# Prentice Hall Mathematics: Course Correlated to: Arizona Academic Standards for Mathematics (Grades 6)

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1 PO 1. Express fractions as ratios, comparing two whole numbers (e.g., ¾ is equivalent to 3:4 and 3 to 4). Strand 1: Number Sense and Operations Every student should understand and use all concepts and skills from the previous grade levels. The standards are designed so that new learning builds on preceding skills and are needed to learn new skills. Communication, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of mathematical strands. Concept 1: Number Sense Understand and apply numbers, ways of representing numbers, the relationships among numbers and different number systems. SE: , , , , TE: 307, web code: aqe-0775, aqe- 0701, aqe-0705 PO 2. Compare two proper fractions, improper fractions, or mixed numbers SE: , , , 202, , 206 TE: 193, web code: aqe-0408, aqe

2 PO 3. Order three or more proper fractions, improper fractions, or mixed numbers. SE: , , , 202, , 206 TE: 193, web code: aqe-0408, aqe PO 4. Determine the equivalency between and among fractions, decimals, and percents in contextual situations. SE: , , , 330, , , , TE: 199, web code: aqe-0409, aqe- 0702, aqe-0705, aqe-0708, aqe

3 PO 5. Identify the greatest common factor for two whole numbers. PO 6. Determine the least common multiple for two whole numbers. SE: , , 180, , 206 TE: 172, web code: aqe-0404, aqe SE: , , 206 TE: 189, web code: aqe-0407 PO 7. Express a whole number as a product of its prime factors, using exponents when appropriate. SE: , , 206 TE: 167, 169, 170 3

4 PO 1. Select the grade-level appropriate operation to solve word problems. web code: aqe-0404, aqe Concept 2: Numerical Operations Understand and apply numerical operations and their relationship to one another. SE: 22-25, 32-41, 44-50, 55-65, 61-66, , , , 251, , , , , , , , , TE: 49, 91, 143, 197, 244, 287, 347, web code: aqe-aqe-0105, aqe- 0775, aqe-0775, aqe-0108, aqe-0109, aqe-0201, aqe-0504, aqe-0505 PO 2. Solve word problems using grade-level appropriate operations and numbers. SE: 22-25, 32-41, 44-50, 55-65, 61-66, , , , 251, , , , , , , , , TE: 48, 62, 317, 417 4

5 PO 3. Apply grade-level appropriate properties to assist in computation. web code: aqe-aqe-0105, aqe- 0775, aqe-0775, aqe-0108, aqe-0109, aqe-0201, aqe-0504, aqe-0505 SE: 12-21, 26-36, 37-47, 51-54, 61-65, , , , , , , , TE: 32, 62, 168, web code: aqe-0102, aqe- 0104, aqe-0106, aqe-0107, aqe-0109, aqe-0201 PO 4. Apply the symbols for or to represent repeating decimals and : to represent ratios, superscripts as exponents. SE: , 280, , , 570, TE: 163, 307 5

6 PO 5. Use grade-level appropriate mathematical terminology. web code: aqe-0775, aqe- 0402, aqe-0701 SE: 65, 74, 128, , 185, 290, , , 341, , 384, 403, 425, 449, 486, 493, 548, 559, 588 TE: 35, 58, 100, 150, 187, 252, 304, 360, 414, 508, 564 PO 6. Simplify fractions to lowest terms. SE: , , , , 237, , , , TE: 177, 185, web code: aqe-0406, aqe- 0775, aqe-0603 PO 7. Add or subtract proper fractions and mixed numbers with unlike denominators with regrouping. SE: , , , , , 301 TE: 225, 226, 230, 252 6

7 web code: aqe-0775, aqe- 0504, aqe-0505, aqe-0553 PO 8. Demonstrate the process of multiplication of proper fractions using models. SE: 260, , web code: aqe-0601 PO 9. Multiply proper fractions. SE: , , , 300 TE:

8 web code: aqe-0601, 0604 PO 10. Multiply mixed numbers. SE: , 280, TE: web code: aqe-0653 PO 11. Demonstrate that division is the inverse of multiplication of proper fractions. SE: , , , 300 TE: 274, web code: aqe

9 PO 12. Divide proper fractions. SE: , , , 300 TE: web code: aqe-0775 PO 13. Divide mixed numbers. SE: , , 300 TE: web code: aqe 0775 PO 14. Solve problems involving fractions or decimals (including money) in contextual situations. SE: 26-30, 32-36, 38-41, 44-47, 56-57, , , , , , 353 TE: 33, 39, 45, 177 9

