Math 2 In Depth Curriculum Guide

 

Math 2 Big Ideas:

Algebra & Functions:

• Quadratic

• Square Root

• Inverse Variation

Geometry:

• Congruence

• Similarity

• Right Triangle Trigonometry

• Special Right Triangles

Statistics & Probability:

• Categorical Data and Two-way Tables

• Addition and Multiplication Rules

• Conditional Probability

• Independent Events

• Experimental & Theoretical Probabilities

Testing Specification:

 

• Num & Quan 3-10%

• Algebra 21-28%

• Functions 18-25%

• Geometry 27-34%

• Stats & Prob 15-22%

 

Important Documents:

 

• NCSCOC - Math 2 Standards

• Math 2 - Math Resources for Instruction (MRIs) - old unpacking documents

• Testing Specifications

• NC Math 2 Google Drive Folder

 

Web Resources:

 

• NCDPI Math Google Site

• DCS High School Math Resources

• Illustrative Mathematics

• Mathematics Assessment Project (MARS - Mathshell)

• Inside Mathematics

• Desmos - Virtual Graphing Calculator - on exam

• Yummy Math

 

Unit 1:  Algebra

Pacing

*Adding, Subtracting, and Multiplying Polynomials

     NC.M2.A-APR.1

• I can add, subtract, and multiply polynomials.

• Write polynomials on the faces of cubes and have students roll the cubes to get problems to add, subtract, and multiply

• Multiplying/factoring matching puzzle

1

*Rational Exponents

     NC.M2.N-RN.1, NC.M2.N-RN.2

• Rational Exponents Investigation  

•  Discovering Properties of Rational Exponents

1

*Simplifying Radical Expressions

     NC.M2.N-RN.1, NC.M2.N-RN.2

• Evaluating Statements about Radicals

• Exponents and Radicals - “I have...you have” activity

• Simplifying Radicals

• Solving radical equations will come later in Unit 2 when students work with the inverse of quadratics

1

*Properties of Rational and Irrational Numbers

     NC.M2.N-RN.3

• Rational and Irrational Numbers 

1

Review & Assessment

1

Total Days

6

 

Unit 2:   Functions

Pacing

C2 U5 L1I 1:  Function Notation

    NC.M2.A-SSE.1, NC.M2.F-IF.4

• Can skip if needed to save time, a good review of function notation that students have learned from Math 1

• Watch Olympic luge runs to start inverse (make sure to look up ahead of time, there are some bad ending luge videos)

1

C2 U1 L1 I1:  On a Roll

     NC.M2.A-CED.1, NC.M2.F-BF.1, NC.M2.F-IF.7

• Include OYO #1, 3, 13

• Need ramps for this activity - can use PVC pipe with holes cut every foot, can stack books as the ramp stand

2

C2 U1 L1 I2:  Power Models

     NC.M2.A-SSE.1, NC.M2.F-IF.9

• Investigating Even and Odd Power Functions

• Focus on the constant of proportionality, end behavior, line of symmetry, asymptotes

• Include OYO #7, 15

1.5

Quiz

.5

*Quadratics Introduction/Review

     NC.M2.F-IF.7, NC.M2.A-CED.1

• Review their previous understanding of quadratics, the graph and factoring.  Students only know how to solve by factoring and graphing at this point.  Think of previous work with pumpkin chunking.

1

C2 U5 L1 I3:  Expanding and Factoring

     NC.M2.A-SSE.1

• Students have already learned how to do this by this point, can skip or use as a good review, but making sure you are using factoring to solve

• Extra practice OYO #11, 12

2

C2 U5 L1 I2:  Designing Parabolas

     NC.M2.F.IF.4, NC.M2.F-BF.1

• Extra practice in OYO #8-10

2

Quiz

.5

C2 U5 L1 I4: Solving Quadratic Equations

     NC.M2.A-SSE.1, NC.M2.N-CN.1, NC.M2.A-REI.4

• Making sure students know when a quadratic would yield 0, 1, or 2 solutions

• Extra practice OYO #13-15

• Proving and Using the Quadratic Formula

• Great video to work with Quadratic Formula - Do The Quad Solve

2

*Complex Numbers

     NC.M2.N-CN.1, NC.M2.A-REI.4

• Can pull from - C3 U5 L2 I2:  Complex #’s with Quadratic Formula - Access here

1

*Complete the Square

     NC.M2.A-SSE.3, NC.M2.F-IF.8

• Have students manipulate algebra tiles, whether physically or virtually, essential for them to visually see about completing the square, do they have too many or not enough squares?

