Vermont State Standards for Mathematics: Grade 7
VT.7.6. Mathematical Understanding: Arithmetic, Number, and Operation Concepts: Students understand arithmetic in computation, and they select and use, in appropriate situations, mental arithmetic, pencil and paper, calculator, and computer.
M7:1. Demonstrates conceptual understanding of rational numbers with respect to percents as a means of comparing the same or different parts of the whole when the wholes vary in magnitude (e.g., 8 girls in a classroom of 16 students compared to 8 girls in a classroom of 20 students, or 20% of 400 compared to 50% of 100); and percents as a way of expressing multiples of a number (e.g., 200% of 50) using models, explanations, or other representations.
M7:2. Demonstrates understanding of the relative magnitude of numbers by ordering, comparing, or identifying equivalent rational numbers across number formats, numbers with whole-number bases and whole-number exponents (e.g., 3^3, 4^3), integers, absolute values, or numbers represented in scientific notation using number lines or equality and inequality symbols.
M7:3. Demonstrates conceptual understanding of operations with integers, exponents, and square roots of perfect square numbers and non-perfect square numbers using models, diagrams, or explanations.
M7:4. Accurately solves problems involving proportional reasoning; percents involving discounts, tax, or tips; and rates. And accurately solves problems involving integers, raising numbers to whole-number powers, and determining square roots of perfect square numbers and non-perfect square numbers.
M7:7. Estimates and evaluates the reasonableness of solutions appropriate to grade level.
M7:8. Applies properties of numbers (greatest common factor [GCF], least common multiple [LCM], composition/decomposition, divisibility, prime factorization, inverses, and identities), and commutative, distributive, and associative properties of operations, and exponents using powers of ten and scientific notation to solve problems and to simplify computations.
VT.7.7. Mathematical Understanding: Geometric and Measurement Concepts: Students use geometric and measurement concepts.
M7:9. Uses properties of angle relationships resulting from two or three intersecting lines (adjacent angles, vertical angles, straight angles, or angle relationships formed by two nonparallel lines cut by a transversal), or two parallel lines cut by a transversal to solve problems.
M7:10. Applies theorems or relationships (triangle inequality or sum of the measures of interior angles of regular polygons) to solve problems.
M7:11. Applies the properties of number of vertices, number of edges, faces, and types of angles, symmetry, to identify and distinguish among three-dimensional shapes (rectangular prisms, triangular prisms, pyramids, cubes) and uses properties to solve problems involving three-dimensional shapes.
M7:12. Applies the concepts of congruency by solving problems on a coordinate plane involving reflections, translations, or rotations.
M7:13. Applies concepts of similarity by solving problems involving scaling up or down and their impact on angle measures, linear dimensions and areas of polygons, and circles when the linear dimensions are multiplied by a constant factor. Describes effects using models or explanations.
M7:14. Demonstrates conceptual understanding of the area of circles or the area or perimeter of composite figures (quadrilaterals, triangles, or parts of circles), and the surface area of rectangular prisms, or volume of rectangular prisms, triangular prisms, or cylinders using models, formulas, or by solving related problems. Expresses all measures using appropriate units.
M7:15. Measures and uses units of measures appropriately and consistently when solving problems across the content strands. Makes conversions within systems.
M7:17. Sketches three-dimensional solids and the nets of prisms, cylinders, and pyramids.
VT.7.8. Mathematical Understanding: Function and Algebra Concepts: Students use function and algebra concepts.
M7:19. Identifies and extends to specific cases a variety of patterns (linear and nonlinear) represented in models, tables, sequences, graphs, or in problem situations; and generalizes a linear relationship using words and symbols; generalizes a linear relationship to find a specific case; or writes an expression or equation using words or symbols to express the generalization of a nonlinear relationship.
