Core Curriculum

MST3 Standard 3 - Mathematics
Students will: •understand the concepts of and become proficient with the skills of mathematics; •communicate and reason mathematically; •become problem solvers by using appropriate tools and strategies; through the integrated study of number sense and operations, algebra, geometry, measurement, and statistics and probability.

MST3.A CONTENT STRAND 2 - Algebra

MST3.I.A Major Understanding 1 - Students will represent and analyze algebraically a wide variety of problem solving situations.

 MST3.I.A.07.01 - Translate two-step verbal expressions into algebraic expressions

MST3.I.A Major Understanding 2 - Students will perform algebraic procedures accurately.

 MST3.I.A.07.02 - Add and subtract monomials with exponents of one MST3.I.A.07.03 - Identify a polynomial as an algebraic expression containing one or more terms MST3.I.A.07.04 - Solve multi-step equations by combining like terms, using the distributive property, or moving variables to one side of the equation MST3.I.A.07.05 - Solve one-step inequalities (positive coefficients only) (See G.07.09) MST3.I.A.07.06 - Evaluate formulas for given input values (surface area, rate, and density problems)

MST3.I.A Major Understanding 3 - Students will recognize, use, and represent algebraically patterns, relations, and functions.

 MST3.I.A.07.07 - Draw the graphic representation of a pattern that can be expressed , as an equation or from table of data MST3.I.A.07.08 - Create algebraic patterns using charts/tables, graphs, equations, and expressions MST3.I.A.07.09 - Build a pattern to develop a rule for determining the sum of the interior angles of polygons MST3.I.A.07.10 - Write an equation to represent a function from a table of values

MST3.CM PROCESS STRAND 3 - Communication

MST3.I.CM Major Understanding 1 - Students will organize and consolidate their mathematical thinking through communication.

 MST3.I.CM.07.01 - Provide a correct, complete, coherent, and clear rationale for thought process used in problem solving MST3.I.CM.07.02 - Provide an organized argument which explains rationale for strategy selection MST3.I.CM.07.03 - Organize and accurately label work

MST3.I.CM Major Understanding 2 - Students will communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

 MST3.I.CM.07.04 - Using both written and verbal form to share organized mathematical ideas through the manipulation of objects, numerical tables, drawings, pictures, charts, graphs, tables, diagrams, models, and symbols MST3.I.CM.07.05 - Answer clarifying questions from others

MST3.I.CM Major Understanding 3 - Students will analyze and evaluate the mathematical thinking and strategies of others.

 MST3.I.CM.07.06 - Analyze mathematical solutions shared by other students MST3.I.CM.07.07 - Compare strategies used and solutions found by others in relation to their own work MST3.I.CM.07.08 - Formulate mathematical questions that elicit, extend, or challenge strategies, solutions, and/or conjectures of others

MST3.I.CM Major Understanding 4 - Students will use the language of mathematics to express mathematical ideas precisely.

 MST3.I.CM.07.09 - Increase their use of mathematical vocabulary and language when communicating with others MST3.I.CM.07.10 - Use appropriate language, representations, and terminology when describing objects, relationships, mathematical solutions, and rationale MST3.I.CM.07.11 - Draw conclusions about mathematical ideas through decoding, comprehension, and interpretation of mathematical visuals, symbols, and technical writing

MST3.CN PROCESS STRAND 4 - Connections

MST3.I.CN Major Understanding 1 - Students will recognize and use connections among mathematical ideas.

 MST3.I.CN.07.01 - Understand and make connections among multiple representations of the same mathematical idea MST3.I.CN.07.02 - Recognize connections between subsets of mathematical ideas MST3.I.CN.07.03 - Connect and apply a variety of strategies to solve problems

MST3.I.CN Major Understanding 2 - Students will understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

 MST3.I.CN.07.04 - Model situations mathematically, using representations to draw conclusions and formulate new situations MST3.I.CN.07.05 - Understand how concepts, procedures, and mathematical results in one area of mathematics can be used to solve problems in other areas of mathematics

MST3.I.CN Major Understanding 3 - Students will recognize and apply mathematics in contexts outside of mathematics.

 MST3.I.CN.07.06 - Recognize and provide examples of the presence of mathematics in their daily lives MST3.I.CN.07.07 - Apply mathematics to solve problems situations that develop outside of mathematics MST3.I.CN.07.08 - Investigate the presence of mathematics in careers and areas or interest MST3.I.CN.07.09 - Recognize and apply mathematics to other disciplines and areas of interest and societal issues

MST3.G CONTENT STRAND 3 - Geometry

MST3.I.G Major Understanding 1 - Students will use visualization and spatial reasoning to analyze characteristics and properties of geometric shapes.

 MST3.I.G.07.01 - Calculate the radius or diameter, given the circumference or area of a circle MST3.I.G.07.02 - Calculate the volume of prisms and cylinders, using a given formula and a calculator MST3.I.G.07.03 - Identify the two-dimensional shapes that make up the faces and bases of three-dimensional shapes (prisms, cylinders, cones, and pyramids) MST3.I.G.07.04 - Determine the surface area of prisms and cylinders, using a calculator and a variety of methods

MST3.I.G Major Understanding 2 - Students will identify and justify geometric relationships, formally and informally.

