 • 8
Top Mathematicians
• Number
• 8.N.1
The student will compare and order real numbers.
• 8.N.2
The student will describe the relationships between the subsets of the real number system.
• 8.N.3
The student will:
a) estimate and determine the two consecutive integers between which a square root lies; and
b) determine both the positive and negative square roots of a given perfect square.
• Algebra
• 8.OA.1
The student will:
a) represent verbal quantitative situations algebraically; and
b) evaluate algebraic expressions for given replacement values of the variables.
• 8.OA.2
The student will perform operations on polynomials, including:
a) applying the laws of exponents to perform operations on expressions;
b) adding, subtracting, multiplying, and dividing polynomials; and
c) factoring completely first- and second-degree binomials and trinomials in one variable.
• 8.OA.3
The student will simplify:
a) square roots of whole numbers and monomial algebraic expressions;
b) cube roots of integers; and
c) numerical expressions containing square or cube roots.
• 8.OA.4
The student will solve:
a) multistep linear equations in one variable algebraically;
b) quadratic equations in one variable algebraically;
c) literal equations for a specified variable;
d) systems of two linear equations in two variables algebraically and graphically; and
e) practical problems involving equations and systems of equations.
• 8.OA.5
The student will:
a) solve multistep linear inequalities in one variable algebraically and represent the solution graphically;
b) represent the solution of linear inequalities in two variables graphically;
c) solve practical problems involving inequalities; and
d) represent the solution to a system of inequalities graphically.
• 8.OA.6
The student will:
a) determine the slope of a line when given an equation of the line, the graph of the line,
or two points on the line;
b) write the equation of a line when given the graph of the line, two points on the line, or the slope and a point on the line; and
c) graph linear equations in two variables.
• 8.OA.7
The student will investigate and analyze linear and quadratic function families and their characteristics both algebraically and graphically, including:
a) determining whether a relation is a function;
b) domain and range;
c) zeros;
d) intercepts;
e) values of a function for elements in its domain; and
f) connections between and among multiple representations of functions using verbal descriptions, tables, equations, and graphs.
• 8.OA.8
The student, given a data set or practical situation, will analyze a relation to determine whether a direct or inverse variation exists, and represent a direct variation algebraically and graphically and an inverse variation algebraically.
• 8.OA.9
The student will collect and analyze data, determine the equation of the curve of best fit in order to make predictions, and solve practical problems, using mathematical models of linear and quadratic functions.
• Geometry
• 8.G.1
The student will use deductive reasoning to construct and judge the validity of a logical argument consisting of a set of premises and a conclusion. This will include:
a) identifying the converse, inverse, and contrapositive of a conditional statement;
b) translating a short verbal argument into symbolic form; and
c) determining the validity of a logical argument.
• 8.G.10
The student will solve problems, including practical problems, involving angles of convex polygons. This will include determining the:
a) sum of the interior and/or exterior angles;
b) measure of an interior and/or exterior angle; and
c) number of sides of a regular polygon.
• 8.G.11
The student will solve problems, including practical problems, by applying properties of circles. This will include determining:
a) angle measures formed by intersecting chords, secants, and/or tangents;
b) lengths of segments formed by intersecting chords, secants, and/or tangents;
c) arc length; and
d) area of a sector.
• 8.G.12
The student will solve problems involving equations of circles.
• 8.G.13
The student will use surface area and volume of three-dimensional objects to solve practical problems.
• 8.G.14
The student will apply the concepts of similarity to two- or three-dimensional geometric figures. This will include:
a) comparing ratios between lengths, perimeters, areas, and volumes of similar figures;
b) determining how changes in one or more dimensions of a figure affect area and/or volume of the figure;
c) determining how changes in area and/or volume of a figure affect one or more dimensions of the figure; and
d) solving problems, including practical problems, about similar geometric figures.
• 8.G.2
The student will use the relationships between angles formed by two lines intersected by a transversal to:
a) prove two or more lines are parallel; and
b) solve problems, including practical problems, involving angles formed when parallel lines are intersected by a transversal.
