Unit Topics
7th Grade Honors and 8th Grade Math will be covering the following topics over the course of District Outcomes. Click on an Outcome to see the District and State Standards* that are being covering throughout the year.
Unit B – Exponents and Scientific Notation Unit E - Solving Linear Equations Unit F - Systems of Linear Equations Unit I - Geometry: Volume of Cones, Cylinders, and Spheres Unit J - Statistical Relationships
*Key = CC.8 - refers to the Common Core - Grade 8 Standard; RP - Ratios and Proportions; NS - Number Sense; EE - Expressions and Equations; G - Geometry; SP - Statistics and Probability; F - Functions Unit A - Irrational Numbers: Students will apply properties and perform operations on rational and irrational numbers. (NS) 1 Identify numbers that are not rational as irrational. Convert numbers into a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, convert decimal expansion which repeats eventually into a rational number. CC.8.NS.1.
2 Use rational approximations of irrational numbers to compare the size of irrational numbers. CC.8.NS.2
3 Locate irrational numbers approximately on a number line diagram. CC.8.NS.2
4 Estimate the value of irrational expressions. CC.8.NS.2
5 Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. CC.8.EE.2
6 Evaluate square roots of small perfect squares and cube roots of small perfect cubes. CC.8.EE.2
Unit B - Exponents and Scientific Notation: Students will evaluate radicals and integer exponents. (EE) 1 Apply the properties of integer exponents to generate equivalent algebraic expressions. CC.8.EE.1
2 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. CC.8.EE.3
3 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. CC.8.EE.4
4 Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities. Interpret scientific notation that has been generated by technology. CC.8.EE.4
Unit C - Functions: Students will define, evaluate, and compare functions. (F) 1 Identify a function as 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 Grade 8.) CC.8.F.1
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.CC.8.F.2
3 Select an equation that defines a linear function, whose graph is a straight line; give examples of functions that are not linear. CC.8.F.3
4 Construct a function to model a linear relationship between two quantities. CC.8.F.4
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). CC.8.F.5
6 Sketch a graph that exhibits the qualitative features of a function that has been described verbally (e.g. A nonlinear, decreasing function). CC.8.F.5
Unit D - Linear Functions : Students will understand the connections between proportional relationships, lines, and linear equations. (EE) 1 Graph and identify proportional relationships, interpreting the unit rate as the slope of the graph. CC.8.EE.5
2 Compare two different proportional relationships represented in different formats such as graphs, equations, and tables. CC.8.EE.5
3 Using similar triangles, calculate the slopes of the corresponding sides to prove the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; write 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. CC.8.EE.6
4 Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. CC.8.F.4
5 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. CC.8.F.4
Outcome E - Solving Linear Equations: Students will analyze and solve linear equations. 1 Create examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. CC.8.EE.7a
2 Solve linear equations in one variable with one solution, infinitely many solutions, or no solutions. Identify the situation (one solution, infinitely many solutions, or no solutions) by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). CC.8.EE.7a
3 Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. CC.8.EE.7b
Outcome F - Systems of Linear Equations: Students will analyze and solve pairs of simultaneous linear equations. (EE) 1 Identify the solution to a system of two linear equations in two variables that intersect on a graph. CC.8.EE.8a
2 Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by examining whether there are no solutions, infinitely many solutions or one solution. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. CC.8.EE.8
3 Solve real-world and mathematical problems using 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. CC.8.EE.8c
Outcome G - Angles and Triangles: Students will understand and apply the Pythagorean Theorem. (G) 1 Establish and apply the facts about the angles created when parallel lines are cut by a transversal. CC.8.G.5 *with terms.
2 Use the Pythagorean Theorem and its converse to determine if the lengths of a triangle’s side represent a right triangle. CC.8.G.6
3 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. CC.8.G.7
4 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. CC.8.G.8
5 Apply the Triangle Sum and Exterior Angle Theorems to establish facts about the angle sum and exterior angles of triangles. CC.8.G.5
6 Use the angle-angle criterion to prove the similarity between a set of given 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. CC.8.G.5
Unit H - Transformations: Students will apply the properties of congruence and similarity using physical models, transparencies, or geometry software. (G) 1 Use the properties of rotations, reflections, and translations to find the pairs of corresponding lines, line segments, angles and parallel lines. For example, if triangle ABC is reflected to A’B’C’, then angle A is congruent to A. CC.8.G.1a, CC.8.G.1b, CC.8.G.1c
2 Match a two-dimensional figure that is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, translations and dilations; given two congruent figures, describe a sequence that exhibits the congruence and similarity between them. CC.8.G.2; CC.8.G.4
3 Describe the effect on the x and y coordinates from dilations, translations, rotations and reflections on two-dimensional figures. CC.8.G.3
Outcome I - Volume of Cylinders, Cones, and Spheres: Students will solve real world and mathematical problems involving volume of cylinders, cones, and spheres. (G) 1 Show and use the formula for the volume of cones and use it to solve real-world and mathematical problems. CC.8.G.9
2 Show and use the formula for the volume of cylinders and use it to solve real-world and mathematical problems. CC.8.G.9
3 Show and use the formula for the volume of spheres and use it to solve real-world and mathematical problems. CC.8.G.9
Unit J - Statistical Relationships: Students will investigate patterns of association in bivariate data. Students will analyze the purposes of different displays. (SP) 1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Identify patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. CC.8.SP.1
2 Show 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. CC.8.SP.2
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. CC.8.SP.3
4 Show 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. CC.8.SP.4
5 Select the appropriate graph to use when presented with different sets of data. |