7.PS.1 Use a variety of strategies to understand new mathematical content and to develop more efficient methods

7.PS.2 Construct appropriate extensions to problem situations 7.PS.3 Understand and demonstrate how written symbols represent mathematical ideas

7.PS.4 Observe patterns and formulate generalizations

7.PS.5 Make conjectures from generalizations 7.PS.6 Represent problem situations verbally, numerically, algebraically, and graphically

7.PS.7 Understand that there is no one right way to solve mathematical problems but that different methods have advantages and disadvantages

7.PS.8 Understand how to break a complex problem into simpler parts or use a similar problem type to solve a problem 7.PS.9 Work backwards from a solution 7.PS.10 Use proportionality to model problems 7.PS.11 Work in collaboration with others to solve problems

7.PS.12 Interpret solutions within the given constraints of a problem 7.PS.13 Set expectations and limits for possible solutions 7.PS.14 Determine information required to solve the problem 7.PS.15 Choose methods for obtaining required information 7.PS.16 Justify solution methods through logical argument 7.PS.17 Evaluate the efficiency of different representations of a problem

7.RP.1 Recognize that mathematical ideas can be supported by a variety of strategies

7.RP.2 Use mathematical strategies to reach a conclusion 7.RP.3 Evaluate conjectures by distinguishing relevant from irrelevant information to reach a conclusion or make appropriate estimates

7.RP.4 Provide supportive arguments for conjectures 7.RP.5 Develop, verify, and explain an argument, using appropriate mathematical ideas and language

7.RP.6 Support an argument by using a systematic approach to test more than one case 7.RP.7 Devise ways to verify results or use counterexamples to refute incorrect statements 7.RP.8 Apply inductive reasoning in making and supporting mathematical conjectures

7.CM.1 Provide a correct, complete, coherent, and clear rationale for thought process used in problem solving

7.CM.2 Provide an organized argument which explains rationale for strategy selection

7.CM.3 Organize and accurately label work

7.CM.4 Share organized mathematical ideas through the manipulation of objects, numerical tables, drawings, pictures, charts, graphs, tables, diagrams, models and symbols in written and verbal form 7.CM.5 Answer clarifying questions from others

7.CM.6 Analyze mathematical solutions shared by others 7.CM.7 Compare strategies used and solutions found by others in relation to their own work

7.CM.8 Formulate mathematical questions that elicit, extend, or challenge strategies, solutions, and/or conjectures of others

7.CM.9 Increase their use of mathematical vocabulary and language when communicating with others 7.CM.10 Use appropriate language, representations, and terminology when describing objects, relationships, mathematical solutions, and rationale 7.CM.11 Draw conclusions about mathematical ideas through decoding, comprehension, and interpretation of mathematical visuals, symbols, and technical writing

7.CN.1 Understand and make connections among multiple representations of the same mathematical idea

7.CN.2 Recognize connections between subsets of mathematical ideas 7.CN.3 Connect and apply a variety of strategies to solve problems

7.CN.4 Model situations mathematically, using representations to draw conclusions and formulate new situations 7.CN.5

Understand how concepts, procedures, and mathematical results in one area of mathematics can be used to solve problems in other areas of mathematics

7.CN.6 Recognize and provide examples of the presence of mathematics in their daily lives 7.CN.7 Apply mathematical ideas to problem situations that develop outside of mathematics 7.CN.8 Investigate the presence of mathematics in careers and areas of interest 7.CN.9 Recognize and apply mathematics to other disciplines, areas of interest, and societal issues

7.R.1 Use physical objects, drawings, charts, tables, graphs, symbols, equations, or objects created using technology as representations 7.R.2 Explain, describe, and defend mathematical ideas using representations 7.R.3 Recognize, compare, and use an array of representational forms 7.R.4 Explain how different representations express the same relationship 7.R.5 Use standard and non-standard representations with accuracy and detail

7.R.6 Use representations to explore problem situations 7.R.7 Investigate relationships between different representations and their impact on a given problem 7.R.8 Use representation as a tool for exploring and understanding mathematical ideas

7.R.9 Use math to show and understand physical phenomena (e.g., make and interpret scale drawings of figures or scale models of objects) 7.R.10 Use math to show and understand social phenomena (e.g., determine profit from sale of yearbooks) 7.R.11 Use math to show and understand mathematical phenomena (e.g., use tables, graphs, and equations to show a pattern underlying a function)

*Number Systems *

7.N.1 Distinguish between the various subsets of real numbers (counting/natural numbers, whole numbers, integers, rational numbers, and irrational numbers) 7.N.2 Recognize the difference between rational and irrational numbers (e.g., explore different approximations of )

7.N.3 Place rational and irrational numbers (approximations) on a number line and justify the placement of the 7.N.4 Develop the laws of exponents for multiplication and division 7.N.5 Write numbers in scientific notation 7.N.6 Translate numbers from scientific notation into standard form 7.N.7 Compare numbers written in scientific notation

