Prentice Hall Mathematics Course Correlated to Kansas Mathematics Content Standards, Knowledge Base Indicators (Grade 7)

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1 Kansas Mathematics Content Standards, Knowledge Base Indicators (Grade 7) Standard 1: Number and Computation The student uses numerical and computational concepts and procedures in a variety of situations. Benchmark 1: Number Sense The student demonstrates number sense for rational numbers, the irrational number pi, and simple algebraic expressions in one variable in a variety of situations. 1. Knows, explains, and uses equivalent representations for rational numbers and simple algebraic expressions including integers, fractions, decimals, percents, and ratios; integer bases with whole number exponents; positive rational numbers written in scientific notation with positive integer exponents; time; and money (2.4.K1a-c) $, e.g., 253,000 is equivalent to 2.53 x 10 5 or x + 5x is equivalent to 6x. 2. Compares and orders rational numbers and the irrational number pi (2.4.K1a) $. 3. Explains the relative magnitude between rational numbers and between rational numbers and the irrational number pi (2.4.K1a). SE/TE: 4, 9, 15, 17, 19, 34-38, 39-43, 45, 48, 64, 72-74, 77, 78, 82, 86, 92, 93-94, 101, , 114, 133, , 140, 144, , 156, 158, 163, , 175, , 180, 191, , 198, 199, 201, 202, 203, 207, 213, 216, 217, 221, 225, 230, 235, 240, , , , 255, 256, 260, 265, 282, , , , , 310, , 316, 322, 332, 338, 340, 341, 3612, 367, 412, 468, 473, , 499, 533, 595, 596, 628, 629, 646, 674, 675, 685, 689 SE/TE: 4, 9, 14, 34-38, 44, 49, 60, 63, 64, 70, 107, 111, 135, 149, , , , 179, 180, 187, 196, 197, , 235, 256, 265, 341, 346, 427, 454, 461, 462, 538, 567, 572, 573, 673, 684, 686, 696 SE/TE: 4, 9, 14, 34-38, 39-44, 49, 60, 63, 64, 70, 107, 111, 135, 149, , , , , 180, 187, 196, 197, 198, 199, , 221, 235, , 256, 265, , , , , 310, , 322, 329, 332, , 338, 340, 341, 346, 361, 367, 412, , , 454, 461, 462, 468, 473, 478, 499, 538, 567, 572, 573, 595, 596, 628, 629, 646, 673, 675, 684, 686, 688, 689, Knows and explains what happens to the product or quotient when (2.4.K1a): 4.a a whole number is multiplied or divided by a rational number greater than zero and less than one, SE/TE: 17-22, 54, 62-63, 64, 75, , 207, , 221, 304, , 316, 318, 321, 333, 341, 402, 407, 483, 562, 687, 703,

2 4b. A whole number is multiplied or divided by a rational number greater than one, 4c. A rational number (excluding zero) is multiplied or divided by zero. 5. Explains and determines the absolute value of rational numbers (2.4.K1a). SE/TE: 17-22, 54, 55, 61, 62-63, 64, 75, 201, , , 221, 240, 305, , 333, 402, 562, 703, SE/TE: 18, 20-22, 28, 48, 52 SE/TE: 34-38, 39-40, 44, 63, 70, 107, , 558, 565, 566, 684 Benchmark 2: Number Systems and Their Properties -- The student demonstrates an understanding of the rational number system and the irrational number pi; recognizes, uses, and describes their properties; and extends these properties to algebraic expressions in one variable. 1. Knows and explains the relationships between natural (counting) numbers, whole numbers, integers, and rational numbers using mathematical models (2.4.K1a, k), e.g., number lines or Venn diagrams. 2. Classifies a given rational number as a member of various subsets of the rational number system (2.4.K1a,k), e.g., - 7 is a rational number and an integer. SE/TE: 4, 5-9, 15, 34-38, 39-44, 45-49, 63, , , 179, , , , 461, 696, SE/TE: 4, 5-9, 15, 34-38, 39-44, 45-49, 63, , , 179, , , , 461, 696, Names, uses, and describes these properties with the rational number system and demonstrates their meaning including the use of concrete objects (2.4.K1a) $: 3a. Commutative properties of addition and multiplication (changing the order of the numbers does not change the solution); 3b. Associative properties of addition and multiplication (changing the grouping of the numbers does not change the solution); 3c. Distributive property [distributing multiplication or division over addition or subtraction, e.g., 2(4 1) = 2(4) 2(1) = 8 2 = 6]; SE/TE: 12-14, 16, 18, 21-22, 38, 43, 62, 64, 716 (TE: T713) SE/TE: 12-14, 16, 18, 21-22, 38, 43, 48, 62, 64, 716 (TE: T713) SE/TE: 30, 50-54, 63, 64, 75, 201, 305, 673, 675, 716 (TE: T713) - 2 -

