NC Math 3 Vance County Schools

Transcription

1 NC Math 3 Vance County Schools Unit Number Topic Number of Days Rationale/Notes 1 Absolute Value & Piecewise Functions 9 days 2 Quadratics 10 days This unit is for the transition year ( ) - Optional unit afterwards, this time can be used for extra time in other units. 3 Polynomials 9 days Add piecewise example while graphing 4 Rationals 8 days Add piecewise example while graphing 5 Geometry: Modeling with Geometry 6 days Gives students a break from the heavy algebra - fits in the pacing guide so that teachers have 5 test per quarter (nine-weeks) 6 Exponential & Logarithms 10 days Add piecewise example while graphing 7 Trigonometry 7 days Introduces idea of radians - radians are used in the circles unit. 8 Geometry: Circles 9 days 9 Geometry: Parallelograms 5 days 10 Statistics 7 days Visit Illustrativemathematics.org for tasks Standards Math 3 Resources for Instruction

2 Day Standard Topics Covered Unit 1 1 NC.M3.A-CED.1 Solve Absolute Value equations and inequalities 2 NC.M3.A-CED.1 Absolute Value Applications *Note: Tolerance problems are an example of applications 3 NC.M3.A-CED.2 NC.M3.A-CED.3 4 NC.M3.A-REI.11 NC.M3.F-BF.3 Graph Absolute Value functions Solve systems of equations (only linear and absolute value functions; using technology) Graph Absolute Value functions using translations *Note: During this day, include explanation of the x-coordinates of the intersections of two functions are the solutions. Also include examples similar to f(x)=1/3g(x). See standard NC.M3.A-REI.11 5 NC.M3.F-IF.2 Piecewise Functions - Evaluate and Graph 6 NC.M3.F-IF.7 Piecewise Functions - Graphing continued, start Key Features Key Features Domain and Range Increasing/Decreasing Intervals Positive/Negative Intervals Relative Max and Min Discontinuous *Note: Only include linear and absolute values in your piecewise functions.

3 7 NC.M3.F-IF.7 Piecewise Functions - Graphing continued, start Key Features 8 Practice/Review 9 Test #1 Unit 2 Key Features Domain and Range Increasing/Decreasing Intervals Positive/Negative Intervals Relative Max and Min Discontinuous *Note: Only include linear and absolute values in your piecewise functions. Unit 2 10 NC.M3.F-BF.3 Graph Quadratics and Transformations in Standard Form and Vertex Form 11 NC.M3.F-IF.7 Convert between standard and vertex form Review Max and Min Applications Identify Key Features 12 NC.M3.F-IF.7 Identify Key Features of Parabolas Include key features from previous unit while adding: End Behavior Rate of Change *Extension: Write quadratic function given vertex and second point 13 NC.M3.F-IF.2 Piecewise Functions (now including quadratics) & Quiz 14 Solve Quadratics by:

4 Factoring Finding Zeros on Graph (Calculator) Taking the Square Root 15 Complex Numbers *Note: At this level you need to only define and do simple simplifying - during the transition year you can include operations Solve by Completing the Square 16 Solve by Quadratic Formula Discriminant Write the quadratic equation given the roots *Extension: Derive quadratic formula from completing the square method *Extension: Write equation using sum and product of roots - derive method from quadratic formula roots 17 NC.M3.F-BF.4 NC.M3.A-CED.3 Inverses - Include Linear Solving Systems of Equations with Quadratic and Linear *Note: Include an application 18 Quadratic Regression Practice Day for the Unit 19 Test #2 *Extension: Solving Quadratic Inequalities

5 Unit 3 20 Multiplying Polynomials Expand using Pascal s triangle Find specific terms using Pascal s triangle 21 NC.M3.A-APR.6 Dividing Polynomials Long Division Synthetic Division 22 NC.M3.A-APR.2 NC.M3.A-SSE.2 NC.M3.A-REI.1 Remainder Theorem Factoring Polynomials using Synthetic Division Solving Polynomials equations by factoring *Note: Limited to cubics only *Note: Sum and Difference of Cubes is new *Extension: Quadratic-like (quartic) 23 NC.M3.A-CED.1 NC.M3.A-SSE.1a NC.M3.A-SSE.1b 24 NC.M3.N-CN.9 NC.M3.A-APR.3 Polynomial applications Cubic Regression Quiz Use Fundamental Theorem of Algebra to write Polynomials Functions given the zeros State zeros and their multiplicity and their effect on the graph Write cubic functions given the zeros using the Sum and Product of Roots *Extension: Use Fundamental Theorem of Roots - use sum & product of roots to write equations with 3 roots, including binomial roots 25 NC.M3.F-IF.7 Graph Polynomials and Identify Key Features:

6 NC.M3.A-CED.2 Include Key features from previous chapters and include: Symmetry Sketch polynomials based on end behavior and zeros 26 NC.M3.A-CED.3 Systems of Equations - Include Linear, Quadratic, and Polynomials (Technology) Practice/Review Day 27 Test #3 28 NC.M3.A-REI.11 Odd and Even Functions *Note: Include Solving equations in calculator of form f(x) = ⅓ g(x) *Note: These concepts are after the test to assure that students do not get confused with the other two concepts of Even and Odd in the unit and to expand the systems concept Unit 4 29 NC.M3.A-CED.2 Graphing Rationals and Identifying Key Featuers 30 NC.M3.F-IF.7 NC.M3.F-IF.9 Compare Key Features between Functions (Linear, Quadratic, Polynomials, Rationals). Compare graphs, equations, tables, and verbal description 31 NC.M3.A-APR.7a Simplify Rational Expressions Multiply and Divide Rational Expressions and State Restrictions 32 NC.M3.A-APR.7b Add and Subtract Rational Expressions (Linear Denominators only) 33 Simplify Complex Fractions Practice All Rational Expressions 34 NC.M3.A-REI.2 NC.M3.A-REI.1 Solve Rational Equations Rational Applications

