Vermont State Standards for Mathematics: Grade 2
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.
M2:1. Demonstrates conceptual understanding of rational numbers with respect to: whole numbers from 0 to 199 using place value, by applying the concepts of equivalency in composing or decomposing numbers (e.g., 34 = 17 + 17; 34 = 29 + 5); and in expanded notation (e.g., 141 = 1 hundred + 4 tens + 1 one or 141 = 100 + 40 + 1) using models, explanations, or other representations; and positive fractional numbers (benchmark fractions: a/2, a/3, or a/4, where a is a whole number greater than 0 and less than or equal to the denominator) as a part to whole relationship in area and set models where the denominator is equal to the number of parts in the whole using models, explanations, or other representations.
M2:2. Demonstrates understanding of the relative magnitude of numbers from 0 to 199 by ordering whole numbers; by comparing whole numbers to each other or to benchmark whole numbers (10, 25, 50, 75, 100, 125, 150, or 175); by demonstrating an understanding of the relation of inequality when comparing whole numbers by using '1 more,' '1 less,' '10 more,' '10 less,' '100 more,' or '100 less'; or by connecting number words and numerals to the quantities they represent using models, number lines, or explanations.
M2:3. Demonstrates conceptual understanding of mathematical operations involving addition and subtraction of whole numbers by solving problems involving joining actions, separating actions, part- whole relationships, and comparison situations; and addition of multiple one-digit whole numbers.
M2:5. Demonstrates understanding of monetary value by adding coins together to a value no greater than $1.99 and representing the result in dollar notation; making change from $1.00 or less, or recognizing equivalent coin representations of the same value (values up to $1.99).
M2:6. Mentally adds and subtracts whole-numbers facts through twenty with accuracy.
M2:7. Estimates and evaluates the reasonableness of solutions appropriate to grade level.
M2:8. Applies properties of numbers (odd, even) and operations (commutative, associative, identity) to solve problems and to simplify computations involving whole numbers.
VT.7.7. Mathematical Understanding: Geometric and Measurement Concepts: Students use geometric and measurement concepts.
M2:9. Uses properties, attributes, composition, or decomposition to sort or classify polygons or objects by a combination of two or more non-measurable or measurable attributes.
M2:11. Identifies three-dimensional shapes (rectangular prisms, triangular prisms, cylinders, or spheres) and their attributes and recognizes them in their environment.
M2:14. Demonstrates conceptual understanding of perimeter and area by using models or manipulatives to surround and cover polygons.
M2:15. Measures and uses units of measures appropriately and consistently, and makes conversions within systems when solving problems across the content strands.
M2:16. Determines elapsed and accrued time as it relates to the patterns of days of the week, months, hours, and tells time to five minutes.
M2:18. Solves problems using a two-dimensional coordinate system (x and y axes - quadrant I) to locate and describe positions on a map.
VT.7.8. Mathematical Understanding: Function and Algebra Concepts: Students use function and algebra concepts.
M2:19. Identifies and extends to specific cases a variety of patterns (linear and non-numeric) represented in models, tables, or sequences by extending the pattern to the next element, or finding a missing element (e.g., 2, 4, 6, ___, 10).
M2:20. Demonstrates a conceptual understanding of linear relationships (y = kx) as a constant rate of change qualitatively (growth - student growing taller) and quantitatively (measurable growth - 2 inches each year) change.
M2:22. Demonstrates conceptual understanding of equality by finding the value that will make an open sentence true (e.g., 2 + __ = 7) (limited to one operation and limited to use addition or subtraction).
VT.7.9. Mathematical Understanding: Statistics and Probability Concepts: Students use statistics and probability concepts.
M2:23. Interprets a given representation (pictographs with one-to-one correspondence, line plots, tally charts, or tables) to answer questions related to the data, or to analyze the data to formulate conclusions.
M2:24. Analyzes patterns, trends, or distributions in data in a variety of contexts by determining or using 'more,' 'less,' or 'equal.'
M2:25. Organizes and displays data using diagrams, models, tally charts, or tables to answer questions related to the data, to analyze the data to formulate conclusions.
M2:26. Uses counting techniques to solve problems involving combinations using a variety of strategies (e.g., student diagrams, organized lists, tables, tree diagrams, or others); (e.g., 'How many ways can you make 50 cents using nickels, dimes, and quarters?')
M2:27. For a probability event in which the sample space may or may not contain equally likely outcomes, uses experimental probability to describe the likelihood or chance of an event using 'more likely,' 'less likely,' 'equally likely,' 'certain,' or 'impossible.'
M2:28. In response to a teacher- or student-generated question or hypothesis, collects appropriate data, organizes the data, displays/represents the data, and makes observations about the data to draw conclusions about the question or hypothesis being tested.
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.
M2:30. Demonstrate understanding of mathematical problem solving and communication through approach and reasoning - the reasoning, strategies, and skills used to solve the problem.
M2:31. Demonstrate understanding of mathematical problem solving and communication through connections - demonstration of observations, applications, extensions, and generalizations.
M2:32. Demonstrate understanding of mathematical problem solving and communication through solution - all of the work that was done to solve the problem, including the answer.
M2:33. Demonstrate understanding of mathematical problem solving and communication through mathematical language - the use of mathematical language in communicating the solution.
M2:34. Demonstrate understanding of mathematical problem solving and communication through mathematical representation - the use of mathematical representation to communicate the solution.
M2:35. Demonstrate understanding of mathematical problem solving and communication through documentation - presentation of the solution.