3 3d. Substitution property (one name of a number can be substituted for another name of the same number), e.g., if a = 2, then 3a = 3 x 2 = 6. This property is applied implicitly as students evaluate algebraic expressions for given values of variables and rewrite algebraic formulas by substituting equivalent expressions (e.g., C = πd = 2πr). SE/TE: 12, 18, 51, 71-75, 81, 93, 98, 103, 105, 122, 124, 125, 132, 205, 210, 256, 332, 419, , 444, , 456, 458, 468, 499, 503, 511, 513, 514, 520, Uses and describes these properties with the rational number system and demonstrates their meaning including the use of concrete objects (2.4.K1a) $: 4a. Identity properties for addition and multiplication (additive identity zero added to any number is equal to that number; multiplicative identity one multiplied by any number is equal to that number); 4b. Symmetric property of equality (if 7 + 2x = 9 then 9 = 7 + 2x); 4c. Zero property of multiplication (any number multiplied by zero is zero); 4d. Addition and multiplication properties of equality (adding/multiplying the same number to each side of an equation results in an equivalent equation); 4e. Additive and multiplicative inverse properties. (Every number has a value known as its additive inverse and when the original number is added to that additive inverse, the answer is zero, e.g., = 0. Every number except 0 has a value known as its multiplicative inverse and when the original number multiplied by its inverse, the answer will be 1, e.g., 8 x 1/8 =1.) 5. Recognizes that the irrational number pi can be represented by approximate rational values, e.g., 22/7 or SE/TE: 12-14, 18, 21-22, 38, 43, 716(T713) This property is applied implicitly in the instructional pages of the SE/TE in examples involving the transformation of formulas and solving problems using formulas. Sample References: SE/TE: 18, 20-22, 28, 48, 52 SE/TE: 16, 83-87, 88-92, , , 123, 124, 125, , , , , , , , , SE/TE: 39, 41, 46, 63, 83-85, 88-92, 98-99, , , 123, 130, , 217, 221, 233, , , 281, 290, 311, 317, , , , , 365, 368, 393, 427, , 526, 716 (T713) SE/TE: , 435, , , 461, 462, 463, 464,

4 Benchmark 3: Estimation -- The student uses computational estimation with rational numbers and the irrational number pi in variety of situations. 1. Estimates quantities with combinations of rational numbers and/or the irrational number pi using various computational methods including mental math, paper and pencil, concrete objects, and/or appropriate technology (2.4.K1a) $. 2. N uses various estimation strategies and explains how they were used to estimate rational number quantities and the irrational number pi (2.4.K1a) $. 3. Recognizes and explains the difference between an exact and approximate answer (2.4.K1a). 4. Determines the appropriateness of an estimation strategy used and whether the estimate is greater than (overestimate) or less than (underestimate) the exact answer and its potential impact on the result (24.K1a). SE/TE: 5-9, 24, 26, 28, 33, 49, 62-63, 64, 65, 74, 77-81, 91, 125, 127, 135, 136, 167, 171, , , , 201, , 208, 210, 218, 225, 226, , , 234, 235, , 290, 297, , , 373, , 420, 423, , 460, 462, , 488, 501, 511, 514, , , 621, 622, 691 SE/TE: 5-9, 24, 26, 28, 33, 49, 62-63, 64, 65, 74, 77-81, 91, 125, 127, 135, 136, 167, 171, , , , 201, , 208, 210, 218, 225, 226, , , 234, 235, , 290, 297, , , 373, , 420, 423, , 460, 462, , 488, 501, 511, 514, , , 621, 622, 691 SE/TE: 5-9, 24, 26, 28, 33, 49, 62-63, 64, 65, 74, 77-81, 91, 125, 127, 135, 136, 167, 171, , , , 201, , 208, 210, 218, 225, 226, , , 234, 235, , 290, 297, , , 373, , 420, 423, , 460, 462, , 488, 501, 511, 514, , , 621, 622, 691 SE/TE: 5-9, 24, 26, 28, 33, 49, 62-63, 64, 65, 74, 77-81, 91, 125, 127, 135, 136, 167, 171, , , , 201, , 208, 210, 218, 225, 226, , , 234, 235, , 290, 297, , , 373, , 420, 423, , 460, 462, , 488, 501, 511, 514, , , 621, 622,

