Mathematics Standards of Learning for Virginia Public Schools (Grade 6) NUMBER AND NUMBER SENSE 6.1 The student will identify representations of a given percent and describe orally and in writing the equivalent relationships among fractions, decimals, and percents. SE/TE: 302-306, 307, 313, 318, 420, 427, 551, 552, 553, 558-559, 560-561, 583, 605 TR: 5-7, Tool Transparencies, 11, 12; 10-1 Practice, Reteaching, Problem Review, Quick Quiz, Teaching Tool Transparency 11, Lesson Enhancement Transparency 52, Chapter 10 Project Master TECH: Technology Master 55 1
6.2 The student will describe and compare two sets of data, using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. 6.3 The student will a) find common multiples and factors, including least common multiple and greatest common factor; b) identify and describe prime and composite numbers; and c) identify and describe the characteristics of even and odd integers. SE/TE: 514-515, 516-517, 518-519, 520-521, 522, 523, 524-525, 526, 530-531, 532-533, 583, 587, 592, 597 TR: 10-1, Tool Transparency, 11, Lesson Enhancement Transparency 52, Chapter 10 Project Master; 10-2; Practice, Reteaching, Problem Review, Quick Quiz, Teaching Tool Transparencies 2, 3, Lesson Enhancement Transparency 49; 10-3, Practice, Reteaching, Problem Review, Quick Quiz, Chapter 10 Project Master; 10-4, Practice, Problem of the Day, Review, Quick Quiz TECH: Technology Masters 51, 52, 53, 55 SE/TE: 271, 275, 276-277, 278-279, 280-281, 282-283, 284, 369, 374, 378, 396, 546, 553, 557 TR: 5-1, Transparency, Problem of the Day, Review, Quick Quiz; 5-2, Tool Transparency 7, Chapter 5 Project Master; 5-3, Practice, Problem of the Day, Review, Quick Quiz, Teaching Tool Transparencies 2, 3, Lesson Enhancement Transparency 20 TECH: Technology Masters 21, 22 2
6.4 The student will compare and order whole numbers, fractions, and decimals, using concrete materials, drawings or pictures, and mathematical symbols. SE/TE: 74-75, 76-77, 97, 133, 148-149, 150-151, 152, 172, 180, 224, 265, 284, 308-309, 310-311, 312, 431, 435, 439, 447 TR: 2-3, Enhancement Transparency 6; 3-3, Practice, Reteaching, Problem Review, Quick Quiz, Teaching Tool Transparency 5, Lesson Enhancement Transparency 9, Chapter 3 Project Master; 5-8, Tool Transparencies 2, 3, 14 TECH: Technology Masters 12, 25 6.5 The student will identify, represent, order, and compare integers. SE/TE: 468-469, 470-471, 533 TR: 9-1, Tool Transparency 5 TECH: Technology Master 44 COMPUTATION AND ESTIMATION 3
6.6 The student will: a) solve problems that involve addition, subtraction, multiplication, and/or division with fractions and mixed numbers, with and without regrouping, that include like and unlike denominators of 12 or less, and express their answers in simplest form; and b) find the quotient, given a dividend expressed as a decimal through thousandths and a divisor expressed as a decimal to thousandths with exactly one non-zero digit. SE/TE: 185-187, 188-189, 190-191, 192-193, 194-195, 196-197, 198, 324-325, 326-327, 328-329, 330-331, 332, 333, 334-335, 336-337, 338, 342-343, 344-345, 346-347, 348-349, 350-351, 352-353, 354 TR: 3-10, Tool Transparency 12, Chapter 3 Project Master; 3-11, Practice, Problem of the Day, Review, Quick Quiz, Teaching Tool Transparency 12; 3-12, Practice, Reteaching, Problem Solving, Quick Quiz, Teaching Tool Transparencies 2, 3; 6-1, Practice, Problem of the Day, Review, Quick Quiz, Teaching Tool Transparency 19, Lesson Enhancement Transparency 25; 6-2, Tool Transparencies 2, 3, 14, Lesson Enhancement Transparencies 26, 27; 6-3, Practice, Reteaching, Problem Solving, Enrichment, Daily Transparency, Problem of the Day, Review, Quick Quiz, Lesson Enhancement Transparency 28, Chapter 6 Project Master, 6-4; Tool Transparency 5, Lesson Enhancement Transparency 29, 6-5; Tool Transparency 14, Lesson Enhancement Transparency 30, 6-6 4
