# SBS:Math Level 10 v4

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Math Level 10 Capacity Matrices

*Resources aligned to the old Math Level 13 v3 which addresses content in the new Math Level 10 v4*

- Math Level 13 Unit - Created by Craig Sherman and Bill Lester

## Contents |

## Number Sense, Properties, and Operations

**Measurement Topic:** *MA.09.H12 Quantitative reasoning is used to make sense of quantities and their relationships in problem situations* Capacity Matrix MA.09.H12

MA.09.H12.03.04 Define appropriate quantities for the purpose of descriptive modeling. (CAS: HS.1.2.a.ii) (CCSS: N-Q.2)

**Measurement Topic:** *MA.10.H11 The complex number system includes real numbers and imaginary numbers* Capacity Matrix MA.10.H11

MA.10.H11.01.04 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.• (CAS: HS.1.1.a.i) (CCSS: N-RN.1)

MA.10.H11.02.04 Rewrite expressions involving radicals and rational exponents using the properties of exponents. (CAS: HS.1.1.a.ii) (CCSS: N-RN.2)

MA.10.H11.04.04 Explain why the sum or product of two rational numbers is rational.• (CAS: HS.1.1.b.i) (CCSS: N-RN.3)

MA.10.H11.05.04 Explain why the sum of a rational number and an irrational number is irrational.• (CAS: HS.1.1.b.ii) (CCSS: N-RN.3)

MA.10.H11.06.04 Explain why the product of a nonzero rational number and an irrational number is irrational.• (CAS: HS.1.1.b.iii) (CCSS: N-RN.3)

MA.10.H11.07.04 Define the complex number i such that i2 = –1, and show that every complex number has the form a + bi where a and b are real numbers. (CAS: HS.1.1.c.i) (CCSS: N-CN.1)

MA.10.H11.08.04 Use the relation i2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. (CAS: HS.1.1.c.ii) (CCSS: N-CN.2)

MA.10.H11.09.04 Solve quadratic equations with real coefficients that have complex solutions. (CAS: HS.1.1.d.i) (CCSS: N-CN.7)

## Patterns, Functions, and Algebraic Structures

**Measurement Topic:** *MA.09.H21 Functions model situations where one quantity determines another and can be represented algebraically, graphically, and using tables* Capacity Matrix MA.09.H21

MA.09.H21.04.04 Graph linear functions and show intercepts.(CAS: HS.2.1.a.i) (CCSS: F-IF.1)

**Measurement Topic:** *MA.09.H23 Expressions can be represented in multiple, equivalent forms* Capacity Matrix MA.09.H23

MA.09.H23.02.04 Interpret complicated expressions by viewing one or more of their parts as a single entity. (CAS: HS.2.3.a.i.2) (CCSS: A-SSE.1b)

**Measurement Topic:** *MA.09.H24 Solutions to equations, inequalities and systems of equations are found using a variety of tools* Capacity Matrix MA.09.H24

MA.09.H24.01.04 Create equations and inequalities in one variable and use them to solve problems (CAS: HS.2.4.a.i) (CCSS: A-CED.1)

MA.09.H24.02.04 Create equations in two or more variables to represent relationships between quantities and graph equations on coordinate axes with labels and scales. (CAS: HS.2.4.a.ii) (CCSS: A-CED.2)

MA.09.H24.04.04 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. (CAS: HS.2.4.a.iv) (CCSS: A-CED.4)

MA.09.H24.05.04 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. (CAS: HS.2.4.b.i) (CCSS: A-REI.1)

**Measurement Topic:** *MA.10.H21 Functions model situations where one quantity determines another and can be represented algebraically, graphically, and using tables* Capacity Matrix MA.10.H21

MA.10.H21.01.04 Graph quadratic functions and show intercepts, maxima, and minima. (CAS: HS.2.1.c.ii) (CCSS: F-IF.7a)

MA.10.H21.02.04 Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. (CAS: HS.2.1.c.vi.1) (CCSS: F-IF.8a)

MA.10.H21.03.04 Use the properties of exponents to interpret expressions for exponential functions. (CAS: HS.2.1.c.vi.2) (CCSS: F-IF.8b)

MA.10.H21.04.04 Determine an explicit expression, a recursive process, or steps for calculation from a context. (CAS: HS.2.1.d.i.1) (CCSS: F-BF.1a)

**Measurement Topic:** *MA.10.H23 Expressions can be represented in multiple, equivalent forms* Capacity Matrix MA.10.H23

MA.10.H23.03.04 Use the structure of an expression to identify ways to rewrite it.

MA.10.H23.04.04 Factor a quadratic expression to reveal the zeros of the function it defines. (CAS: HS.2.3.b.i.1) (CCSS: A-SSE.3a)

MA.10.H23.05.04 Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. (CAS: HS.2.3.b.i.2) (CCSS: A-SSE.3b)

MA.10.H23.06.04 Explain that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. (CAS: HS.2.3.c.i) (CCSS: A-APR.1)

**Measurement Topic:** *MA.10.H24 Solutions to equations, inequalities and systems of equations are found using a variety of tools* Capacity Matrix MA.10.H24

MA.10.H24.01.04 Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x-p)2=q that has the same solutions. Derive the quadratic formula from this form. (CAS: HS.2.4.c.ii.1) (CCSS: A-REI.4a)

MA.10.H24.02.04 Solve quadratic equations by inspection, taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation. (CAS: HS.2.4.c.ii.2) (CCSS: A-REI.4b)