5 Benchmark 4: Computation -- The student models, performs, and explains computation with positive rational numbers and integers in variety of situations. 1. Computes with efficiency and accuracy using various computational methods including mental math, paper and pencil, concrete objects, and appropriate technology (2.4.K1ac) $. SE/TE: 4, 5-9, 11-15, 16, 17-22, 28, 29, 30, 33, 38, 39-44, 45-49, 50-54, 55, 60, 61, 62-63, 64, 65, 70, 75, 77, 79, 81, 91, 125, 130, 155, 167, 186, , 191, , , , , 221, 225, 227, 232, 234, 235, 240, 245, 250, 252, 255, 290, 294, 302, 304, , , 317, , 321, , , , 337, 341, 373, 392, 402, 407, 412, 473, 474, 483, 562, 653, 673, 684, 687, , Performs and explains these computational procedures (2.4.K1a): 2a. N adds and subtracts decimals from ten millions place through hundred thousandths place; 2b. N multiplies and divides a four-digit number by a two-digit number using numbers from thousands place through thousandths place; 2c. N multiplies and divides using numbers from thousands place through thousandths place by 10; 100; 1,000;.1;.01;.001; or single-digit multiples of each, e.g., or 54.3 x 300; 2d. N adds, subtracts, multiplies, and divides fractions and expresses answers in simplest form; 2e. N adds, subtracts, multiplies, and divides integers; 2f. N uses order of operations (evaluates within grouping symbols, evaluates powers to the second or third power, multiplies or divides in order from left to right, then adds or subtracts in order from left to right) using whole numbers; SE/TE: 11-15, 16, 22, 28, 38, 50, 61, 62, 64, 70, 130, 155, 684 SE/TE: 4, 17-22, 28, 240, 562, 684, 699, 705, 707 SE/TE: 19-22, 28, 29, 52-53, 56, 64, 235, 305, 402, 562, 684, , SE/TE: 191, , , , , 212, 218, 221, 225, 232, 234, 294, 304, 341, 392, 407, 412, 653, 687, 708 SE/TE: 39-44, 45-49, 54, 63, 64, 65, 70, 81, 130, 167, 186, 201, 252, 255, 473, 474, 483, 684 SE/TE: 50-54, 55, 56, 60, 62-63, 64, 70, 71, 130, , 180, 190, 230, 402,

6 2g. Simplifies positive rational numbers raised to positive whole number powers; 2h. Combines like terms of a first-degree algebraic expression. 3. Recognizes, describes, and uses different ways to express computational procedures, e.g., 5 2 = 5 + ( 2) or 49 x 23 = (40 x 23) + (9 x 23) or 49 x 23 = (49 x 20) + (49 x 3) or 49 x 23 = (50 x 23) Finds prime factors, greatest common factor, multiples, and the least common multiple (2.4.K1d). 5. finds percentages of rational numbers (2.4.K1a, c) $, e.g., 12.5% x $40.25 = n or 150% of 90 is what number? (For the purpose of assessment, percents will not be between 0 and 1.) SE/TE: , , 146, 148, 155, , 178, 180, 181, 190, 196, 250, 341, 402, 419, , 458, 461, 462, 468, 478, 515, 520, , 647, 673, 674, 686 Students simplify algebraic expressions as they transform formulas to solve for a given variable. Sample References: SE/TE: 11-13, 16, 17-20, 21, 39-43, 45-48, 50-53, 64, 191, , , , , 212, 341 SE/TE: 136, , , 150, , 155, 163, 165, 177, , 180, 181, 186, 190, 193, 198, 203, , 235, 243, 274, 321, 341, 373, 647, 674, 686 SE/TE: , , , , , 317, , , , , 337, , 340, 341, 346, 356, 388, 418, 430, 436, 488, 498, 511, 562, 595, 675, 689 Standard 2: Algebra The student uses algebraic concepts and procedures in variety of situations. Benchmark 1: Patterns -- The student recognizes, describes, extends, develops, and explains the general rule of pattern in variety of situations. 1. Identifies, states, and continues a pattern presented in various formats including numeric (list or table), algebraic (symbolic notation), visual (picture, table, or graph), verbal (oral description), kinesthetic (action), and written using these attributes: 1a. counting numbers including perfect squares, cubes, and factors and multiples (number theory) (2.4.K1a); SE/TE: 21, 71, 116, 131, 134, 136, 211, 220, 279, 335, 395, 448, 458, , , 506, 514, 567,

