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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.
M4:30. Demonstrate understanding of mathematical problem solving and communication through approach and reasoning - the reasoning, strategies, and skills used to solve the problem.
M4:32. Demonstrate understanding of mathematical problem solving and communication through solution - all of the work that was done to solve the problem, including the answer.
M4:33. Demonstrate understanding of mathematical problem solving and communication through mathematical language - the use of mathematical language in communicating the solution.
M4:34. Demonstrate understanding of mathematical problem solving and communication through mathematical representation - the use of mathematical representation to communicate the solution.
M4:35. Demonstrate understanding of mathematical problem solving and communication through documentation - presentation of the solution.
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.
M4:1. Demonstrates conceptual understanding of rational numbers with respect to: whole numbers from 0 to 999,999 through equivalency, composition, decomposition, or place value using models, explanations, or other representations; and positive fractional numbers (benchmark fractions: a/2, a/3, a/4, a/5, a/6, a/8, or a/10, 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, set, or linear models where the number of parts in the whole are equal to, and a multiple or factor of the denominator; and decimals as hundredths within the context of money, or tenths within the context of metric measurements (e.g., 2.3 cm) using models, explanations, or other representations.
M4:2. Demonstrates understanding of the relative magnitude of numbers from 0 to 999,999 by ordering or comparing whole numbers; and ordering, comparing, or identifying equivalent proper positive fractional numbers; or decimals using models, number lines, or explanations.
M4:3. Demonstrates conceptual understanding of mathematical operations by describing or illustrating the relationship between repeated subtraction and division (no remainders); the inverse relationship between multiplication and division of whole numbers; or the addition or subtraction of positive fractional numbers with like denominators using models, number lines, or explanations.
M4:4. Accurately solves problems involving multiple operations on whole numbers or the use of the properties of factors and multiples; and addition or subtraction of decimals and positive proper fractions with like denominators. (Multiplication limited to 2 digits by 2 digits, and division limited to 1 digit divisors.)
M4:6. Mentally adds and subtracts whole numbers through twenty and multiplies whole numbers through twelve with accuracy.
M4:7. Estimates and evaluates the reasonableness of solutions appropriate to grade level.
M4:8. Applies properties of numbers (odd, even, factor, multiple, 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.
M4:11. Uses properties or attributes (shape of bases or number of lateral faces) to identify, compare, or describe three-dimensional shapes (rectangular prisms, triangular prisms, cylinders, or spheres). Identifies components (faces, edges, and vertices) of three-dimensional shapes (cubes and rectangular prisms).
M4:13. Demonstrates conceptual understanding of similarity by applying scales on maps, or applying characteristics of similar figures (same shape, but not necessarily the same size) to identify similar figures, or to solve problems involving similar figures. Describes relationships using models or explanations.
M4:14. Demonstrates conceptual understanding of perimeter of polygons, and the area of rectangles, polygons, or irregular shapes on grids using a variety of models, manipulatives, or formulas. Expresses all measures using appropriate units.
M4:15. Measures and uses units of measures appropriately and consistently, and makes conversions within systems when solving problems across the content strands.
M4:16. Determines elapsed and accrued time to the 1/4 hour.
M4:18. Solves problems using the Cartesian coordinate system (Quadrant I) to locate coordinates and to represent data from tables.
M4:9. Uses properties or attributes of angles (number of angles) or sides (number of sides, length of sides, parallelism, or perpendicularity) to identify, describe, or distinguish among triangles, squares, rectangles, rhombi, trapezoids, hexagons, or octagons; or classify angles relative to 90o as more than, less than, or equal to. Recognizes symmetrical figures and uses symmetry to identify and classify figures.
VT.7.8. Mathematical Understanding: Function and Algebra Concepts: Students use function and algebra concepts.
M4:19. Identifies and extends to specific cases a variety of patterns (linear and nonlinear) represented in models, tables or sequences; and writes a rule in words or symbols to find the next case.
M4:21. Demonstrates conceptual understanding of algebraic expressions by using letters or symbols to represent unknown quantities to write simple linear algebraic expressions involving any one of the four operations; or by evaluating simple linear algebraic expressions using whole numbers.
M4:22. Demonstrates conceptual understanding of equality by showing equivalence between two expressions using models or different representations of the expressions, by simplifying numerical expressions where left to right computations may be modified only by the use of parentheses (expressions consistent with the parameters of M(FandA)-4-3), and by solving one-step linear equations of the form ax = c, x +/-b = c, where a, b, and c are whole numbers with a not equal to 0.
VT.7.9. Mathematical Understanding: Statistics and Probability Concepts: Students use statistics and probability concepts.
M4:23. Interprets a given representation (line plots, tables, bar graphs, pictographs, or circle graphs) to answer questions related to the data, to analyze the data to formulate or justify conclusions, to make predictions, or to solve problems.
M4:24. Analyzes patterns, trends, or distributions in data in a variety of contexts by determining or using measures of central tendency (median or mode), or range.
M4:25. 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, or to make predictions.
M4:26. Uses counting techniques to solve problems in context involving combinations or simple permutations (e.g., given a map, determines the number of paths from point A to point B) using a variety of strategies (e.g., organized lists, tables, tree diagrams, or others).
M4:27. For a probability event in which the sample space may or may not contain equally likely outcomes, determines the theoretical probability of an event and expresses the result as part to whole (e.g., two out of five).
M4:28. In response to a teacher- or student-generated question or hypothesis, collects appropriate data, organizes the data, displays/represents the data, analyzes the data to draw conclusions about the questions or hypothesis being tested.
M4:29. Uses experimental probability, records the outcomes, and describes the likelihood of an event as a value from 0 through 1 (for events that are certain to occur) written as either a ratio or as part to whole (e.g., 7 out of 10).
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