Math II Pacing Guide - tutorcharlotte.net · 4 N-RN.2 Radical & Rational Exponent Rules Simplifying Radicals ... two-variables lesson and 20 A-REI.7 A-REI.11 Solving Non-Linear and

Math II Pacing Guide

*Note – We have included review and test days in this pacing guide, but it is teacher discretion as to when to include

quizzes.

*** In the possible resources column, Algebra I, Geometry, and Algebra II Workbooks are referenced often. These are the Glencoe McGraw-Hill student workbooks that come with our textbooks:

Algebra I = Math A Geometry = Math BC, Volume I Algebra II = Math BC, Volume II

Unit 1 – Math I Review Day Standard Topics Learning Targets Possible Resources

1 Intro to Course and get to know

students

2 A-REI.10 F-IF.5

F-BF.1a

Review Linear Equations &

Inequalities & Recursion

I can identify the parts of a linear equation

I can solve and graph a linear equation and inequality

I can describe the domain and range of a function

I can relate a linear function to its informal recursive formula (Next-Now)

Linear Equations & Inequalities Worksheet (Go to Wiki)

Graphing & Slope-Intercept Form Worksheet (See Wiki)

Graphing Slope-Intercept Form of Inequalities Worksheet (See Wiki)

3 A-SSE.1a A-SSE.3 A-APR.1 F-BF.1b

Basic Exponent Rules &

Polynomial Operations

I can simplify expression using rules of exponents (adding like terms, multiplying powers, and power of a power)

I can add and subtract any two polynomial expression

I can multiply up to 3 linear expressions

4 N-RN.2 Radical & Rational

Exponent Rules Simplifying

Radicals

I can rewrite expressions involving radicals and rational exponents using the properties of exponents

I can simplify radical expressions

Algebra II Workbook pages 109 – 111

Rational Exponents Worksheet (See Wiki)

5 F-IF.2

Quiz or TEST Function Notation

I can use function notation

I can evaluate functions for inputs their domains

Function Notation Worksheet (See Wiki)

Unit 2 – Quadratics

Day Standard Topics Learning Targets Possible Resources

6 F-IF.4 F-IF.5 F-BF.3

Parts of a Quadratic Function & Graphing

Quadratics

I can identify the vertex, axis of symmetry, x and y-intercepts, and domain of a quadratic function from the graph

I can identify the vertex, y-intercept, and whether the parabola opens up or down from the from standard or vertex form of the equation of the quadratic

I can shift a quadratic graph both horizontally and vertically and describe how these shifts affect the equation

Algebra II Workbook page 59

Intro to Quads Worksheet (See Wiki)

Graphing Quadratics Worksheet (See Wiki)

7 A-REI.4b A-SSE.2 A-REI.1

Solving Quadratics from equations, and

graphs

I can identify the zeros of a quadratic using the graph

I can solve a basic quadratic using algebra (ex. X2 – 20 = 5) and explain the steps

I can solve a quadratic by factoring when the leading coefficient is one and explain the steps

Algebra II Workbook pages 61 – 63 (Graphing)

Algebra II Workbook pages 65 – 68 (Factoring)

Solving Quadratics by Graphing WS (See Wiki)

Kuta Software WS – Factor and Solve Equations (See Wiki)

Factoring with Multiple Methods WS (See Wiki) – Long & Short Versions

8 A-REI.4b A-APR.3

Solving Quadratics using

the Quadratic Formula &

Relating solution back to the

Graph

I can solve a quadratic by using the quadratic formula

I can recognize when a quadratic has no real solution

I can use the solutions of a quadratic to construct (sketch) a rough graph of the function

Algebra I Workbook pages 182 – 184


Solve with Quadratic Formula Worksheet (See Wiki)

9 F-IF.9 Comparing the key features of Quadratics in

different forms

I can compare and contrast the key features (vertex, y-int, zeros, etc) of two or more quadratics give in different forms (i.e. Given a graph of one and the algebraic expression for the other, identify which has the larger maximum)

