math 3 outcomes (teacher guide) 2018

Pacing is based on a semester schedule with 90 minute classes. Buncombe County Schools 2018-2019

Math 3 Outcomes (Instruction Guide)

10 days

Students graph and analyze piecewise functions. They identify key features and interpret them in context. Students recognize absolute value functions as a type of piecewise function. They describe transformations of the absolute value function including 𝑓(𝑘𝑥). Students solve absolute value equations and inequalities algebraically and use them to solve problems.

Outcome 1: I can graph and analyze key features of piecewise functions. (3 days) a. I can identify and interpret key features of a piecewise

function in context given a graph, table, or description.F-IF.4 b. I can use function notation to evaluate piecewise functions for

a given x and interpret what it means in context.F-IF.2 c. I can graph a piecewise function to show key features.F-IF.7 d. Honors: I can build a linear piecewise function.F-BF.1

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The course begins with piecewise functions to allow students the opportunity to review functions studied during previous courses. Students should be familiar with identifying key features. A focus, for piecewise functions, is on the domain for the different pieces of the function. Consider exposing students to absolute value functions as a type of piecewise function prior to the more extensive study in the following outcomes. Students have been using function notation since Math 1. Include more complex use of function notation such as 𝑓(𝑎) + 2𝑓(𝑏) where 𝑎 and 𝑏 belong to different parts of the domain. Students should be able to graph in simple cases and use technology, such as Desmos, in more complex cases.

Outcome 2: I can graph and analyze key features of absolute value functions. (3 days)

a. I can graph an absolute value function to show key features.F-IF.7 b. I can identify and interpret key features of an absolute value

function in context given a graph, table, or description.F-IF.4 c. I can describe the effect of a transformation on the graph and

table of an absolute value function.F-BF.3 d. Honors: I can graph and identify key features of non-linear

absolute value functions.F-IF.4

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Absolute value is a new function for students. Consider reviewing the definition of absolute value (developed in middle grades) as students identify the key features of the function. The intent is for students to revisit the transformations from Math 2 and add the new transformation 𝑓(𝑘𝑥) with a focus on absolute value functions. Revisit the transformations in the polynomial and trigonometric modules. Students should describe the transformations’ effect on the graph and the table. Continue reinforcing the key features. Students should be flexible in describing the transformations given a function 𝑓(𝑥) where 𝑓(𝑥) is not limited to the parent function.

Outcome 3: I can solve absolute value equations and inequalities. (3 days) a. I can create absolute value equations and inequalities from

context.A-CED.1,2 b. I can solve absolute value equations and inequalities using

graphs and tables.A-CED.1, A-REI.11 c. I can solve absolute value equations algebraically and justify

each step in the solving process.A-REI.1, A-SSE.1 d. I can identify if a solution to an absolute value equation is

extraneous. A-REI.2 e. Honors: I can solve non-linear absolute value equations and

inequalities.A-REI.11

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Prior to this outcome, consider providing students review of solving one and two step linear equations during warmups and homework. Connect the algebraic process of solving absolute value equations to the concept of it being a piecewise function. A-REI.11 includes solving a variety of one variable equations such as, |2𝑥 + 1| = | − 4𝑥 − 5|, using graphs and tables.


10 days

Students extend their understanding of exponential functions by building rules and rewriting the rates of change for contextual situations. They define logarithms and use them to solve exponential equations. Students identify inverse functions, describe their characteristics and write them for linear, exponential, and quadratic functions.

