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Math: Grade 1, Semester 1 Math: Grade 1, Semester 2 Math: Grade 2, Semester 1 Math: Grade 2, Semester 2 Math: Grade 3, Semester 1 Math: Grade 3, Semester 2

Printed on October 15, 2015

Math: Grade 1, Semester 1 Matter, Form and Function Big Idea: We use mathematical modeling with a variety of classes of functions to solve applications such as in biology and finance, and to form a basis for the study of mechanics and calculus. MA.1.01 - Create, interpret and analyze trigonometric ratios that model real-world situations. (Week 01 Week 05) Essential Questions: ‣ "Why is modeling an indispensable tool? ‣ Why do we represent phenomena in multiple ways?" Skills: ‣ A. Sine, cosine, and tangent ratios and Pythagorean Theorem ‣ B. Define the six trigonometric functions in terms of right triangles. ‣ C. Determine which quadrants have positive and negative trigonometric values ‣ D. Derive sine and cosine law ‣ E. Solving triangles (using law of sine and cosine) ‣ F. Use the law of sines, law of cosines to solve applied problems. ‣ G. Use the inverses of the sine, cosine, and tangent to solve problems. Concepts: ‣A. Unit circle ‣ B. Six trigonometric functions ‣ C. Related angles ‣ D. Sine law , cos law ‣ E. Angle of elevation and angle of depression Evidence: Problem Set 1.8 - BA #3, ST #6d Problem Set 3.1 - BA #6, 10, ST #9 Problem Set 3.2 - BA #5, ST #7c Problem Set 3.3 - BA #7, ST #8 Problem Set 3.6 - BA #1, ST # 8 Texts & References: Math Connections 2a sections 1.8, 3.1 - 3.4 , 3.6, 3.7 See materials in Unit Materials folder: https://drive.google.com/drive/folders/0B9KK7ZY6QeS3dGlETUVNQ0c2em8 Capstone Connection: Determine the dimensions of the sustainable houses Grand Challenge Connections: Improve the use of alternative energies to reduce our reliance on extracted fuel sources,Increase efficient use of our land through improved use of arid areas,Increase industrial base for Egypt,Recycle and retain garbage for recycling Topic: Right triangle trig

MA.1.02 - Apply the relationships between 2-D and 3-D objects in modeling situations (Week 06 - Week 10)

Printed on October 15, 2015

Essential Questions: Why is the world 3-D? Skills: ‣ A. Draw 2-D cross-sections of a representation of a 3-D object. ‣ B. Identify three dimensional objects created by rotations of two dimensional objects ‣ C. Describe 3-D shapes ‣ D. Create 3-D shapes Concepts: ‣ A. Cross section ‣ B. 2-Dimensional objects ‣ C. 3-Dimensional objects ‣ D. Classifying regular polyhedra Evidence: Problem Set 5.1 BA:p 466 # 1 a, b, ST:466 # 1 c Assessment in "2D Representations of 3D Objects" Texts & References: Math Connections Geometry 2b Section 5.1 See materials in the Unit Materials Folder: https://drive.google.com/drive/folders/0B10u0LfTYd6hflM3QkZnM0JCM1B6bzR5T3F6dktnN0RkdFBJb3RpS XdBLTRuMlVIbVZGWW8 Capstone Connection: Building house Grand Challenge Connections: Reduce urban congestion and its impact,Increase opportunities for Egyptians to stay and work in Egypt Topic: 2-D/3-D Objects

MA.1.03 - Understand similarity and use the concept for scaling to solve problems (Week 06 - Week 10) Essential Questions: Why are relationships predictable? Skills: ‣ A. Determine axes of similarity ‣ B. Draw the image of a shape (using reduction and magnification) ‣ C. Solve problems and applications using proportionality theorems ‣ D. Prove the angle bisector theorem ‣ E. Stretching and Shrinking Angles and Areas ‣ F. Stretching and Shrinking Volumes ‣ G. Finding the scaling factor(area and volume) ‣ H. Solve problems related to geometric shapes " Concepts: ‣A. Similarity ‣ B. Transformation( reduction and magnification) ‣ C. Proportionality ‣ D. Parallel lines and proportional parts ‣ E. Angle bisectors Evidence: Geometry Packet Basic Application- page 4, page 16 #7, page 25 bottom chart Geometry Packet Strategic Thinking Pages 12, 18 Math Connections Geometry 2a, 2.10 BA - #5