10 F-IF.8 F-IF.5 F-BF.1b N-Q.1 N-Q.2 N-Q.3

Modeling Real World Situations with Quadratic Functions

I can interpret the equation and graph of a quadratic that models a real world situation (ex. Projectile motion, area, profit…)

I can solve and interpret the solutions of a quadratic in context

I can describe an appropriate domain of a quadratic function in context

I can explain the effect of a shift in context

Projectile Motion Worksheet (See Wiki)

Story Problems I & II Worksheets (See Wiki)

11 Review Build your own Quadratic Worksheet (See Wiki)

12 TEST

Unit 3 - Exponential Functions


13 F-IF.4 F-IF.5

F-IF.7e F-BF.3

Parts of an Exponential Function & Graphing

Exponentials

I can identify the parts of an exponential equation (base, exponent, and growth or decay) and relate the equation to the informal recursive formula (NEXT-NOW)

I can identify the y-intercept, growth or decay, and where the function levels off from the graph of an exponential (hinting at the concept of asymptotes without actually teaching the terminology)

I can shift an exponential graph both horizontally and vertically and describe how these shifts affect the equation

Algebra I Workbook Pages 185 – 188


Exponentials – Creating Equations WS (See Wiki)

Exponentials – Shape WS (See Wiki)

Exponentials – Translations WS (See Wiki)

14 A-CED.1 A-SSE.3c

Solving Exponentials

with Graphs and Common Bases

I can solve an exponential function by graphing using technology

I can solve an exponential function by finding a common base on both sides of the equation (ex. 9x = 27 can be rewritten as (32)x = 33)

Algebra II Workbook page 117 (Common Bases)

Solving Exponential Equations without Logs (See Wiki)

15 A-CED.1 Solving Exponentials

with Logs

I can use common logarithms to solve exponential equations (At this point, students just need to use common logs and not explain why they work)

Solving Exponential Equations with Logs Worksheet (See Wiki)

16 F-IF.4 A-CED.1 F-BF.1b N-Q.1 N-Q.2 N-Q.3

Modeling Real Life Situations

with Exponentials

I can interpret the equation and graph of an exponential that models a real world situation (ex. Population growth or decay, interest, half life…)

I can solve and interpret the solutions of an exponential in context

I can explain the effect of a shift in context

Algebra I Workbook Pages 189 – 192

Purchasing a Used Car WS (See Wiki)

17 Review Exponential Function Worksheet (See Wiki)

Exponential Functions Multiple Choice Practice (See Wiki)

18 TEST

Unit 4 - Systems of Equations & Inequalities


19 A-REI.11 Solving Linear Systems of Equations

I can solve a linear system by graphing both equations and finding the point of intersection (by hand and using technology)

I can identify when a system has zero, one or many solutions from the equations or graphs

I can solve a systems of linear equations using substitution (Teachers may discuss elimination at this point, but emphasize that it only works with linear systems)


Algebra II Workbook pages 25, 28

Solving linear equations in two-variables lesson and worksheet (See Wiki)

20 A-REI.7 A-REI.11

Solving Non-Linear and Mixed

Systems of Equations

I can solve a non-linear or mixed system by graphing both equations and finding the point of intersection (using technology)

I can identify when a system has zero, one or two solutions from the graphs

I can solve a systems of non-linear or mixed equations using substitution (ex. f(x) = 3x - 3 and g(x) = x2 – 1)


Smart Lesson for solving non-linear systems (See Wiki)

21 A-CED.1 A-CED.2 A-CED.3

Modeling Systems of Equations

I can create equations to model real world situations

I can solve systems of equations that model real world situations and explain the solutions in context

Smart Lesson for Word Problems – Game (See Wiki)

Systems of Equations Word Problems Worksheets (See Wiki)

22 A-REI.10 A-CED.3

Graphing Systems of Linear and Non-Linear

Inequalities

I can graph a linear or nonlinear inequality in the coordinate plane

I can graph a system of linear inequalities and understand that a solution is any point in the area where the shading overlaps

I can graph a system of non- linear or mixed inequalities and understand that a solution is any point in the area where the shading overlaps

