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### 8.NS Number Sense and Operations

- 8.NS.A Know that there are numbers that are not rational, and approximate them by rational numbers.
- 8.NS.A.1 Explore the real number system.
- 8.NS.A.1.a Know the differences between rational and irrational numbers.
- 8.NS.A.1.b Understand that all rational numbers have a decimal expansion that terminates or repeats.
- 8.NS.A.1.c Convert decimals which repeat into fractions and fractions into repeating decimals.
- 8.NS.A.1.d Generate equivalent representations of rational numbers.

- 8.NS.A.2 Estimate the value and compare the size of irrational numbers and approximate their locations on a number line.
- Checkpoint opportunity

- 8.NS.A.1 Explore the real number system.

### 8.EEI Expressions, Equations and Inequalities

- 8.EEI.A Work with radicals and integer exponents.
- 8.EEI.A.1 Know and apply the properties of integer exponents to generate equivalent expressions.
- 8.EEI.A.2 Investigate concepts of square and cube roots.
- 8.EEI.A.2.a Solve equations of the form x² = p and x³ = p, where p is a positive rational number.
- 8.EEI.A.2.b Evaluate square roots of perfect squares less than or equal to 625 and cube roots of perfect cubes less than or equal to 1000.
- 8.EEI.A.2.c Recognize that square roots of non-perfect squares are irrational.

- 8.EEI.A.3 Express very large and very small quantities in scientific notation and approximate how many times larger one is than the other.
- 8.EEI.A.4 Use scientific notation to solve problems.
- 8.EEI.A.4.a Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used.
- 8.EEI.A.4.b Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities.

- Checkpoint opportunity

- 8.EEI.B Understand the connections between proportional relationships, lines and linear equations.
- 8.EEI.B.5 Graph proportional relationships.
- 8.EEI.B.5.a Interpret the unit rate as the slope of the graph.
- 8.EEI.B.5.b Compare two different proportional relationships.

- 8.EEI.B.6 Apply concepts of slope and y-intercept to graphs, equations and proportional relationships.
- 8.EEI.B.6.a Explain why the slope (m) is the same between any two distinct points on a non-vertical line in the Cartesian coordinate plane.
- 8.EEI.B.6.b 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.

- Checkpoint opportunity

- 8.EEI.B.5 Graph proportional relationships.
- 8.EEI.C Analyze and solve linear equations and inequalities and pairs of simultaneous linear equations.
- 8.EEI.C.7 Solve linear equations and inequalities in one variable.
- 8.EEI.C.7.a Create and identify linear equations with one solution, infinitely many solutions or no solutions.
- 8.EEI.C.7.b Solve linear equations and inequalities with rational number coefficients, including equations and inequalities whose solutions require expanding expressions using the distributive property and combining like terms.

- 8.EEI.C.8 Analyze and solve systems of linear equations.
- 8.EEI.C.8.a Graph systems of linear equations and recognize the intersection as the solution to the system.
- 8.EEI.C.8.b Explain why solution(s) to a system of two linear equations in two variables correspond to point(s) of intersection of the graphs.
- 8.EEI.C.8.c Explain why systems of linear equations can have one solution, no solution or infinitely many solutions.
- 8.EEI.C.8.d Solve systems of two linear equations.

- Checkpoint opportunity

- 8.EEI.C.7 Solve linear equations and inequalities in one variable.

### 8.GM Geometry and Measurement

- 8.GM.A Understand congruence and similarity using physical models, transparencies or geometry software.
- 8.GM.A.1 Verify experimentally the congruence properties of rigid transformations.
- 8.GM.A.1.a Verify that angle measure, betweeness, collinearity and distance are preserved under rigid transformations.
- 8.GM.A.1.b Investigate if orientation is preserved under rigid transformations.

- 8.GM.A.2 Understand that two-dimensional figures are congruent if a series of rigid transformations can be performed to map the pre-image to the image.
- 8.GM.A.2.a Describe a possible sequence of rigid transformations between two congruent figures.

