MST3.I.A Major Understanding 1 - Students will represent and analyze algebraically a wide variety of problem solving situations.
- Translate two-step verbal expressions into algebraic expressions|
MST3.I.A Major Understanding 2 - Students will perform algebraic procedures accurately.
- Add and subtract monomials with exponents of one|
- Identify a polynomial as an algebraic expression containing one or more terms
- Solve multi-step equations by combining like terms, using the
distributive property, or moving variables to one side of the equation
- Solve one-step inequalities (positive coefficients only) (See G.07.09)
- 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.
- Draw the graphic representation of a pattern that can be expressed , as an equation or from table of data|
- Create algebraic patterns using charts/tables, graphs, equations, and expressions
- Build a pattern to develop a rule for determining the sum of the interior angles of polygons
- 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.
- Provide a correct, complete, coherent, and clear rationale for thought process used in problem solving|
- Provide an organized argument which explains rationale for strategy selection
- 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.
- 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|
- Answer clarifying questions from others
MST3.I.CM Major Understanding 3 - Students will analyze and evaluate the mathematical thinking and strategies of others.
- Analyze mathematical solutions shared by other students|
- Compare strategies used and solutions found by others in relation to their own work
- 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.
- Increase their use of mathematical vocabulary and language when communicating with others|
- Use appropriate language, representations, and terminology when describing objects, relationships, mathematical solutions, and rationale
- 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.
- Understand and make connections among multiple representations of the same mathematical idea|
- Recognize connections between subsets of mathematical ideas
- 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.
- Model situations mathematically, using representations to draw conclusions and formulate new situations|
- 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.
- Recognize and provide examples of the presence of mathematics in their daily lives|
- Apply mathematics to solve problems situations that develop outside of mathematics
- Investigate the presence of mathematics in careers and areas or interest
- 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.
- Calculate the radius or diameter, given the circumference or area of a circle|
- Calculate the volume of prisms and cylinders, using a given formula and a calculator
- Identify the two-dimensional shapes that make up the faces and bases of three-dimensional shapes (prisms, cylinders, cones, and pyramids)
- 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.
- Identify the right angle, hypotenuse, and legs of a right triangle|
- Explore the relationship between the lengths of the three sides of a right triangle (Pythagorean Theorem)
- Find a missing angle when given angles of a quadrilateral
- Use the Pythagorean Theorem to determine the unknown length of a side of a right triangle
- 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.
- 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.
- Calculate distance using a map scale|
- Convert capacities and volumes within a given system
- Identify customary and metric units of mass
- Convert mass within a given system
- Calculate unit price using proportions
- Compare unit prices
- Convert money between different currencies with the use of an exchange rate table and calculator
- Draw central angles in a given circle using a protractor (circle graphs)
- Determine the tool and technique to measure with an appropriate level of precision:
MST3.I.M Major Understanding 3 - Students will develop strategies for estimating measurements.
- Identify the relationships between relative error and magnitude
when dealing with large numbers (e.g., money, population)|
- Estimate surface area
- Determine personal references for customary /metric units of mass
- 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.
- Distinguish between the various subsets of real numbers (counting/natural numbers, whole numbers, integers, rational numbers, irrational numbers)|
- Recognize the difference between rational and irrational numbers (e.g., explore different approximations of Pi)
- Place rational and irrational numbers (approximations) on a number line and justify the placement of the numbers
- Develop the laws of exponents for multiplication and division
- Write numbers in scientific notation
- Translate numbers from scientific notation into standard form
- Compare numbers written in scientific notation
- Find the common factors and greatest common factor of two or more numbers
- Determine multiples and least common multiple of two or more numbers
- 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.
- Simplify expressions using order of operations Note: Expressions may include absolute value and/or integral exponents greater than 0|
- Add and subtract integers
- Multiply and divide integers
- Add and subtract two integers (with and without the use of a number line)
- 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)
- Recognize and state the value of the square root of a perfect square (up to 225)
- Determine the square root of non-perfect squares using a calculator
- Classify irrational numbers as non-repeating/non-terminating decimals
MST3.I.N Major Understanding 3 - Students will compute accurately and make reasonable estimates.
- 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)|
- 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.
- Use a variety of strategies to understand new mathematical content and to develop more efficient methods|
- Construct appropriate extensions to problem situations
- 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.
- Observe patterns and formulate generalizations|
- Make conjectures from generalizations
- 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.
- Understand that there is no one right way to solve mathematical problem but that different methods have advantages and disadvantages|
- Understand how to break a complex problem into simpler
parts or use a similar problem type to solve a problem
- Work backwards from a solution
- Use proportionality to model problems
- 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.
- Interpret solutions within the given constraints of a
- Set expectations and limits for possible solutions
- Determine information required to solve the problem
- Choose methods for obtaining required information
- Justify solution methods through logical argument
- 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.
- Use physical objects, drawings, charts, tables, graphs, symbols, equations or objects created using technology as representations|
- Explain, describe, and defend mathematical ideas using representations
- Recognize, compare, and use an array of representational forms
- Explain how different representations express the same relationship
- 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.
- Use representations to explore problem situations|
- Investigate relationships between different representations and their impact on a given problem
- 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
- Use mathematics to show and understand physical phenomena
(e.g., make and interpret scale drawings of figures or scale models of objects)|
- Use mathematics to show and understand social phenomena (e.g., determine profit from sale of yearbooks)
- 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.
- 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.
- Use mathematical strategies to reach a conclusion|
- 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.
- Provide supportive arguments for conjectures|
- Develop, verify, and explain an argument, using appropriate mathematical ideas and language
- Support an argument by using a systematic approach to test more than one case
- 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.
- 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.
- Identify and collect data using a variety of methods|
- Display data in a circle graph
- Convert raw data into double bar graphs and double line graphs
- Calculate the range for a given set of data
- Select the appropriate measure of central tendency
- 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.
- Identify and explain misleading statistics and graphs|
MST3.I.S Major Understanding 3 - Students will understand and apply concepts of probability.
- Interpret data to provide the basis for predictions and to establish experimental probabilities|
- Determine the validity of sampling methods to predict outcomes
- Predict the outcome of an experiment
- Design and conduct an experiment to test predictions
- Compare actual results to predicted results