Algebra I Workbook pages 113 – 115 (Linear only)

23 A-CED.3 Modeling Systems of Inequalities

I can create inequalities to represent constraints

I can solve systems of inequalities that model real world situations and explain the solutions in context

(ex. Determine if solutions are viable or nonviable in a modeling context. This does not include the full linear programming process)

Algebra I Workbook page 116

Defining regions using Inequalities WS (See Wiki)

24 Review Systems of Equations & Inequalities Worksheet (See Wiki)

25 TEST

Unit 5 – Additional Functions

Day Standard Topics Learning Targets

26 F-IF.7b F-BF.3

Equations & Graphs of additional Functions

I can identify and graph a simple square root, cube root, absolute value, and rational functions by hand

I can describe the domain of simple square root, cube root, absolute value, and rational functions from the equation or graph

I can identify types of graphs and the key features of each. (This is a good time to complete a function family tree or chart)

I can extent my knowledge of horizontal and vertical shifts to these new functions

Families of Functions Table (See Wiki)

Graphing Functions Worksheet (See Wiki)

Algebra I Workbook Pages 197 – 200 (Square Roots) & pages 221 – 223 (Rational)

Algebra II Workbook pages 153 – 155 (Rational)

27 A-REI.2 A-CED.4 A-SSE.1b

Solving Radical & Rational

Equations

I can solve a simple radical equation in one variable and identify extraneous solutions

I can solve a simple rational equation in one variable and identify extraneous solutions

I can solve literal equations for a given variable (ex. Rearrange Ohm’s law V = IR to highlight resistance R)

Algebra I Workbook Pages 209 – 212 (Radicals)

28 F-IF.7 Graphing Piecewise & Step

Functions

I can graph a piecewise function consisting of 2 linear equations

I can graph a piecewise function consisting of a mix linear and non-linear equations

I can graph a basic step function



Step Functions WS (See Wiki)

29 A-CED.3 Review (Include systems

of equations with these new functions on the

review day)

Transformations Worksheet (See Wiki)

30 TEST

ALGEBRA Benchmark – Review 2 Days and Test 1 Day on Units 1 - 5

Unit 6 – Transformations


34 Review Basic Geometry & Directed Line

Segments

I can find the length and midpoint of a segment

I can use segment addition to find the length of line segments

I can find the point that partitions a line segment in a given ratio

(Ex. Given A(3, 2) and B(6, 11), Find the point that divides the line segment AB two-thirds of the way from A to B. (The point two-thirds of the way from A to B has x-coordinate two-thirds of the way from 3 to 6 and y coordinate two-thirds of the way from 2 to 11. So, (5, 8) is the point that is two-thirds from point A to point B).

Algebra I Workbook Pages 215 – 216 (Distance & Midpoint)

35 G-CO.2 G-CO.4 G-CO.5

Represent Translations in

the Plane

I can describe the different types of transformations (translations, reflections, rotations, dilations)

I can compare transformations that preserve distance and angle measure (rigid transformations) to those that do not.

I can use graph paper, transparency paper, and technology to model translations.

I can describe a translation as a function that uses points in the coordinate plane as inputs and produce points as outputs.

I can define a translation to be a transformation that shifts points a specified distance along a line parallel to a specified axis (either right/left or up/down)

Translations Worksheet (See Wiki)

36 G-CO.2 G-CO.3 G-CO.4 G-CO.5

Represent Reflections in the

Plane

I can use graph paper, transparency paper, and technology to model reflections.

I can describe a reflection as a function that uses points in the coordinate plane as inputs and produce points as outputs.

I can define a reflection to be a transformation that moves a figure along a line perpendicular to a line of symmetry an equal distance from it.

I can describe the reflections that will carry a figure onto itself.

Reflections on a coordinate plane activity (See Wiki)

Photo activity for Symmetry (See Wiki)

Reflections Worksheet (See Wiki)

37 G-CO.2 G-CO.3 G-CO.4 G-CO.5

Represent Rotations in the

Plane

I can use graph paper, transparency paper, and technology to model rotations about a point.