(continued) 6.6 The student will: a) solve problems that involve addition, subtraction, multiplication, and/or division with fractions and mixed numbers, with and without regrouping, that include like and unlike denominators of 12 or less, and express their answers in simplest form; and b) find the quotient, given a dividend expressed as a decimal through thousandths and a divisor expressed as a decimal to thousandths with exactly one non-zero digit. 6.7 The student will use estimation strategies to solve multistep practical problems involving whole numbers, decimals, and fractions (rational numbers). 6.8 The student will solve multistep consumer application problems involving fractions and decimals and present data and conclusions in paragraphs, tables, or graphs. Planning a budget will be included. (continued) TE: Tool Transparency 14, Lesson Enhancement Transparency 31, Chapter 6 Project Master TECH: Technology Masters 15, 26, 27, 28, 29, 30, Interactive CD-ROM Lesson 6 SE/TE: 90-93, 94-97, 160-161, 342-343, 366-369, 554-557 TR: 2-6; enhancement Transparency 7, 2-7; Practice, Reteaching, Problem Review, Quick Quiz, Teaching Tool Transparencies 2, 3, 6-4; Tool Transparency 5, Lesson Enhancement Transparency 29, 7-1; Transparency, Problem of the Day, Review, Quick Quiz, 10-9; Tool Transparency 22, Lesson Enhancement Transparency 51 SE/TE: 13, 48, 85, 94, 104, 107, 159, 160, 161, 166, 167, 173, 192, 209, 211, 222, 225, 227, 243, 478, 501, 533, 566, 579, 608 MEASUREMENT 5
6.9 The student will compare and convert units of measures for length, area, weight/mass, and volume within the U.S. Customary system and the metric system and estimate conversions between units in each system:* a) length part of an inch (1/2. 1/4, and 1/8) inches, feet, yards, miles, millimeters, centimeters, meters, and kilometers; b) weight/mass ounces, pounds, tons, grams, and kilograms; c) liquid volume cups, pints, quarts, gallons, milliliters, and liters; and d) area square units * The intent of this standard is for students to make ballpark comparisons and not to memorize conversion factors between U.S. Customary and metric units. SE/TE: 215, 216-217, 218-219, 220-221, 222-223, 224 TR: 4-2; Enhancement Transparencies 13, 14, 4-3; Practice, Reteaching, Problem Solving, Enrichment, Daily Transparency, Problem of the Day, Review, Quick Quiz, Lesson Enhancement Transparency 15 TECH: Technology Master 16 6.10 The student will estimate and then determine length, weight/mass, area, and liquid volume/capacity, using standard and nonstandard units of measure. SE/TE: 228-229, 230-231, 232, 233, 234-235, 236, 237, 238-239, 240-241, 254-255, 256-257, 258 TR: 4-4; Tool Transparency 11, Lesson Enhancement Transparency 17; 4-5; Tool Transparencies 2, 3; 4-6; Practice, Reteaching, Problem Review, Quick Quiz, Teaching Tool Transparency 10, Chapter 4 Project Master; 4-9; Practice, Reteaching, Problem Solving, Quick Quiz, Lesson Enhancement Transparency 6
