Vermont State Standards for Mathematics: Grade 5
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.
M5:1. Demonstrates conceptual understanding of rational numbers with respect to: whole numbers from 0 to 9,999,999 through equivalency, composition, decomposition, or place value using models, explanations, or other representations; positive fractional numbers (proper, mixed number, and improper) (halves, fourths, eighths, thirds, sixths, twelfths, fifths, or powers of ten [10, 100, 1000]), decimals (to thousandths), or benchmark percents (10%, 25%, 50%, 75% or 100%) as a part to whole relationship in area, set, or linear models using models, explanations, or other representations.
M5:2. Demonstrates understanding of the relative magnitude of numbers by ordering, comparing, or identifying equivalent positive fractional numbers, decimals, or benchmark percents within number formats (fractions to fractions, decimals to decimals, or percents to percents); or integers in context using models or number lines.
M5:3. Demonstrates conceptual understanding of mathematical operations by describing or illustrating the meaning of a remainder with respect to division of whole numbers using models, explanations, or solving problems.
M5:4. Accurately solves problems involving multiple operations on whole numbers or the use of the properties of factors, multiples, prime, or composite numbers; and addition or subtraction of fractions (proper) and decimals to the hundredths place. (Division of whole numbers by up to a two-digit divisor.)
M5:6. Mentally multiplies and divides whole numbers through twelve with accuracy.
M5:7. Estimates and evaluates the reasonableness of solutions appropriate to grade level.
M5:8. Applies properties of numbers (odd, even, factor, multiple, prime, composite, divisibility, remainders, composition/decomposition) to solve problems and to simplify computations.
VT.7.7. Mathematical Understanding: Geometric and Measurement Concepts: Students use geometric and measurement concepts.
M5:9. Uses properties or attributes of angles (right, acute, or obtuse) or sides (number of congruent sides, parallelism, or perpendicularity) to identify, describe, classify, or distinguish among different types of triangles (right, acute, obtuse, equiangular, or equilateral) or quadrilaterals (rectangles, squares, rhombi, trapezoids, or parallelograms).
M5:11. Uses properties or attributes (shape of bases, number of lateral faces, or number of bases) to identify, compare, or describe three-dimensional shapes (rectangular prisms, triangular prisms, cylinders, spheres, pyramids, or cones).
M5:12. Demonstrates conceptual understanding of congruency by matching congruent figures using reflections, translations, or rotations (flips, slides, or turns), or as the result of composing or decomposing shapes using models or explanations.
M5:13. Demonstrates conceptual understanding of similarity by describing the proportional effect on the linear dimensions of polygons when scaling up or down while preserving the angles of polygons, or by solving related problems (including applying scales on maps). Describes effects using models or explanations.
M5:14. Demonstrates conceptual understanding of perimeter of polygons, and the area of rectangles or right triangles through models, manipulatives, or formulas, the area of polygons or irregular figures on grids, and volume of rectangular prisms (cubes) using a variety of models, manipulatives, or formulas. Expresses all measures using appropriate units.
M5:15. Measures and uses units of measures appropriately and consistently, and makes conversions within systems when solving problems across the content strands.
M5:16. Determines elapsed and accrued time to the nearest minute.
M5:18. Solves problems using the Cartesian coordinate system (all quadrants) to locate coordinates and to represent data from tables.
VT.7.8. Mathematical Understanding: Function and Algebra Concepts: Students use function and algebra concepts.
M5:19. Identifies and extends to specific cases a variety of patterns (linear and nonlinear) represented in models, tables, sequences, or in problem situations; and writes a rule in words or symbols for finding specific cases of a linear relationship.
M5:20. Demonstrates a conceptual understanding of linear relationships (y = kx) as a constant rate of change by identifying, describing, or comparing situations that represent constant rates of change.
M5:21. Demonstrates conceptual understanding of algebraic expressions by using letters to represent unknown quantities to write linear algebraic expressions involving any two of the four operations; or by evaluating linear algebraic expressions using whole numbers.
M5:22. Demonstrates conceptual understanding of equality by showing equivalence between two expressions using models or different representations of the expressions (expressions consistent with the parameters of M(FandA)-5-3), by solving one-step linear equations of the form ax = c, x +/-b = c, or x/a = c, where a, b, and c are whole numbers with a not equal to 0; or by determining which values of a replacement set make the equation (multistep of the form ax +/-b = c where a, b, and c are whole numbers with a not equal to 0) a true statement (e.g., 2 x + 3 = 11, (x: x = 2, 3, 4, 5)).
VT.7.9. Mathematical Understanding: Statistics and Probability Concepts: Students use statistics and probability concepts.
M5:23. Interprets a given representation (tables, bar graphs, circle graphs, or line graphs) to answer questions related to the data, to analyze the data to formulate or justify conclusions, to make predictions, or to solve problems.
M5:24. Analyzes patterns, trends, or distributions in data in a variety of contexts by determining or using measures of central tendency (mean, median, or mode) or range to analyze situations, or to solve problems.
M5:25. Identifies or describes representations or elements of representations that best display a given set of data or situation, consistent with the representations required in M5:23. Organizes and displays data using line plots, bar graphs, tally charts and frequency charts, or tables to answer question related to the data, to analyze the data to formulate or justify conclusions, to make predictions, or to solve problems.
M5:26. Uses counting techniques to solve problems in context involving combinations using a variety of strategies (e.g., organized lists, tables, tree diagrams, or others); or determines the possible outcomes for a sample space that contains equally likely outcomes.
M5:27. For a probability event in which the sample space may or may not contain equally likely outcomes, determines the experimental or theoretical probability of an event and expresses the result as a fraction.
M5:28. In response to a teacher- or student-generated question or 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 connections to real-world situations.
M5:29. Uses experimental probability, evaluates the possible outcomes, and describes the likelihood or chance of an event as a ratio of actual times the event occurred to the number of trials written as either a ratio or as part to whole.
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.
M5:30. Demonstrate understanding of mathematical problem solving and communication through approach and reasoning - the reasoning, strategies, and skills used to solve the problem.
M5:31. Demonstrate understanding of mathematical problem solving and communication through connections - demonstration of observations, applications, extensions, and generalizations.
M5:32. Demonstrate understanding of mathematical problem solving and communication through solution - all of the work that was done to solve the problem, including the answer.
M5:33. Demonstrate understanding of mathematical problem solving and communication through mathematical language - the use of mathematical language in communicating the solution.
M5:34. Demonstrate understanding of mathematical problem solving and communication through mathematical representation - the use of mathematical representation to communicate the solution.
M5:35. Demonstrate understanding of mathematical problem solving and communication through documentation - presentation of the solution.