I can describe a rotation as a function

Website for Rotation of Polygons (See Wiki)

Rotations Worksheet (See Wiki)

that uses points in the coordinate plane as inputs and produce points as outputs.

I can define a rotation to be a transformation that moves a figure along an arc with a specified angle about a specified center.

I can describe the rotations that will carry a figure onto itself.

38 G-CO.2 G-CO.5 G-CO.6

Perform multiple transformations

I can perform a combination of transformations.

I can identify the transformations that will graph a given preimage onto its image (and reverse).

I can predict the effect of a rigid transformation on a given figure.

Calculator Activity for multiple transformations (See Wiki)

39 G-CO.2 G-SRT.1a G-SRT.1b

Represent Dilations in the

Plane

I can use graph paper, transparency paper, and technology to model dilations about a point.

I can compare transformations that preserve distance and angle measure (rigid transformations) to those that do not.

I can verify experimentally the following properties about dilations given by a center and a scale factor: o A dilation takes a line not passing

through the center of dilation to a parallel line, and leaves a line passing through the center unchanged.

o A dilation of a line segment is longer or shorter in the ratio given by the scale factor

Geometry Workbook pages 165 – 168

40 Review Multi-Transformation Activity (See Wiki)

Transformation Worksheet (See Wiki)

Transformation Jeopardy (See Wiki)

41 TEST

Unit 7 – Triangle Properties & Proofs


42 G-CO.10

Classifying Triangles

I can classify a triangle by its sides and angles.

I can determine whether or not three lengths will form a triangle.

I can determine the range of the length of the third side of a triangle.

I can use the converse of the Pythagorean Theorem to determine whether or not a triangle is acute, right, or obtuse. (May need to review Pythagorean Theorem)

Geometry Workbook pages 101, 103 & 150

Triangle Inequality Lab (See Wiki)

43-44 G-CO.6 G-CO.7 G-CO.8

Congruent Triangles

Define congruence in terms of rigid transformations (Congruent figures have the same shape and sizes as preserved in rigid transformations)

I can perform a rigid transformation and identify corresponding sides and angles in two triangles

I can extend the definition of congruence in terms of rigid transformations to explain that triangles are congruent if and only if all corresponding pairs of sides and all corresponding pairs of angles are congruent (CPCTC).

I can determine whether two triangles are congruent using appropriate postulate (ASA, SSS, SAS, or none)

Geometry Workbook page 61

Congruence Worksheets for SSS, SAS, ASA, AAS – 3 total (See Wiki)

45-46 G-CO.7 G-CO.8

Proving Triangles Congruent

I can prove triangles are congruent.

I can prove that segments or angles are congruent using congruent triangles and CPCTC. (Method of proof is preference of student)

Geometry Workbook pages 62 - 71

47 G-CO.7 G-CO.8 G.CO.10

More Proof I can continue to prove triangles (and corresponding parts) are congruent.

I can prove that the angles in a triangle add to 180.

I can prove that the segment joining the midpoints of two sides of a triangle is parallel to the third side and half the length.


48 Review

49 TEST

Unit 8 – Trigonometry *Honors Classes should include Law of Sines, Law of Cosines, and the area formula A = ½(ab)Sin(C) in this

unit Day Standard Topics Learning Targets

50 G-GPE.1 Review Pythagorean

Theorem & Use to Derive the Equation of a

Circle

I can use Pythagorean Theorem to find missing sides in a right triangle.

I can use Pythagorean Theorem to derive the equation of a circle given the center and radius

Geometry Workbook page 149 (Pythag Thm)

Geometry Workbook pages 185 – 188 (Circles)

51 G-SRT.8 Special Right Triangles (45-45-

90)

I can use special right triangles(45-45-90) to solve for a missing side

*This is a good discovery lesson for students


52 G-SRT.8 Special Right Triangles (30-60-

90 & Combinations of

both)

I can derive the relationships in a 30-60-90 triangle (Discovery Lesson)

I can use special right triangles to solve for a missing side

I can solve problems involving multiple triangles with missing sides using special right triangles


Special Right Triangles Worksheet (See Wiki)

Multi-Step Special Right Triangles Worksheet (See Wiki)

53 G-SRT.6 G-SRT.7

Right Triangle Trigonometry

I can identify the sides of right triangles as they relate to an acute angle (opposite, adjacent, hypotenuse).

