Math Curriculum - Grade12 also available as a printable PDF . 1. Number & Operations Essentials Skills: 1. Understand numbers, ways of representing numbers, relationships among numbers and number systems 2. Understand meanings of operations and how they relate to one another 3. Compute fluently. 4. Make reasonable estimates and relate the estimates to solutions Important to Know • Use complex numbers as solutions to quadratic equations that do not have real solutions • Identify the properties of vectors • Perform vector addition and multiplication (dot and cross) • Use permutations and combinations as counting techniques . 2. Algebra Essential Skills: 1. Understand patterns, relations and functions 2. Represent and analyze mathematical situations and structures using algebraic symbols 3. Use mathematical models to represent and understand quantitative relationships 4. Analyze change in various contexts 5. Use paper and pencil to demonstrate skills prior to using technology Important to Know • Generalize patterns using explicitly defined and recursively defined functions • Represent relations and logarithmic, exponential, and trig functions in various forms • Identify quantitative relationships in a situation and determine classes of functions that might model the relationship • Translate, solve and test the reasonableness of word problems into mathematical symbolic expressions (linear quadratic, non-linear) • Approximate and interpret rates of change from graphical and numerical data . 3. Geometry Essential Skills: 1. Analyze characteristics and properties of two-and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships 2. Specify locations and describe spatial relationships using coordinate geometry and other representational systems 3. Apply transformations and use symmetry to analyze mathematical situations 4. Use visualization, spatial reasoning, and geometric modeling to solve problems 5. Use paper and pencil to demonstrate skills prior to using technology Important to Know • Use visual tools such as networks to represent and solve problems • Sketch 3-D figures from different perspectives • Explore relationships (including congruence and similarity) among classes of 2-D and 3-D geometric objects • Investigate conjectures about 2-D and 3-D objects and solve problems involving them • Draw and construct representations of 2-D and 3-D geometric objects using a variety of tools (graphing calculators, CAD) • Visualize 3-D objects from different perspectives and analyze their cross sections • Use vertex-edge graphs to model and solve problems • Use Cartesian coordinates and other coordinate systems, such as navigational, polar, and spherical systems, to analyze geometric situations • Investigate conjectures and solve problems involving 2-D and 3-D objects represented with Cartesian and 3-D coordinate systems • Use geometric ideas to solve problems in, and gain insights into, other disciplines and other areas of interest such as art and architecture . 4. Measurement Essential Skills: 1. Understand measurable attributes of objects and the units, systems, and processes of measurement 2. Apply appropriate techniques, tools, ad formulas to determine measurements 3. Use paper and pencil to demonstrate skills prior to using technology Important to Know • Make decisions about units and scales that are appropriate for problem situations involving measurement • Analyze precision, accuracy and approximate error in measurement • Apply informal concepts of successive approximation, upper and lower bounds, and limit in measurement situation • Use unit analysis to check measurement computations . 5. Data Analysis & Probability Essential Skills: 1. Select and use appropriate statistical methods to analyze data 2. Develop and evaluate inferences and predictions that are based on data 3. Understand and apply basic concepts of probability 4. Use paper and pencil to demonstrate skills prior to using technology Important to Know • Understand the differences among various kinds of studies and which types of inferences can legitimately be drawn from each • Know the characteristics of well-designed studies including the role of randomization in surveys and experiments • Use theoretical and experimental probability to form predictions • Understand the meaning of measurement data and categorical data, of univariate and bivariate data, and of the term variable • For univariate measurement data display the distribution, describe its shape, and select and calculate summary statistics • For bivariate measurement data display a scatterplot, describe its shape, and determine regression coefficients, regression equations, and correlation coefficients using technological tools • Display and discuss bivariate data where at least one variable is categorical • Recognize how linear formations of univariate data affect shape, center, and spread • Identify trends in bivariate data and find functions that model the data or transform the data so that they can be modeled . 6. Problem Solving Essential Skills: 1. Work individually and as a member of a group in formulating and solving problems 2. Build new mathematical knowledge through problem solving 3. Identify and solve problems that arise in mathematics and in other contexts 4. Apply and adapt a variety of appropriate strategies, including choosing appropriate computations, to solve problems 5. Monitor and reflect on the process of mathematical problem solving Important to Know • Identify needed information to solve a problem • Use the following strategies: act it out, make a physical model, draw a diagram, make a chart or table, generalize, look for a pattern, guess/check/revise, working backwards, solve a simpler problem • Translate from words to mathematical symbols • Identify relevant and irrelevant information • Solve multi-step problems • Judge the reasonableness of solutions • Use an open sentence (algebraic equation to symbolize a problem situation and solve the equation to find a solution to the problem • Identify problems that are similar in structure • Generalize a problem solving situation to there content areas • Exhibit a project that includes a flow chart or outline of a problem solving process • Use strategies with geometric theorems and proofs • Choose an appropriate computer program to help solve problems and display evidence . 7. Reasoning and Proof K-12 Essential Skills 1. Recognize reasoning and proof as a fundamental aspect of mathematics 2. Make and investigate mathematical conjectures 3. Develop and evaluate mathematical arguments and proofs 4. Select and use various types of reasoning and methods of proof . 8. Communication Essential Skills 1. Organize and consolidate mathematical thinking through communication 2. Communicate mathematical thinking coherently and clearly to peers, teachers, and others 3. Analyze and evaluate the mathematical thinking and strategies of others 4. Use the language of mathematics to express mathematical ideas precisely Important to Know Oral • Explain fluently and sequentially what method was used to get an answer • Validate and generalize solutions to a problem Written • Explain fluently and sequentially what method was used to get an answer • Validate and generalize solutions • Explain mathematical processes • Record observations and investigations using appropriate math symbols and terms • Keep weekly math journal using math concepts Visual • Use concrete materials to model mathematical ideas • Use tables, charts and graphs to make presentations Kinesthetic • Use body language to demonstrate mathematical ideas . 9. Connections Essential Skills 1. Recognize and use connections among mathematical ideas 2. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole 3. Recognize and apply mathematics in contexts outside of mathematics . 10. Representation K-12 Essential Skills 1. Create and use representations to organize, record, and communicate mathematical ideas 2. Select, apply, and translate among mathematical representations to solve problems 3. Use representations to model and interpret physical, social, and mathematical phenomena
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