8th Grade Math

Standard - CC.2.2.7.B.3
Model and solve real-world and mathematical problems by using and connecting numerical, algebraic, and/or graphical representations.

Unit 1 - Transformations

Demonstrate an understanding of geometric transformations.

Unit 2 - Slope & Linear Relationships

Unit 3 - System of Equations

I can identify rotations, reflections, and translations.

I can apply properties of rotations, reflections, and translations.

I can describe the effect of translations, rotations, and reflections on two-dimensional figures using coordinates.

Apply properties of geometric transformations to verify congruence or similarity.

I can apply properties of rotations, reflections, and translations.

I can describe a sequence of transformations that exhibits the congruence between two congruent figures.

I can describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

I can describe a sequence of transformations that exhibits the similarity between two given similar two-dimensional figures.

Analyze and describe linear relationships between two variables, using slope.

Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.

I can 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.

I can calculate the slope of a line from various representations (i.e. graph, table, two points).

Understand the connections between proportional relationships, lines, and linear equations.

I can derive the equation y = mx for a line through the origin.

I can derive the equation y = mx + b for a line intercepting the vertical axis at b.

Write, solve, graph, and interpret linear equations in one variable, using various methods.

Solve linear equations that have rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

Write and identify linear equations in one variable with one solution, infinitely many solutions, or no solutions.

Write, solve, graph, and interpret linear equations in two variables, using various methods.

Interpret solutions to a system of two linear equations in two variables as points of intersection of their graphs because points of intersection satisfy both equations simultaneously.

Solve systems of two linear equations in two variables algebraically and estimate solutions by graphing the equations. Solve simple cases by inspection.

Solve real-world and mathematical problems leading to two linear equations in two variables.

Unit 4 - Volume & Functions

Apply volume formulas of cones, cylinders, and spheres.

I can evaluate expressions at specific values of their variables

I can find volume by applying formulas

I can solve real-world and mathematical problems

Represent or interpret functional relationships between quantities using tables, graphs, and descriptions.

I can describe the functional relationship between two quantities by analyzing a graph (where the function is increasing or decreasing, linear or nonlinear)

I can sketch or determine a graph that exhibits features of a function that has been described verbally

I can determine whether a relation is a function by looking at a graph, table, or set of ordered pairs

Define, evaluate, and compare functions displayed algebraically, graphically, or numerically in tables or by verbal descriptions.

I can construct a function to model a linear relationship between two quantities

I can determine the rate of change and initial value of a function from a description of a relationship or from two points

I can interpret the rate of change and initial value of a linear function in terms of the situation it models

I can translate fluently between different representations of linear functions

I can compare properties of two functions, each represented in a different way

I can interpret the equation of y=mx+b as defining a linear function whose graph is a straight line

I can give examples of functions that are not linear

Unit 5 - Real Numbers and the Pythagorean Theorem

Represent and use expressions and equations to solve problems involving integer exponents.

I can understand the properties of integer exponents.

I can apply the properties of integer exponents to generate equivalent expressions without a calculator.

I can estimate very large or very small numbers using scientific notation.

I can express how many times larger or smaller a number is from another in scientific notation.

I can perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used.

I can express answers in scientific notation and choose units of appropriate size for measurements of very large or very small quantities

Eligible Content - M06.B-E.1.1.1 Write and evaluate numerical expressions involving whole-number exponents.

Represent and use expressions and equations to solve problems involving radicals.

Apply concepts of rational and irrational numbers.

I can 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.

I can evaluate square roots of perfect squares (up to and including 12^2) and cube roots of perfect cubes (up to and including 5^3) without a calculator

Determine whether a number is rational or irrational. For rational numbers, show that the decimal expansion terminates or repeats (limit repeating decimals to thousandths).

I can estimate the value of irrational numbers without a calculator

I can use rational approximations of irrational numbers to compare and order irrational numbers.

I can locate/identify rational and irrational numbers at their approximate locations on a number line.

I can convert a terminating or repeating decimal to a rational number

Solve problems involving right triangles by applying the Pythagorean theorem.

I can apply the converse of the Pythagorean theorem to show a triangle is a right triangle.

I can apply the Pythagorean theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two dimensions.

I can apply the Pythagorean theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in three dimensions

I can apply the Pythagorean theorem to find the distance between two points in a coordinate system.

Unit 6 - Data

Analyze and interpret bivariate data displayed in multiple representations.

Understand that patterns of association can be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table.

I can construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities.

I can describe patterns such as clustering, outliers, positive or negative correlation, linear association, and nonlinear association.

I can identify a line of best fit by judging the closeness of the data points to the line, for scatter plots that suggest a linear association.

I can use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.

I can construct a two-way table summarizing data on two categorical variables collected from the same subjects.

I can interpret a two-way table summarizing data on two categorical variables collected from the same subjects.

I can use relative frequencies calculated for rows or columns to describe possible associations between the two variables.

Standard - CC.2.1.7.D.1
Analyze proportional relationships and use them to model and solve real-world and mathematical problems.

I can describe a sequence of transformations that exhibits the similarity between two given similar two-dimensional figures. (Unit 1 - Lesson 2)

Standard - CC.2.2.7.B.1
Apply properties of operations to generate equivalent expressions.

Standard - CC.2.2.7.B.3
Model and solve real-world and mathematical problems by using and connecting numerical, algebraic, and/or graphical representations.

I can derive the equation y = mx + b for a line intercepting the vertical axis at b. (Unit 2 - Lesson 2)

CC.2.3.6.A.1
Apply appropriate tools to solve real-world and mathematical problems involving area, surface area, and volume.

I can derive the equation y = mx + b for a line intercepting the vertical axis at b. (Unit 2 - Lesson 2)

I can interpret the rate of change and initial value of a linear function in terms of the situation it models. (Unit 4 - Lesson 3)

Eligible Content - M06.A-N.3.1.3 Locate and plot integers and other rational numbers on a horizontal or vertical number line; locate and plot pairs of integers and other rational numbers on a coordinate plane.

I can describe the functional relationship between two quantities by analyzing a graph (where the function is increasing or decreasing, linear or nonlinear) (Unit 4 - Lesson 2)

Eligible Content - M07.A-N.1.1.3 Apply properties of operations to multiply and divide rational numbers, including real-world contexts; demonstrate that the decimal form of a rational number terminates or eventually repeats.

Eligible Content - M07.C.G.1.1.1 Solve problems involving scale drawings of geometric figures, including finding length and area.

Find the area and circumference of a circle. Solve problems involving area and circumference of a circle(s). Formulas will be provided.

Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Formulas will be provided.