# SBS:Math Level 08 v4

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Math Level 08 Capacity Matrices

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

- Math Level 11 Unit - Created by Kelly Messenger
- Math Level 11 Unit - Created by Maria Dorsey

## Contents |

## 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)