I can define the three trigonometric ratios by comparing the ratios of corresponding sides of similar right triangles in relation to an acute angle

I can recognize that in similar right triangles the sine, cosine, and tangent ratios of corresponding angles are constant

I can explain the relationship between the sine and cosine of complementary angles (acute angles in the same triangle) given varied examples (ie, the sine of angle A is equal to the cosine of angle B)

*Discovery Activity with comparing triangles


Trigonometric Ratios Worksheet (See Wiki)

54 G-SRT.8 Right Triangle Trigonometry

I can use trigonometric ratios to solve for a missing side in a right triangle

I can use inverse trig ratios to solve for a missing angle in a right triangle


Solving right triangles Worksheet (See Wiki)

Inverse trigonometric ratios Worksheet (See Wiki)

55 G-SRT.8 Right Triangle Trigonometry Applications

I can identify angles of elevation and depression in a real world situation

I can use right triangle trig to model and


solve real world applications

I can interpret the solution to a real world application including unit and evaluating reasonability

56 G-SRT.8 Mixed Right Triangles

I can use Pythagorean Theorem, special right triangles, and right triangle trigonometry

I can determine an appropriate method for finding missing parts of right triangles using varied examples

I can solve a right triangle using the appropriate method

57 Review Trig Jeopardy (See Wiki)

58 TEST

Unit 9 – Surface Area & Volume


59 G-MG.1 Review 2-Dimensional

Shapes & Areas 3-Dimensional

Figures

I can identify and find the areas of 2-Dimensional Figures (Does not include regular polygons)

I can identify the different 3-Dimensional Shapes

I can identify the bases and faces of 3-Dimensional Figures

I can explain the concepts of Lateral Area, Surface Area, and Volume

Formula Sheet (See Wiki) – Use throughout Units 9 & 10

60 G-MG.1 Lateral Area & Surface Area of

Prisms & Cylinders

I can find the lateral area and surface area of prisms & cylinders

I can solve real world applications involving surface areas of prisms and cylinders

(Does not include solids with regular polygons as bases)


61 G-MG.1 Lateral Area & Surface Area of

Pyramids & Cones

I can find the lateral area and surface area of pyramids & cones

I can solve real world applications involving surface areas of pyramids and cones


62 G-MG.1 Volume of 3-Dimensional

Figures

I can find the volume of prisms, pyramids, cylinders, and cones

I can solve real world applications involving volume of 3-dimensional figures


Prism - Luxor Problem (See Wiki)

63 G-MG.1 Surface Area & Volume of

Spheres

I can find the surface area and volume of spheres

I can solve real world applications involving surface area and volume of spheres


64 Review

65 TEST

Unit 10 – Modeling


66 G-CO.13 G-GMD.4

Make Geometric Constructions

& Shapes of two-

dimensional cross-sections of three-

dimensional objects &

Three-dimensional objects generated by

rotations of two-dimensional objects

I can construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle

I can identify the shapes of two-dimensional cross sections of three-dimensional objects.

I can identify three-dimensional objects generated by rotations of two-dimensional objects.

I can classify and describe real world objects using measures and properties of geometric shapes.

Slicing up food items (pound cake, apples, oranges, etc) is a great way to show cross-sections

Party Supply stores sell various objects that can be opened from flat to 3-dimensional and is a great way to illustrate rotations of 2-dimensional objects

67-69 G-MG.2 G-MG.3

Concepts of density based on area and

volume &

Geometric methods to solve design problems

I can apply concepts of density based on area and volume in modeling situations (examples: persons per square mile, BTUs per cubic foot, etc…).