Outcome 4: I can use exponential functions to model and solve problems. (4 days) a. I can create equivalent forms of an exponential function using

exponent properties to reveal rates. A-CED.1,2, A-SSE.3c, F-BF.1 b. I can solve exponential equations & inequalities using graphs

and tables. A-CED.1, A-REI.11 c. I can rewrite any real number as the power of another real

number.F-LE.4 d. I can solve exponential equations using logarithms and justify

each step in the solving process.F-LE.4, A-REI.1 e. Honors: I can build and solve exponential equations using e

and the natural logarithm. F-BF.1, F-LE.4, A-REI.1

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Students studied exponential functions in Math 1. The extension, in Math 3, is for students to be able to rewrite the growth/decay factor and interpret what it means in context. Consider reviewing the power to a power exponent rule for this outcome. A-REI.11 includes solving a variety of one variable equations such as, 4(1.23)3 = 7(2.5)3, using graphs and tables. Students should understand logarithms are a way to rewrite numbers with the same base. They use that understanding to solve exponential equations without the use of the laws of logarithms. For further explanation refer to the Math 3 Math Resource for Instruction document.

Outcome 5: I can identify and represent the inverse of a function. (2 days) a. I can create a table and a graph of an inverse given any

representation of a function.F-BF.4a,c b. I can determine if an inverse function exists from a graph,

table, or equation.F-BF.4b c. I can describe domains of a function where an inverse function

exists.F-BF.4 d. Honors: I can verify that two functions are inverses by

substituting one function into the other and interpreting the result.F-BF.4a, A-SSE.1b, A-SSE.2

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Students should reason with a variety of function types, both traditional and non-traditional. These functions can be presented as graphs and tables. Students should also be able to restrict the domain of a function in order to describe when an inverse function exists. Students should be able to use and interpret interval notation, inequalities, and words to describe restricted domains. (Interval notation was used in Math 2.)

Outcome 6: I can write the inverse function of a given function. (3 days) a. I can write the inverse function of a linear function using

algebraic reasoning.F-BF.4c b. I can write the inverse function of an exponential function

using algebraic reasoning.F-BF.4c c. I can write the inverse function of a quadratic function by

restricting the domain and using algebraic reasoning.F-BF.4c d. Honors: I can write the inverse of functions in the form 𝑓(𝑥) =𝑎𝑥5 + 𝑐 and 𝑓(𝑥) = 7

3+ 𝑐.F-BF.4

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The outcome is specific to the types of functions the F-BF.4 standard references. Students will need to rewrite quadratics by completing the square in order to write the inverse function of a quadratic function. The process of completing the square was studied in Math 2. As an honors extension, consider having students find the inverse of one or both types of functions. The intent of this extension is to strengthen students algebraic skills.


12 days

Students extend their understanding of polynomial functions to include those with a degree of 3 or higher. They identify and interpret key features. They connect the zeros of the function to the graph. Students use multiple representations of polynomial functions to model and solve problems.

Outcome 7: I can analyze key features of a polynomial function emphasizing the connections between the zeros, factors and its graph. (4 days) a. I can graph a polynomial function, using technology, to show

key features.A.CED.2 b. I can identify and interpret key features of a polynomial

function in context using graphs and tables.F-IF.4, 7 c. I can sketch a graph to show key features of a polynomial

function written in factored form.A.APR.3, F-IF.7 d. I can create a polynomial function (in factored form) from the

zeros and a point on the graph of a function.F-BF.1a e. Honors: I can create the polynomial function in standard form

given the zeros and a point on the graph of the function.F-BF.1a

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This module approaches the study of polynomials by first studying the key features and characteristics of polynomial functions followed by a deeper study with the algebraic concepts. The outcome begins with students graphing and identifying key features of polynomial functions. Next, students identify the key features (intercepts and end behavior) from factored form and sketch the polynomial graph using these key features. (Sketches may lack some precision). Students reverse the process by using the key features to write the factored form of the polynomial function. Key features can be given as a graph, description, or ordered pairs. Creating the polynomial functions is an opportunity to connect back to the transformation 𝑘𝑓(𝑥).