M7:20. Demonstrates conceptual understanding of linear relationships (y = kx; y = mx + b) as a constant rate of change by solving problems involving the relationship between slope and rate of change, by describing the meaning of slope in concrete situations, or informally determining the slope of a line from a table or graph; and distinguishes between constant and varying rates of change in concrete situations represented in tables or graphs; or describes how change in the value of one variable relates to change in the value of a second variable in problem situations with constant rates of change.
M7:21. Demonstrates conceptual understanding of algebraic expressions by using letters to represent unknown quantities to write algebraic expressions (including those with whole-number exponents or more than one variable); or by evaluating algebraic expressions (including those with whole-number exponents or more than one variable); or by evaluating an expression within an equation (e.g., determine the value of y when x = 4 given y = 5 x3 - 2).
M7:22. Demonstrates conceptual understanding of equality by showing equivalence between two expressions (expressions consistent with the parameters of the left- and right-hand sides of the equations being solved at this grade level) using models or different representations of the expressions, solving multistep linear equations of the form ax +/-b = c with a not equal to 0, ax +/-b = cx +/-d with a, c not equal to 0, and (x/a) +/-b = c with a not equal to 0, where a, b, c and d are whole numbers; or by translating a problem-solving situation into an equation consistent with the parameters of the type of equations being solved for this grade level.
VT.7.9. Mathematical Understanding: Statistics and Probability Concepts: Students use statistics and probability concepts.
M7:23. Interprets a given representation (circle graphs, scatter plots that represent discrete linear relationships, or histograms) to analyze the data to formulate or justify conclusions, to make predictions, or to solve problems.
M7:24. Analyzes patterns, trends, or distributions in data in a variety of contexts by solving problems using measures of central tendency (mean, median, or mode), dispersion (range or variation), or outliers to analyze situations to determine their effect on mean, median, or mode; and evaluates the sample from which the statistics were developed (bias).
M7:25. Identifies or describes representations or elements of representations that best display a given set of data or situation, consistent with the representations required in M7:23. Organizes and displays data using line graphs or histograms, bar graphs, tables, frequency tables, line plots, and stem-and-leaf plots to answer question related to the data, to analyze the data to formulate or justify conclusions, or to make predictions.
M7:26. Uses counting techniques to solve problems in context involving combinations using a variety of strategies (e.g., organized lists, tables, tree diagrams, area models, Fundamental Counting Principle, or others); or determines the possible outcomes for a sample space that may or may not contain equally likely outcomes.
M7:27. For a probability event in which the sample space may or may not contain equally likely outcomes, determines the experimental or theoretical probability of a simple event or an event in a problem-solving situation.
M7:28. In response to a teacher- or student-generated question, makes a hypothesis, collects appropriate data, organizes the data, appropriately displays/represents numerical and/or categorical data, analyzes the data to draw conclusions about the questions or hypothesis being tested, and when appropriate makes predictions, asks new questions, or makes connection to real-world situations.
M7:29. Compares and contrasts theoretical and experimental probabilities of events; and uses theoretical or experimental probabilities to determine the fairness of a game. Represents probabilities using fractions, decimals, or percents.
VT.7.10. Mathematical Problem Solving: Applications: Students use concrete, formal, and informal strategies to solve mathematical problems, apply the process of mathematical modeling, and extend and generalize mathematical concepts. Students apply mathematics as they solve scientific and technological problems or work with technological systems.
M7:30. Demonstrate understanding of mathematical problem solving and communication through approach and reasoning - the reasoning, strategies, and skills used to solve the problem.
M7:31. Demonstrate understanding of mathematical problem solving and communication through connections - demonstration of observations, applications, extensions, and generalizations.
M7:32. Demonstrate understanding of mathematical problem solving and communication through solution - all of the work that was done to solve the problem, including the answer.
M7:33. Demonstrate understanding of mathematical problem solving and communication through mathematical language - the use of mathematical language in communicating the solution.
M7:34. Demonstrate understanding of mathematical problem solving and communication through mathematical representation - the use of mathematical representation to communicate the solution.
M7:35. Demonstrate understanding of mathematical problem solving and communication through documentation - presentation of the solution.