# SBS:Math Level 08 v4

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Resources aligned to the old Math Level 11 v3 addresses content in the new Math Level 08 v4

## Number Sense, Properties, and Operations

Measurement Topic: MA.08.811 In the real number system, rational and irrational numbers are in one to one correspondence to points on the number line Capacity Matrix MA.08.811

MA.08.811.04.04 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions. (CAS: 8.1.1.c) (CCSS: 8.NS.2)

MA.08.811.05.04 Apply the properties of integer exponents to generate equivalent numerical expressions. (CAS: 8.1.1.d) (CCSS: 8.EE.1)

MA.08.811.06.04 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. (CAS: 8.1.1.e) (CCSS: 8.EE.2)

MA.08.811.08.04 Use numbers expressed in the form of a single digit times a whole-number power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. (CAS: 8.1.1.g) (CCSS: 8.EE.3)

MA.08.811.09.04 Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities. (CAS: 8.1.1.h.i) (CCSS: 8.EE.4)

## Patterns, Functions, and Algebraic Structures

Measurement Topic: MA.08.821 Linear functions model situations with a constant rate of change and can be represented numerically, algebraically, and graphically.

MA.08.821.01.04 Describe the connections between proportional relationships, lines, and linear equations. (CAS: 8.2.1.a) (CCSS: 8.EE)

MA.08.821.02.04 Graph proportional relationships, interpreting the unit rate as the slope of the graph. (CAS: 8.2.1.b) (CCSS: 8.EE.5)

MA.08.821.04.04 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. (CAS: 8.2.1.d) (CCSS: 8.EE.6)

MA.08.821.05.04 Derive the equation y=mx for a line through the origin and the equation y=mx+b for the line intercepting the veritcal axis at b. (CAS: 8.2.1.e) (CCSS: 8.EE.6)

Measurement Topic: MA.08.822 Properties of algebra and equality are used to solve linear equations and systems of equations Capacity Matrix MA.08.822

MA.08.822.01.04 Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. (CAS: 8.2.2.a.i) (CCSS: 8.EE.7a)

MA.08.822.02.04 Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. (CAS: 8.2.2.a.ii) (CCSS: 8.EE.7b)

MA.08.822.04.04 Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. (CAS: 8.2.2.b.ii) (CCSS: 8.EE.8b)

MA.08.822.05.04 Solve real-world and mathematical problems leading to two linear equations in two variables. (CAS: 8.2.2.b.iii) (CCSS: 8.EE.8c)

Measurement Topic: MA.08.823 Graphs,tables and equations can be used to distinguish between linear and nonlinear functions Capacity Matrix MA.08.823

MA.08.823.02.04 Show that the graph of a function is the set of ordered pairs consisting of an input and the corresponding output. (CAS: 8.2.3.a.ii) (CCSS: 8.F.1)

MA.08.823.03.04 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). (CAS: 8.2.3.a.iii) (CCSS: 8.F.2)

MA.08.823.05.04 Construct a function to model a linear relationship between two quantities. (CAS: 8.2.3.b.i) (CCSS: 8.F.4)

MA.08.823.06.04 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. (CAS: 8.2.3.b.ii) (CCSS: 8.F.4)

MA.08.823.07.04 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. (CAS: 8.2.3.b.iii) (CCSS: 8.F.4)

MA.08.823.08.04 Describe qualitatively the functional relationship between two quantities by analyzing a graph. (CAS: 8.2.3.b.iv) (CCSS: 8.F.5)

## Data Analysis, Statistics, and Probability

Measurement Topic: MA.08.831 Visual displays and summary statistics of two-variable data condense the information in data sets into usable knowledge Capacity Matrix MA.08.831

MA.08.831.01.04 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. (CAS: 8.3.1.a) (CCSS: 8.SP.1)

MA.08.831.02.04 Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. (CAS: 8.3.1.b) (CCSS: 8.SP.1)

MA.08.831.03.04 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. (CAS: 8.3.1.c) (CCSS: 8.SP.2)

MA.08.831.04.04 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. (CAS: 8.3.1.d) (CCSS: 8.SP.3)

MA.08.831.05.04 Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. (CAS: 8.3.1.e.i) (CCSS: 8.SP.4)

MA.08.831.06.04 Use relative frequencies calculated for rows or columns to describe possible association between the two variables. (CAS: 8.3.1.e.ii) (CCSS: 8.SP.4)

## Shape, Dimension, and Geometric Relationships

Measurement Topic: MA.08.841 Transformations of objects can be used to define the concepts of congruence and similarity Capacity Matrix MA.08.841

MA.08.841.02.04 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. (CAS: 8.4.1.b) (CCSS: 8.G.3)

MA.08.841.03.04 Demonstrate that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations. (CAS: 8.4.1.c) (CCSS: 8.G.2)

MA.08.841.04.04 Given two congruent figures, describe a sequence of transformations that exhibits the congruence between them. (CAS: 8.4.1.d) (CCSS: 8.G.2)

MA.08.841.06.04 Given two similar two-dimensional figures, describe a sequence of transformations that exhibits the similarity between them. (CAS: 8.4.1.f) (CCSS: 8.G.4)

MA.08.841.07.04 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. (CAS: 8.4.1.g) (CCSS: 8.G.5)

Measurement Topic: MA.08.842 Direct and indirect measurement can be used to describe and make comparisons Capacity Matrix MA.08.842

MA.08.842.01.04 Explain a proof of the Pythagorean Theorem and its converse. (CAS: 8.4.2.a) (CCSS: 8.G.6)

MA.08.842.02.04 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. (CAS: 8.4.2.b) (CCSS: 8.G.7)

MA.08.842.03.04 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. (CAS: 8.4.2.c) (CCSS: 8.G.8)

MA.08.842.04.04 State the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. (CAS: 8.4.2.d) (CCSS: 8.G.9)