I can solve design problems by applying geometric methods (examples: designing an object or structure to satisfy physical constraints or minimize cost, working with typographic grid systems based on ratios).

Area & Volume word problems Worksheet (See Wiki)

Surface Area & Volume Applications Worksheet (See Wiki)

Population Density worksheet (See Wiki)

Population Density Project (See Wiki)

Cash Crops modeling problem (See Wiki)

70 Present Solutions Students should present solutions to some of the application problems that were completed on the previous days.

GEOMETRY Benchmark – 2 Days Review and 1 Test Day on Units 6 - 10

Unit 11 – Probability

Day Standard Topic Learning Targets

74 S-CP.1 S-CP.4

Vocabulary & Basic Probability

I can identify events, outcomes and sample spaces for a given situation (Ex. What is the sample space for rolling a die? (Ex. What is the sample space for randomly selecting one letter from the word MATHEMATICS? ) (Ex. Describe different subsets of outcomes for rolling a die using a single category or characteristic.)

I can calculate basic probabilities from a situation or table (probability = favorable/total)

Probability I PowerPoint (See Wiki)

Intro to Probability Worksheet (See Wiki)

75 S-CP.1

Vocabulary, Notation, & Venn Diagrams

I can describe events as unions, intersections, and complements (Ex. Describe the following subset of outcomes for choosing one card from a standard deck of cards as the intersection of two events: {queen of hearts, queen of diamonds – so Queen & Red is the intersection of these two events}.

I can use a Venn Diagram to represent outcomes and determine probabilities for unions, intersections, and complements of events

PowerPoint for Probability II (See Wiki) – Could be used here and with conditional probability

Probability Practice Worksheet (See Wiki)

76 S-CP.2 S-CP.7

Probability Rules & Independence

I can find the probability of the union of two events using the formula P(A or B) = P(A) + P(B) – P(A and B) (Ex. Given the situation of drawing a card from a standard deck of cards, calculate the probability of the following:

a. drawing a red card or a king b. drawing a ten or a spade c. drawing a four or a queen d. drawing a black jack or a club e. drawing a red queen or a spade)

I can describe what it means for two events to be independent

I can determine if two events are independent if the probability of A and B occurring together is the product of their probabilities (Ex. For the situation of drawing a card from a standard deck of cards, consider the two events of “draw a diamond” and “draw an ace.”

Probability Practice Worksheet (See Wiki)

Determine if these two events are independent.

77 Practice & Quiz Day? PowerPoint of practice problems (See Wiki)

78 S-CP.3 S-CP.4 S-CP.6

Two-Way Tables & Conditional Probabilities

I can create a two-way table from a set of data

I can explain conditional probabilities in context of a situation

I can determine conditional probabilities from a two-way table

I can find conditional probabilities using the formula P(A│B) = P(A and B)/P(B)

Probability Tutorial (See Wiki)

Conditional Probability Practice Worksheet (See Wiki)

79 S-CP.3 S-CP.5 S-IC.2

Independence & Conditional

Probabilities, Modeling Probabilities

I can determine if two events are independent if P(A│B) = P(A)

I can explain probability, conditional probability and independence in everyday language and apply the concepts to real world situation (Ex. Felix is a good chess player and a good math student. Do you think that the events “being good at playing chess” and “being a good math student” are independent or dependent? Justify your answer. (Ex. Juanita flipped a coin 10 times and got the following results: T, H, T, T, H, H, H, H, H, H. Her math partner Harold thinks that the next flip is going to result in tails because there have been so many heads in a row. Do you agree? Explain why or why not.

Notes & examples for probability and independence (See Wiki)

Another worksheet for conditional probability (See Wiki)

80 Review Probability Review Worksheet (See Wiki)

81 TEST

MSL Review – 5 Days

*This pacing guide accounts for 86 days of the semester which should allow for teacher and school flexibility.

Documents

Math II Pacing Guide - tutorcharlotte.net · 4 N-RN.2 Radical & Rational Exponent Rules Simplifying Radicals ... two-variables lesson and 20 A-REI.7 A-REI.11 Solving Non-Linear and