7 1b. positive rational numbers including arithmetic and geometric sequences (arithmetic: sequence of numbers in which the difference of two consecutive numbers is the same, geometric: a sequence of numbers in which each succeeding term is obtained by multiplying the preceding term by the same number) (2.4.K1a), e.g., 2, 1/2, 3, 1/3, 4, 1/4, ; SE/TE: 21, 71, 116, 131, 134, 136, 158, , 220, 279, 289, 295, 335, , , 458, , , , 506, 514, 567, 605 1c. Geometric figures (2.4.K1f); SE/TE: 220, 245, 254, 289, , , 395, 396, 448, , 474, d. Measurements (2.4.K1a); SE/TE: 71, 162, , , 476, 480, e. Things related to daily life (2.4.K1a) $, e.g., tide, moon cycle, or temperature. SE/TE: 71, 131, , , , 480, Generates a pattern (2.4.K1a). SE/TE: 21, 71, 116, 131, 134, 136, 158, , , 220, 245, 254, 279, 289, 295, 335, , , 395, 396, 448, 458, , , , 506, 514, 567, Extends a pattern when given a rule of one or two simultaneous changes (addition, subtraction, multiplication, division) between consecutive terms (2.4.K1a), e.g., find the next three numbers in a pattern that starts with 3, where you double and add 1 to get the next number; the next three numbers are 7, 15, and states the rule to find the n th term of a pattern with one operational change (addition or subtraction) between consecutive terms (2.4.K1a), e.g., given 3, 5, 7, and 9; the n th term is 2n +1. (This is the explicit rule for the pattern.) SE/TE: 21, 71, 116, 131, 134, 136, 158, , 220, 279, 289, 295, 335, , , 458, , , , 506, 514, 567, 605 SE/TE: 220, 279, 335, , , , 506, 514, 567,

8 Benchmark 2: Variables, Equations, and Inequalities -- The student uses variables, symbols, positive rational numbers, and algebraic expressions in one variable to solve linear equations and inequalities in variety of situations. 1. Knows and explains that a variable can represent a single quantity that changes (2.4.K1a), e.g., daily temperature. 2. Knows, explains, and uses equivalent representations for the same simple algebraic expressions (2.4.K1a), e.g., x + y + 5x is the same as 6x + y. 3. Shows and explains how changes in one variable affects other variables (2.4.A1a), e.g., changes in diameter affects circumference. 4. Explains the difference between an equation and an expression. SE/TE: 12, 18, 51, 53, 71-75, 76, 77-81, 82, 83-87, 88-92, 93-97, , , , , , 121, , 124, 125, 135, 139, 159, 203, 205, 206, , , 217, 222, 225, 233, 234, 235, 240, 241, 250, 255, 259, , 266, , , 279, 281, 283, 284, 290, 310, , 317, 324, , , 337, 341, 346, 350, 351, , 356, , 386, 393, 406, , , , 427, , 431, , , , , 463, 468, 479, , , , 493, 494, , 502, , 506, , 511, 515, 520, , 538, 539, , 547, 553, 558, , 566, 567, 578, 595, 600, 611, 618, 623, 634, 685, 692 SE/TE: 88, 94 SE/TE: 21, 31, 66, 71, 76, 196, 407, , 418, 424, 436, 447, 448, 453, 479, , , , 601 SE/TE: 71-75, 77-81, 82, 83-87, 88-92, 93-97, , , , 124, 125, 163, 167, 203, 205, 206, , , 217, 222, 225, 233, 234, 235, 240, 250, 255, 256, 259, , 266, , 281, 290, 310, , 317, 324, , , 341, 346, 350, 351, 386, 418, 429, , 468, , 493, , 506, 510, , 543, 547, 685,

