Download The Number System vocabulary related to real numbers in

MATHEMATICS 8 PACING GUIDE
The Number System
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vocabulary related to real numbers in classroom discussions and assignments.
the definition of rational and irrational numbers.
fractions being another way to express division.
use vocabulary related to rational and irrational numbers: natural, whole, integer, rational, irrational, real numbers, square
root, cube root, perfect squares, and perfect cubes.
define rational and irrational numbers
express rational numbers as repeating and terminating decimals.
convert between fractions and decimals (including common repeating decimals).
determine between which two consecutive integers a square root and/or cube root lies.
locate irrational numbers on a number line (include both square and cube roots).
apply the concepts of rational and irrational numbers in real-world problems.
10 days
Expressions and Equations – Part 1
Linear Equations and Roots
 vocabulary related to roots, expressions, and equations in classroom discussions and assignments.
 balance being a required condition for equations.
the limitations of a solution.
 equations by writing, interpreting and solving.
 solve equations that involve square and cube roots.
 use vocabulary related to roots, expressions, and equations: coefficient, like-terms, distributive property, inverse operations,
square root, cube root, perfect square, and perfect cube.
 solve multiple-step equations – include equations with rational number coefficients, applying the distributive property, and
combining like terms.
 understand that linear one-variable equations can have one solution (x = a), no solution (a = b), or an infinite number of
solutions (a = a).
 write and solve equations that are based upon real-world situations/word problems.
 solve equations of the form x^2 = p and x^3 = p (include solutions of roots approximated to the nearest tenth).
 evaluate the roots of perfect squares and perfect cubes – including fractions (i.e. sq. rt. of 144/169).
Integer Exponents
 the rules of exponents.
 simplify products and quotients of monomial expressions using the rules of exponents.
 simplify numeric and variable expressions with exponents (including negative and zero exponents).
 use the rules of exponents to compare the magnitude of numbers.
Scientific Notation
 Scientific Notation by writing, simplifying, and interpreting expressions.
 convert numbers from Scientific Notation to standard form and vice versa.
 compare the magnitude of two numbers written in Scientific Notation.
 perform basic operations on numbers written in Scientific Notation.
QUARTERLY ONE
30 days
Expressions and Equations – Part 2
Proportional Relationships, Lines, and Linear Equations
 proportional relationships being represented in different ways.
 proportionality being inherent in slope (rate of change).
 a variety of phenomena and relationships that can be modeled and analyzed using equations, tables, and/or graphic
representations.
 the y-intercept represents where the function crosses the y-axis; as well, as an initial amount.
 how the slope and y-intercept relate to the equation.
 express and compare proportional relationships of real-world situations using equations, tables, and graphs.
determine the slope of a function given a graph and two ordered pairs – including slopes that are undefined or zero.
 interpret a unit rate as a slope.
 determine the y-intercept given an equation or a graph.
 interpret the meaning of a y-intercept in a real-world situation.
 write an equation in slope-intercept form given a graph.
Systems of Two Linear Equations
 vocabulary related to systems in classroom discussions and assignments.
 how and why the number of solutions depend on the relationship between two linear equations.
 different ways to solve a system of equations and when to utilize each method.
 how to write, interpret, and solve a system of equations for real-world applications.
 use vocabulary related to systems of equations: system of equations, solution to a system, substitution, and linear combinations.
 identify linear systems having one solution, no solution, or infinitely many solutions.
 solve systems of equations by using the methods of graphing, substitution, and adding/subtracting (linear combinations).
 choose the most efficient method of solving a system of linear equations.
 model real-world problems using a linear system.
22 days
Functions
Defining and Comparing Functions
 vocabulary related to functions in classroom discussions and assignments.
 functions having a rule that assigns to each in put exactly one output.
 relations and functions being displayed as ordered pairs, in mapping diagrams, and on graphs.
 the difference between linear and non-linear relationships.
 functions being used to model real life situations.
 use vocabulary related to functions: relation, function, mapping diagram, and vertical line test.
 compare relations displayed as a set of ordered pairs, in a table, or on a graph.
 determine if a relation forms a function – including the vertical line test.
 compare and contrast linear and non-linear functions.
 create and analyze story graphs – including determining if intervals are increasing, decreasing, or if it remains constant.
Linear Functions
 vocabulary related to functions in classroom discussions and assignments.
 the translation of word problems into equations.
 the coefficient of x being the rate of change; and that the initial value is the constant.
 parallel lines having the same slope; and that intersecting lines have different slopes.
 use vocabulary related to linear functions: linear function, coefficient, rate of change, and the initial value of the function.
21 days
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translate word problems into equations.
compare linear functions represented in various ways (table, description, equation).
identify that the initial value is the constant in the equation (written in slope-intercept form).
recognize that functions that are parallel have the same rate of change; and functions that intersect have different rates of change.