10 web code: aqe-0106, aqe- 0107, aqe-0108, aqe-0109 PO 15. Simplify numerical expressions using the order of operations with grade-appropriate operations on number sets. SE: 16-20, 32-36, 38-41, 44-47, , , 152 TE: 18, 33 web code: aqe-0105, aqe- 0107, aqe-0108, aqe-0109, aqe-0308, aqe-0504, aqe-0775 Concept 3: Estimation Use estimation strategies reasonably and fluently. PO 1. Solve grade-level appropriate problems using estimation. SE: 32-38, 53, , , , , 356 TE: 34, 213, 253,

11 PO 2. Use estimation to verify the reasonableness of a calculation (e.g., Is 5/9 x 3/7 more than 1?). web code: aqe-0553, aqe SE: 32-38, 53, , , , , 356 TE: 35, 213, web code: aqe-0553, aqe PO 3. Round to estimate quantities in contextual situations (e.g., round up or round down). SE: 8-10, 32, 125, 210, , 352 TE: 9,

12 PO 4. Estimate and measure for the area and perimeter of polygons using a grid. web code: aqe-0709 SE: , 431, , PO 5. Verify the reasonableness of estimates made from calculator results within a contextual situation. TE: 427, 428, 434, 445 Strand 2: Data Analysis, Probability, and Discrete web code: aqe-0903, aqe SE: 42, 138, 163, 180, 232, 237, 280, 437, 440, Every student should understand and use all concepts and skills from the previous grade levels. The standards are designed so that new learning builds on preceding skills and are needed to learn new skills. Communication, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of mathematical strands. Concept 1: Data Analysis (Statistics) Understand and apply data collection, organization and representation to analyze and sort data. PO 1. Formulate questions to collect data in contextual situations. SE: 48, 61-69, 70-73, 74-77, 80-83, 86-90, 93-97, 202, 239, , 325, 345, , 431, 437, 457, 461, TE: 62, 75, 81,

13 PO 2. Construct a histogram, line graph, scatter plot, or stem-and-leaf plot with appropriate labels and title from organized data. PO 3. Interpret simple displays of data including double bar graphs, tally charts, frequency tables, circle graphs, and line graphs. web code: aqe-0201, aqe- 0202, aqe-0203, aqe-0204, aqe-0205, aqe-0206, aqe-0507, aqe-0753, aqe-1004 SE: 74-77, 78-79, 80-83, 84, 86-90, 93-97, 239, 507 TE: 75, 81, 87 web code: aqe-0203, aqe- 0204, aqe-0205, aqe-0206 SE: 74-77, 78-79, 80-83, 84, 86-90, 93-97, 239, 507 TE: 75, 81, 87 13

14 PO 4. Answer questions based on simple displays of data including double bar graphs, tally charts, frequency tables, circle graphs, and line graphs. web code: aqe-0203, aqe- 0204, aqe-0205, aqe-0206 SE: 74-77, 78-79, 80-83, 84, 85-90, , 102, 239, 325, 345, 507 TE: 81, 93 web code: aqe aqe- 0204, aqe-0205, aqe-0506 PO 5. Find the mean, median (odd number of data points), mode, range, and extreme values of a given numerical data set. SE: 60-65, 66-69, 70-73, 93-97, 99, , 102, 103, 202 TE: 63, 67, 94 14

15 PO 6. Identify a trend (variable increasing, decreasing, remaining constant) from displayed data. web code: aqe-0201, aqe- 0202, aqe-0206 SE: 60-65, 66-69, 70-73, 93-97, 99, , 102, 103, 202, 325, 345 TE: 63, 71 web code: aqe-0201, aqe- 0202, aqe-0206 PO 7. Compare trends in data related to the same investigation. SE: 325, 345 TE:

16 PO 8. Solve contextual problems using bar graphs, tally charts, and frequency tables. SE: 70-73, 74-77, 78-79, 84, 93-97, , 102 TE: 72, 94 web code: aqe-0202, aqe- 0203, aqe-0205 Concept 2: Probability Understand and apply the basic concepts of probability. PO 1. Name the possible outcomes for a SE: , , , 510 probability experiment. TE: 477, web code: aqe-0775 PO 2. Express probabilities of a single event as a decimal. SE: , , , , , 511 TE: 489,

17 web code: aqe-1002, aqe- 0775, aqe-1004, aqe-1005 PO 3. Predict the outcome of a grade-level appropriate probability experiment. PO 4. Record the data from performing a gradelevel appropriate probability experiment. SE: , 492, 498, 499, , 504, , 507, , 510 TE: 489, web code: aqe-1005 SE: 493, 498, 499, 504, 506 TE:

18 PO 5. Compare the outcome of an experiment to predictions made prior to performing the experiment. SE: 492, 498, 499, TE: PO 6. Make predictions from the results of student-segenerated experiments using objects (e.g., coins, 492, 498, 499, spinners, number cubes, cards). TE:

19 PO 7. Compare the results of two repetitions of the same grade-level appropriate probability experiment. SE: 492, 498, 499, 504 TE: Concept 3: Discrete Systematic Listing and Counting Understand and demonstrate the systematic listing and counting of possible outcomes. PO 1. Determine all possible outcomes involving a SE: , , 510 combination of three sets of three items, using a systematic approach (e.g., 3 different shirts, 3 different pairs of pants, and 3 different belts). TE: web code: aqe

20 PO 2. Determine all possible arrangements given a set with four or fewer objects using a systematic list, table or tree diagram when order is not important. SE: , , 510 TE: web code: aqe-1001 Concept 4: Vertex-Edge Graphs Understand and apply vertex-edge graphs. PO 1. Find the shortest route on a map from one site to another (vertex-edge graph). Strand 3: Patterns, Algebra, and Functions Every student should understand and use all concepts and skills from the previous grade levels. The standards are designed so that new learning builds on preceding skills and are needed to learn new skills. Communication, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of mathematical strands. Concept 1: Patterns Identify patterns and apply pattern recognition to reason mathematically. PO 1. Communicate a grade-level appropriate SE: , 112, 123, , 152 recursive pattern, using symbols or numbers. TE:

21 PO 2. Extend a grade-level appropriate iterative pattern. PO 3. Solve grade-level appropriate iterative pattern problems. web code: aqe-0301 SE: 42, , 112, 123, , 152 TE: web code: aqe-0301 SE: 42, , 112, 123, , 152 TE: web code: aqe

22 Concept 2: Functions and Relationships Describe and model functions and their relationships. PO 1. Describe the rule used in a simple gradelevel appropriate function (e.g., T-chart, SE: , , , 566 input/output model). TE: 556, web code: aqe-1107 Concept 3: Algebraic Representations Represent and analyze mathematical situations and structures using algebraic representations. PO 1. Evaluate expressions involving the four basic operations by substituting given fractions for the variable (e.g., n +3, when n = ½ ). SE: , 204, , , TE: 163, web code: aqe-0402, aqe

23 PO 2. Use variables in contextual situations. SE: , , , , , , 148, 149, , 152 TE: 119, 125, 132, web code: aqe-0302, aqe- 0303, aqe-0304, aqe-0305, aqe-0306, aqe-0307 PO 3. Translate a written phrase to an algebraic expression (e.g., The quotient of m and 5 is m /5 or m 5) SE: , 117, , 149, , 563 PO 4. Translate a phrase written in context into an algebraic expression (e.g., Write an expression to describe the situation: John has x pieces of candy and buys three more. x + 3). TE: 115, web code: aqe-0302, aqe- 0303, aqe-0453 SE: , 117, , 149, , 563 TE: 114,

24 web code: aqe-0302, aqe- 0303, aqe-0453 PO 5. Solve one-step equations with one variable represented by a letter or symbol, using inverse operations with whole numbers. SE: , , , , 149, , 152, , , , 254, 265 TE: 125, 131, 135 Concept 4: Analysis of Change Analyze change in a variable over time and in various contexts. PO 1. Identify values on a given line graph or SE: 74-77, , 102 scatter plot (e.g., Given a line showing wages earned per hour, what is the wage at five hours?). web code: aqe-0304, aqe- 0775, aqe-0506 TE: 76 24

25 web code: aqe-0203 Strand 4: Geometry and Measurement Every student should understand and use all concepts and skills from the previous grade levels. The standards are designed so that new learning builds on preceding skills and are needed to learn new skills. Communication, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of mathematical strands. Concept 1: Geometric Properties Analyze the attributes and properties of 2- and 3- dimensional shapes and develop mathematical arguments about their relationships. PO 1. Classify polygons by their attributes (e.g., number of sides, length of sides, angles, parallelism, perpendicularity). SE: 379, , , , 407, , 410, TE: 381, web code: aqe-0775, aqe- 0804, aqe-0805, aqe

26 PO 2. Draw a geometric figure showing specified properties, such as parallelism and perpendicularity. SE: , , , , , 410, TE: 368, web code: aqe-0807 PO 3. Classify prisms, pyramids, cones, and cylinders by base shape and lateral surface shape. SE: 448, , 453, 456, , , 470 TE: 450, web code: aqe-0908, aqe PO 4. Classify 3-dimensional figures by their attributes. SE: , , , 470, TE: 450,