Outcome 8: I can reason with multiple representations to solve polynomial equations. (6 days) a. I can factor a polynomial function with degree of 3 or less.A-

SSE.2 b. I can divide a polynomial expression and determine if the

divisor is a factor of the expression.A.APR.2,6 c. I can apply the Remainder Theorem by evaluating 𝑓(𝑐)to

determine if (𝑥 − 𝑐)is a factor of 𝑓(𝑥).A-APR.2 d. I can solve polynomial equations with real solutions.A-APR.3, A-

CED.1, A-REI.11 e. I can apply the Fundamental Theorem of Algebra to

determine the number and potential types of zeros for a polynomial function.N-CN.9

f. Honors: I can find all solutions to a cubic polynomial equation including non-real solutions.A-REI.1, A-REI.11

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Factoring quadratics is a focus in Math 1. In Math 3, students should be able to factor special cases such as a difference or sum of cubes, factoring with a GCF, and factor by grouping. Consider dividing polynomials using the area model. Students should use any method to solve polynomial equations. A-REI.11 includes all function types and should be reviewed after Module C with rational functions and trigonometric functions. It is not solving a system of equations. These solutions should only be the x-coordinate of the intersecting functions.


8 days

Students use geometry and algebra concepts to model and solve problems. Geometry concepts include perimeter, area, volume. Contextual situations include density, design and optimization.

Outcome 9: I can use perimeter, area and volume formulas to solve problems. ( 3 days) a. I can describe the two-dimensional cross-sections of three-

dimensional objects.G-GMD.4 b. I can describe three-dimensional objects generated by

rotations of two-dimensional objects.G-GMD.4 c. I can calculate the volume of a prism, pyramid, cylinder, cone

or sphere.G-GMD.3 d. I can determine the value of a specific measurement when

given the volume of a prism, pyramid, cylinder, cone or sphere and all other necessary measurements.G-GMD.3

e. I can decompose a figure into familiar pieces and use them to solve problems involving perimeter, area, and volume.G-GMD.3, G-

MG.1 f. Honors: I can use Cavalieri’s Principle to compare the volume of

two figures.G-GMD.3

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The outcome begins with cross sections and rotations which provides the opportunity to define a prism, pyramid, cylinder, cone, and sphere. Students should explore all types of cross sections and generalize for cross sections that are parallel to the base and those that are perpendicular to the base. Students studied volume in 8th grade. Review area formulas for figures that can be possible bases of a prism or pyramid. This includes the area of a circle, triangle and parallelogram. Students should know the formulas in this outcome, as it is unclear whether the formulas are provided for them on the EOC. Consider having students distinguish between figures that are compositions of two or more figures added together and those that are subtracted. See examples below.

Outcome 10: I can apply geometric concepts to solve problems. (4 days) a. I can apply concepts of density based on area or volume to

solve problems.G-MG.1 b. I can create functions to model relationships within geometric

figures. G-MG.1 c. I can use geometric and algebraic concepts to solve design

problems.G-MG.1 d. I can use geometric and algebraic concepts to solve

optimization problems.G-MG.1 e. I can define the points of concurrency of triangles (centroid,

incenter, and circumcenter) and identify their properties.G-CO.10 f. Honors: I can design and describe measurements of a 3D figure

that satisfies given constraints.G-MG.1

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Students may be familiar with density, from science, where density is mass per volume (ex. gold’s density is 19.32 g/cm3). Student understanding of density should extend to population density (ex. Asheville’s population density in 2016 was 1,948 people/mi2). Students should be flexible when solving density problems. When given the density, and either the area or the volume, students can solve for the unknown quantity. Students should attend to precision with units and use the units as a way to understand the problem and guide their solution. For examples for design and optimization problems refer to the Math 3 Math Resource for Instruction document. Recognize that points of concurrency are not directly related to the other standards in this module. These concepts are included here because the properties of points of concurrency can be emphasized to solve problems.

In the figure to the left, the hemisphere and cone are added together.

In this figure, the cone has been removed/ subtracted out of the cube.


