Math Curriculum - Grade 9 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 • Perform operations with scientific notation • Explain the effects of multiplication , division, and computing powers and roots on the magnitudes of quantities • Perform operations with real numbers accurately and efficiently, using mental computation or paper and pencil calculations for simple cases, and technology for more complicated cases • Develop and use strategies to estimate the results of rational number computations and judge the reasonableness of those results . 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 • Represent relations and linear and quadratic functions in various forms • Analyze functions of one variable by investigating rates of change, intercepts and zeros • Perform transformation such as arithmetically combining commonly used functions • Interpret representations of linear and quadratic functions • Identify the equivalent forms of expressions, equations, inequalities and relations • Write and solve equivalent forms of equations, inequalities and systems of equations • Use symbolic algebra to represent and explain mathematical relationships • Identify quantitative relationships in a situation and determine classes of functions that might model the relationship • Translate word problems into mathematical symbolic expressions • Judge the meaning usefulness, and reasonableness of solutions • 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 • Create and critique inductive and deductive arguments concerning geometric relationships with congruence, similarity, and the Pythagorean Theorem • Define the properties of known 2-D and 3-D objects • Use coordinate geometry to represent and examine the properties of geometric shapes • Use geometric models to represent and explain numerical and algebraic relationships • Identify and solve problems with rational and algebraic expressions using angles and/or parallel and perpendicular lines • Describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling, using coordinate geometry • Use 2-D representations of 3-D objects to visualize and solve problems involving surface area and volume of: prisms, cylinders, pyramids, cones, and spheres • Calculate missing measurements of similar figures using ratio and proportion • Apply the triangle congruency postulates and theorems to geometric proofs • Analyze properties and determine attributes of 2-D shapes • Use trigonometric relationships to determine lengths and angle measures • Use Cartesian coordinates and other coordinate systems, such as navigational, to analyze geometric situations • Investigate conjectures and solve problems involving 2-D shapes represented with Cartesian coordinates • Understand and represent translations, reflections, rotations, and dilations of objects in the plane by using sketches and coordinates • 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 • Select and compute with appropriate standard metric units to measure length, area, volume, weight, capacity, and temperature • Use common benchmarks to select appropriate methods for estimating measurements • Select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision • Use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and circles • Develop strategies to find the area of more complex shapes • Use strategies and formulas to determine the surface area and volume of selected prisms, pyramids, cylinders, and cones • Solve simple problems involving rates and derived measurements for such attributes as velocity and density • Analyze precision, accuracy and approximate error in measurement situations • 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 • Formulate questions, design studies, and collect data about a characteristic shared by two populations or different characteristics within one population • Understand histograms, parallel box plots, and scatterplots and use them to display data • Understand the differences among various kinds of studies and which types of inferences can legitimately be drawn from each • Use theoretical and experimental probability to form predictions . 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 other content areas • Exhibit a project that includes a flow chart or outline of a problem solving process . 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. Communications 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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