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Geometry Packet Strategic Thinking page 31 #4, page 36, page 38 Texts & References: Geometry Packet in the Unit Materials Folder pages 1 to 25 https://drive.google.com/drive/folders/0B10u0LfTYd6hfkllWmNyWHcwRDdRWXJ5T05peldMVFBtemtscTczU 1lDaEVvaWo4aTZ6bDg Math Connections 2a 1.10 Math Connections Geometry 2a, 2.9, 2.10 Geometry Packet in the Unit Materials Folder pages 27 to 38 Capstone Connection: Building house Grand Challenge Connections: Reduce urban congestion and its impact,Increase opportunities for Egyptians to stay and work in Egypt,Increase industrial base for Egypt,Recycle and retain garbage for recycling Topic: Similarity, scaling

MA.1.04 - Apply volume formulas (pyramid, cones, spheres, prisms) (Week 06 - Week 10) Essential Questions: How does what we measure influence how we measure? Skills: ‣ A. Derive the formulas of areas and volumes ‣ B. Determine area and volume of different shapes and figures ‣ C. Determine volume of a composite figures Concepts: ‣ A. Area ‣ B. Volume ‣ C. Composite figures Evidence: Math Connections 5.3 Basic Application #3 Math Connections 5.4 Strategic Thinking #7 Texts & References: Math Connections 2b 5.3-5.4 See materials in Unit Materials folder: https://drive.google.com/drive/folders/0B10u0LfTYd6hfjJHNDFJTGpkVlQ1S040Z2JIOWhRS3JENkFQUzNV VzdZNEM2QlNLckU1Mlk Capstone Connection: Building house Grand Challenge Connections: Reduce urban congestion and its impact,Increase opportunities for Egyptians to stay and work in Egypt Topic: Volume

MA.1.05 - Create, interpret and analyze functions, particularly linear and step functions that model real-world situations. (Week 11 - Week 13) Essential Questions: ‣ Why is modeling an indispensable tool? ‣ Why do we represent phenomena in multiple ways?

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‣ How does data help make sense of the world around us? Skills: ‣ A. Given data, create functions that model applied situation. Calculate a least squares regression line, understand its properties, compute and interpret correlation for data ‣ B. Interpret the functions based on the real-world situation they model ‣ C. Analyze the functions and their characteristics. Explain the different properties of the algebraic function and its graph. ‣ D. Identify, interpret and describe real-world step functions ‣ E. Analyze direct and inverse variations based on the real-world situation they model. ‣ F. Graph linear, piecewise, absolute value and step functions ‣ G . Find the inverse of some functions algebraically and graphically and determine if the inverse is a function. (Also: Distinguish between "inverse variation" and "inverse function.") ‣ H. Solve real life application on functions Concepts: ‣A. Linear functions ‣B. Piecewise function ‣C. Absolute-Value Functions ‣D. STEP function ‣E. Direct variation ‣F. Inverse variation ‣G. Regression ‣H. Correlation ‣I. Correlation coefficient ‣j. Slope ‣K. Intercepted part ‣L. Composition of Functions ‣M.Translation of linear function Evidence: Quiz : https://drive.google.com/drive/folders/0B9KK7ZY6QeS3NGZVd25rbWhmS2c Math Connections 1a Basic Application Problem Set 4.5 #1 Strategic Thinking Problem Set 4.5 #6 Math Connections 1b Basic Application Problem Set 6.1 #2, Problem Set 6.3 # 3, Problem Set 6.4 #6 a through c, Problem set 6.6 # 2 (any of them) Strategic Thinking Problem Set 6.1 #8, Problem Set 6.4 #6 d, Problem Set 6.6 #6c Texts & References: Math Connections 1A 3.4 - 3.6, 4.4 - 4.5 Math Connections 1B 6.1 - 6.4, 6.6 https://www.youtube.com/watch?v=npBg0Ynv4D0 See material in Unit Materials folder Capstone Connection: Building house Grand Challenge Connections: Reduce urban congestion and its impact,Increase opportunities for Egyptians to stay and work in Egypt Printed on October 15, 2015