10 days

Students are introduced to rational functions. They graph and identify key features. They operate with rational expressions building upon their understanding of operations with rational numbers. Students build and solve rational equations using tables, graphs, and algebraic reasoning.

Outcome 11: I can graph and analyze key features of rational functions. (3 days) a. I can graph a rational function to show key features.A-CED.2, F-IF.7 b. I can use graphs and tables to identify and interpret key

features of rational functions, including asymptotes and points of discontinuity.F-IF.4,7

c. I can rewrite a rational expression in simplest form.A-SSE.2, A-APR.6 d. I can rewrite a rational expression to determine

discontinuities.F-IF.7, A-SSE.1,2 e. Honors: I can explain why rational functions have asymptotes

and discontinuities.SMP7, 2

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This module approaches the study of rational functions by first studying the key features (intercepts, increasing/decreasing, end behavior, horizontal/vertical asymptotes, and discontinuities) and characteristics of rational functions followed by a deeper study with the algebraic concepts. At a minimum, students should be able to analyze a rational function for a given value of 𝑥 and determine if there is a discontinuity. Students should have an opportunity to discuss the difference between an asymptote and a hole. Rewriting the rational function allows students to recognize discontinuities and their relationship to functions.

Outcome 12: I can operate with rational expressions. (3 days) a. I can add or subtract two rational expressions (limited to

denominators that are linear expressions).A-APR.7a b. I can multiply two rational expressions.A-APR.7b c. I can divide two rational expressions.A-APR.7b d. Honors: I can rewrite rational expressions that involve

multiple operations or include more than two rational expressions.A-APR.7 In

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Build upon student understanding of operations with fractions to reason with the operations of rational expressions.

Outcome 13: I can build and solve rational equations. (3 days) a. I can create a rational equation from context.A-CED.1, 2 b. I can solve rational equations using graphs and tables.A-CED.1, A-

REI.11 c. I can solve rational equations algebraically and justify each

step in the solving process.A-REI.1, 2 d. I can identify extraneous solutions to a rational equation.A-REI.2 e. Honors: I can explain how extraneous solutions may be

produced when solving a rational equation using algebraic reasoning.A-REI.2

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A common problem type for rational equations in context is combined rate problems such as “Peter can mow the lawn in 40 minutes and John can mow the lawn in 60 minutes. How long will it take for them to mow the lawn together?”


15 days

Students prove properties of parallelograms. They analyze and apply relationships between angles, arcs, and line segments of a circle. Students use the relationships to solve problems. They understand the proportional relationships within circles to calculate arc length, area of a sector and radians.

Outcome 14: I can prove properties of parallelograms and apply them in other proofs. (4 days) a. I can construct a logical argument to prove a theorem about

the sides of parallelograms.G-CO.11 b. I can construct a logical argument to prove theorems about the

angles of different types of parallelograms.G-CO.11 c. I can construct a logical argument to prove theorems about the

diagonals of different types of parallelograms.G-CO.11 d. I can apply theorems about parallelograms to prove given

statements and to solve problems. G-CO.14 e. Honors: I can critique a given proof and revise if necessary.SMP3 In

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Students developed proofs in Math 2 that included paragraph, flow and two-column. Prior knowledge from Math 2 that will need to be reviewed includes congruent triangles and parallel lines. A parallelogram is defined as a quadrilateral with opposite sides parallel. Given that definition, students should prove opposite sides are congruent; adjacent angles are supplementary; and opposite angles are congruent. Students should prove the properties of the diagonals of parallelograms and be able to identify the parallelogram given the properties of the diagonals. The special parallelograms are rhombus, rectangle, and square.