• Vertex Form and Completing the Square from Core-Plus Course 3

2

Quiz

.5

*Vertex Form

   NC.M2.A-SSE.3, NC.M2.F-IF.8

• Vertex Form and Completing the Square from Core-Plus Course 3

1

*Quadratic Key Features

     NC.M2.A-SSE.1, NC.M2.F-IF.7, NC.M2.F-IF.9

• Representing Quadratic Functions Graphically

1

Quiz

.5

*Inverse of Quadratics - Square Root Functions

     NC.M2.A-SSE.1, NC.M2.A-REI.2, NC.M2.F-IF.7, NC.M2.F-IF.9

• Have students discuss inverse and what they think it means, have them discover square root functions by learning they are in the inverse of quadratic functions and what that means

1

*Solving Square Root Functions

     NC.M2.A-REI.1, NC.M2.A-CED.1

• Several Activities - Illustrative Mathematics - “Canoe Trip” and “Who Wins the Race” 

• Tsunami Speeds 

1

Quiz

.5

*Transformations of Functions

      NC.M2.F-BF.3

• Have students stand up and do these as “Mathercises” having them move their body and arms as you change the function - Mathercises with Arms

• Square Root Card Sort Translations - pg. 335

1.5

Review & Assessment

2

Total Days

24.5

 

Unit 3:  Solving Systems

Pacing

C2 U5 L2 I1:  Supply and Demand

    NC.M2.A-CED.2, NC.M2.A-CED.3, NC.M2.A-REI.2, NC.M2.A-REI.11

• At the end of investigation, review ALL possibilities of solutions for a linear and inverse system, including different positions to give number of solutions

1.5

C2 U5 L2 I2:  Making More by Charging Less

     NC.M2.A-CED.2, NC.M2.A-CED.3, NC.M2.A-REI.7

•  Include OYO #3, 7-10, 13

1.5

*Create and Solve Systems of All Functions

     NC.M2.A-CED.3, NC.M2.A-REI.11

• Nonlinear Systems with Radicals Practice

• Use desmos.com to graph nonlinear systems

1

*Solving Systems Algebraically

• Card Sort - MARS - Students are given a variety of different rules and they have to figure out whether they are always, sometimes, or never equivalent in whatever method they choose

• The cycle shop (system of 3 equations)

1

Review & Assessment

1.5

Total Days

6.5

 

Unit 4:  Geometry 

Pacing

C2 U3 L2 I1:  Modeling Rigid Transformations

    NC.M2.F-IF.1, NC.M2.F-IF.2, NC.M2.G-CO.2, NC.M2.G-CO.4, NC.M2.G-CO.5

• Another activity to teach transformations

• Start off watching “The Tech of Shrek” or “Making of Avatar” - students can see how where transformation of geometry is applied in animation

• Discuss similarity vs. congruence of the figures

• Stress the importance of “rigidness” of these transformation

• CPMP Tools

3

C2 U3 L2 I2:  Modeling Size Transformations

      G-SRT.1, NC.M2.F-IF.1, NC.M2.F-IF.2, NC.M2.G-CO.2, NC.M2.G-SRT.1, NC.M2.G-SRT.2

• The investigation only deals with a center of (0,0)

• Discuss similarity vs. congruence of the figures

• CPMP Tools

• Evaluating Statements about Enlargements

1

*Combining Transformations

     NC.M2.F-IF.1, NC.M2.F-IF.2, NC.M2.G-CO.2, NC.M2.G-CO.4, NC.M2.G-CO.5

• Practice doing two or more transformation - sequence transformations 

• Discuss similarity vs. congruence of the figures

• Translation Cafe

• Making Shrek Dance

• CPMP Tools

• Card matching activity - Representing and Combining Transformations

1

*Symmetry in Rotations and Reflections

     NC.M2.G-CO.3

• Rotations, Reflections, and Symmetry

1

Review & Assessment

1.5

Total Days

7.5

 

Unit 5:  Triangles and Trigonometry  

Pacing

*Rigidness & Properties of Rigid Motion

     NC.M2.G-CO.5

• Can pull from Course 1, Unit 6, Lesson 1, Investigation 1, questions #5-7 - using linkage strips to make quadrilaterals, as you add a diagonal what happens to the shape and why is that important?

