PO 2. Identify irrational numbers. SE/TE: 4-8: Exploring Square Roots and Irrational Numbers, TECH: itext; PH Presentation Pro CD-ROM;

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1 Arizona Mathematics Standards Articulated by Grade Level Strands 1-5, Performance Objectives (Grade 8) STRAND 1: NUMBER SENSE AND OPERATIONS Concept 1: Number Sense Locate rational numbers on a number line. SE/TE: 1-3: Integers and Absolute Value, 16-21; 1-4: Adding and Subtracting Integers, Identify irrational numbers. SE/TE: 4-8: Exploring Square Roots and Irrational Numbers, Classify numbers as rational or irrational. SE/TE: 4-3: Comparing and Ordering Rational Numbers, ; 4-8: Exploring Square Roots and Irrational Numbers, Concept 2: Numerical Operations Select the grade level appropriate operation to solve word problems. SE/TE: 1-4: Adding and Subtracting Integers, 22-26; 1-5: Multiplying and Dividing Integers, 28-32; 2-1: Solving One-Step Equations, 61-66; 2-2: Solving Two-Step Equations, 69-72; 2-4: Solving Multi-Step Equations, 78-82; 2-6: Solving Inequalities by Adding or Subtracting, 90-95; 2-7: Solving Inequalities by Multiplying or Dividing, ; 2-8: Solving Two-Step Inequalities, ; 4-4: Adding and Subtracting Rational Numbers, ; 4-5: Multiplying and Dividing Rational Numbers, ; 4-9: The Pythagorean Theorem, ; 6-3: Percents and Proportions, ; 6-4: Percents and Equations, ; 6-5: Percent of Change, ; 6-6: Markup and Discount, ; 6-8: Simple and Compound Interest,

2 Select the grade level appropriate operation to solve word problems. SE/TE: 7-2: Exponents and Multiplication, ; 7-3: Exponents and Division, Solve word problems using grade level appropriate operations and numbers. SE/TE: Real-World Snapshots: 56-57, , , , , , , , , , , ; 1-4: Adding and Subtracting Integers, 22-26; 1-5: Multiplying and Dividing Integers, 28-32; 2-1: Solving One-Step Equations, 61-66; 2-2: Solving Two-Step Equations, 69-72; 2-4: Solving Multi-Step Equations, 78-82; 2-6: Solving Inequalities by Adding or Subtracting, 90-95; 2-7: Solving Inequalities by Multiplying or Dividing, ; 2-8: Solving Two-Step Inequalities, ; 4-4: Adding and Subtracting Rational Numbers, ; 4-5: Multiplying and Dividing Rational Numbers, ; 4-9: The Pythagorean Theorem, ; 6-3: Percents and Proportions, ; 6-4: Percents and Equations, ; 6-5: Percent of Change, ; 6-6: Markup and Discount, ; 6-8: Simple and Compound Interest, ; 7-2: Exponents and Multiplication, ; 7-3: Exponents and Division, Determine the square of an integer. SE/TE: 4-8: Exploring Square Roots and Irrational Numbers,

3 Determine the square root of an integer. SE/TE: 4-8: Exploring Square Roots and Irrational Numbers, PO 5. PO 6. PO 7. Identify squaring and finding square roots as inverse operations. Apply grade level appropriate properties to assist in computation. Apply the symbols to represent square root, ± to represent roots, {} as grouping symbols. SE/TE: 4-8: Exploring Square Roots and Irrational Numbers, SE/TE: 1-4: Adding and Subtracting Integers, 22-26; 1-5: Multiplying and Dividing Integers, 28-32; 2-1: Solving One-Step Equations, 61-66; 2-2: Solving Two-Step Equations, 69-72; 2-4: Solving Multi-Step Equations, 78-82; 2-6: Solving Inequalities by Adding or Subtracting, 90-95; 2-7: Solving Inequalities by Multiplying or Dividing, ; 2-8: Solving Two-Step Inequalities, ; 4-4: Adding and Subtracting Rational Numbers, ; 4-5: Multiplying and Dividing Rational Numbers, ; 4-9: The Pythagorean Theorem, ; 6-3: Percents and Proportions, ; 6-4: Percents and Equations, ; 6-5: Percent of Change, ; 6-6: Markup and Discount, ; 6-8: Simple and Compound Interest, ; 7-2: Exponents and Multiplication, ; 7-3: Exponents and Division, SE/TE: 1-1: Algebraic Expressions and the Order of Operations, 5-10; 4-8: Exploring Square Roots and Irrational Numbers,