 MST3.I.G.07.05 - Identify the right angle, hypotenuse, and legs of a right triangle MST3.I.G.07.06 - Explore the relationship between the lengths of the three sides of a right triangle (Pythagorean Theorem) MST3.I.G.07.07 - Find a missing angle when given angles of a quadrilateral MST3.I.G.07.08 - Use the Pythagorean Theorem to determine the unknown length of a side of a right triangle MST3.I.G.07.09 - Determine whether a given triangle is a right triangle by applying the Pythagorean Theorem and using a calculator

MST3.I.G Major Understanding 4 - Students will apply coordinate geometry to analyze problem solving situations.

 MST3.I.G.07.10 - Graph the solution set of an inequality (positive coefficients only) on a number line (See A.07.05)

MST3.M CONTENT STRAND 4 - Measurement

MST3.I.M Major Understanding 1 - Students will determine what can be measured and how, using appropriate methods and formulas.

 MST3.I.M.07.01 - Calculate distance using a map scale MST3.I.M.07.02 - Convert capacities and volumes within a given system MST3.I.M.07.03 - Identify customary and metric units of mass MST3.I.M.07.04 - Convert mass within a given system MST3.I.M.07.05 - Calculate unit price using proportions MST3.I.M.07.06 - Compare unit prices MST3.I.M.07.07 - Convert money between different currencies with the use of an exchange rate table and calculator MST3.I.M.07.08 - Draw central angles in a given circle using a protractor (circle graphs) MST3.I.M.07.09 - Determine the tool and technique to measure with an appropriate level of precision: mass

MST3.I.M Major Understanding 3 - Students will develop strategies for estimating measurements.

 MST3.I.M.07.10 - Identify the relationships between relative error and magnitude when dealing with large numbers (e.g., money, population) MST3.I.M.07.11 - Estimate surface area MST3.I.M.07.12 - Determine personal references for customary /metric units of mass MST3.I.M.07.13 - Justify the reasonableness of mass of an object

MST3.N CONTENT STRAND 1 - Number Sense & Operations

MST3.I.N Major Understanding 1 - Students will understand numbers, multiple ways of representing numbers, relationships among numbers, and number systems.

 MST3.I.N.07.01 - Distinguish between the various subsets of real numbers (counting/natural numbers, whole numbers, integers, rational numbers, irrational numbers) MST3.I.N.07.02 - Recognize the difference between rational and irrational numbers (e.g., explore different approximations of Pi) MST3.I.N.07.03 - Place rational and irrational numbers (approximations) on a number line and justify the placement of the numbers MST3.I.N.07.04 - Develop the laws of exponents for multiplication and division MST3.I.N.07.05 - Write numbers in scientific notation MST3.I.N.07.06 - Translate numbers from scientific notation into standard form MST3.I.N.07.07 - Compare numbers written in scientific notation MST3.I.N.07.08 - Find the common factors and greatest common factor of two or more numbers MST3.I.N.07.09 - Determine multiples and least common multiple of two or more numbers MST3.I.N.07.10 - Determine the prime factorization of a given number and write in exponential form

MST3.I.N Major Understanding 2 - Students will understand meanings of operations and procedures, and how they relate to one another.

 MST3.I.N.07.11 - Simplify expressions using order of operations Note: Expressions may include absolute value and/or integral exponents greater than 0 MST3.I.N.07.12A - Add and subtract integers MST3.I.N.07.12B - Multiply and divide integers MST3.I.N.07.13 - Add and subtract two integers (with and without the use of a number line) MST3.I.N.07.14 - Develop a conceptual understanding of negative and zero exponents with a base of ten and relate to fractions and decimals (e.g., 10 to the negative second power = .01 = 1/100) MST3.I.N.07.15 - Recognize and state the value of the square root of a perfect square (up to 225) MST3.I.N.07.16 - Determine the square root of non-perfect squares using a calculator MST3.I.N.07.17 - Classify irrational numbers as non-repeating/non-terminating decimals

MST3.I.N Major Understanding 3 - Students will compute accurately and make reasonable estimates.

 MST3.I.N.07.18 - Identify the two consecutive integers 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) MST3.I.N.07.19 - Justify the reasonableness of answers using estimation

MST3.PS PROCESS STRAND 1 - Problem Solving

MST3.I.PS Major Understanding 1 - Students will build new mathematical knowledge through problem solving.

 MST3.I.PS.07.01 - Use a variety of strategies to understand new mathematical content and to develop more efficient methods MST3.I.PS.07.02 - Construct appropriate extensions to problem situations MST3.I.PS.07.03 - Understand and demonstrate how written symbols represent mathematical ideas

MST3.I.PS Major Understanding 2 - Students will solve problems that arise in mathematics and in other contexts.

 MST3.I.PS.07.04 - Observe patterns and formulate generalizations MST3.I.PS.07.05 - Make conjectures from generalizations MST3.I.PS.07.06 - Represent problem situations verbally, numerically, algebraically, and graphically

MST3.I.PS Major Understanding 3 - Students will apply and adapt a variety of appropriate strategies to solve problems.