QUARTERLY TWO
Geometry – (Topics 9 – 12)
Congruence and Similarity
 vocabulary related to congruence and similarity in classroom discussions and assignments.
 the impact of transformations on geometric figures.
 how an angle of rotation dictates the orientation of the image.
 the corresponding parts of congruent figures.
 characteristics and properties of similar and congruent figures.
 a figure being congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and/or
translations.
 figures being similar if a scale factor produces proportional corresponding sides; and corresponding sides have the same slope.
 measurements that can be found using indirect methods.
 use vocabulary related to congruence and similarity: transformation, translation, image, reflection, vertex, arrow notation,
rotation, angle of rotation, congruent, rigid motions, dilation, and scale factor.
 perform transformations by rotating, reflecting dilating, and translating images.
 write the set of transformation(s) used to move a pre-image to an image.
 name the corresponding parts (angles and sides) of congruent figures.
 apply a scale factor to geometric figures to create similar figures.
 understand that the slope of corresponding parts (non-vertical sides) is the same on similar triangles.
 understand that corresponding sides of similar figures are proportional.
 determine side lengths of similar figures by indirect measurements.
Reasoning and Proof
 vocabulary related to angles in classroom discussions and assignments.
 the relationships among the various angles in geometric figures and parallel lines.
 the measure of an exterior angle is equal to the sum of the measures of its two remote interior angles.
 use vocabulary related to geometry: corresponding angles, alternate interior angles, transversal, adjacent angles, exterior angles,
remote interior angles, vertical angles, and similar figures.
 identify corresponding and alternate interior angles.
 determine that two lines are parallel if corresponding angles and/or alternate interior angles are congruent.
 identify that the sum of the measures of the interior angles of a triangle, supplementary angles, and straight angles have 180
degrees.
 determine the measures of the angles of a triangle given numeric and algebraic clues.
 identify the remote interior angles of an exterior angle of a triangle.
 demonstrate how to use angle relationships to determine if two triangles are similar.
Pythagorean Theorem
 vocabulary related to proofs and the Pythagorean Theorem.
 mathematical proofs.
 how and when to apply the Pythagorean Theorem.
 use vocabulary related to proofs and the Pythagorean Theorem: theorem, hypotenuse, leg, and converse.
20 days
Geometry
Topics 9 – 12 will be
on Quarterly Three.
(Geometry Topic 13
will be on Quarterly
Four.)
10 days
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use reasons (properties, definitions, or given facts) to complete a proof.
determine the missing side lengths of a right triangle in real-world and mathematical problems in two- and three-dimensions by
applying the Pythagorean Theorem.
determine the distance between two points on a coordinate graph using the Pythagorean Theorem.
10 days
QUARTERLY THREE
Geometry – continued (Topic 13)
Surface Area and Volume
 vocabulary related to geometry in classroom discussions and assignments.
 characteristics between three dimensional objects.
 the representations of two-dimensional figures can be used to understand the surfaces of three-dimensional objects.
 apply vocabulary related to three-dimensional objects: net, cone, cylinder, sphere, surface area, volume, height, base, lateral
area, slant, vertex, and radius.
 use nets to assist in finding the surface area of objects.
 determine the surface area of cylinders, cones, and spheres.
 recognize that the volume of a cone is one-third of the volume of a cylinder with the same base and height.
develop and apply strategies and formulas for calculating the volume of cones, cylinders, and spheres.
 determine a missing dimension by applying formulas for volume.
12 days
Statistics
Scatter Plots
 vocabulary related to scatter plots in classroom discussions and assignments.
 a variety of phenomena and relationships that can be modeled and analyzed using scatter plots.
 the inherent proportionality in the slope of a line.
 use vocabulary related to scatter plots - including cluster, trend line, linear/non-linear associations, positive/negative
associations, and outliers.
 recognize and describe patterns in scatter plots such as positive/negative association; clustering; outliers; and linear/non-linear
associations.
 construct and interpret scatter plots to investigate relationships between two quantities.
 informally construct a line of best fit and assess the model fit by judging the closeness of the data points.
 construct, interpret, and write a line of best fit for scatter plots; and use the line to make predictions.
Analyzing Categorical Data
 vocabulary related to data in classroom discussions and assignments.
 two-way frequencies by constructing and interpreting data.
 relative frequencies describe an association between the two variables.
 use vocabulary related to data: bivariate data, measurement data, categorical data, two-way frequency table, and two-way
relative frequency table.
 determine if data is categorical or measurement.
 construct and interpret two-way frequency tables.
 interpret relative frequencies calculated in rows or columns.
QUARTERLY FOUR
23 days