*Number Theory *

7.N.8 Find the common factors and greatest common factor of two or more numbers

7.N.9 Determine multiples and least common multiple of two or more numbers

7.N.10 Determine the prime factorization of a given number and write in exponential form

*Operations *

7.N.11 Simplify expressions using order of operations (Note: Expressions may include absolute value and/or integral exponents greater than 0.) 7.N.12 Add, subtract, multiply, and divide integers 7.N.13 Add and subtract two integers (with and without the use of a number line) 7.N.14 Develop a conceptual understanding of negative and zero exponents with a base of ten and relate to fractions and decimals (e.g., 10

^{-2}= .01 = 1/100)7.N.15 Recognize and state the value of the square root of a perfect square (up to 225) 7.N.16 Determine the square root of non-perfect squares using a calculator 7.N.17 Classify irrational numbers as non-repeating/non-terminating decimals

Estimation

7.N.18 Identify the two consecutive whole numbers between which the square root of a non-perfect square whole number less than 225 lies (with and without the use of a number line)

7.N.19 Justify the reasonableness of answers using estimation

7.A.1 Translate two-step verbal expressions into algebraic expressions

*
Students will perform algebraic procedures accurately. *

7.A.2 | Add and subtract monomials with exponents of one | |

7.A.3 | Identify a polynomial as an algebraic expression containing one or more terms |

7.A.4 Solve multi-step equations by combining like terms, using the distributive property, or moving variables to one side of the equation 7.A.5 Solve one-step inequalities (positive coefficients only) (See 7.G.10) 7.A.6 Evaluate formulas for given input values (surface area, rate, and density problems)

*Patterns, Relations, and Functions*

7.A.7 Draw the graphic representation of a pattern from an equation or from a table of data

7.A.8 Create algebraic patterns using charts/tables, graphs, equations, and expressions 7.A.9 Build a pattern to develop a rule for determining the sum of the interior angles of polygons 7.A.10 Write an equation to represent a function from a table of values

7.G.1 Calculate the radius or diameter, given the circumference or area of a circle 7.G.2 Calculate the volume of prisms and cylinders, using a given formula and a calculator 7.G.3 Identify the two-dimensional shapes that make up the faces and bases of three-dimensional shapes (prisms, cylinders, cones, and pyramids) 7.G.4 Determine the surface area of prisms and cylinders, using a calculator and a variety of methods

7.G.5 Identify the right angle, hypotenuse, and legs of a right triangle 7.G.6 Explore the relationship between the lengths of the three sides of a right triangle to develop the Pythagorean Theorem 7.G.7 Find a missing angle when given angles of a quadrilateral 7.G.8 Use the Pythagorean Theorem to determine the unknown length of a side of a right triangle 7.G.9 Determine whether a given triangle is a right triangle by applying the Pythagorean Theorem and using a calculator

*Students
will apply coordinate geometry to analyze problem solving situations.
*

*Coordinate Geometry*

7.G.10 |
Graph the solution set of an inequality (positive coefficients only) on a number line (See 7.A.5) |

7.M.1 Calculate distance using a map scale 7.M.2 Convert capacities and volumes within a given system 7.M.3 Identify customary and metric units of mass 7.M.4 Convert mass within a given system 7.M.4 Calculate unit price using proportions 7.M.4 Compare unit prices 7.M.4 Convert money between different currencies with the use of an exchange rate table and a calculator 7.M.4 Draw central angles in a given circle using a protractor (circle graphs)

*Tools and Methods *

7.M.9 Determine the tool and technique to measure with an appropriate level of precision: mass

7.M.10 Identify the relationships between relative error and magnitude when dealing with large numbers (e.g., money, population) 7.M.11 Estimate surface area 7.M.12 Determine personal references for customary /metric units of mass 7.M.13 Justify the reasonableness of the mass of an object

7.S.1 Identify and collect data using a variety of methods

*Organization and Display of Data*

7.S.2 Display data in a circle graph

7.S.3 Convert raw data into double bar graphs and double line graphs

*Analysis of Data *

7.S.4 Calculate the range for a given set of data 7.S.5 Select the appropriate measure of central tendency 7.S.6 Read and interpret data represented graphically (pictograph, bar graph, histogram, line graph, double line/bar graphs or circle graph)

*Predictions from Data*

7.S.7 Identify and explain misleading statistics and graphs

7.S.8 Interpret data to provide the basis for predictions and to establish experimental probabilities 7.S.9 Determine the validity of sampling methods to predict outcomes 7.S.10 Predict the outcome of an experiment 7.S.11 Design and conduct an experiment to test predictions 7.S.12 Compare actual results to predicted results

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Table of
Contents |
Prekindergarten |
Kindergarten |
Grade 1 |
Grade 2 |
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Grade 3 |
Grade 4 |
Grade 5 |
Grade 6 | Grade 8 | ||

Integrated Algebra | Geometry | Algebra 2 and Trigonometry |

1/25/05