4 PO 8. Use grade level appropriate mathematical terminology. SE/TE: Writing in Math: 9, 14, 19, 26, 31, 37, 42, 50, 54, 65, 67, 71, 77, 81, 88, 93, 101, 105, 107, 110, 120, 125, 127, 132, 140, 144, 149, 155, 161, 166, 173, 178, 188, 194, 199, 203, 209, 214, 219, 224, 230, 236, 246, 251, 256, 163, 169, 275, 280, 284, 290, 296, 307, 312, 318, 323, 329, 335, 340, 346, 348, 353, 357, 358, 369, 380, 386, 390, 394, 400, 411, 416, 424, 428, 433, 438, 445, 446, 450, 453, 458, 464, 474, 480, 484, 487, 492, 498, 504, 509, 514, 521, 526, 536, 543, 545, 550, 555, 561, 566 PO 8. PO 9. Use grade level appropriate mathematical terminology. Calculate the missing value in a percentage problem. SE/TE: Writing in Math: 573, 578, 584, 593, 598, 603, 609, 614, 618, 624, 630, 641, 646, 651, 656, 661, 666, 670, 677, 681, 685, 690 SE/TE: 6-3: Percents and Proportions, ; 6-4: Percents and Equations, ; 6-5: Percent of Change, ; 6-6: Markup and Discount, ; 6-8: Simple and Compound Interest, PO 10. Convert standard notation to scientific notation and vice versa. PO 11. Simplify numerical expressions using the order of operations with grade appropriate operations on number sets. SE/TE: 7-1: Scientific Notation, ; 7-2: Exponents and Multiplication, ; 7-3: Exponents and Division, ; 7-4: Power Rules, SE/TE: 1-7: Powers and Exponents, 39-43; 2-3: Simplifying Algebraic Expressions, Concept 3: Estimation 4

5 Solve grade level appropriate problems using estimation. SE/TE: 6-2: Estimating With Percents, ; estimation: 10, 26, 31, 42, 71, 143, 250, 251, 260, 281, 316, 327, 328, 351, 451, 475, 492, 498, 503, 507, 509 Use estimation to verify the reasonableness of a calculation. (e.g., Is 32 the square root of 64?) Use estimation to verify the reasonableness of a calculation. (e.g., Is 32 the square root of 64?) Express answers to the appropriate place or degree of precision. (e.g., time and money) Verify the reasonableness of estimates made from calculator results within a contextual situation SE/TE: estimation: 10, 26, 31, 42, 71, 143, 250, 251, 260, 281, 314, 316, 327, 328, 351, 451, 475, 492, 498, 503, 507, 509 SE/TE: Investigation: Precision and Greatest Possible Error, 486 SE/TE: estimation: 10, 26, 31, 42, 71, 143, 250, 251, 260, 281, 314, 316, 327, 328, 351, 451, 475, 492, 498, 503, 507, 509 STRAND 2: DATA ANALYSIS, PROBABILITY, AND DISCRETE MATHEMATICS Concept 1: Data Analysis (Statistics) Formulate questions to collect data in contextual situations. SE/TE: 10-1: Displaying Frequency, ; 10-3: Stem-and-Leaf Plots, ; 10-4: Boxand-Whisker Plots, ; 10-7: Choosing an Appropriate Graph,

6 Construct box and whisker plots. SE/TE: 10-4: Box-and-Whisker Plots, PO 5. PO 6. PO 7. Determine the appropriate type of graphical display for a given data set. Interpret box-and-whisker plots, circle graphs and scatter plots Interpret box-and-whisker plots, circle graphs and scatter plots Answer questions based on box-andwhisker plots, circle graphs and scatter plots. Solve problems in contextual situations using the mean, median, mode, and range of a given data set. Formulate reasonable predictions based on a given set of data. SE/TE: 10-7: Choosing an Appropriate Graph, SE/TE: 10-4: Box-and-Whisker Plots, ; 10-5: Making Predictions From Scatter Plots, ; 10-6: Circle Graphs, SE/TE: 10-4: Box-and-Whisker Plots, ; 10-5: Making Predictions From Scatter Plots, ; 10-6: Circle Graphs, SE/TE: 1-6: Using Integers With Mean, Median, and Mode, SE/TE: 10-5: Making Predictions From Scatter Plots,