Outcome 15: I can analyze and apply relationships between the angles and arcs in circles. (3 days) a. I can identify and define the types of arcs, angles, lines, and line

segments in a circle.G-C.2 b. I can apply the relationship between a central angle and its

intercepted arc to solve problems.G-C.2 c. I can apply the relationship between an inscribed angle and its

intercepted arc to solve problems.G-C.2 d. I can determine the measures of angles and arcs formed by two

intersecting chords.G-C.2 e. I can determine the measures of angles and arcs formed by two

lines (secants and/or tangents) that intersect outside of a circle.G-C.2

f. Honors: I can construct a logical argument to prove theorems about angles and their intercepted arcs.G-CO.14

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Circles are studied in 7th grade; therefore, the definition, parts of a circle (including the vocabulary for those parts) and the notation used to identify the parts should be a focus. Consider using technology such as GeoGebra or Desmos/Geometry while studying circles. Students should become flexible in strategically adding auxiliary lines such as radii or chords to help solve problems. Applications of inscribed angles include:

• the arcs between parallel chords of a circle are congruent • an angle inscribed in a semicircle is a right angle • opposite angles in an inscribed quadrilateral are supplementary


Outcome 16: I can analyze and apply relationships between line segments in a circle. (4 days) a. I can apply the relationship between the perpendicular bisector

of a chord and the center of the circle to solve problems.G-C.2 b. I can apply the relationship between congruent chords in a

circle to solve problems.G-C.2 c. I can apply the relationship between the radii and the tangent

lines to solve problems.G-C.2 d. I can determine the lengths of parts of two intersecting chords

in a circle.G-C.2 e. I can determine the lengths of segments created by a secant

and a tangent or two secants that intersect outside of a circle.G-

C.2 f. Honors: I can construct a logical argument to prove theorems

about angles and line segments of a circle.G-CO.14

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Students should understand the relationship between the perpendicular bisector and the center of a circle in that given two of the criteria the other must also be true. Relationships between congruent chords should include:

• equidistant from the center • they intercept congruent arcs

Consider identifying the relationship between lengths of chords/tangents/secants by the location of the intersection (inside the circle, on the circle, and outside the circle). Students can use the same relationship for all three cases (product of the lengths from intersection to the point on the circle are equal). For more information see Power of a Point by NCTM Illuminations

Outcome 17: I can analyze and apply proportional relationships between angles, arcs, and sectors of a circle to solve problems. (3 days) a. I can apply the proportional relationship between the

intercepted arc, radius, and radian measure of an angle in a circle to solve problems.G-C.5, F-TF.1

b. I can determine the arc length of an arc intercepted by an inscribed or central angle.G-C.5

c. I can determine the area of a sector.G-C.5 d. I can apply arc length and area of sectors to solve problems of

unknown length and area.G-C.5, G-CO.14 e. Honors: I can determine the perimeter or area of a geometric

figure composed of circles, triangles and/or parallelograms.G-C.5

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Students should understand radians as a unit of measure to describe the size of an angle. Specifically, they should know and be able to use the fact that a radian is the quotient of the arc length and the radius to solve problems. For example, given the radian measure and the arc length find the radius. Students should be able to calculate arc lengths and areas given angle measures in degrees or radians. It is not a focus of the Math 3 standards for students to convert between degrees and radians. The intent is for students to understand both as a measure of an angle and be flexible in using either to solve problems.


7 days

Students extend their understanding of the trigonometric ratios to build functions that model periodic change. They understand the relationships between the ratios and points on the circle. Students graph and interpret key features within context.

Outcome 18: I can represent and identify points on a circle in the coordinate plane. (3 days) a. I can write the equation of a circle given its center and radius.G-

GPE.1 b. I can rewrite the equation of a circle to identify its center and

radius. G-GPE.1, A-SSE.1

c. I can use sine and cosine ratios to determine the coordinates of any point on a circle given the radius of one unit and angle of rotation. F-TF.2, F-IF.1

d. Honors: I can use sine and cosine ratios to determine the coordinates of any point on a circle given the radius and angle of rotation. F-TF.2 In

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Students should understand how the equation of the circle is connected to the definition of a circle (all points equidistant from a given point). Consider having students investigate the connection to the Pythagorean Theorem / Distance Formula. Students will need to use the process of completing the square (previously studied in Math 2 and used when writing the inverse of a quadratic function earlier in Math 3) to rewrite the equation of a circle. The standard F-TF.2 refers to the “unit circle” as a way to define a circle centered at the origin with a radius of 1 unit. It is not the intent of the standard for students to study or discover additional properties of the unit circle. Students should use the unit circle to develop an understanding of the

• sine function as the relationship between an angle measure in radians to the y coordinate • cosine function as the relationship between an angle measure in radians to the x coordinate.