7 35 NC.M3.A-CED.1 Solving Systems of Equations - Include previous functions with Rationals (Technology) Practice/Review 36 Test #4 *Optional Extension: Inverse of Rational Functions Unit 5 37 NC.M3.G-GMD.3 Volume Formulas Include tasks from Illustrative Mathematics **Recommendation: Go over formulas then do the Centerpiece tasks and The Great Egyptian Pyramids task with the students. Have the students work on the Dr. Appointment task in small groups, or individually. 38 NC.M3.G-GMD.4 NC.M3.G-MG.1 3D Visuals and Cross-Sections Include tasks from Illustrative Mathematics Visuals of 3d figures: 3D Cross-Sections: **Recommendation: Use websites to discuss and explain 3D visuals and cross-sections during lecture. Then have students complete Tennis Balls in a Can task from Illustrative Mathematics website. 39 NC.M3.G-CO.10 Review theorems from Math 2 standard NC.M2.G-CO.9 Properties of Centers of Triangles (Centroid, Incenter, Circumcenter) 40 NC.M3.G-CO.10 Continue Properties of Centers of Triangles

8 41 Practice 42 Test #5 Unit 6 43 NC.M3.F-IF.7 NC.M3.F-IF.9 NC.M3.F-LE.3 NC.M3.A-CED.2 Graphing Exponentials and Comparing Key Features 44 NC.M3.A-SSE.3c NC.M3.A-CED.1 NC.M3.A-SSE.1a NC.M3.A-SSE.1b Write an equivalent form of an exponential expression/equation using the properties of exponents *Note: For example the expression 1.15t can be rewritten as (1.151/12)12t t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%. Exponential Applications (Pert and Half-life) 45 NC.M3.F-LE.4 Introduction to Logs Properties of Logs - Condense and expand 46 NC.M3.A-REI.1 Solve Log Equations 47 NC.M3.F-LE.4 NC.M3.A-REI.1 Solve exponential equations - Include some with and without like bases Change of Base Formula 48 NC.M3.A-REI.1 Solve Natural Log Equations and Exponential Equations with base e Include Applications 49 NC.M3.F-BF.4 Find and Graph Inverses

9 50 NC.M3.F.BF.1a; b Building Functions by combining standard function types 51 Exponential Regression and Practice 52 Test #6 Unit 7 53 NC.M3.F-TF.1 Angles in the Coordinate Plane Radian measure Coterminal Angles Reference Angles Put degrees and radians on the unit circle 54 NC.M3.F-TF.2 Create Unit Circle 55 NC.M3.F-IF.1 NC.M3.F-TF.2 56 NC.M3.F-TF.2 NC.M3.F-TF.5 NC.M3.F-IF.7 Evaluate sine and cosine (including from Unit Circle) Graph sine and cosine Identify Key Features - Include key features from previous units and add periodicity 57 NC.M3.F-TF.5 NC.M3.F-IF.4 Real-world modeling problems *Note: Sine functions only 58 Practice/Review 59 Test #7

10 Unit 8 60 NC.M3.G-C.2 Circles and Lines that intersect them 61 NC.M3.G-C.2 Arcs & Chords 62 NC.M3.G-C.2 Inscribed Angles 63 NC.M3.G-C.2 Angles and Relationships Segments and Relationships 64 ` Practice & Quiz 65 NC.M3.G-C.5 Sector Area and Arc Length *Note: You can introduce radians here, or reintroduce Sector Area and Arc Length in the Trig unit 66 NC.M3.G-GPE.1 Circles in the Coordinate Plane - Graphing Circles Use Pythagorean Theorem to write equation using center and radius Use Completing the Square to write equation in standard form 67 Practice 68 Test #8 Unit 9 69 NC.M3.G-CO.11 NC.M3.G-CO NC.M3.G-CO.11 NC.M3.G-CO.14 Parallelograms *Note: Focus on proofs mentioned in standard NC.M3.G-CO.11 throughout the unit Rhombus, Rectangle, Square

11 71 NC.M3.G-CO.11 NC.M3.G-CO NC.M3.G-CO.11 NC.M3.G-CO.14 Kites and Trapezoids Practice proofs and set up and solve problems for any of the special quadrilaterals 73 Test #9 Unit NC.M3.S-IC.3 Introduction to Experiments and Simulations (Water-Water Activity) 75 NC.M3.S-IC.4 NC.M3.S-IC.5 Simulations Use Simulations to determine margin of error Use Simulations to determine difference between two samples are statistically significant 76 NC.M3.S-IC.3 Distinguish between types of Studies Experiments Observational Studies Surveys Simulations 77 NC.M3.S-IC1 Making Inferences about Populations Parameter of interest Statistics What is the best study to use? Activity: Random Rectangle

12 78 NC.M3.S-IC.6 Evaluate Articles 79 Review/Practice *Extension: Design a Simulation 80 Test # Review Day Pacing guide was made with the 2016 Spring semester in mind with 82 days of school due to snow. Extra days can be used as buffer days within the semester or review days at the end for the final exam.