MST3.I.A Major Understanding 1 - Students will represent and analyze algebraically a wide variety of problem solving situations.
- Translate verbal sentences into algebraic inequalities|
- Write verbal expressions that match given mathematical expressions
- Describe a situation involving relationships that matches a given graph
- Create a graph given a description or an expression for a situation involving a linear or nonlinear relationship
- Use physical models to perform operations with polynomials
MST3.I.A Major Understanding 2 - Students will perform algebraic procedures accurately.
- Multiply monomials|
- Divide monomials
- Add and subtract polynomials (integer coefficients)
- Multiply a binomial by a monomial or a binomial (integer coefficients)
- Divide a polynomial by a monomial (integer coefficients) Note: The degree of the denominator is less than or equal to the degree of the numerator for all variables.
- Factor algebraic expressions using the GCF
- Factor a trinomial in the form ax squared + bx + c; a=1 and c having no more than three sets of factors
- Apply algebra to determine the measure of angles formed by or contained in parallel lines cut by a transversal and by intersecting lines
- Solve multi-step inequalities and graph the solution set on a number line
- Solve linear inequalities by combining like terms, using the distributive property, or moving variables to one side of the inequality (include multiplication or division of inequalities by a negative number)
MST3.I.A Major Understanding 3 - Students will recognize, use, and represent algebraically patterns, relations, and functions.
- Understand that numerical information can be represented in multiple ways: arithmetically, algebraically, and graphically|
- Find a set of ordered pairs to satisfy a given linear numerical pattern (expressed algebraically); then plot the ordered pairs and draw the line
- Define and use correct terminology when referring to function (domain and range)
- Determine if a relation is a function
- Interpret multiple representations using equation, table of values, and graph
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.
- Use 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.
- Construct the following using a straight edge and compass:
Segment congruent to a segment
Angle congruent to an angle
MST3.I.G Major Understanding 2 - Students will identify and justify geometric relationships, formally and informally.
- Identify pairs of vertical angles as congruent|
- Identify pairs of supplementary and complementary angles
- Calculate the missing angle in a supplementary or complementary pair
- Determine angle pair relationships when given two parallel lines cut by a transversal
- Calculate the missing angle measurements when given two parallel lines cut by a transversal
- Calculate the missing angle measurements when given two intersecting lines and an angle
MST3.I.G Major Understanding 3 - Students will apply transformations and symmetry to analyze problem solving situations.
- Describe and identify transformations in the plane, using proper function notation (rotations, reflections, translations, and dilations)|
- Draw the image of a figure under rotations of 90 and 180 degrees
- Draw the image of a figure under a reflection over a given line
- Draw the image of a figure under a translation
- Draw the image of a figure under a dilation
- Identify the properties preserved and not preserved under a reflection, rotation, translation, and dilation
MST3.I.G Major Understanding 4 - Students will apply coordinate geometry to analyze problem solving situations.
- Determine the slope of a line from a graph and explain the meaning of slope as a constant rate of change|
- Determine the y-intercept of a line from a graph and be able to explain the y-intercept
- Graph a line using a table of values
- Determine the equation of a line given the slope and the y-intercept
- Graph a line from an equation in slope-intercept form (y = mx + b )
- Solve systems of equations graphically (only linear, integral solutions, y = mx + b format, no vertical/horizontal lines)
- Graph the solution set of an inequality on a number line
- Distinguish between linear and nonlinear equations ax² + bx + c; a=1 (only graphically)
- Recognize the characteristics of quadratics in tables, graphs, equations, and situations
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.
- Solve equations/proportions to convert to equivalent measurements within metric and customary measurement systems
Note: Also allow Fahrenheit to Celsius and vice versa|
MST3.N CONTENT STRAND 1 - Number Sense & Operations
MST3.I.N Major Understanding 2 - Students will understand meanings of operations and procedures, and how they relate to one another.
- Develop and apply the laws of exponents for multiplication and division|
- Evaluate expressions with integral exponents
- Read, write, and identify percents less than 1% and greater than 100%
- Apply percents to: Tax
MST3.I.N Major Understanding 3 - Students will compute accurately and make reasonable estimates.
- Estimate a percent of quantity, given an application|
- 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 problem|
- 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 from 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|