MST Standard 3 Math:
Grade 7
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Through the integrated study of number sense and operations, algebra, geometry, measurement,
and statistics and probability, 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;
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Algebra
Students will represent and analyze algebraically a wide variety of problem solving situations.
Variables and Expressions
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7.A.1 |
Translate two-step verbal expressions into algebraic expressions
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Algebra
Students will perform algebraic procedures accurately.
Equations and Inequalities
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7.A.6 |
Evaluate formulas for given input values (surface area, rate, and density problems)
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7.A.5 |
Solve one-step inequalities (positive coefficients only) (See 7.G.10)
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7.A.4 |
Solve multi-step equations by combining like terms, using the distributive property, or moving variables to one side of the equation
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Algebra
Students will recognize, use, and represent algebraically patterns, relations, and functions.
Patterns, Relations, and Functions
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7.A.8 |
Create algebraic patterns using charts/tables, graphs, equations, and expressions
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7.A.9 |
Build a pattern to develop a rule for determining the sum of the interior angles of polygons
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7.A.10 |
Write an equation to represent a function from a table of values
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7.A.7 |
Draw the graphic representation of a pattern from an equation
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Algebra
Students will perform algebraic procedures accurately.
Variables and Expressions
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7.A.2 |
Add and subtract monomials with exponents of one
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7.A.3 |
Identify a polynomial as an algebraic expression containing one or more terms
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Communication
Students will organize and consolidate their mathematical thinking through communication.
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7.CM.2 |
Provide an organized argument which explains rationale for strategy selection
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7.CM.3 |
Organize and accurately label work
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7.CM.1 |
Provide a correct, complete, coherent, and clear rationale for thought process used in problem solving
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Communication
Students will communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
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7.CM.5 |
Answer clarifying questions from others
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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
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Communication
Students will analyze and evaluate the mathematical thinking and strategies of others.
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7.CM.8 |
Formulate mathematical questions that elicit, extend, or challenge strategies, solutions, and/or conjectures of others
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7.CM.7 |
Compare strategies used and solutions found by others in relation to their own work
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7.CM.6 |
Analyze mathematical solutions shared by others
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Communication
Students will use the language of mathematics to express mathematical ideas precisely.
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7.CM.11 |
Draw conclusions about mathematical ideas through decoding, comprehension, and interpretation of mathematical visuals, symbols, and technical writing
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7.CM.10 |
Use appropriate language, representations, and terminology when describing objects, relationships, mathematical solutions, and rationale
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7.CM.9 |
Increase their use of mathematical vocabulary and language when communicating with others
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Connections
Students will recognize and use connections among mathematical ideas.
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7.CN.3 |
Connect and apply a variety of strategies to solve problems
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7.CN.2 |
Recognize connections between subsets of mathematical ideas
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7.CN.1 |
Understand and make connections among multiple representations of the same mathematical idea
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Connections
Students will understand how mathematical ideas interconnect and build on one another to produce a coherent whole.
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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
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7.CN.4 |
Model situations mathematically, using representations to draw conclusions and formulate new situations
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Connections
Students will recognize and apply mathematics in contexts outside of mathematics.
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7.CN.9 |
Recognize and apply mathematics to other disciplines, areas of interest, and societal issues
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7.CN.6 |
Recognize and provide examples of the presence of mathematics in their daily lives
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7.CN.8 |
Investigate the presence of mathematics in careers and areas of interest
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7.CN.7 |
Apply mathematical ideas to problem situations that develop outside of mathematics
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Geometry
Students will use visualization and spatial reasoning to analyze characteristics and properties of geometric shapes.
Shapes
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7.G.1 |
Calculate the radius or diameter, given the circumference or area of a circle
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7.G.2 |
Calculate the volume of prisms and cylinders, using a given formula and a calculator
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7.G.3 |
Identify the two-dimensional shapes that make up the faces and bases of three-dimensional shapes (prisms, cylinders, cones, and pyramids)
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7.G.4 |
Determine the surface area of prisms and cylinders, using a calculator and a variety of methods
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Geometry
Students will identify and justify geometric relationships, formally and informally.
