Number and Numeracy SE/TE: 43, 49, , , 457, 459, 479


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1 Ohio Proficiency Test for Mathematics, New Graduation Test, (Grade 10) Mathematics Competencies Competency in mathematics includes understanding of mathematical concepts, facility with mathematical skills, and application of concepts and skills to problemsolving situations. Assessment will focus on using mathematics, appropriate for the end of tenth grade to solve problems. To the extent possible, items and tasks will have realworld contexts including the use of practical applications, real data, and numbers often associated with situations and problems encountered in the workplace and in daily life. The development of the mathematics competencies was predicted upon students having access to scientific calculators during assessment. Number and Numeracy 1. Represent and use real numbers in a variety of equivalent forms. * Incorporates ninthgrade outcome #2: Compare, order, and determine equivalence of fractions, decimals, percents, whole numbers, and integers. 2. Estimate and compute with real numbers. * Incorporates ninthgrade outcome #1: Compute with whole numbers, fractions, and decimals. 3. Apply rates, ratios, proportions, and percents. * Incorporates ninthgrade outcome #3: Solve and use proportions. * Incorporates ninthgrade outcome #5: Solve problems and make applications involving percentages. SE/TE: 43, 49, , , 457, 459, 479 TR: Teaching Guide: 21, 22, 44, 91, 111, 116 Skills Practice: 21, 22, 44, 91, 111, 116 SE/TE: 43, 49, 118, , 380, 457, 459, 479 TR: Teaching Guide: 21, 22, 44, 91, 111, 116 Skills Practice: 21, 22, 44, 91, 111, 116 SE/TE: 206, , 621, 630 TR: Teaching Guide: 510, 119, 142 Skills Practice: 510, 119,
2 Algebra and Functions 4. Write, interpret, simplify, evaluate, and/or use algebraic expressions and formulas. * Incorporates ninthgrade outcome #15: Solve simple number sentences and use formulas. * Incorporates ninthgrade outcome #16: Evaluate algebraic expressions (simple substitutions). SE/TE: , , , , , , , , , , , , , , , , TR: Teaching Guide: Chapters 11, 12, 13, 14 Skills Practice: Chapters 11, 12, 13, Use linear equations and inequalities. SE/TE: 169, 295, 300, 316, , , TR: Teaching Guide: 52, 76, 79, 81, 82, 136 Skills Practice: 52, 76, 79, 81, 82, Represent a mathematical relationship using a table, graph, symbols, and words, and describe how a change in the value of one variable affects the value of a related variable. 7. Create and analyze graphs of linear and simple nonlinear functions. SE/TE: 2, , , , , , , , , 662 TR: Teaching Guide: 73, 74, 75, 76, 77, 131, 144, 145 Skills Practice: 73, 74, 75, 76, 77, 131, 144, 145 SE/TE: 2, , , , , , , , , , , 662 TR: Teaching Guide: 73, 74, 75, 76, 77, 131, 144, 145 Skills Practice: 73, 74, 75, 76, 77, 131, 144,
3 Geometry and Measurement 8. Apply angle relationships to situations involving intersecting lines, perpendicular lines, and parallel lines. * Incorporates ninthgrade outcome #9: Recognize, classify, and use characteristics of lines and simple twodimensional figures. 9. Recognize and apply characteristics of congruent and similar figures. 10. Apply visualization, spatial sense, and properties of twodimensional figures and threedimensional objects. * Incorporates ninthgrade outcome #9: Recognize, classify, and use characteristics of lines and simple twodimensional figures. 