MA.10.H24.03.04 Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b. (CAS: HS.2.4.c.ii.3) (CCSS: A-REI.4b)

MA.10.H24.04.04 Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. (CAS: HS.2.4.d.iii) (CCSS: A-REI.7)

**Measurement Topic:** *MA.11.H21 Functions model situations where one quantity determines another and can be represented algebraically, graphically, and using tables* Capacity Matrix MA.11.H21

MA.11.H21.01.04 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. (CAS: HS.2.1.b.i) (CCSS: F-IF.4)

MA.11.H21.02.04 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. (CAS: HS.2.1.b.ii) (CCSS: F-IF.5)

MA.11.H21.03.04 Calculate and interpret the average rate of change of a function over a specified interval. Estimate the rate of change from a graph. (CAS: HS.2.1.b.iii) (CCSS: F-IF.6)

MA.11.H21.05.04 Graph piecewise-defined functions, including step functions. (CAS: HS.2.1.c.iii) (CCSS: F-IF.7b)

MA.11.H21.06.04 Graph cube root functions. (CAS: HS.2.1.c.iii) (CCSS: F-IF.7b)

MA.11.H21.07.04 Graph absolute value functions. (CAS: HS.2.1.c.iii) (CCSS: F-IF.7b)

MA.11.H21.08.04 Graph square root functions. (CAS: HS.2.1.c.iii) (CCSS: F-IF.7b)

MA.11.H21.10.04 Graph logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. (CAS: HS.2.1.c.v) (CCSS: F-IF.7e)

MA.11.H21.11.04 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). (CAS: HS.2.1.c.vi.3) (CCSS: F-IF.9)

MA.11.H21.12.04 Determine an explicit expression, a recursive process, or steps for calculation from a context. (CAS: HS.2.1.d.i.1) (CCSS: F-BF.1a)

MA.11.H21.13.04 Combine standard function types using arithmetic operations. (CAS: HS.2.1.d.i.2) (CCSS: F-BF.1b)

MA.11.H21.15.04 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k, 9 and find the value of k given the graphs. (CAS: HS.2.1.e.i) (CCSS: F-BF.3)

## Data Analysis, Statistics, and Probability

**Measurement Topic:** *MA.09.H31 Visual displays and summary statistics condense the information in data sets into usable knowledge* Capacity Matrix MA.09.H31

MA.09.H31.06.04 Informally assess the fit of a function by plotting and analyzing residuals (CAS: HS.3.1.a.i) (CCSS: S-ID.1)

**Measurement Topic:** *MA.10.H33 Probability models outcomes for situations in which there is inherent randomness* Capacity Matrix MA.10.H33

MA.10.H33.01.04 Describe events as subsets of a sample space using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events. (CAS: HS.3.3.a.i) (CCSS: S-CP.1)

MA.10.H33.02.04 Explain that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. (CAS: HS.3.3.a.ii) (CCSS: S-CP.2)

MA.10.H33.03.04 Using the conditional probability of A given B as P(A and B)/P(B), interpret the independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B. (CAS: HS.3.3.a.iii) (CCSS: S-CP.3)

MA.10.H33.04.04 Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. (CAS: HS.3.3.a.iv) (CCSS: S-CP.4)

MA.10.H33.05.04 Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. (CAS: HS.3.3.a.v) (CCSS: SCP.5)

MA.10.H33.06.04 Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model. (CAS: HS.3.3.b.i) (CCSS: S-CP.6)

MA.10.H33.07.04 Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model. (CAS: HS.3.3.b.ii) (CCSS: S-CP.7)

## Shape, Dimension, and Geometric Relationships

**Measurement Topic:** *MA.10.H42 Concepts of similarity are foundational to geometry and its applications* Capacity Matrix MA.10.H42

MA.10.H42.01.04 Show that a dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. (CAS: HS.4.2.a.i.1) (CCSS: G-SRT.1a)

MA.10.H42.02.04 Show that the dilation of a line segment is longer or shorter in the ratio given by the scale factor.

MA.10.H42.03.04 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar. (CAS: HS.4.2.a.ii) (CCSS: G-SRT.2)

MA.10.H42.04.04 Explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. (CAS: HS.4.2.a.iii) (CCSS: G-SRT.2)

MA.10.H42.05.04 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.• (CAS: HS.4.2.a.iv) (CCSS: G-SRT.3)

MA.10.H42.06.04 Prove theorems about triangles. (CAS: HS.4.2.b.i) (CCSS: G-SRT.4)

MA.10.H42.08.04Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. (CAS: HS.4.2.b.iii) (CCSS: G-SRT.5)

MA.10.H42.09.04 Explain that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. (CAS: HS.4.2.c.i) (CCSS: G-SRT.6)

MA.10.H42.10.04 Explain and use the relationship between the sine and cosine of complementary angles (CAS: HS.4.2.c.ii) (CCSS: G-SRT.7)

MA.10.H42.11.04 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems (CAS: HS.4.2.c.iii) (CCSS: G-SRT.8)

**Measurement Topic:** *MA.10.H44 Attributes of two- and three-dimensional objects are measurable and can be quantified* Capacity Matrix MA.10.H44

MA.10.H44.01.04 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone.æ (CAS: HS.4.4.a.i) (CCSS: G-GMD.1)

MA.10.H44.02.04 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. (CAS: HS.4.4.a.ii) (CCSS: G-GMD.3)