variables by inspection.
 
I can estimate the point(s) of intersection for a system of two equations in two unknowns by graphing the equations.
 
Document Camera
Calculators
Promethean Board
Clicker Devices
Internet
Number lines
Scissors
Tape
Compass
Protractors
Algebra Scales
M3 Tiles
Integer Cards
Dice
Integer Robots
M3 Notebooks
Walk a thon cards
Geogebra
I-MAC computers
Snap Cubes
Formative may include:
Clicker Quizzes
Problem Sets
Thumbs up
Bell ringers
Modeling
Spot Checks
Exit Slips
In class questioning
Computer Printouts
Small Dry-erase board work
 
Summative Assessment will be at the end of week 23. It will consist of approximately 20 multiple choice questions, 2 to 4 short answer questions, and an extended response.
 
24-29
8.G.1abc Verify experimentally the properties of rotations, reflections, and translations:
a. Lines are taken to lines, and line segments to line segments of the same length.
b. Angles are taken to angles of the same measure.
c. Parallel lines are taken to parallel lines.
 
8.G.2 Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.
 
8.G.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
 
8.G.4 Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.
 
8.G.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the three angles appear to form a line, and give an argument in terms of transversals why this is so.
 
8.G.6 Explain a proof of the Pythagorean Theorem and it’s converse.
 
8.G.7 Apply the Pythagorean theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
 
8.G.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system
 
8.G.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
 
Rotation
Center of rotation
Rotational symmetry
Transformation
Image
Translation
Reflection
Line of symmetry Reflection
Translation
Dilations    
Similar figures
Corresponding parts
Congruent
Similar figures
Scale drawing Scale
Scale model
Dilations
proofs
Legs
Hypotenuse
Pythagorean theorem
Circles
Radius
Diameter Circumference
Pi
Sector
Central angle
Composite figure
Area
Perimeter
Surface area Regular pyramid
Similar solids
Volume
I can define & identify rotations, reflections, and translations.
 
I can identify corresponding sides & corresponding angles.
Understand prime notation to describe an image after a translation, reflection, or rotation.
 
I can identify center of rotation.
I can identify direction and degree of rotation.
 
I can identify line of reflection.
 
I can use physical models, transparencies, or geometry software to verify the properties of rotations, reflections, and translations (ie. Lines are taken to lines and line segments to line segments of the same length, angles are taken to angles of the same measure, & parallel lines are taken to parallel lines.)
 
I can define congruency.
Identify symbols for congruency.
 
I can apply the concept of congruency to write congruent statements.
 
I can reason that a 2-D figure is congruent to another if the second can be obtained by a sequence of rotations, reflections, translation.
 
I can describe the sequence of rotations, reflections, translations that exhibits the congruence between 2-D figures using words.
 
I can describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
 
I can describe the effects of dilations, translations, rotations, & reflections on 2-D figures using coordinates.
 
I can define similar figures as corresponding angles are congruent and corresponding sides are proportional.
 
I can recognize symbol for similar.
 
I can apply the concept of similarity to write similarity statements.
 
I can reason that a 2-D figure is similar to another if the second can be obtained by a sequence of rotations, reflections, translation, or dilation.
 
I can describe the sequence of rotations, reflections, translations, or dilations that exhibits the similarity between 2-D figures using words and/or symbols.
 
 
 
 
I can define similar triangles
 
I can define and identify transversals
 
I can identify angles created when parallel line is cut by transversal (alternate interior, alternate exterior, corresponding, vertical, adjacent, etc.)
 
I can justify that the sum of interior angles equals 180. (For example, arrange three copies of the same triangle so that the three angles appear to form a line.)
 
I can justify that the exterior angle of a triangle is equal to the sum of the two remote interior angles.
 
I can use Angle-Angle Criterion to prove similarity among triangles. (Give an argument in terms of transversals why this is so.)
 
I can define key vocabulary: square root, Pythagorean Theorem, right triangle, legs a & b, hypotenuse, sides, right angle, converse, base, height, proof.
 
I can identify the legs and hypotenuse of a right triangle.
 
I can explain a proof of the Pythagorean Theorem.
 
I can explain a proof of the converse of the Pythagorean Theorem.
 
I can recall the Pythagorean theorem and its converse.
 
I can solve basic mathematical Pythagorean theorem problems and its converse to find missing lengths of sides of triangles in two and three-dimensions.
 
I can apply Pythagorean theorem in solving real-world problems dealing with two and three-dimensional shapes.
 
I can determine how to create a right triangle from two points on a coordinate graph.
 
I can use the Pythagorean Theorem to solve for the distance between the two points.
 
I can identify and define vocabulary:
cone, cylinder, sphere, radius,
diameter, circumference, area,
volume, pi, base, height
Know formulas for volume of cones, cylinders, and spheres.
 
I can compare the volume of cones, cylinders, and spheres.
 
I can determine and apply appropriate volume formulas in order to solve mathematical and real-world problems for the given shape.
 
I can, given the volume of a cone, cylinder, or sphere, find the radii, height, or approximate for π.
Document Camera
Calculators
Promethean Board
Clicker Devices
Internet
Number lines
Scissors
Tape
Compass
Protractors
Algebra Scales
M3 Tiles
Integer Cards
Dice
Integer Robots
M3 Notebooks
Walk a thon cards
Geogebra
I-MAC computers
Snap Cubes
In class questioning
Computer Printouts
Small Dry-erase board work
 
Summative Assessments will be at the end of week 26 and 29. It will consist of approximately 10-15  multiple choice questions, 2 to 4 short answer questions, and an extended response. This unit will be divided between transformations/triangles and volume so there will be two summatives.
 
30-33
8.SP.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.
 
8.SP.2 Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.
 
8.SP.3 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. (For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.)
 
8.SP.4 Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?
Measures of central tendency Mean
Median
Mode
Stem-and-leaf plot
Stems
Leaves
Measures of variation
Range
Quartiles
Outlier
Box-and-whisker plot
Histogram
Outcomes bivariate
I can describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association
 
I can construct scatter plots for bivariate measurement data
 
I can interpret scatter plots for bivariate (two different variables such as distance and time) measurement data to investigate patterns of association between two quantities
 
 
 
 
 
I can know that straight lines are used to model relationships between two quantitative variables
 
I can informally assess the model fit by judging the closeness of the data points to the line.
 
I can fit a straight line within the plotted data.
 
I can interpret the meaning of the slope and intercept of a linear equation in terms of the situation
 
I can solve problems using the equation of a linear model.
Document Camera
Calculators
Promethean Board
Clicker Devices
Internet
Number lines
Scissors
Tape
Compass
Protractors
Algebra Scales
M3 Tiles
Integer Cards
Dice
Integer Robots
M3 Notebooks
Walk a thon cards
Geogebra
I-MAC computers
Snap Cubes
In class questioning
Computer Printouts
Small Dry-erase board work
 
Summative Assessment will be at the end of week 33. It will consist of approximately 20 multiple choice questions, 2 to 4 short answer questions, and an extended response.
 
 
 
 
 
 
 
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