9 5. Solves (2.4.K1a, e) $: 5a. One-step linear equations in one variable with positive rational coefficients and solutions, e.g., 7x = 28 or x + 3/4 = 7 or x/3 = 5; 5b. Two-step linear equations in one variable with counting number coefficients and constants and positive rational solutions; 5c. One-step linear inequalities with counting numbers and one variable, e.g., 3x > Explains and uses the equality and inequality symbols (=,, <,, >, ) and corresponding meanings (is equal to, is not equal to, is less than, is less than or equal to, is greater than, is greater than or equal to) to represent mathematical relationships with rational numbers (2.4.K1a) $. 7. knows the mathematical relationship between ratios, proportions, and percents and how to solve for a missing term in a proportion with positive rational number solutions and monomials (2.4.K1a, c) $, e.g., 8. evaluates simple algebraic expressions using positive rational numbers (2.4.K1c) $, e.g., if x = 3/2, y = 2, then 5xy + 2 = 5(3/2)(2) + 2 = 17. SE/TE: 77-81, 82, 83-87, 88-92, 112, 116, 120, , 124, 186, 195, 206, 211, 216, 217, 221, 222, 240, 245, 259, 316, , 324, 326, , 346, 351, , 365, 386, 393, 480, 507, 558, , 685, 687 SE/TE: 94-97, , , 111, 121, 123, 124, 125, 144, 155, 163, , 225, 233, 234, , 266, , , 279, 281, 283, 284, 290, 310, , 317, , 337, 418, 455, 468, 558, 685, 687 SE/TE: , , , 123, 124, 125, 135, 139, 216, 492, 558, 673, 685 SE/TE: 12-14, 21-22, 51-54, 63, 70, 83-85, 88-92, , , , 135, 139, , 172, , 180, 187, 197, 211, 235, 240, 250, 256, , 346, , 673, , 696 SE/TE: , , 251, , , , , 280, , 284, 285, , 289, , , , , , 317, , , , , 337, , 340, 341, , 346, 350, 356, 361, 377, , 397, 406, 412, 418, 430, 436, 463, 488, 498, 506, 511, 525, 538, 553, 562, 567, 572, 595, , 622, 628, 658, 673, 675, 688, 689 SE/TE: 12, 18, 51, 71-75, 81, 93, 98, 103, 105, 122, 124, 125, 132, 205, 210, 256, 332, , 456, 468, 499, 520,

10 Benchmark 3: Functions -- The student recognizes, describes, and analyzes linear relationships in variety of situations. 1. Recognizes constant and linear relationships using various methods including mental math, paper and pencil, concrete objects, and graphing utilities or appropriate technology (2.4.K1a, e-g) $. 2. Finds the values and determines the rule through two operations using a function table (input/output machine, T-table) (2.4.K1f). 3. Demonstrates mathematical relationships using ordered pairs in all four quadrants of a coordinate plane (2.4.K1g). 4. Describes and/or gives examples of mathematical relationships that remain constant (2.4.K1e-g) $, e.g., you will get $10.00 to do a job, no matter how long it takes for you to do it. SE/TE: 71, , , , , 493, , , , 510, 511, , 514, 515, 517, , 539, , , 547, 553, 558, 563, , 566, 567, 584, 600, 611, 618, 634, 674, 692 SE/TE: 31, 66, 71, 76, , , , 493, 495, , , 510, 511, , 514, , , , 553, , 566, 567, 584, 611, 634, SE/TE: , 488, , 493, , , 514, , 526, , , 539, , 548, , , 572, 578, 580, 583, 584, 595, 600, 605, , , 623, 646, , 693 SE/TE: ,

11 Benchmark 4: Models -- The student generates and uses mathematical models to represent and justify mathematical relationships in variety of situations. 1. Knows, explains, and uses mathematical models to represent and explain mathematical concepts, procedures, and relationships. Mathematical models include: 1a. Process models (concrete objects, pictures, diagrams, number lines, hundred charts, measurement tools, multiplication arrays, division sets, or coordinate grids) to model computational procedures, algebraic relationships, and mathematical relationships and to solve equations (1.1.K1-5, 1.2.K1-4, 1.3.K1-4, 1.4.K1-2, 1.4.K5, 2.1.K1a-b, 2.1.K1e. 2.1.K2-4, 2.2.K1-3, 2.2.K5-6, 2.3.K1, 3.1.K9, 3.2.K1-3, 3.2.K9, 3.3.K1-4, 3.4.K1, 4.2.K4-6) $; 1b. Place value models (place value mats, hundred charts, base ten blocks, or unifix cubes) to compare, order, and represent numerical quantities and to model computational procedures (1.1.K1, 1.4.K2) $; 1c. Fraction and mixed number models (fraction strips or pattern blocks and decimal and money models (base ten blocks or coins to compare, order, and represent numerical quantities (1.1.K1, 1.3.K5, 1,4,K2, 2.2.K7-8, 4.1.K3) $: 1d. Factor trees to find least common multiple and greatest common factor and to model prime factorization (1.4.K4); 1e. Equations and inequalities to model numerical relationships (2.2.K5) SE/TE: 16, 17, 24, 34-35, 39-43, 45, 53, 64, 78, 82, 83-85, 89, 94-95, , , , 117, 145, 153, 156, 158, 164, 167, 173, 180, 187, 191, 194, 203, 207, 242, , 276, , , , 298, 303, , 316, , 324, , , 426, SE/TE: 15, , SE/TE: 151, 153, 156, 158, 164, 191, , 202, 207, 213 SE/TE: SE/TE: 29, 53, 71, 77-81, 82, 83-87, 88-92, 94-97, , , 106, , , , 121, , 124, 125, 203, , 216, 226, 236, 255, 260, , 266, , , 281, 283, 284, , 324, , , , 493, 494, 498, , 502, , , 539, , , 566, 595,

