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WPS Math - Integrated Math III
Core Connections Integrated III is the third course in a four-year sequence of rigorous college preparatory mathematics courses that starts with Core Connections Integrated I and continues through Calculus. It aims to apply and extend what students have learned in previous courses by focusing on finding connections between multiple representations of functions, transformations of different function families, finding zeros of polynomials and connecting them to graphs and equations of polynomials, modeling periodic phenomena with trigonometry, and understanding the role of randomness and the normal distribution in making statistical conclusions.
On a daily basis, students in Core Connections Integrated III use problem-solving strategies, questioning, investigating, analyzing critically, gathering and constructing evidence, and communicating rigorous arguments justifying their thinking. Under teacher guidance, students learn in collaboration with others while sharing information, expertise, and ideas.
The course is well balanced between procedural fluency (algorithms and basic skills), deep conceptual understanding, strategic competence (problem solving), and adaptive reasoning (extension and transference). The lessons in the course meet all of the content standards, including the “plus” standards, of Appendix A of the Common Core State Standards for Mathematics. The course imbeds the CCSS Standards for Mathematical Practice as an integral part of the lessons in the course.
Unit | Timeframe | Big Ideas (Statements or Essential Questions) | Major Learning Experiences from Unit |
|---|---|---|---|
Chapter 1 Investigations and Functions | 5 days | Where can I start? Did I do anything similar in previous courses that I can extend here? Is there another approach? Will a graph help? | -Work with your team and use graphing technology to help you explore functions, and you will present your results to the class. -Further develop your understanding of what it means to investigate a function and you will learn about families of functions. |
Chapter 2 Transformations of Parent Graphs | 10 days | What does the structure of this equation tell me about its graph? | -Review how to shift, stretch, compress, and reflect the graph of . You will write an equation in graphing form for the family of quadratic functions. -Apply the concepts of transformations to other parent functions, and you will learn that transforming each parent function creates a family of functions. Write an equation in graphing form for a family of functions. Will learn how the graphing form of a function allows you to determine the transformations needed to graph the function. -Review a method for rewriting a quadratic equation in standard form into graphing form, both for parabolas and circles. |
Chapter 4 Normal Distributions | 6 days | Can I write a research question? Can I identify bias in questions? Can I design an experiment? Can I analyze a normal distribution? How can I apply the mathematics I have learned to model this situation? How can I design a survey or experiment to get the information I need. | Create a survey and learn how to avoid bias in creating survey questions. Perform an experiment and contrast other experiments with observational studies such as opinion surveys. Construct relative frequency histograms. |
Chapter 5 Inverses | 8 days | Can I write equations of inverses for simple functions by “undoing”? Can I create the graph of the inverses of functions? Can I convert from logarithmic form to exponential form and vice versa? Can I write equations of transformed graphs and/or sketch their graphs? | Examine relationships, called inverses, which “undo” the actions of functions. Investigate multiple representations of inverse functions. Learn what happens when you “stack” function machines with their inverses. Investigate logarithms, which are the inverses of exponential functions and learn to transform its graphs. |
Chapter 6 Simulating Sampling Variability | 6 days | Can I set up a simulation to model an event? Can I run a hypothesis test? Can I reason about the results of the hypothesis test? What tools can I use to simulate the situation? What predictions can I make? What conclusions can I draw from the results? | Perform simulations to determine complex probabilities. Conduct a statistical hypothesis test. Observe the effect of sample size on sample-to-sample variability. Use a hypothesis test to determine whether two results in an experiment are truly different. Evaluate decisions and strategies based on area models of probability. |
Chapter 7 Logarithms And Triangles | 10 days | Can I solve logarithmic and exponential equations? Can I write equations of exponential functions in the form y=abx ? Can I write equations of inverses of more complicated functions, including those that require a restricted domain? | - learn some important properties of logarithms that will enable the solving of equations. - use these skills to solve a murder mystery, “The Case of the Cooling Corpse.” - investigate how to solve for side lengths and angle measures in triangles given different types of information about a triangle - focus on developing tools to calculate missing side lengths and angle measures in any triangle |
Chapter 8 Polynomials | 10 days | Can I sketch the graph of a polynomial function without using a graphing calculator, and write a polynomial equation from a graph? Can I represent solutions to polynomial functions using imaginary and complex numbers? Can I apply my knowledge of area models and factoring to polynomial division in order to write polynomials in factored form? | -Describe the graph of a polynomial given its equation in factored form. -Generalize and explain results of polynomial investigations. -Write exact equations for the graphs of polynomial functions when given the x-intercepts and one additional point. -Write equations of quadratic functions when given complex roots and know that complex roots come in complex conjugate pairs. -Identify the number of real and complex roots of a polynomial function by its graph. -Recognize that a polynomial function of degree n will always have roots. -Use polynomial division to determine factors of polynomials. -Use the Rational Zeros Theorem, the Remainder Theorem, the Factor Theorem, and polynomial division to determine all roots of polynomials with degree greater than 2. -Factor expressions using patterns of polynomial identities. -Apply knowledge of polynomial equations to real world problems. |
Chapter 9 Trigonometric Functions | 10 days | How can I use what I know about right-triangle trigonometry to describe functions determined by angles in a circle? | - use the understanding of the trigonometric ratios in right triangles to build an understanding of two new functions - recognize and create multiple representations of the functions y=sin(θ) and y=cos(θ) - discover relationships between the unit circle and the graphs of these functions - measure angles using radians - apply skills of transforming parent graphs to graph a function family whose parent function is y=sin(x) - develop general equations for trigonometric functions - learn about a property of these functions called a period |
Chapter 11.1 Rational Expressions | 3-4 days?? | Can I use the different properties of the number 1 to rewrite and simplify rational expressions? Can I use my understanding of operations on fractions to add, subtract, multiply and divide rational expressions? | -Analyze and compare rational expressions. -Multiply and divide rational expressions in order to simplify them. -Add and subtract rational expressions in order to simplify them. -Use all four operations (multiply, divide, add and subtract) to simplify rational expressions. |