27 web code: aqe-0908, 0911 PO 5. Compare attributes of 2-dimensional figures with 3-dimensional figures. SE: , , , , TE: 451, web code: aqe-0905, aqe- 0909, aqe-0910, aqe-0911 PO 6. Draw triangles with appropriate labels. SE: 372, , , , , 406, TE: 381, 383,

28 PO 7. Identify supplementary or complementary angles. PO 8. Identify the diameter, radius, and circumference of a circle or sphere. web code: aqe-0904, aqe- 0805, aqe-0808 SE: , , 410 TE: web code: aqe-0807, 0808 SE: , , , , 470, 471 TE: 440, web code: aqe-0906, aqe

29 PO 9. Draw a 2-dimensional shape with a given number of lines of symmetry. PO 1. Identify reflections and translations using pictures. SE: , , TE: web code: aqe-0807, aqe Concept 2: Transformation of Shapes Apply spatial reasoning to create transformations and use symmetry to analyze mathematical situations. SE: , , 410, 553 TE: 404, web code: aqe-0808 PO 2. Perform elementary transformations to create a tessellation. SE: TE:

30 PO 1. Graph a polygon in the first quadrant using ordered pairs. web code: aqe-0808 Concept 3: Coordinate Geometry Specify and describe spatial relationships using coordinate geometry and other representational systems. SE: , 553 TE: 549, Interactive Textbook 11-8 PO 2. State the missing coordinate of a given figure in the first quadrant of a coordinate grid using geometric properties (e.g., Find the coordinates of the missing vertex of a rectangle when two adjacent sides are drawn.). SE: , , 566 TE:

31 PO 1. Determine the appropriate measure of accuracy within a system for a given contextual situation (e.g., Would you measure the length of your bedroom wall using inches or feet?). Interactive Textbook 11-8 Concept 4: Measurement - Units of Measure - Geometric Objects Understand and apply appropriate units of measure, measurement techniques, and formulas to determine measurements. SE: , , , 254, , , 297, , 300, , , TE: 247, 252, web code: aqe-0605, 0606 PO 2. Determine the appropriate tool needed to measure to the needed accuracy. SE: 185 (# 33, 34), 186, 206 (#16), 298 TE:

32 PO 3. Determine a linear measurement to the appropriate degree of accuracy. web code 0406 SE: 185 (# 33, 34), 206 (#16), , , TE: web code: aqe-0605, aqe- 0606, aqe-0653 PO 4. Measure angles using a protractor. SE: , 377, 378, TE: 368,

33 PO 5. Convert within a single measurement system (U.S. customary or metric) (e.g., How many ounces are equivalent to 2 pounds?). PO 6. Solve problems involving the perimeter of polygons. web code: aqe-0802, aqe SE: , , 300, TE: web code: aqe-0606 SE: , 431, , , TE: 428, 434, web code: aqe-0903, aqe- 0905, aqe

34 PO 7. Determine the area of triangles. SE: , , 470 TE: web code: aqe-0905 PO 8. Distinguish between perimeter and area in contextual situation. PO 9. Solve problems for the areas of parallelograms (includes rectangles). SE: , , , , 471, 470, TE: 428, 429, 441, web code: aqe-0905, aqe- 0906, aqe-0907, aqe-1053 SE: , , , 470 TE: 427,

35 PO 10. Identify parallelograms having the same perimeter or area. PO 11. Determine the actual measure of objects using a scale drawing or map. web code: aqe-0904, aqe SE: TE: web code: aqe-0775 SE: , , 356, TE: 327, web code: aqe

36 Strand 5: Structure and Logic Every student should understand and use all concepts and skills from the previous grade levels. The standards are designed so that new learning builds on preceding skills and are needed to learn new skills. Communication, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of mathematical strands. Concept 1: Algorithms and Algorithmic Thinking Use reasoning to solve mathematical problems in contextual situations. PO 1. Discriminate necessary information from SE: xxxiv-xli, 49-50, 55, 91-92, 103, , unnecessary information in a given grade-level , 207, appropriate word problem. TE: 50, 92, web code: aqe-0604 PO 2. Analyze algorithms for computing with decimals. SE: 22-25, 26-31, 32-37, 38-42, 44-47, 51, 61-65, TE: 21, 37, 45, 62 web code: aqe-0105, aqe- 0106, aqe-0108, aqe

37 Concept 2: Logic, Reasoning, Arguments, and Mathematical Proof PO 1. Solve a simple logic problem from given information (e.g., Which of three different people live in which of three different colored houses?). Evaluate situations, select problem-solving strategies, draw logical conclusions, develop and describe solutions and recognize their applications. SE: 371 (#16), 378, 379, 385, 390 (#24-28), TE: 385,

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