12 1f. Function tables to model numerical and algebraic relationships (2.3.K1-2) 1g. Coordinate planes to model relationships between ordered pairs and linear equations (2.3.K1) 1h. Two- and three-dimensional geometric models (geoboards) 1i. Geometric models (spinners, targets, or number cubes), process models (coins, pictures, or diagrams), and tree diagrams to model probability (4.1.K1, 4.1.K4) $; 1j. Frequency tables, bar graphs, line graphs, circle graphs, Venn diagrams, charts, tables, single stem-and-leaf plots, scatter plots, and box-and-whisker plots to organize and display data (4.2.K1) $; 1k. Venn diagrams to sort data and show relationships (1.2.K1-2). SE/TE: , , 493, , 500, 512, 514 SE/TE: , 488, , 493, , , 514, , 526, , , 539, , 548, , , 572, 578, 580, 583, 584, 595, 600, 605, , , 623, 646, , 693 SE/TE: 17, 50, 88, 94, 95, 151, 153, 164, 202, 242, 246, 247, , 295, 298, SE/TE: 627, , 635, , 642, , , , 659, 663, 669, , 672, 677, 695 SE/TE: 3, 11, 35, 37, 43, 49, 56-59, 66-67, 69, 71, , 168, 172, 175, 176, 185, 195, 201, 226, 239, , 249, , 256, 284, 294, 299, 305, , 316, 320, 327, 331, 355, , 395, 396, 401, 455, , , , 512, 514, 517, , 542, , , , , , 591, , , , , 612, , 619, , 622, 627, 634, 639, 641, 657, 668, , , 682, 690, 692, 694 SE/TE: 149, 591 Standard 3: Geometry The student uses geometric concepts and procedures in variety of situations. Benchmark 1: Geometric Figures and Their Properties -- The student recognizes geometric figures and compares their properties in variety of situations. 1. Recognizes and compares properties of twoand three-dimensional figures using concrete objects, constructions, drawings, appropriate terminology, and appropriate technology (2.4.K1h). SE/TE: 15, 32-33, 51, 53-54, 79, , 159, 195, 259, , 273, 279, 283, 284, 289, 315, , 352, , 362, , 368, , , , , 396, 398, , , , 425, 431, , , 441, , 448, , , 459, , 462, 463, 479, 498, 526, 546,

13 2. Classifies regular and irregular polygons having through ten sides as convex or concave. 3. identifies angle and side properties of triangles and quadrilaterals (2.4.K1h): 4. Sum of the interior angles of any triangle is 180 ; 5. Sum of the interior angles of any quadrilateral is 360 ; 6. Parallelograms have opposite sides that are parallel and congruent; 7. Rectangles have angles of 90, opposite sides are congruent; 8. Determines if a triangle can be constructed given sides of three different lengths (2.4.K1h). 9. Generates a pattern for the sum of angles for 3-, 4-, 5-, n-sides polygons (2.4.K1a). 10. Describes the relationship between the diameter and the circumference of a circle (2.4.K1h). SE/TE: 15, 32-33, 51, 53-54, 79, 159, 254, 259, , 273, 279, 283, 284, 289, 315, 352, , 362, , 368, , , , , 396, 398, , , 424, 425, 431, , , 440, 442, , 459, , 462, 463, 479, 498, 526, 546, 605 SE/TE: 15, 32-33, 51, 53-54, 79, 159, 254, 259, , 273, 279, 283, 284, 289, 315, 360, , 368, , , , , 396, 398, , , 424, 425, 431, , , 440, 442, , 459, , 462, 463, 479, 498, 526, 546, 605 SE/TE: , 368, , 378 SE/TE: SE/TE: , , 413, 425, 460, 462, 526 SE/TE: 6, 15, 51, 53-54, 79, 245, 267, , 283, , 378, 380, 406, 411, 413, , 444, 456, 458 Students learn and apply the Pythagorean Theorem that relates the lengths of the sides in a right triangle. SE/TE: 431, , 457, 459, 461, 462, 463, 510, 526, 531, 567, 675, 691 SE/TE: , 378 SE/TE: , 444, 461, 462, 567, 673, 691, 715 (TE: T713)