(continued) 6.10 The student will estimate and then determine length, weight/mass, area, and liquid volume/capacity, using standard and nonstandard units of measure. 6.11 The student will determine if a problem situation involving polygons of four or fewer sides represents the application of perimeter or area and apply the appropriate formula. 6.12 The student will: a) solve problems involving the circumference and/or area of a circle when given the diameter or radius; and b) derive approximations for pi from measurements for circumference and diameter, using concrete materials or computer models. (continued) TECH: Technology Masters 17, 18, Interactive CD-ROM Lesson 4 SE/TE: 210-211, 212-213, 214, 228-229, 230-231, 232, 233, 234-235, 236, 237, 238-239, 240-241 TR: 4-1; Enhancement Transparency 12, Chapter 4 Project Master; 4-4, Tool Transparency 11, Lesson Enhancement Transparency 17; 4-5; Tool Transparencies 2, 3; 4-6; Practice, Reteaching, Problem Review, Quick Quiz, Teaching Tool Transparency 10, Chapter 4 Project Master TECH: Technology Masters 17, 18, Interactive CD-ROM Lesson 4 SE/TE: 246-247, 248-249, 250-251, 252-253 TR: 4-7; Tool Transparency 23, Chapter 4 Project Master; 4-8; Practice, Problem of the Day, Review, Quick Quiz, Lesson Enhancement Transparency 18 TECH: Technology Masters 19, 20 7
6.13 The student will: a) estimate angle measures, using 45 degrees, 90 degrees, and 180 degrees as referents, and use the appropriate tools to measure the given angles; and b) measure and draw right, acute, and obtuse angles and triangles. SE/TE: 412-413, 414-415, 416-417, 418-419, 420, 424-425, 426-427, 428-429, 430-431 TR: 8-2; Tool Transparencies 2, 3, 8-3; Practice, Reteaching, Problem Review, Quick Quiz, Teaching Tool Transparencies 6, 17, Lesson Enhancement Transparency 37, Chapter 8 Project Master; 8-4; Tool Transparency 6; 8-5; Practice, Reteaching, Problem solving, Quick Quiz TECH: Technology Masters 37, 38, 39, Interactive CD-ROM Lesson 8 8
GEOMETRY 6.14 The student will identify, classify, and describe the characteristics of plane figures including similarities, differences, and defining properties. 6.15 The student will determine congruence of segments, angles, and polygons by direct comparison, given their attributes. Examples of noncongruent and congruent figures will be included. 6.16 The student will construct the perpendicular bisector of a line segment and an angle bisector. 6.17 The student will sketch, construct models of, and classify solid figures (rectangular prisms, cones, cylinders, and pyramids). SE/TE: 432-433, 434-435, 436-437, 438-439 TR: 8-6; Tool Transparency 20, Lesson Enhancement Transparencies 38, 39; 8-7; Enhancement Transparencies 40, 41 TECH: Technology Masters 40, 41 SE/TE: 544-545, 546 TR: 10-7; Tool Transparencies 2, 3, 6, 16, 17, Chapter 10 Project Master TECH: Technology Master 54 SE/TE: 459 SE/TE: 580-581, 582-583 TR: 11-1; Enhancement Transparency 53 TECH: Technology Master 57 PROBABILITY AND STATISTICS 9
6.18 The student, given a problem situation, will collect, analyze, display, and interpret data in a variety of graphical methods, including a) line, bar, and circle graphs; b) stem-and-leaf plot; and c) box-and-whisker plots. Circle graphs will be limited to halves, fourths, and eighths. 