Embedded Credit – Content Standards and Objectives Alignment Matrix

Teachers and Administrators who completed the matrix:

Recommendation that embedded credit be awarded: Yes □ No □ Provide rationale for decision

Embedded Credit Course Standards and Objectives
(Transition Math for Seniors) / Alignment to Host Course Standards and objectives
(Machine Tool Technology) / Content Alignment / How Standards and/or objectives that do not have strong alignment will be delivered /
Strong Align-ment / Moderate Align-ment / Weak or No Align-ment /
M.TMS.RN.1
Use units as a way to understand and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. / MA.31, MA.34, MA.35, 1903.3, 1905.3, 1903.6, 1903.15, 1905.9, 1903.14, 1905.1, 1905.3, 1907.13, 1907.15,1907.19 / X
M.TMS.RN.2
Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. / MA.31, MA.34, MA.35, 1903.3,1903.6, 1903.14, 1903.15, 1905.1, 1907.13, 1907.15, 1907.19
1905.3, 1905.9 / X
M.TMS.CNS.1
Solve quadratic equations with real coefficients that have complex solutions. / MA. 14, MA.17, MA.31, MA. 11, MA.12, 1907.18, 1909.1, 1907.1 / X
M.TMS.SSE.1
Use the structure of an expression to identify ways to rewrite it. For example, see x4-y4 as x22-y22, thus recognizing it as a difference of squares that can be factored as (x2-y2)(x2+y2). / MA.31, MA.34, 1905.3, 1905.9, 1907.9, 1907.15, 1903.6, 1903.15, 1903.3, 1903.14, 1903.15,1905.1, 1905.12, 1907.4 / X
M.TMS.SSE.2
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
a.  Factor a quadratic expression to reveal the zeros of the function it defines.
b.  Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. / MA.31, MA.34, MA.35, 1903.6, 1903.12, 1903.14, 1905.1, 1905.3 / X
M.TMS.SSE.3
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. / MA.31, MA.35, 1903.15, 1903.3, 1905.9, 1903.6, 1905.1, MA.34, 1903.12, 1903.14, 1905.3 / X
M.TMS.SSE.4
Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of the two moving objects has greater speed. / MA.31, MA.35, 1903.15, 1903.3, 1905.9, 1903.6, 1905.1, MA.34, 1903.12, 1903.14, 1905.3, 1903.15, 1905.6, 1905.11, 1907.1,1907.9, 1907.12 / X
M.TMS.SSE.5
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; 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. / MA.31, MA. 35, MA.34, MA.35, 1903.3, 1903.4, 1903.8,1905.1,1905.2,1905.3, 1905.6, 1905.7,1905.9, 1905.17 / X
M.TMS.SSE.6
Solve linear equations in one variable. / MA.31, MA.34, 1903.3,1903.6,1903.12, 1903.14,1903.15 1905.1, 1905.3, 1905.6, 1905.9, 1905.10 / X
M.TMS.APR.1
Understand 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. / MA.31, MA.32, 1903.3, 1905.1, 1905.3, 1905.9, 1907.9, 1907.15, 1909.1, 1909.3, 1909.5, 1909.16, 1908.17, 1909.19 / X
M.TMS.ACE.1
Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions and simple rational and exponential functions. / MA.31, MA.34, 1903.6, 1909.3, 1909.6, 1909.12, 1909.12, 1909.12, 1909.16, 1909.17, 1907.15, 1903.7, 1903.12, 1903.14, 1903.15. 1905.1, 1905.3, 1905.9, 1905.10 / X
M.TMS.ACE.2
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. / MA.31, MA.34, 1903.6,1905.3, 1905.6, 1905.10, 1905.9,1907.15,1909.6, 1909.12, 1909.16, 1909.17, 1903.7, 1903.12, 1903.14 / X
M.TMS.ACE.3
Represent constraints by equations or inequalities and by systems of equations and/or inequalities and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. / MA.31, MA.34, MA.32, MA.35, 1903.2, 1903.3, 1903.6, 1903.15, 1905.1, 1903.5, 1905.9, 1907.9, 1907.11 / X
M.TMS.ACE.4
Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. / MA.31, MA. 34, MA.32, MA.35,!903.2, 1903.3, 1903.6, 1903.15, 1905.1, 1905.3, 1905.9, 1907.9, 1907.11 / X
M.TMS.REI.1
Solve simple rational and radical equations in one variable and give examples showing how extraneous solutions may arise. / MA.31, MA.34, 1903.4, 1903.6, 1903.9, 1905.1, 1909.3, 1905.3, 1905.5, 1905.9, 1905.11, 1903.3, 1909.1,1903.15, 1905.19, 1907.9, 1907.25 / X
M.TMS.REI.2
Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. / MA.31, MA.34, 1903.4, 1903.6, 1903.9, 1905.1, 1909.3, 1905.3, 1905.5, 1905.9, 1905.11, 1903.3, 1909.1,1903.15, 1905.19, 1907.9, 1907.25 / X
M.TMS.REI.3
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. Construct a viable argument to justify a solution method. / MA.31, MA.34, 1903.4, 1903.6, 1903.9, 1905.1, 1909.3, 1905.3, 1905.5, 1905.9, 1905.11, 1903.3, 1909.1,1903.15, 1905.19, 1907.9, 1907.25 / X
M.TMS.REI.4
Solve quadratic equations in one variable. Use the method of completing the square to transform any quadratic equation in x into an equation of the form x-p2=q that has the same solutions. Derive the quadratic formula from this form. Solve quadratic equations by inspection (e.g., x2=49), taking square roots, completing the square, the quadratic formulas and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a±bi for real numbers a and b. / MA.31, MA.34, 1903.3, 1905.9, 1905.10,1907.9, 1907.20, 1909.1, 1905.5, 1909.12, 1909.16, 1909.23 / X
M.TMS.REI.5
Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produced a system with the same solutions. / MA.31, MA.34, 1903.3, 1905.9, 1905.10,1907.9, 1907.20, 1909.1, 1905.5, 1909.12, 1909.16, 1909.23 / X
M.TMS.REI.6
Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. / X / Itunesu course-Math Ready
M.TMS.REI.7
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 fx=g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. / X / Itunesu course-Math Ready
M.TMS.REI.8
Solve systems of linear equations exactly and approximately (e.g. with graphs), focusing on pairs of linear equations in two variables. / MA.31, MA.34, 1903.3, 1903.6, 1903.15, 1905.1, 1905.3, 1905.10, 1905.15, 1907.9, 1907.15, 1909.1 / X
M.TMS.REI.9
Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality) and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. / MA.31, MA.34, 1903.3, 1903.6, 1903.15, 1905.1, 1905.3,1905.10, 1905.15, 1907.9, 1907.15, 1909.1 / X
M.TMS.IF.1
Understand a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x in an element of its domain, them f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y=f(x). / MA.31, MA.34, 1903.3, 1903.12, 1903.14, 1903.15, 1905.1, 1905.6, 1907.9, 1907.13, 1909.1, 1903.3, 1909.12, 1909.16 / X
M.TMS.IF.2
Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. / MA.31, MA.34, MA.5, MA.25, MA.27, MA.28, MA.30, 1905.3, MA.7, 1903..5, 1905.21, 1905.23, 1907.7, 1907.17, 1909.18 / X
M.TMS.IF.3
Interpret the parameters in a linear or exponential function in terms of a context. / MA.31, MA.34, 1903.3, 1903.12, 1903.14, 1903.15, 1905.1, 1905.6, 1907.9, 1907.13, 1909.1, 1903.3, 1909.12, 1909.16 / X
M.TMS.IF.4
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. Key features include: intercepts; intervals where the function is increasing, decreasing, positive or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. / MA.31, MA.34, 1903.3, 1903.12, 1903.14, 1903.15, 1905.1, 1905.6, 1907.9, 1907.13, 1909.1, 1903.3, 1909.12, 1909.16 / X
M.TMS.IF.5
Distinguish between situations that can be modeled with linear functions and with exponential functions. / MA.31, MA.34, MA.35, 1909.1, 1909.13, 1909.14, 1909.15, 1909.16, 1909.17, 1909.25 / X
M.TMS.IF.6
Interpret the equation y=mx+b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. / MA.31, MA.34, MA.35, 1903.3, 1903.13, 1903.15, 1905.7, 1905.15, 1907.9, 1907.22, 1907.24 / X
M.TMS.IF.7
Describe qualitatively the functional relationship between two quantities by analyzing a graph. / X / Itunesu course- Math Ready
M.TMS.IF.8
Identify the effect on the graph of replacing f(x) by fx+k, kfx, fkx, and f(x+k) for specific values of k (both positive and negative); find the value of k given the graphs. / MA.31, MA.34, MA.35, 1907.22, 1909.1, 1909.13, 1909.14,1909.15,1909.16, 1909.25 / X
M.TMS.IF.9
Graph functions expressed symbolically and show key features of he graph, by hand in simple cases and using technology for more complicated cases.
a.  Graph linear and
quadratic functions
and show intercepts,
maxima, and minima.
