Vermont State Standards for Mathematics: Grade 1
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.
M1:1. Demonstrates conceptual understanding of rational numbers with respect to whole numbers from 0 to 100 using place value (a grouping system wherein a digit's place in a number denotes its value; e.g., in 34, 3 represents 3 tens, or 30); by applying the concepts of equivalency in composing or decomposing numbers (e.g., 12 = 7 + 5); and in expanded notation (e.g., 41 = 4 tens + 1 one or 41 = 40 + 1) using models, explanations, or other representations. Shows correct sequence of ordinal and cardinal numbers and compares cardinal numbers 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 part/whole relationships of benchmark fractions with models, diagrams, or written or verbal/scribed response.
M1:2. Demonstrates understanding of the relative magnitude of numbers from 0 to 100 by ordering whole numbers; by comparing whole numbers to each other or to benchmark numbers (10, 25, 50); by showing the relationship between whole numbers (1 more, 1 less; 10 more, 10 less); or by connecting number words and numerals to the quantities they represent using models, representations, or number lines. Apply number parameters consistent with M1:1.
M1:3. Demonstrates conceptual understanding of mathematical operations involving addition and subtraction by solving problems involving situations in which one adds to, takes from, puts together, and takes apart, or adds.
M1:4. Accurately solves problems in and out of context involving addition and subtraction using whole numbers.
M1:5. Demonstrates understanding of monetary value of coins and adds coins together to a value no greater than $1.00.
M1:6. Mentally adds and subtracts whole-number facts through ten with accuracy.
M1:7. Estimates and evaluates the reasonableness of solutions appropriate to grade level.
M1:8. Applies properties of numbers (odd, even, composition/decomposition [5 is the same as 2 + 3]) and operations (commutative, 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.
M1:9. Uses attributes, composition, or decomposition to sort or classify polygons (triangles, squares, rectangles, rhombi, trapezoids, and hexagons) or objects by a combination of two non-measurable or measurable attributes. Recognizes and names polygons and circles in their environment.
M1:11. Identifies objects in the environment given an example of a three-dimensional shape (e.g., show a wooden cylinder and students identify common objects of the same shape).
M1:15. Selects an appropriate tool with which to measure length, temperature, weight, and volume, and uses nonstandard units for linear measurement and weight.
M1:16. Determines elapsed and accrued time as it relates to the patterns of days of the week, yesterday, today, tomorrow and tells time to the half hour.
M1:18. Find and name locations with simple relationships (i.e., near, far, above, below, next to, up, down, right, left).
VT.7.8. Mathematical Understanding: Function and Algebra Concepts: Students use function and algebra concepts.
M1:19. Identifies and extends to specific cases a variety of patterns including sequences of shapes, sounds, movement, colors, letters, and numbers by extending the pattern to the next one, two, or three elements.
M1:20. 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).
M1:22. Demonstrates conceptual understanding of equality by showing equivalence between two expressions (4+1=5; 2+3=5) by solving one-step equations involving whole number addition or subtraction using models, verbal explanations, or written equations.
VT.7.9. Mathematical Understanding: Statistics and Probability Concepts: Students use statistics and probability concepts.
M1:23. Interprets a given representation (models, tally charts, pictographs with one-to-one correspondence, and tables) through written or verbal/scribed response to answer questions related to the data, or to analyze the data to formulate conclusions.
M1:24. Analyzes patterns, trends, or distributions in data in a variety of contexts using 'more,' 'less,' or 'equal.'
M1:25. Organizes and displays data using diagrams, models, or tally charts through written or verbal/scribed response to answer questions related to the data, to analyze the data to formulate conclusions.
M1:27. 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').
M1:28. In response to a teacher- or student-generated question or hypothesis, collects appropriate data to answer the question or hypothesis being tested through written or verbal/scribed response.
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.
M1:30. Demonstrate understanding of mathematical problem solving and communication through approach and reasoning - the reasoning, strategies, and skills used to solve the problem.
M1:31. Demonstrate understanding of mathematical problem solving and communication through connections - demonstration of observations, applications, extensions, and generalizations.
M1:32. Demonstrate understanding of mathematical problem solving and communication through solution - all of the work that was done to solve the problem, including the answer.
M1:33. Demonstrate understanding of mathematical problem solving and communication through mathematical language - the use of mathematical language in communicating the solution.
M1:34. Demonstrate understanding of mathematical problem solving and communication through mathematical representation - the use of mathematical representation to communicate the solution.
M1:35. Demonstrate understanding of mathematical problem solving and communication through documentation - presentation of the solution.