- 8.GM.A.3 Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates.
- 8.GM.A.4 Understand that two-dimensional figures are similar if a series of transformations (rotations, reflections, translations and dilations) can be performed to map the pre-image to the image.
- 8.GM.A.4.a Describe a possible sequence of transformations between two similar figures.

- 8.GM.A.5 Explore angle relationships and establish informal arguments.
- 8.GM.A.5.a Derive the sum of the interior angles of a triangle.
- 8.GM.A.5.b Explore the relationship between the interior and exterior angles of a triangle.
- 8.GM.A.5.c Construct and explore the angles created when parallel lines are cut by a transversal.
- 8.GM.A.5.d Use the properties of similar figures to solve problems.

- Checkpoint opportunity

- 8.GM.A.1 Verify experimentally the congruence properties of rigid transformations.
- 8.GM.B Understand and apply the Pythagorean Theorem.
- 8.GM.B.6 Use models to demonstrate a proof of the Pythagorean Theorem and its converse.
- 8.GM.B.7 Use the Pythagorean Theorem to determine unknown side lengths in right triangles in problems in two- and three-dimensional contexts.
- 8.GM.B.8 Use the Pythagorean Theorem to find the distance between points in a Cartesian coordinate system.
- Checkpoint opportunity

- 8.GM.C Solve problems involving volume of cones, pyramids and spheres.
- 8.GM.C.9 Solve problems involving surface area and volume.
- 8.GM.C.9.a Understand the concept of surface area and find surface area of pyramids.
- 8.GM.C.9.b Understand the concepts of volume and find the volume of pyramids, cones and spheres.

- Checkpoint opportunity

- 8.GM.C.9 Solve problems involving surface area and volume.

### 8.DSP Data Analysis, Statistics and Probability

- 8.DSP.A Investigate patterns of association in bivariate data.
- 8.DSP.A.1 Construct and interpret scatter plots of bivariate measurement data to investigate patterns of association between two quantities.
- 8.DSP.A.2 Generate and use a trend line for bivariate data, and informally assess the fit of the line.
- 8.DSP.A.3 Interpret the parameters of a linear model of bivariate measurement data to solve problems.
- 8.DSP.A.4 Understand the patterns of association in bivariate categorical data displayed in a two-way table.
- 8.DSP.A.4.a Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects.
- 8.DSP.A.4.b Use relative frequencies calculated for rows or columns to describe possible association between the two variables.

- Checkpoint opportunity

### 8.F Functions

- 8.F.A Define, evaluate and compare functions.
- 8.F.A.1 Explore the concept of functions. (The use of function notation is not required.)
- 8.F.A.1.a Understand that a function assigns to each input exactly one output.
- 8.F.A.1.b Determine if a relation is a function.
- 8.F.A.1.c Graph a function.

- 8.F.A.2 Compare characteristics of two functions each represented in a different way.
- 8.F.A.3 Investigate the differences between linear and nonlinear functions.
- 8.F.A.3.a Interpret the equation y = mx + b as defining a linear function, whose parameters are the slope (m) and the y-intercept (b).
- 8.F.A.3.b Recognize that the graph of a linear function has a constant rate of change
- 8.F.A.3.c Give examples of nonlinear functions.

- Checkpoint opportunity

- 8.F.A.1 Explore the concept of functions. (The use of function notation is not required.)
- 8.F.B Use functions to model relationships between quantities.
- 8.F.B.4 Use functions to model linear relationships between quantities.
- 8.F.B.4.a Explain the parameters of a linear function based on the context of a problem.
- 8.F.B.4.b Determine the parameters of a linear function.
- 8.F.B.4.c Determine the x-intercept of a linear function.

- 8.F.B.5 Describe the functional relationship between two quantities from a graph or a verbal description.
- Checkpoint opportunity

- 8.F.B.4 Use functions to model linear relationships between quantities.