Consider reviewing right triangle trigonometric ratios, from Math 2, when beginning this study. The honors extension is for students to generalize beyond the unit circle and be able to determine the coordinates on a circle given the radius, 𝑟,as (𝑟𝑐𝑜𝑠𝜃, 𝑟𝑠𝑖𝑛𝜃).

Outcome 19: I can use trigonometric functions to model and solve problems. (3 days) a. I can graph sine and cosine functions and identify key features

including period, amplitude, and midline. F-IF.4, F-IF.7 b. I can use the sine function to model patterns of periodic

change. F-TF.5 c. I can interpret key features of a sine function in context given a

graph, table, function rule or description.F-TF.5, F-IF.4 d. Honors: I can use the cosine function to model patterns of

periodic change.F-TF.5

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F-TF.1 states students should understand the radian measure of an angle is the domain for trigonometric functions; therefore, graphs of sine and cosine functions should focus on using radians. Students will graph sine and cosine functions to analyze and identify key features. Next, students will model contextual situations using the sine function. The honors extension is to also model using the cosine function. Modeling with the sine function provides students the opportunity to revisit transformations.


6 days

Students use statistical reasoning to draw conclusions. They distinguish between the different types of statistical studies. They understand the role of random sampling. Students use data from surveys or simulations to make inferences and draw conclusions.

Outcome 20: I can use statistical reasoning to draw conclusions from experiments and studies. (6 days) a. I can distinguish between, justify the use of, and recognize the

limitations of sample surveys, experiments, and observational studies. S-IC.1, 3

b. I can describe representative samples that allow inferences to be made about a population.S-IC.1

c. I can use data from a sample survey to estimate the true population mean or proportion, with a margin of error. S-IC.1, 3, 4

d. I can determine if results from an experiment are statistically significant and justify appropriate conclusions. S-IC.3, 5

e. I can use statistical reasoning to evaluate reports based on data. S-IC.6

f. Honors: I can create and answer a statistical question using the four steps of the statistical process.S-IC.1,3,4,5

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Students should be able to distinguish between the types of studies including understanding how randomization should be used in each. For instance, observational studies typically do not use randomization while it is essential to a well-designed experiment. Student descriptions of representative samples should focus on random sampling methods that create samples which are representative of the population of interest (the population about which the sample is used to make inferences). The intent of the S-IC.4 and S-IC.5 is for students to use simulation. Students used simulations in 7th grade and Math 2 to explore probability. Through the use of simulation, students develop an understanding of margin of error and statistical significance. Students should understand that the margin of error allows us to decide statistical significance because any sample statistic which lies outside the margin of error is “statistically significant” (meaning it is not likely to happen just by chance alone, according to the simulation results.)

3 days

Students extend their understanding of the different types of functions. Students solve non-linear systems of equations using graphs and tables.

Outcome 21: I can solve systems of equations or inequalities and interpret the solution in context. (3 days) a. I can compare key features of two functions each with a

different representation.F-IF.9 b. I can create a system of equations and/or inequalities to model

a situation in context.A-CED.3 c. I can identify values in the solution set and describe solution(s)

in the context of a situation. A-CED.3 d. Honors: I can solve a system algebraically containing a

quadratic and the equation of a circle.A-REI.1

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This module allows the opportunity to review all functions. Students should be able to compare key features of any two functions represented differently (e.g., one as a table and one as a function rule). Focus on using the graphs and tables to identify and compare key features. Students apply their knowledge of building the different functions to create systems of equations. They are not expected to solve complex systems algebraically, but should focus on more efficient methods such as tables, graphs, and using technology. The honors extension is solving some systems algebraically.


