# SBS:Math Level 11 v4

Go back to main Math v4 page

Math Level 11 Capacity Matrices

*Resources aligned to the old Math Level 14 v3 which addresses content in the new Math Level 11 v4*

- Math Level 14 Unit - Created by Craig Sherman and Bill Lester (
*Teacher versions of the assessments are available on the T:/*)

## Contents |

## Number Sense, Properties, and Operations

**Measurement Topic:** *MA.11.H12 Quantitative reasoning is used to make sense of quantities and their relationships in problem situations* Capacity Matrix MA.11.H12

MA.11.H12.03.04 Define appropriate quantities for the purpose of descriptive modeling. (CAS: HS.1.2.a.iv) (PFL)

**Measurement Topic:** *Functions and their Graphs*

MA.20.H11.05.04 Find and apply inverse functions

## Patterns, Functions, and Algebraic Structures

**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.H24.05.04 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.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.

**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.H21.09.04 Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. (CAS: HS.2.1.c.iv) (CCSS: F-IF.7c)

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.H21.15.04 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)

MA.11.H21.17.04 Use radian measure of an angle as the length of the arc on the unit circle subtended by the angle. (CAS: HS.2.1.f.i) (CCSS: F-TF.1)

MA.11.H21.18.04 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. (CAS: HS.2.1.f.ii) (CCSS: F-TF.2)

**Measurement Topic:** *MA.11.H22 Quantitative relationships in the real world can be modeled and solved using functions* Capacity Matrix MA.11.H22

MA.11.H22.01.04 For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology. (CAS: HS.2.2.a.iv) (CCSS: F-LE.4)

MA.11.H22.02.04 Choose the trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. (CAS: HS.2.2.c.i) (CCSS: F-TF.5)

**Measurement Topic:** *MA.11.H23 Expressions can be represented in multiple, equivalent forms* Capacity Matrix MA.11.H23

MA.11.H23.02.04 Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. (CAS: HS.2.3.b.ii) (CCSS: A-SSE.4)

MA.11.H23.04.04 Rewrite simple rational expressions in different forms. (CAS: HS.2.3.g) (CCSS: A-APR.6)

MA.11.H23.07.04 State and apply the Remainder Theorem. (CAS: HS.2.3.d.i) (CCSS: A-APR.2)

MA.11.H23.08.04 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. (CAS: HS.2.3.d.ii) (CCSS: A-APR.3)

MA.11.H23.09.04 Prove polynomial identities and use them to describe numerical relationships. (CAS: HS.2.3.e.i) (CCSS: A-APR.4)

**Measurement Topic:** *MA.11.H24 Solutions to equations, inequalities and systems of equations are found using a variety of tools* Capacity Matrix MA.11.H24

MA.11.H24.06.04 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. (CAS: HS.2.4.b.ii) (CCSS: A-REI.2)

MA.11.H24.07.04 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately. (CAS: HS.2.4.e.ii) (CCSS: A-REI.11)

## 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.H31.05.04 Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. (CAS: HS.3.1.b.ii.1) (CCSS: S-ID.6a)

MA.09.H31.06.04 Informally assess the fit of a function by plotting and analyzing residuals. (CAS: HS.3.1.b.ii.2) (CCSS: S-ID.6b)

**Measurement Topic:** *MA.11.H31 Visual displays and summary statistics condense the information in data sets into usable knowledge* Capacity Matrix MA.11.H31

MA.11.H31.04.04 Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages and identify data sets for which such a procedure is not appropriate. (CAS: HS.3.1.a.iv) (CCSS: S-ID.4)

MA.11.H31.05.04 Use calculators, spreadsheets, and tables to estimate areas under the normal curve. (CAS: HS.3.1.a.v) (CCSS: S-ID.4)

**Measurement Topic:** *MA.11.H32 Statistical methods take variability into account supporting informed decisions making through quantitative studies designed to answer specific questions* Capacity Matrix MA.11.H32

MA.11.H32.02.04 Decide if a specified model is consistent with results from a given data-generating process. (CAS: HS.3.2.a.ii) (CCSS: S-IC.2)

MA.11.H32.03.04 Identify the purposes of and differences among sample surveys sample surveys, experiments, and observational studies; explain how randomization relates to each. (CAS: HS.3.2.b.i) (CCSS: S-IC.3)

MA.11.H32.04.04 Use data from a sample survey to estimate a population mean or proportion. (CAS: HS.3.2.b.ii) (CCSS: S-IC.4)

MA.11.H32.05.04 Develop a margin of error through the use of simulation models for random sampling. (CAS: HS.3.2.b.iii) (CCSS: S-IC.4)