Geometric Relationships
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7.G.5 |
Identify the right angle, hypotenuse, and legs of a right triangle
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7.G.6 |
Explore the relationship between the lengths of the three sides of a right triangle to develop the Pythagorean Theorem
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7.G.7 |
Find a missing angle when given angles of a quadrilateral
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7.G.8 |
Use the Pythagorean Theorem to determine the unknown length of a side of a right triangle
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7.G.9 |
Determine whether a given triangle is a right triangle by applying the Pythagorean Theorem and using a calculator
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Geometry
Students will apply coordinate geometry to analyze problem solving situations.
Coordinate Geometry
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7.G.10 |
Graph the solution set of an inequality (positive coefficients only) on a number line (See 7.A.5)
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Measurement
Students will determine what can be measured and how, using appropriate methods and formulas.
Units of Measurement
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7.M.3 |
Identify customary and metric units of mass
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7.M.4 |
Convert mass within a given system
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7.M.5 |
Calculate unit price using proportions
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7.M.6 |
Compare unit prices
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7.M.7 |
Convert money between different currencies with the use of an exchange rate table and a calculator
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7.M.8 |
Draw central angles in a given circle using a protractor (circle graphs)
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7.M.2 |
Convert capacities and volumes within a given system
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7.M.1 |
Calculate distance using a map scale
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Measurement
Students will determine what can be measured and how, using appropriate methods and formulas.
Tools and Methods
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7.M.9 |
Determine the tool and technique to measure with an appropriate level of precision: mass
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Measurement
Students will develop strategies for estimating measurements.
Estimation
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7.M.10 |
Identify the relationships between relative error and magnitude when dealing with large numbers (e.g., money, population)
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7.M.11 |
Estimate surface area
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7.M.12 |
Determine personal references for customary /metric units of mass
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7.M.13 |
Justify the reasonableness of the mass of an object
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Number Sense and Operations
Students will understand numbers, multiple ways of representing numbers, relationships among numbers, and number systems.
Number Systems
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7.N.3 |
Place rational and irrational numbers (approximations) on a number line and justify the placement of the numbers
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7.N.4 |
Develop the laws of exponents for multiplication and division
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7.N.7 |
Compare numbers written in scientific notation
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7.N.6 |
Translate numbers from scientific notation into standard form
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7.N.5 |
Write numbers in scientific notation
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7.N.1 |
Distinguish between the various subsets of real numbers (counting/natural numbers, whole numbers, integers, rational numbers, and irrational numbers)
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7.N.2 |
Recognize the difference between rational and irrational numbers (e.g., explore different approximations of n)
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Number Sense and Operations
Students will understand numbers, multiple ways of representing numbers, relationships among numbers, and number systems.
Number Theory
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7.N.10 |
Determine the prime factorization of a given number and write in exponential form
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7.N.9 |
Determine multiples and least common multiple of two or more numbers
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7.N.8 |
Find the common factors and greatest common factor of two or more numbers
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Number Sense and Operations
Students will understand meanings of operations and procedures, and how they relate to one another.
Operations
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7.N.16 |
Determine the square root of non-perfect squares using a calculator
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7.N.17 |
Classify irrational numbers as non-repeating/non-terminating decimals
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7.N.15 |
Recognize and state the value of the square root of a perfect square (up to 225)
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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)
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7.N.13 |
Add and subtract two integers (with and without the use of a number line)
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7.N.11 |
Simplify expressions using order of operations Note: Expressions may include absolute value and/or integral exponents greater than 0.
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7.N.12 |
Add, subtract, multiply, and divide integers
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Number Sense and Operations
Students will compute accurately and make reasonable estimates.
Estimation
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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)
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7.N.19 |
Justify the reasonableness of answers using estimation
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Problem Solving
Students will build new mathematical knowledge through problem solving.
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7.PS.1 |
Use a variety of strategies to understand new mathematical content and to develop more efficient methods
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7.PS.2 |
Construct appropriate extensions to problem situations
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7.PS.3 |
Understand and demonstrate how written symbols represent mathematical ideas
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Problem Solving
Students will solve problems that arise in mathematics and in other contexts.
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7.PS.4 |
Observe patterns and formulate generalizations
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7.PS.5 |
Make conjectures from generalizations
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7.PS.6 |
Represent problem situations verbally, numerically, algebraically, and graphically
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Problem Solving
Students will apply and adapt a variety of appropriate strategies to solve problems.