Standards Alignment

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N-C

N.9

A-SS

E.1

A-SS

E.2

A-SS

E.3c

A-AP

R.2

A-AP

R.3

A-AP

R.6

A-AP

R.7

A-CE

D.1

A-CE

D.2

A-CE

D.3

A-RE

I.1

A-RE

I.2

A -RE

I.11

F -IF

.1

F-IF

.2

F-IF

.4

F-IF

.7

F-IF

.9

F -BF

.1

F -BF

.3

F -BF

.4

F-LE

.3

F-LE

.4

F-TF

.1

F-TF

.2

F-TF

.5

1a x 1b x 1c x

1d* x 2a x 2b x 2c x

2d* x 3a x x 3b x x 3c x x 3d x

3e* x

4a x x x x 4b x x 4c x 4d x x

4e* x x x 5a a,c 5b b 5c x

5d* b x a 6a c 6b c 6c c

6d* x

7a x 7b x x 7c x x 7d a

7e* a 8a x 8b x x 8c x 8d x x x 8e x 8f* x x


Standards Alignment continued

Out

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N- C

N.9

A-SS

E.1

A-SS

E.2

A-SS

E.3c

A-AP

R.2

A-AP

R.3

A-AP

R.6

A-AP

R.7

A-CE

D.1

A-CE

D.2

A-CE

D.3

A-RE

I.1

A-RE

I.2

A-RE

I.11

F -IF

.1

F -IF

.2

F-IF

.4

F -IF

.7

F-IF

.9

F -BF

.1

F-BF

.3

F -BF

.4

F-LE

.3

F-LE

.4

F-TF

.1

F-TF

.2

F-TF

.5

G-GP

E.1

SMP

11a x x 11b x x 11c x x 11d x x x

11e* 2, 7 12a a 12b b 12c b

12d* x 13a x x 13b x x 13c x x 13d x

13e* x

18a x

18b x x

18c x x

18d* x

19a x x

19b x

19c x x

19d* x

Out

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N-C

N.9

A -SS

E.1

A-SS

E.2

A-SS

E.3c

A-AP

R.2

A-AP

R.3

A-AP

R.6

A-AP

R.7

A-CE

D.1

A-CE

D.2

A-CE

D.3

A-RE

I.1

A-RE

I.2

A-RE

I.11

F -IF

.1

F-IF

.2

F-IF

.4

F -IF

.7

F -IF

.9

F-BF

.1

F -BF

.3

F-BF

.4

F-LE

.3

F-LE

.4

F-TF

.1

F -TF

.2

F-TF

.5

G-GP

E.1

21a x

21b x

21c x

21d* x


Standards Alignment Continued

Out

com

e/

Lear

ning

Ta

rget

G-CO

.10

G-CO

.11

G-CO

.14

G-C.

2

G -C.

5

G-GM

D.3

G -GM

D.4

G-M

G.1

F-TF

.1

SMP

9a x 9b x 9c x 9d x 9e x x 9f* x 10a x 10b x 10c x 10d x 10e x 10f* x

14a x 14b x 14c x 14d x

14e* 3 15a x 15b x 15c x 15d x 15e x 15f* x 16a x 16b x 16c x 16d x 16e x 16f* x 17a x x 17b x 17c x 17d x x

17e* x

Out

com

e/

Lear

ning

Ta

rget

S-IC

.1

S-IC

. 3

S-IC

.4

S-IC

.5

S-IC

. 6

20a x x

20b x

20c x x x

20d x x

20e x

20f* x x x x

math 3 outcomes (teacher guide) 2018

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