Applications: PH.1.08, PH.1.09, PH.1.11, PH.1.12, ME.1.02, ME.1.04, CH.3.15, Topic: linear, piecewise, absolute value

MA.1.06 - Analyze, display and describe quantitative data with a focus on standard deviation. (Week 14 Week 14) Essential Questions: ‣ How can graphical displays be manipulated to present misleading information? ‣ How can data analysis be used to predict future happenings? ‣ Does the data always lead to the truth? Why or why not? Skills: ‣ A. Describe the overall pattern (shape, center, spread) of a distribution and identify any major departures from the pattern (like outliers). ‣ B. Make a histogram, dotplot, boxplot or stemplot to display small sets of data and interpret the data. ‣ C. Identify the shape of a distribution (symmetric or skewed) from a dotplot, stemplot, or histograms ‣ D. Calculate and interpret measures of center (mean, median) and spread (IQR, standard deviation). ‣ E. Use appropriate graphs and numerical summaries to compare distributions of quantitative variables. Concepts: ‣ A. Shape, center, spread ‣ B. Outliers ‣ C. histogram ‣ D. Dotplot ‣ E. Boxplot ‣ F. Stemplot ‣ G. Skewed ‣H. Symmetric ‣I. IQR ‣ J. Standard deviation Evidence: The Practice of Statistics Section (1-2) Exercises Basic Application #38 a Strategic Thinking #49b section (1-3) Exercises Basic Application Check Your Understanding #1,2,3 Strategic Thinking #98b, c Chapter 1 Chapter Review Exercises Strategic Thinking R1.3 Texts & References: Starnes, Daren - Tabor, Josh - Yates, Daniel - Moore, David, The Practice of Statistics, New York: W.H. Freeman, 2015, 5th Edition

Printed on October 15, 2015

Exploring Data (Chapter 1) Capstone Connection: geometry and measurement Grand Challenge Connections: Address the exponential population growth and prepare for the impact,Improve the use of alternative energies to reduce our reliance on extracted fuel sources,Reduce urban congestion and its impact,Increase opportunities for Egyptians to stay and work in Egypt,Increase industrial base for Egypt Topic: Quantitative data

Printed on October 15, 2015

Math: Grade 1, Semester 2 Energy Force and Power Big Idea: We use mathematical modeling with a variety of classes of functions to solve applications such as in biology and finance, and to form a basis for the study of mechanics and calculus. MA.1.07 - Create, interpret and analyze quadratic functions that model real-world situations. (Week 01 Week 04) Essential Questions: ‣ Why do we need an imaginary world? ‣ How can things be real and imaginary? Skills: ‣ A. Use first and second differences to create models that represent data ‣ B. Interpret the functions based on the real-world situation they model. ‣ C. Analyze the functions and their characterisitcs. Explain the different properties of the algebraic function and its graph ‣ D. Review solving quadratic equations using completing squares ‣ E. Find the inverse of a quadratic function graphically and algebraically (completing the square) and determine how to make the inverse a function. ‣ F. Graph quadratic function ‣ G. Relation between roots of quadratic function and the coefficient ‣ H. Form Quadratic equation ‣ I. Related roots ‣ J. Parabola: focus, directrix, ‣ K.Write quadratic equation in parabolic form ‣ L. Real life application on parabola ‣ M. Use the quadratic formula to find real solutions to quadratic equations; identify graphically and algebraically when a quadratic equation has no real solution ‣ N. Use the quadratic formula to find complex solutions to quadratic equations ‣ O. Represent complex numbers three ways: as ordered pairs, graphically on the coordinate plane, and in the form a+bi ‣ I. Add, subtract, multiply, and divide complex numbers Concepts: ‣ A. Quadratic Function ‣ B. First and second differences ‣ C. Completing the square ‣ D.complex numbers ‣ E. parabola ‣F. Focus ‣ G. Argand diagram ‣ H. related roots Evidence: Math Connections 3A Algebra 2 Basic Application Problem Set 1.2 #5a Math Connections 3A Algebra 2 Basic Application Problem Set 1.5 #3