a.  Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. / MA.31, MA.34, MA.35, 1909.1, 1903.4, 1907.7, 1903.7, 1903.8, 1903.13, 1905.16, 1907.15, 1907.19 / X
M.TMS.IF.10
Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. / MA.31, MA.34, MA.35, 1905.1,1905.6, 1905.9,1905.15, 1907.15,1907.25, 1909.1, 1909.12, 1909.13,1909.15,1909.16 / X
M.TMS.IF.11
Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
a.  Use the process of factoring and completing the square in a quadratic function to show zeroes, extreme values, and symmetry of the graph, and to interpret these in terms of a context. / MA.31, MA.34, MA.35, 1909.14, 1909.15,1909.16,1909.17, 1909.1, 1909.3 / X
M.TMS.IF.12
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). / MA.31, MA.34, MA.35, 1903.3, 1903.15, 1905.1, 1905.3, 1905.6, 1907.9, 1907.11, 1907.15, 1907.25, 1909.1 / X
M.TMS.BF.1
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a
relationship, or two input-output pairs (include reading these from a table). (CCSS.Math.Content.HSF-LE.A.2) / MA.31, MA.34, MA.35, 1903.5, 1903.6, 1903.14,1903.15, 1905.1, 1905.3, 1905.10, 1907.4, 1907.9, 1907.15,1909.1, 1909.3, 1909.5, 1909.6, 1909.12-18 / X
M.TMS.BF.2
Write a function that describes a relationship between two quantities.
a.  Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to a model.
b.  Compose functions. For example, if Tyis the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(ht) is the temperature at the location of the weather balloon as a function of time. / MA.31, MA.34, MA.35, 1903.5, 1903.6, 1903.14,1903.15, 1905.1, 1905.3, 1905.10, 1907.4, 1907.9, 1907.15,1909.1, 1909.3, 1909.5, 1909.6, 1909.12-18 / X
M.TMS.GMD.1
Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s Principle, and informal limit arguments. / MA.31, MA.34, MA.35, 1903.4, 1903.6, 1903.8, 1903.15, 1905.1, 1905.2,1905.3, 1905.9, 1907.9,1907.11,1907.15 / X
M.TMS.GMD.2
Give an informal argument using Cavalieri’s Principle for the formulas for the volume of a sphere and other solid figures. / MA.31, MA.34, MA.35, 1903.4, 1903.7, 1903.12, 1905.1, 1905.3, 1905.9, 1907.1, 1907.11, 1907.15, 1907.24, 1909.1,1909.3, 1909.12-18 / X
M.TMS.GPE.1
Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, 3) lies on the circle centered at the origin and containing the point (0, 2). / MA.31, MA.34, MA.35, 1909.12-18, 1909.19-1909.22, 1909.23,1909.25 / X
M.TMS.GPE.2
Use coordinates to compute perimeters and areas of triangles and rectangles, e.g. using the distance formula. / MA.31, MA.34, MA.35, 1909.12-18, 1909.19-1909.22, 1909.23,1909.25 / X
M.TMS.MG.1
Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with topographic grid systems based on ratios). / MA.31, MA.34, MA.35, 1903.4, 1903.7, 1903.8, 1905.1, 1905.3, 1905.6, 1905.9, 1907.7, 1907.11, 1907.15, 1909.1, 1909.3, 1909.12-18 / X
M.TMS.MG.2
Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot). / MA.31, MA.34, MA.35, 1903.1, 1903.2, 1903.3, 1903.15, 1905.2, 1905.9, 1905.10, 1907.15, 1907.25, 1909.1, 1909.27 / X
M.TMS.SPI.1
Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. Interpret linear models. / MA.31, MA.34, MA.1, MA.2, 1903.3, MA.5, MA.7, MA.25, 1903.5, 1903.6, 1905.3, 1905.9, 1905.16, 1907.17 / X
M.TMS.SPI.2
Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of data. / MA.31, MA.34, MA.1, MA.2, 1903.3, MA.5, MA.7, MA.25, 1903.5, 1903.6, 1905.3, 1905.9, 1905.16, 1907.17 / X
M.TMS.SPI.3
Know that straight lines are widely used to model relationships between two quantitative variables. 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 on the line. / MA.31, MA.34, MA.1, MA.2, 1903.3, MA.5, MA.7, MA.25, 1903.5, 1903.6, 1905.3, 1905.9, 1905.16, 1907.17 / X
M.TMS.SPI.4
Represent data with plots on the real number line (dot plots, histograms, and box plots). / MA.31, MA.34, MA.1, MA.2, 1903.3, MA.5, MA.7, MA.25, 1903.5, 1903.6, 1905.3, 1905.9, 1905.16, 1907.17 / X