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7.PS.7 |
Understand that there is no one right way to solve mathematical problems but that different methods have advantages and disadvantages
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7.PS.8 |
Understand how to break a complex problem into simpler parts or use a similar problem type to solve a problem
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7.PS.9 |
Work backwards from a solution
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7.PS.10 |
Use proportionality to model problems
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7.PS.11 |
Work in collaboration with others to solve problems
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Problem Solving
Students will monitor and reflect on the process of mathematical problem solving.
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7.PS.12 |
Interpret solutions within the given constraints of a problem
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7.PS.13 |
Set expectations and limits for possible solutions
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7.PS.14 |
Determine information required to solve the problem
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7.PS.15 |
Choose methods for obtaining required information
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7.PS.16 |
Justify solution methods through logical argument
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7.PS.17 |
Evaluate the efficiency of different representations of a problem
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Reasoning and Proof
Students will recognize reasoning and proof as fundamental aspects of mathematics.
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7.RP.1 |
Recognize that mathematical ideas can be supported by a variety of strategies
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Reasoning and Proof
Students will make and investigate mathematical conjectures.
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7.RP.2 |
Use mathematical strategies to reach a conclusion
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7.RP.3 |
Evaluate conjectures by distinguishing relevant from irrelevant information to reach a conclusion or make appropriate estimates
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Reasoning and Proof
Students will develop and evaluate mathematical arguments and proofs.
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7.RP.4 |
Provide supportive arguments for conjectures
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7.RP.5 |
Develop, verify, and explain an argument, using appropriate mathematical ideas and language
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Reasoning and Proof
Students will select and use various types of reasoning and methods of proof.
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7.RP.8 |
Apply inductive reasoning in making and supporting mathematical conjectures
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7.RP.7 |
Devise ways to verify results or use counterexamples to refute incorrect statements
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7.RP.6 |
Support an argument by using a systematic approach to test more than one case
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Representation
Students will create and use representations to organize, record, and communicate mathematical ideas.
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7.R.5 |
Use standard and non-standard representations with accuracy and detail
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7.R.4 |
Explain how different representations express the same relationship
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7.R.1 |
Use physical objects, drawings, charts, tables, graphs, symbols, equations, or objects created using technology as representations
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7.R.2 |
Explain, describe, and defend mathematical ideas using representations
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7.R.3 |
Recognize, compare, and use an array of representational forms
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Representation
Students will select, apply, and translate among mathematical representations to solve problems.
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7.R.6 |
Use representations to explore problem situations
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7.R.7 |
Investigate relationships between different representations and their impact on a given problem
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7.R.8 |
Use representation as a tool for exploring and understanding mathematical ideas
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Representation
Students will use representations to model and interpret physical, social, and mathematical phenomena.
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7.R.11 |
Use mathematics to show and understand mathematical phenomena (e.g., use tables, graphs, and equations to show a pattern underlying a function)
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7.R.9 |
Use mathematics to show and understand physical phenomena (e.g., make and interpret scale drawings of figures or scale model of objects)
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7.R.10 |
Use mathematics to show and understand social phenomena (e.g., determine profit from sale of yearbooks)
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Statistics and Probability
Students will collect, organize, display, and analyze data.
Collection of Data
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7.S.1 |
Identify and collect data using a variety of methods
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Statistics and Probability
Students will collect, organize, display, and analyze data.
Organization and Display of Data
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7.S.3 |
Convert raw data into double bar graphs and double line graphs
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7.S.2 |
Display data in a circle graph
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Statistics and Probability
Students will collect, organize, display, and analyze data.
Analysis of Data
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7.S.4 |
Calculate the range for a given set of data
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7.S.5 |
Select the appropriate measure of central tendency
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7.S.6 |
Read and interpret data represented graphically (pictograph, bar graph, histogram, line graph, double line/bar graphs or circle graph)
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Statistics and Probability
Students will make predictions that are based upon data analysis.
Data
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7.S.7 |
Identify and explain misleading statistics and graphs
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Statistics and Probability
Students will understand and apply concepts of probability.
Probability
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7.S.8 |
Interpret data to provide the basis for predictions and to establish experimental probabilities
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7.S.9 |
Determine the validity of sampling methods to predict outcomes
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7.S.10 |
Predict the outcome of an experiment
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7.S.11 |
Design and conduct an experiment to test predictions
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7.S.12 |
Compare actual results to predicted results
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