Printed on October 15, 2015

Math Connections 3A Algebra 2 Strategic Thinking Problem Set 1.2 #5a, #5c Math Connections 3A Algebra 2 Strategic Thinking Problem Set 1.5 #5 Texts & References: Math Connections 3A Algebra 2 sections 1.2, 1.3 pages 11 - 36 Math Connection Algebra 1B Sections 8.4 Math Connections 3A Algebra 2 sections 1.5 See materials in Unit Materials folder Capstone Connection: using the graphs of quadratic function in modeling solar cell Grand Challenge Connections: Reduce urban congestion and its impact,Increase opportunities for Egyptians to stay and work in Egypt Applications: PH.1.10, PH.1.08, PH.1.09, PH.1.11, PH.1.12, ME.1.04, Topic: Quadratic function

MA.1.08 - Create, interpret and analyze exponential and logarithmic functions that model real-world situations. (Week 05 - Week 07) Essential Questions: ‣ "Why is modeling an indispensable tool? ‣ Why do we represent phenomena in multiple ways? ‣ How does data help make sense of the world around us? ‣ Why do we need laws/rules?" Skills: ‣ A. Use different properties of exponential and logarithmic functions ‣ B. Interpret and manipulate rational exponents ‣ C. Use exponential functions to describe growth and decay ratios ‣ D. Construct exponential growth and decay functions to fit given data ‣ E. Solve compound interest problems. ‣ F. Reveal and explain different properties of the exponential function and its graph ‣ G. Graph exponential functions, find its domain and range ‣ H. Describe the inverse of an exponential function as a logarithm ‣ G. Graph logarithmic functions, find its domain and range. ‣ I. prove the logarithm rules ‣ J. solve logarithmic and exponential equations ‣ K. solve real life application Concepts: ‣ A. Exponential functions ‣ B. Logarithmic function ‣C. Growth ‣D. Decay Evidence: Basic Application - Math Connections 3A Problem Set 2.8 p.213, # 3a, b or Quiz in Unit Materials folder: https://drive.google.com/drive/folders/0B9KK7ZY6QeS3cEpJZGlYNzFzWVk Strategic Thinking - Math Connections 3A Problem Set 2.6 p.197, 6d, e, Math Connections 3a P.221 #10 d, e, Math Connections 3a Problem Set 2.8p.213, 3c, d Texts & References: Math Connections 3a sections 2.1 - 2.8 and pages 217-226

Printed on October 15, 2015

http://betterlesson.com/community/document/219143/unit-08day-06-notes-guided-practice-properties-of-logs-logarithmspdf For graph: https://www.desmos.com/calculator See materials in Unit Materials folder: https://drive.google.com/drive/folders/0B9KK7ZY6QeS3cEpJZGlYNzFzWVk Capstone Connection: inform alternative energy geometries, using graphs in solar cells Grand Challenge Connections: Reduce urban congestion and its impact,Improve Sources of Clean Water,Reduce pollution fouling our air water and grounds Applications: CH.2.03, PH.1.11, PH.1.12, PH.1.09, PH.1.08, ES.3.06, ES.2.09, CH.1.06, Topic: Exponential, Logarithmic

MA.1.09 - Create, interpret and analyze trigonometric functions that model real-world situations. (Week 08 Week 11) Essential Questions: ‣ Why is modeling an indispensable tool? ‣ Why do we represent phenomena in multiple ways? Skills: ‣ A. Relate the coordinates of points on the unit circle to the sine and cosine of angles ‣ B. Extend the domain of trigonometric functions using the unit circle (convert between radians and degrees) ‣ C. Draw and identify positive, negative, and co-terminal angles of rotation ‣ D. Describe the inverses of the sine, cosine and tangent functions and explain the relationship between sine, cosine, tangent and their inverses ‣ E. Identify different characteristics of sine, cosine and tangent functions: shape, domain, range, amplitude, intercepts, max/min, period, asymptotes. ‣ F Use technology to explore and analyze various functions.. ‣ G. Describe the transformations that shift and stretch a trigonometric function ‣ H Interpret the functions created based on the real-world situation they model. Concepts: ‣ A. Trigonometric functions. ‣ B. Coordinates ‣ C. Graphs of sine, cosine and tangent functions ‣ D. Inverses of the sine, cosine and tangent functions ‣ E. Shape, domain, range, amplitude, intercepts, max/min, period, asymptotes. ‣ F. Domain of trigonometric functions ‣ G. Positive, negative, and co-terminal angles of rotation ‣ H. Shift and stretch a trigonometric function Evidence: Math Connections Book 3A Basic Application: P.274 #2a,b,c P.280 #10a,b,c,d Strategic Thinking: P.264 #3 P274 #2d,e, #3b P.280 #10e,f P.289 #6b Texts & References: Math Connections 3a sections 3.1 - 3.6