11. Use measurement techniques including scale drawings, formulas, and geometric relationships to find length, perimeter, area, surface area, and volume. * Incorporates ninthgrade outcome #10: Find the perimeters (circumference) and areas of polygons (circles). * Incorporates ninthgrade outcome #11: Find surface areas and volumes of rectangular solids. SE/TE: , , , , TR: Teaching Guide: 73, 74, 75, 76, 77, 131 Skills Practice: 73, 74, 75, 76, 77, 131 SE/TE: 340, , 546, 621, 625 TR: Teaching Guide: 81, 119, 127, 142 Skills Practice: 81, 119, 127, 142 SE/TE: , 281, , , 292, 293, , , 340, , , 546, 548, 558 TR: Teaching Guide: 69, 73, 75, 77, 81, 84, 85, 119, 127 Skills Practice: 69, 73, 75, 77, 81, 84, 85, 119, 127 SE/TE: 14, 21, , 275, , , , , , , , 456, , , 662 TR: Teaching Guide: 13, 14, 51, 52, 53, 54, 55, 56, 57, 58, 59, 510, 511, 73, 74, 75, 76, 77, 84, 103, 117, 131 Skills Practice: 13, 14, 51, 52, 53, 54, 55, 56, 57, 58, 59, 510, 511, 73, 74, 75, 76, 77, 84, 103, 117,
4 Data Analysis and Probability 12. Create, interpret and/or analyze tables, charts, and graphs involving data. * Incorporates ninthgrade outcome #12: Read, interpret, and use tables, charts, maps, and graphs to identify patterns, note trends, and draw conclusions. 13. Choose and apply measures of central tendency (mean, median, and mode) and variability (range and visual displays of distribution). * Incorporates ninthgrade outcome #14: Compute averages. 14. Represent and interpret the possible outcomes for a mathematical situation and calculate possibilities. * Incorporates ninthgrade outcome #13: Use elementary notions of probability. SE: 2633, 5758, 66, 68, 98, 138, 191, 197, 221, , 260, 293, 295, , , , 560, 561, , 591, 655, , 662 TR: Teaching Guide: 17, 18, 24, 26, 33, 43, 57, 63, 67, 610, Skills Practice: 17, 18, 24, 26, 33, 43, 57, 63, 67, 610, SE: 340, 347, 501 TR: Teaching Guide: 81, 82, 119 Skills Practice: 81, 82, 119 SE: 2633, 5758, 66, 68, 98, 138, 191, 197, 221, , 260, 293, 295, , , , 560, 561, , 591, 655, , 662 TR: Teaching Guide17, 18, 24, 26, 33, 43, 57, 63, 67, 610, 75, 78, 79, 107, 146, 147 Skills Practice17, 18, 24, 26, 33, 43, 57, 63, 67, 610, 4
5 Mathematical Processes Competencies represent important processes that cross all the mathematics content domains. The contexts for items and tasks assessing these mathematical processes will be drawn from the content associated with competencies Communicate mathematical ideas, reasoning, and solutions through the use of appropriate mathematical terminology, notations, symbols, definitions, models and other representations. SE/TE: 4, 9, 12, 28, 46, 49, 55, 61, 66, 67, 93, 94, 103, 109, 169, 179, 191, 206, 220, , 286, 292, 310, 340, 354, 367, 388, , 396, , , , 413, 436, 473, 492, 494, 501, 545, 555, 570, 574, 582, 621, 638, 650 TR: Teaching Guide: 12, 13, 17, 22, 24, 25, 26, 32, 34, 35, 52, 54, 57, 510, 63, 64, 74, 75, 78, 81, 83, 91, 95, 96, 97, 98, 101, 107, 115, 118, 127 Skills Practice: 12, 13, 17, 22, 24, 25, 26, 32, 34, 35, 52, 54, 57, 510, 63, 64, 74, 75, 78, 81, 83, 91, 95, 96, 97, 98, 101, 107, 115, 118, Apply problem solving strategies and evaluate processes, strategies, calculations, and solutions to verify reasonableness; and use mathematical reasoning to validate and/or generalize approaches, arguments, strategies, and solutions. SE/TE: 2630, 3033, 3439, 7886, , 221, , , 281, , , 320, , , 440, , 505, , TR: Teaching Guide: 17, 18, 19, 28, 46, 67, 69, 78, 79, 710, 97, 98, 107, 119, 132, 146 Skills Practice: 17, 18, 19, 28, 46, 67, 69, 78, 79, 710, 97, 98, 107, 119, 132,
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