 MST3.I.PS.07.07 - Understand that there is no one right way to solve mathematical problem but that different methods have advantages and disadvantages MST3.I.PS.07.08 - Understand how to break a complex problem into simpler parts or use a similar problem type to solve a problem MST3.I.PS.07.09 - Work backwards from a solution MST3.I.PS.07.10 - Use proportionality to model problems MST3.I.PS.07.11 - Work in collaboration with others to solve problems

MST3.I.PS Major Understanding 4 - Students will monitor and reflect on the process of mathematical problem solving.

 MST3.I.PS.07.12 - Interpret solutions within the given constraints of a problem MST3.I.PS.07.13 - Set expectations and limits for possible solutions MST3.I.PS.07.14 - Determine information required to solve the problem MST3.I.PS.07.15 - Choose methods for obtaining required information MST3.I.PS.07.16 - Justify solution methods through logical argument MST3.I.PS.07.17 - Evaluate the efficiency of different representations of a problem

MST3.R PROCESS STRAND 5 - Representation

MST3.I.R Major Understanding 1 - Students will create and use representations to organize, record, and communicate mathematical ideas.

 MST3.I.R.07.01 - Use physical objects, drawings, charts, tables, graphs, symbols, equations or objects created using technology as representations MST3.I.R.07.02 - Explain, describe, and defend mathematical ideas using representations MST3.I.R.07.03 - Recognize, compare, and use an array of representational forms MST3.I.R.07.04 - Explain how different representations express the same relationship MST3.I.R.07.05 - Use standard and nonstandard representations with accuracy and detail

MST3.I.R Major Understanding 2 - Students will select, apply, translate among mathematical representations to solve problems.

 MST3.I.R.07.06 - Use representations to explore problem situations MST3.I.R.07.07 - Investigate relationships between different representations and their impact on a given problem MST3.I.R.07.08 - Use representation as a tool for exploring and understanding mathematical ideas

MST3.I.R Major Understanding 3 - Students will use representations to model and interpret physical, social, and mathematical phenomena

 MST3.I.R.07.09 - Use mathematics to show and understand physical phenomena (e.g., make and interpret scale drawings of figures or scale models of objects) MST3.I.R.07.10 - Use mathematics to show and understand social phenomena (e.g., determine profit from sale of yearbooks) MST3.I.R.07.11 - Use mathematics to show and understand mathematical phenomena (e.g., use tables graphs, and equations to show a pattern underlying a function)

MST3.RP PROCESS STRAND 2 - Reasoning & Proof

MST3.I.RP Major Understanding 1 - Students will recognize reasoning and proof as fundamental aspects of mathematics.

 MST3.I.RP.07.01 - Recognize that mathematical ideas can be supported using a variety of strategies

MST3.I.RP Major Understanding 2 - Students will make and investigate mathematical conjectures.

 MST3.I.RP.07.02 - Use mathematical strategies to reach a conclusion MST3.I.RP.07.03 - Evaluate conjectures by distinguishing relevant and irrelevant information to reach a conclusion or make appropriate estimates

MST3.I.PS Major Understanding 3 - Students will develop and evaluate mathematical arguments and proofs.

 MST3.I.RP.07.04 - Provide supportive arguments for conjectures MST3.I.RP.07.05 - Develop, verify, and explain an argument, using appropriate mathematical ideas and language MST3.I.RP.07.06 - Support an argument by using a systematic approach to test more than one case MST3.I.RP.07.07 - Devise ways to verify results or use counterexamples to refute incorrect statements

MST3.I.RP Major Understanding 4 - Students will select and use various types of reasoning and methods of proof.

 MST3.I.RP.07.08 - Apply inductive reasoning in making and supporting mathematical conjectures

MST3.S CONTENT STRAND 5 - Statistics and Probability

MST3.I.S Major Understanding 1 - Students will collect, organize, display, and analyze data.

 MST3.I.S.07.01 - Identify and collect data using a variety of methods MST3.I.S.07.02 - Display data in a circle graph MST3.I.S.07.03 - Convert raw data into double bar graphs and double line graphs MST3.I.S.07.04 - Calculate the range for a given set of data MST3.I.S.07.05 - Select the appropriate measure of central tendency MST3.I.S.07.06 - Read and interpret data represented graphically (pictograph, bar graph, histogram, line graph, double line/bar graphs or circle graph)

MST3.I.S Major Understanding 2 - Students will make predictions that are based upon data analysis.

 MST3.I.S.07.07 - Identify and explain misleading statistics and graphs

MST3.I.S Major Understanding 3 - Students will understand and apply concepts of probability.

 MST3.I.S.07.08 - Interpret data to provide the basis for predictions and to establish experimental probabilities MST3.I.S.07.09 - Determine the validity of sampling methods to predict outcomes MST3.I.S.07.10 - Predict the outcome of an experiment MST3.I.S.07.11 - Design and conduct an experiment to test predictions MST3.I.S.07.12 - Compare actual results to predicted results

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