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Capstone Connection: inform alternative energy geometries, using graphs in solar cells Grand Challenge Connections: Reduce urban congestion and its impact,Increase industrial base for Egypt Topic: Trigonometric graphs

MA.1.10 - Prove and apply trigonometric identities (Week 08 - Week 11) Essential Questions: Can things change and still be the same? Skills: ‣ A. Derive and apply the Pythagorean Identities ‣ B. Manipulate and apply cofunction Identities" Concepts: ‣ A. Trigonometric identities ‣ B. Pythagorean Identities ‣ C. Cofunction Identities Evidence: Basic Application: Math Connections 3A Algebra 2 Page 315 3.47 any of those problems Strategic Thinking: Students create a trigonometric identity that involves cosine, sine and tangent. Texts & References: Math Connections 3A Algebra 2 pages 307 - 316 Capstone Connection: inform alternative energy geometries. Grand Challenge Connections: Increase industrial base for Egypt Topic: Trigonometric identities

MA.1.11 - Create, interpret and analyze systems of linear functions that model real-world situations. (Week 12 - Week 14) Essential Questions: ‣ Why is modeling an indispensable tool? ‣ Why do we represent phenomena in multiple ways? ‣ How do humans make informed decisions, given multiple options? ‣ What factors affect our decisions and how dothese factors relate to mathematical models? Skills: ‣ A. Solve a system of two equations and two unknowns by graphing and algebraic methods ‣ B. Interpret the solution of a system in context of the situation ‣ D. Represent a system as a matrix ‣ E. Apply matrix operations to solve a system ‣ F. Use matrices to represent real-world situations and interpret their solution ‣ G. Reduce matrices to RREF and interpret the meaning ‣ H. Determine and interpret optimal solutions and the constraints to real-world situations using Linear Programming ‣ I Write objective functions Concepts: ‣ A. System ‣ B. System of equations ‣ C. Unknowns

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‣ D. Graphing methods ‣ E. Algebraic methods ‣F. Matrix ‣ G. Operations ‣ A. Linear Programming ‣ B. Objective functions ‣ C. Feasible regions ‣ D. Constraints ‣ E. Optimal solution Evidence: Math Connections Geometry 2B Basic Application Problem Set 6.4 #7a Math Connections Geometry 2B Basic Application Page 631, #6.49 Math Connections Algebra 2 3A Basic Application Page 332 # 3 a, b Math Connections Algebra 2 3A Basic Application Page 352 # 3 a, b Math Connections Geometry 2B Strategic Thinking Problem Set 6.4 #7b Math Connections Geometry 2B Strategic Thinking Page 631, #6.50 Math Connections Algebra 2 3A Basic Application Page 352 # 3c Texts & References: Math Connections 2b, sections 6.1 - 6.5 Math Connections 3a sections 4.1 - 4.4 Capstone Connection: Modeling with Energy Grand Challenge Connections: Address the exponential population growth and prepare for the impact,Improve the use of alternative energies to reduce our reliance on extracted fuel sources,Increase industrial base for Egypt Topic: Systems, determinant, constraint

MA.1.12 - Apply determinants and their properties in real-world situations (Week 12 - Week 14) Essential Questions: ‣ Why use shortcuts? ‣ Why is it essential to have different ways of reaching solutions? Skills: ‣ A. Use the properties of determinants to determine the value of a determinant ‣ B. Solve real-world applications of determinants particularly finding the area of parallelogram and triangle. ‣ C. Solve a system of linear equations using Cramer's Rule Concepts: ‣ A. Determinants ‣ B. Value of a determinant ‣ C. Area, parallelogram and triangle. ‣D. Matrices ‣ E. System of equations ‣ F. Cramer's Rule Evidence: Unit in Materials Folder: Determinants

Printed on October 15, 2015

Basic Application: Page 24 #41 - 48 Basic Application: Page 25 #59 Str...