1

*Triangle Congruence

     NC.M2.G-CO.8, NC.M2.G-SRT.3

• Interactive applet

• Evaluating Conditions for Congruence

• Can pull from Course 1, Unit 6, Lesson 1, Investigation 1 - Congruent Shapes - Extra practice OYO #4-6

2

*Similarity and Congruence in Triangle Transformations

     NC.M2.G-CO.6, NC.M2.G-CO.7, NC.M2.G-SRT.2, NC.M2.G-SRT.3

• Similar Triangles - Meredith Navigating the 7 C’s

• Practice for triangle congruence (no proof)

1

Quiz

.5

C2 U7 L1 I1:  Connecting Angles Measures

    NC.M2.G-SRT.6, NC.M2.G-SRT.8

• Standard specifically says to use side ratios to lead the the definitions of trig ratios - meaning you should not just tell them the trig ratios, they need to discover the relationship

2

C2 U7 L1 I2:  Measuring without Measuring

    NC.M2.G-SRT.6, NC.M2.G-SRT.8

• Make sure students do OYO #20 on page 481 for complementary angles

• Angle of elevation lab with clinometer

1.5

C2 U7 L1 I3:  What’s the Angle?

     NC.M2.G-SRT.6, NC.M2.G-SRT.8

• This video is a great video to introduce here Getting Triggy With It

1

*Special Right Triangles

     NC.MW.G-SRT.12

• 45-45-90 & 30-60-90

• Discovering Special Right Triangles

• Special Right Triangles

1.5

*Trigonometry Practice

     NC.M2.G-SRT.8

• Just some added time to practice more - could have students make up real life scenarios and then other students must draw and solve

• Trig Practice from Word Problems

1.5

Review & Assessment

2

Total Days

14

 

Unit 6:  Proofs

Pacing

*Prove Theorems About Lines and Angles

     NC.M2.G-CO.9

• Vertical angles are congruent

• When a transversal crosses parallel lines, alternate interior angles are congruent

• When a transversal crosses parallel lines, corresponding angles are congruent

• Points are on a perpendicular bisector of a line segment if and only if they are equidistant from the endpoints of the segment

• Use congruent triangles to justify why the bisector of an angle is equidistant from the sides of the angle

2

*Prove Theorems About Triangles

     NC.M2.G-CO.10, NC.M2.G-SRT.4

• Triangle construction

• A line parallel to one side of a triangle divides the other two sides proportionally and its converse

• The Pythagorean Theorem

• Sum of measures of the interior angles of triangle is 180 degrees

• An exterior angle of a triangle is equal to the sum of its remote interior angles

• The base angles of an isosceles triangle are congruent

• The segment joining the midpoints of two sides of a triangle is parallel to the third side and half the length

2

*Use Similarity to Prove and Solve

     NC.M2.G-SRT.2, NC.M2.G-SRT.4

• I can determine the height of a rocket

• Practice with Similarity Proofs

2

Review & Assessment

1.5

Total Days

7.5

 

Unit 7:  Probability  

Pacing

C1 U8 L1 I1:  Probability Distributions

     NC.M2.S-CP.1

• Excellent place to have students gather their own data or have data that is relevant to the students in your classroom

• Student exploration to begin probability discussions

• Can access investigation here

2

C1 U8 L1 I2:  The Addition Rule

     NC.M2.S-CP.7

• Think of the words “and” and “or;”  you have more of chance to get “red or black” - so when we are working with fractions, you add them to make the number larger (if we multiplied fractions, it makes our number even smaller, which relates to the “and” because it is harder to get a “red and blank”)

2

C1 U8 L2 I1:  When It’s A 50-50 Chance?

     NC.M2.S-IC.2

• Can skip #6-8 if needed

1

Quiz

.5

C2 U8 L1 I1:  Multiplication Rule

     NC.M2.S-CP.8

• The area and array models are awesome representations of this

• Can reference what we said under “The Addition Rule” with and or or - “and” makes something harder to get; therefore, the probability will be smaller, the way to get a smaller number with fractions is when you multiply them

2

C2 U8 L1 I2:  Conditional Probability

     NC.M2.S-CP.3, NC.M2.S-CP.4, NC.M2.S-CP.4, NC.M2.S-CP.6

• Probability games

• Conditional probability

2

Review & Assessment

2

Total Days

11.6

 

Total Days: 77.5 days

 

Honors Math 2:

Trig Unit: Law of Sines and Law of Cosines - G-SRT.9, G-SRT.11

• C2 U7 L2 I1 and I2

Transformations with animations

Operations with complex numbers

Standards to be Address Throughout the Course:  

• Function notation

• Interpret meaning of numbers in context - NC.M2.A-SSE.1

• Key features of all graphs - NC.M2.F-IF.4

• Theoretical and practice domain and range

• Justify and explain steps

• Proofs in general - not just two-column

• Include units with all work (no naked numbers)