• 8.G.3
The student will solve problems involving symmetry and transformation. This will include:
a) investigating and using formulas for determining distance, midpoint, and slope;
b) applying slope to verify and determine whether lines are parallel or perpendicular;
c) investigating symmetry and determining whether a figure is symmetric with respect to a line or a point; and
d) determining whether a figure has been translated, reflected, rotated, or dilated, using coordinate methods.
• 8.G.4
The student will construct and justify the constructions of:
a) a line segment congruent to a given line segment;
b) the perpendicular bisector of a line segment;
c) a perpendicular to a given line from a point not on the line;
d) a perpendicular to a given line at a given point on the line;
e) the bisector of a given angle,
f) an angle congruent to a given angle;
g) a line parallel to a given line through a point not on the line; and
h) an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
• 8.G.5
The student, given information concerning the lengths of sides and/or measures of angles in triangles, will solve problems, including practical problems. This will include:
a) ordering the sides by length, given angle measures;
b) ordering the angles by degree measure, given side lengths;
c) determining whether a triangle exists; and
d) determining the range in which the length of the third side must lie.
• 8.G.6
The student, given information in the form of a figure or statement, will prove two triangles are congruent.
• 8.G.7
The student, given information in the form of a figure or statement, will prove two triangles are similar.
• 8.G.8
The student will solve problems, including practical problems, involving right triangles. This will include applying:
a) the Pythagorean Theorem and its converse;
b) properties of special right triangles; and
c) trigonometric ratios.
• 8.G.9
The student will verify and use properties of quadrilaterals to solve problems, including practical problems.
• Measurement and Geometry
• 8.MD.10
The student will solve area and perimeter problems, including practical problems, involving composite plane figures.
• 8.MD.5
The student will use the relationships among pairs of angles that are vertical angles, adjacent angles, supplementary angles, and complementary angles to determine the measure of unknown angles.
• 8.MD.6
The student will:
a) solve problems, including practical problems, involving volume and surface area of cones and square-based pyramids; and
b) describe how changing one measured attribute of a rectangular prism affects the volume and surface area.
• 8.MD.7
The student will:
a) given a polygon, apply transformations, to include translations, reflections, and dilations, in the coordinate plane; and
b) identify practical applications of transformations.
• 8.MD.8
The student will construct a three-dimensional model, given the top or bottom, side, and front views.
• 8.MD.9
The student will:
a) verify the Pythagorean Theorem; and
b) apply the Pythagorean Theorem.
• Statistics & Probability
• 8.SP.11
The student will:
a) compare and contrast the probability of independent and dependent events; and
b) determine probabilities for independent and dependent events.
• 8.SP.12
The student will:
a) represent numerical data in boxplots;
b) make observations and inferences about data represented in boxplots; and
c) compare and analyze two data sets using boxplots.
• 8.SP.13
The student will
a) represent data in scatterplots;
b) make observations about data represented in scatterplots; and
c) use a drawing to estimate the line of best fit for data represented in a scatterplot.
• Patterns, Functions and Algebra
• 8.PFA.2.14
The student will:
a) evaluate an algebraic expression for given replacement values of the variables; and
b) simplify algebraic expressions in one variable.
• 8.PFA.2.15
The student will:
a) determine whether a given relation is a function; and
b) determine the domain and range of a function.
• 8.PFA.2.16
The student will:
a) recognize and describe the graph of a linear function with a slope that is positive, negative, or zero;
b) identify the slope and y-intercept of a linear function, given a table of values, a graph, or an equation in y = mx + b form;
c) determine the independent and dependent variable, given a practical situation modeled by a linear function;
d) graph a linear function given the equation in y = mx + b form; and
e) make connections between and among representations of a linear function using verbal descriptions, tables, equations, and graphs.
• 8.PFA.2.17
The student will solve multistep linear equations in one variable with the variable on one or both sides of the equation, including practical problems that require the solution of a multistep linear equation in one variable.
• 8.PFA.2.18
The student will solve multistep linear inequalities in one variable with the variable on one or both sides of the inequality symbol, including practical problems, and graph the solution on a number line.