Math Curriculum - Seventh Grade also available as a printable PDF . 1. Number and Operations Essential 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 them to solutions. Important to Know: • Solve word problems using decimals, fractions and mixed numbers • Compare and order decimals, fractions, and mixed numbers efficiently and find their approximate locations on a number line • Use factors, multiples, and prime factorizations to solve problems • Explain the effects of arithmetic operations with decimals, fractions, and mixed numbers • Use the associative and commutative properties of addition and multiplication and distributive property of multiplication over addition to simplify computations with decimals, fractions, and mixed numbers • Use integers to represent and compare quantities • Explain the effects of arithmetic operations with integers • Use inverse relationships of addition /subtraction, multiplication/division to simplify computations and solve problems • Use a variety of methods and tools for computing with decimals, fractions, and mixed numbers that include: mental computation, estimation, calculators or computers, and paper and pencil • Evaluate any whole number to any whole number exponent • Compute efficiently with decimals, fractions, mixed numbers, and integers • Recognize and generalize equivalent representations for any fraction . 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: • Use parentheses accurately to group numbers for applying operations • Apply formulas to problem situations • Describe problems involving ratios, proportions, and percents with algebraic expressions • Solve linear equations with one variable using +, -, x, / • Evaluate algebraic expressions • Interpret graphs of problem situations describing linear relationships • Construct graphs describing real world problems; and assign and label scales to axes • Construct tables to describe a linear problem situation • Write a linear equation to represent a real world problem • Symbolize, using variables, the relations between addition, subtraction, multiplication, and division . 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: • Describe and classify relationships among 3 to 10 sided polygons using their properties • Describe the simple shapes within a complex shape • Define acute, right, obtuse and straight angles • Plot known quadrilaterals on the coordinate plane and examine their characteristics • Describe sizes, positions, and orientations of shapes under the following informal transformations: flips, turns, slides and scaling • Identify line and rotational symmetry of regular polygons • Recognize known shapes from different perspectives • Draw quadrilaterals using specified properties (side lengths and angle measurements) • Draw 2-D representations of prisms, pyramids, cones, spheres, and cylinders v Recognize and apply geometric ideas and relationships in areas outside the mathematics classroom, such as art, science and everyday life . 4. Measurement Essential Skills: 1. Understand measurable attributes of objects and the units, systems, and processes of measurement 2. Apply appropriate techniques, tools, and formulas to determine measurements 3. Use paper and pencil to demonstrate skills prior to using technology Important to Know: • Select and compute with appropriate standard metric units to measure length, area, volume, weight, capacity, and temperature • Use a protractor to measure angles through 360 degrees • Understand relationships among units and convert from one unit to another within the same system • 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 consistent units of measure in problem solving . 5. Data Management and 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: • Select, create, and use appropriate graphical representations of data including double bar and stacked bar graphs • Use mean, median, mode in problem solving and data analysis • Represent probability as a ratio from 0 through 1 • Compare probable outcomes within an experiment • 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, work 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 . 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 K-12 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 phenomenon
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