MA.11.H32.06.04 Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. (CAS: HS.3.2.b.iv) (CCSS: S-IC.5)

MA.11.H32.07.04 Define and explain the meaning of significance, both statistical (using p-values) and practical (using effect size). (CAS: HS.3.2.b.v)

MA.11.H32.08.04 Evaluate reports based on data. (CAS: HS.3.2.b.vi) (CCSS: S-IC.6)

## Shape, Dimension, and Geometric Relationships

**Measurement Topic:** *MA.09.H41 Objects in the plane can be transformed, and those transformations can be described and analyzed mathematically* Capacity Matrix MA.09.H41

MA.09.H41.08.04 Specify the transformations that will carry a given figure onto another. (CAS: HS.4.1.a.viii) (CCSS: GCO.5)

MA.09.H41.09.04 Make formal geometric constructions with a variety of tools and methods. (CAS: HS.4.1.d.i) (CCSS: G-CO.12)

MA.09.H41.10.04 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. (CAS: HS.4.1.d.ii) (CCSS: G-CO.13)

**Measurement Topic:** *MA.09.H43 Objects in the plane can be described and analyzed algebraically * Capacity Matrix MA.09.H43

MA.09.H43.02.04 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems.æ (CAS: HS.4.3.a.ii.2) (CCSS: G-GPE.5)

MA.09.H43.03.04 Find the point on a directed line segment between two given points that partitions the segment in a given ratio. (CAS: HS.4.3.a.ii.3) (CCSS: G-GPE.6)

MA.09.H43.04.04 Use coordinates and the distance formula to compute perimeters of polygons and areas of triangles and rectangles. (CAS: HS.4.3.a.ii.4) (CCSS: G-GPE.7)

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

MA.10.H42.07.04 Prove that all circles are similar.• (CAS: HS.4.2.b.ii) (CCSS: G-C.1)

MA.10.H42.12.04 Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1. (CAS: HS.4.2.d.i)(CCSS: F-TF.8)

MA.10.H42.13.04 Use the Pythagorean identity to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle. (CAS: HS.4.2.d.ii)(CCSS: F-TF.8)

MA.10.H42.14.04 Identify and describe relationships among inscribed angles, radii, and chords.• (CAS: HS.4.2.e.i) (CCSS: G-C.2)

MA.10.H42.15.04 Construct the inscribed and circumscribed circles of a triangle. (CAS: HS.4.2.e.ii) (CCSS: G-C.3)

MA.10.H42.16.04 Prove properties of angles for a quadrilateral inscribed in a circle. (CAS: HS.4.2.e.iii) (CCSS: G-C.3)

MA.10.H42.17.04 Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality. (CAS: HS.4.2.f.i) (CCSS: G-C.5)

MA.10.H42.18.04 Derive the formula for the area of a sector. (CAS: HS.4.2.f.ii) (CCSS: G-C.5)

**Measurement Topic:** *MA.10.H43 Objects in the plane can be described and analyzed algebraically* Capacity Matrix MA.10.H43

MA.10.H43.01.04 Derive the equation of a circle of given center and radius using the Pythagorean Theorem. (CAS: HS.4.3.a.i.1) (CCSS: G-GPE.1)

MA.10.H43.02.04 Complete the square to find the center and radius of a circle given by an equation. (CAS: HS.4.3.a.i.2) (CCSS: G-GPE.1)

MA.10.H43.03.04 Derive the equation of a parabola given a focus and directrix. (CAS: HS.4.3.a.i.3) (CCSS: G-GPE.2)

MA.10.H43.04.04 Use coordinates to prove simple geometric theorems algebraically.• (CAS: HS.4.3.a.ii.1) (CCSS: G-GPE.4)

**Measurement Topic:** *MA.11.H44 Attributes of two- and three-dimensional objects are measurable and can be quantified* Capacity Matrix MA.11.H44

MA.11.H44.03.04 Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects. (CAS: HS.4.4.b.i) (CCSS: G-GMD.4)

**Measurement Topic:** *MA.11.H45 Objects in the real world can be modeled using geometric concepts * Capacity Matrix MA.11.H45

MA.11.H45.01.04 Use geometric shapes, their measures, and their properties to describe objects. (CAS: HS.4.5.a.i) (CCSS: G-MG.1)

MA.11.H45.02.04 Apply concepts of density based on area and volume in modeling situations. (CAS: HS.4.5.a.ii) (CCSS: G-MG.2)

MA.11.H45.03.04 Apply geometric methods to solve design problems. (CAS: HS.4.5.a.iii) (CCSS: G-MG.3)