14 Benchmark 2: Measurement and Estimation -- The student estimates, measures, and uses measurement formulas in variety of situations. 1. Determines and uses rational number approximations (estimations) for length, width, weight, volume, temperature, time, perimeter, and area using standard and nonstandard units of measure (2.4.K1a) $. 2. Selects and uses measurement tools, units of measure, and level of precision appropriate for a given situation to find accurate rational number representations for length, weight, volume, temperature, time, perimeter, area, and angle measurements (2.4.K1a) $. 3. Converts within the customary system and within the metric system (2.4.K1a). 4. Recognizes and states perimeter and area formulas for circles, squares, rectangles, triangles, and parallelograms (2.4.K1h). 5. knows and uses perimeter and area formulas for circles, squares, rectangles, triangles, and parallelograms (2.4.K1h). 6. Finds perimeter and area of two-dimensional composite figures of circles, squares, rectangles, and triangles (2.4.K1h). SE/TE: 6, 24, 26-28, 33, 49, 201, 225, 226, , 233, 234, 265, , 420, , 436, , 460, 472, 673, 691 SE/TE: 12, 15, 22, 23-28, 29, 33, 35, 38, 41-44, 47-49, 51, 53, 61, 63, 64, 79, 132, 138, 162, 166, 183, 185, 195, 200, 201, 205, , 215, 221, , 226, , 231, 233, 234, 245, , 251, 259, 265, 266, , , 280, 321, 326, 345, 350, , 370, , 401, 402, , , , , , , , , , 459, , 462, 463, 464, 498, , 519, 531, 543, 546, 567, , 687, SE/TE: 23-28, 29, 63, 64, , 233, 234, 251, , 283, 356, 403, 488, 498, 511, 567, SE/TE: 6, 15, 51, 53-54, 132, 195, 201, 221, 335, , , , 427, 436, , 454, , 459, , 462, 463, 479, 498, 514, 526, 546, 567, 673, 675, 691, 715 (TE: T713) SE/TE: 6, 15, 51, 53-54, 132, 195, 201, 221, 335, , , , 427, 436, , 454, , 459, , 462, 463, 479, 498, 514, 526, 546, 567, 673, 675, 691, 715 (TE: T713) SE/TE: 6, 15, 51, 53-54, 132, 195, 201, 221, 335, , , , 427, 436, , 454, , 459, , 462, 463, 479, 498, 514, 526, 546, 567, 673, 675, 691, 715 (TE: T713)

15 7 uses given measurement formulas to find (2.4.K1h): 7a. Surface area of cubes, SE/TE: , 461, 691, 715 (TE: T713) 7b. Volume of rectangular prisms. SE/TE: 133, , , 461, 462, 463, 673, 691, 715 (TE: T713) 8. Finds surface area of rectangular prisms using concrete objects (2.4.K1h). 9. Uses appropriate units to describe rate as a unit of measure (2.4.K1a), e.g., miles per hour. 10. Finds missing angle measurements in triangles and quadrilaterals (2.4.K1h). SE/TE: SE/TE: 22, 47-48, 162, 183, , , 266, 271, 274, 280, 282, 284, 285, 326, 341, 397, 494, 506, 514, 519, 531, 546, 567, 622, 673, 688 SE/TE: 272, , 368, 373, , 378 Benchmark 3: Transformational Geometry -- The student recognizes and performs transformations on two- and three-dimensional geometric figures in variety of situations. 1. Identifies, describes, and performs single and multiple transformations [reflection, rotation, translation, reduction (contraction/shrinking), enlargement (magnification/growing)] on a two-dimensional figure (2.4.K1a). 2. Identifies three-dimensional figures from various perspectives (top, bottom, sides, corners) (2.4.K1a). 3. Draws three-dimensional figures from various perspectives (top, bottom, sides, corners) (2.4.K1a). SE/TE: 245, 259, , 273, , 280, 283, 284, , 341, 356, 478, 538, 548, , , , 563, , 566, 567, 584, 590, 646, 674, 675, 688, 693 SE/TE: 133, , 396, , 441, , 448, , 461, 462, 463 SE/TE: , 441, , Generates a tessellation (2.4.K1a). SE/TE: 551 Benchmark 4: Geometry From An Algebraic Perspective -- The student relates geometric concepts to number line and coordinate plane in variety of situations. 1. Finds the distance between the points on a number line by computing the absolute value of their difference (2.4.K1a). SE/TE: 34-38,