6.19 The student will describe the mean, median, and mode as measures of central tendency, describe the range, and determine their meaning for a set of data. SE/TE: 6-7, 8-9, 10, 16-17, 18-19, 20, 21, 24-25, 26-27, 28, 29, 30-31, 32-33, 34-35, 36-37, 38 TR: 1-1; Enhancement Transparency 1; 1-3; Practice, Reteaching, Problem Review, Quick Quiz; 1-4; Practice, Reteaching, Problem Solving, Quick Quiz, Teaching Tool Transparency 22, Lesson Enhancement Transparency 4, Chapter 1 Project Master; 1-5; Practice, Reteaching, Problem Solving, Enrichment, Daily Transparency, Problem of the Day, Review, Quick Quiz; 1-6; Practice, Reteaching, Problem Review, Quick Quiz TECH: Technology Masters 2, 3, Interactive CD-ROM Spreadsheet/Grapher Tool SE/TE: 42-43, 44-45, 46-47, 48-49, 52, 55, 186 TR: 1-7; Transparency, Problem of the Day, Review, Quick Quiz; 1-8; Tool Transparencies 2, 3 TECH: Technology Master 4, Interactive CD-ROM Lesson 1 10
6.20 The student will: a) make a sample space for selected experiments and represent it in the form of a list, chart, picture, or tree diagram; and b) determine and interpret the probability of an event occurring from a given sample space and represent the probability as a ratio, decimal, or percent, as appropriate for the given situation. SE/TE: 626-627, 628-629, 630-631, 632-633, 635, 636-637, 638, 642-643, 644-645, 646, 647. 648-649, 650, 651, 652-653, 644 TR: 12-1; Enhancement Transparency 58; 12-2; Practice, Reteaching, Problem Review, Quick Quiz; 12-3; Practice, Reteaching, Problem Solving, Quick Quiz, Teaching Tool Transparencies 2, 3, Lesson Enhancement Transparency 59, Chapter 12 Project Master; 12-4; Tool Transparencies 2, 3; 12-5; Practice, Reteaching, Problem Review, Quick Quiz; 12-6; Practice, Reteaching, Problem Solving, Quick Quiz, Chapter 12 Project Master TECH: Technology Masters 60, 61, 62, 63, 64; Interactive CD-ROM Lesson 12 11
PATTERNS, FUNCTIONS, AND ALGEBRA 6.21 The student will investigate, describe, and extend numerical and geometric patterns, including triangular numbers, patterns formed by powers of 10, and arithmetic sequences. 6.22 The student will investigate and describe concepts of positive exponents, perfect squares, square roots, and, for number greater than 10, scientific notation. Calculators will be used to develop exponential patterns. SE/TE: 87, 102-106, 133, 189, 205, 327, 575 TR: 2-9; Transparency, Problem of the Day, Review, Quick Quiz TECH: Technology Master 9, Interactive CD-ROM Lesson 2 SE/TE: 78-79, 80-81, 82, 83, 153, 154-155, 156, 157, 251, 276, 505 TR: 2-4; Tool Transparencies 2, 3, 23, Chapter 2 Project Master; 3-4; Tool Transparency 23 TECH: Technology Masters 6, 7, 13 12
6.23 The student will: a) model and solve algebraic equations, using concrete materials; b) solve one-step linear equations in one variable, involving whole number coefficients and positive rational solutions; and c) use the following algebraic terms appropriately: variable, coefficient, term, and equation. SE/TE: 118-119, 120-121, 122-123, 124-125, 169, 170-171, 172, 195, 196-197, 198, 334-335, 336-337, 338, 392-393, 394-395, 396, 498-499, 500-501, 502 TR: 2-12; Transparency, Problem of the Day, Review, Quick Quiz; 2-13; Transparency, Problem of the Day, Review, Quick Quiz, Chapter 2 Project Master; 3-7; Practice, Reteaching, Problem Solving, Quick Quiz, Teaching Tool Transparencies 2, 3; 3-12; Practice, Problem of the Day, Review, Quick Quiz, Teaching Tool Transparencies 2, 3; 6-3; Practice, Reteaching, Problem Solving, Quick Quiz, Lesson Enhancement Transparency 28, Chapter 6 Project Master; 7-6; Practice, Reteaching, Problem Solving, Quick Quiz, Teaching Tool Transparencies 2, 3; 9-7; Practice, Problem of the Day, Review, Quick Quiz, Teaching Tool Transparencies 7, 8, Lesson Enhancement Transparency 47, Chapter 9 Project Master; TECH: Technology Masters 10, 14, 15, 28, 35, 50 13