16 2. Uses all four quadrants of a coordinate plane to (2.4.K1g): 2a. Identify in which quadrant or on which axis a point lies when given the coordinates of a point, SE/TE: , 488, , 493, , , 514, , 526, , , 539, , 548, , , 572, 578, 580, 583, 584, 595, 600, 605, , , 623, 646, , 693 2b. Plot points, SE/TE: , 488, , 493, , , 514, , 526, , , 539, , 548, , , 572, 578, 580, 583, 584, 595, 600, 605, , , 623, 646, , 693 2c. Identify points, SE/TE: , 488, , 493, , , 514, , 526, , , 539, , 548, , , 572, 578, 580, 583, 584, 595, 600, 605, , , 623, 646, , 693 2d. List through five ordered pairs of a given line. SE/TE: , 488, , 493, , , 514, , , , , , 566, 583, 600, 674, Uses a given linear equation with whole number coefficients and constants and a whole number solution to find the ordered pairs, organize the ordered pairs using a T-table, and plot the ordered pairs on the coordinate plane (2.4.K1e-g). 4. Examines characteristics of two-dimensional figures on a coordinate plane using various methods including mental math, paper and pencil, concrete objects, and graphing utilities or other appropriate technology (2.4.A1g). SE/TE: 488, , 493, 513, 514, , 538, 539, 564, 566, 583, 595, 618, 674, 692 SE/TE: 526, 548, , , 565, 566, 567, 675, 693 Standard 4: Data -- The student uses concepts and procedures of data analysis in variety of situations. Benchmark 1: Probability -- The student applies the concepts of probability to draw conclusions and to make predictions and decisions including the use of concrete objects in variety of situations. 1. Finds the probability of a compound event composed of two independent events in an experiment or simulation (2.4.K1i) $. SE/TE: 627, , 635, , 642, , , , 659, 663, 669, , 672, 677,

17 2. Explains and gives examples of simple or compound events in an experiment or simulation having probability of zero or one. SE/TE: , 640, uses a fraction, decimal, and percent to represent the probability of (2.4.K1c): 3a. a simple event in an experiment or simulation; SE/TE: , , 642, , , , 659, 663, 669, , 672, 677, 695 3b. a compound event composed of two independent events in an experiment or simulation. 4. Finds the probability of a simple event in an experiment or simulation using geometric models (2.4.K1i), e.g., using spinners or dartboards, what is the probability of landing on 2? The answer is ¼,.25, or 25%. SE/TE: 635, 636, 638, 640, , , , 659, 663, , 672, 677, 695 SE/TE: 632, 641, 650, 652, 657, 658, 677 Benchmark 2: Statistics -- The student collects, organizes, displays, and explains numerical (rational numbers) and non-numerical data sets in variety of situations with special emphasis on measures of central tendency. : 1. organizes, displays, and reads quantitative (numerical) and qualitative (non-numerical) data in a clear, organized, and accurate manner including a title, labels, categories, and rational number intervals using these data displays (2.4.K1j) $ 1a. Frequency tables; SE/TE: 58, , 611, 620, 622 1b. Bar, line, and circle graphs; SE/TE: 56, 195, 305, 309, 327, , , 514, 536, 545, , , 580, , 600, , 612, 619, 620, 622, 674, 682, 690, 694 1c. Venn diagrams or other pictorial displays; SE/TE: 35, 43, 66-67, 249, 252, 308, 588,

18 1d. Charts and tables; SE/TE: 3, 11, 37, 43, 49, 57, 59, 69, 71, 127, 168, 172, 175, 176, 185, 201, 226, 239, , 253, 256, 284, 294, 299, 316, 320, 331, , 396, 401, 455, , , , 512, 514, 542, , 569, , 579, 581, 583, 585, , , , 609, 613, , 622, 627, 634, 639, 657, 668, 692, 694 1e. Stem-and-leaf plots (single); SE/TE: , 619, 621, 622, 641, 675 1f. Scatter plots; SE/TE: , 621, 622, 634 1g. Box-and-whiskers plots. SE/TE: , 621, Selects and justifies the choice of data collection techniques (observations, surveys, or interviews) and sampling techniques (random sampling, samples of convenience, or purposeful sampling) in a given situation. 3. Conducts experiments with sampling and describes the results. 4. Determines the measures of central tendency (mode, median, mean) for a rational number data set (2.4.K1a) $. 5. Identifies and determines the range and the quartiles of a rational number data set (2.4.K1a) $. 6. Identifies potential outliers within a set of data by inspection rather than formal calculation (2.4.K1a) $, e.g., consider the data set of 1, 100, 101, 120, 140, and 170; the outlier is 1. SE/TE: 576, 581, 589, 591, , 680 SE/TE: , 621, 622, 680 SE/TE: 56-60, 63, 64, 65, 196, 235, 259, 337, 341, 382, 515, 572, , , 619, 675, 684 SE/TE: 41-43, , 619 SE/TE: 57-60,

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