7 PO 8. Compare trends in data related to the same investigation. SE/TE: 10-1: Displaying Frequency, ; 10-2: Reading Graphs Critically, ; 10-5: Making Predictions From Scatter Plots, PO 9. Solve contextual problems using scatter plots, box-and-whiskers plots, and double line graphs of continuous data. SE/TE: 10-4: Box-and-Whisker Plots, ; 10-5: Making Predictions From Scatter Plots, PO 10. Evaluate the effects of missing or incorrect data on the results of an investigation. (e.g., Susie s teacher recorded a 39 instead of a 93 for her last quiz, what will happen to Susie s average?) PO 11. Identify a line of best fit for a scatter plot. PO 12. Distinguish between causation and correlation. SE/TE: 10-2: Reading Graphs Critically, SE/TE: 10-5: Making Predictions From Scatter Plots, SE/TE: 10-2: Reading Graphs Critically, ; 10-5: Making Predictions From Scatter Plots, Concept 2: Probability 7

8 Determine the probability that a specific event will occur in a 2-stage probability experiment. SE/TE: 11-4: Theoretical and Experimental Probability, ; 11-5: Independent and Dependent Events, Solve contextual situations using probability. (e.g., If the probability of Michelle making a free throw is 0.25, what is the probability that she will make six free throws in a row?) Predict the outcome of a grade level appropriate probability experiment. SE/TE: 11-1: Counting Outcomes, ; 11-4: Theoretical and Experimental Probability, ; 11-5: Independent and Dependent Events, SE/TE: 11-4: Theoretical and Experimental Probability, PO 5. PO 6. Record the data from performing a grade level appropriate probability experiment. Compare the outcome of an experiment to predictions made prior to performing the experiment. Distinguish between independent and dependent events. SE/TE: 11-1: Counting Outcomes, ; 11-4: Theoretical and Experimental Probability, SE/TE: 11-1: Counting Outcomes, ; 11-4: Theoretical and Experimental Probability, SE/TE: 11-5: Independent and Dependent Events,

9 PO 7. Compare the results of two repetitions of the same grade level appropriate probability experiment. SE/TE: 11-1: Counting Outcomes, ; 11-4: Theoretical and Experimental Probability, Concept 3: Discrete Mathematics Systematic Listing and Counting Determine all possible outcomes involving the combination of two or more sets of objects. (e.g. If you roll a 6 sided number cube 4 times how many possible outcomes are possible?) Determine all possible arrangements given a set. (e.g. How many ways can you arrange a set of 7 books on a shelf? ) SE/TE: 11-1: Counting Outcomes, ; 11-2: Permutations, SE/TE: 11-3: Combinations, Concept 4: Vertex-Edge Graphs Solve contextual problems represented by vertex edge graphs. SE/TE: 5-7: Scale Models and Maps, STRAND 3: PATTERNS, ALGEBRA, AND FUNCTIONS Concept 1: Patterns Communicate a grade level appropriate iterative or recursive pattern, using symbols or numbers. SE/TE: 8-4: Solve a Simpler Problem and Look for a Pattern,

10 Extend a grade level appropriate iterative or recursive pattern. SE/TE: 8-4: Solve a Simpler Problem and Look for a Pattern, Solve grade level appropriate iterative or recursive pattern problems. SE/TE: 8-4: Solve a Simpler Problem and Look for a Pattern, Concept 2: Functions and Relationships Describe the rule used in a simple grade level appropriate function (e.g., T-chart, input/output model). Distinguish between linear and nonlinear functions, given graphic examples Distinguish between linear and nonlinear functions, given graphic examples Determine whether a graph or table are related to a given equation of the form y=ax 2 where a is a natural number. Identify independent and dependent variables for a contextual situation. SE/TE: 12-4: Writing Rules for Linear Functions, SE/TE: 12-2: Functions, ; 12-3: Graphing Linear Functions, ; 12-4: Writing Rules for Linear Functions, ; 12-6: Quadratic and Other Nonlinear Functions, Resource Pro CD-ROM TECH: Computer Test Generator CD-ROM; PH SuccessNet; SE/TE: 12-3: Graphing Linear Functions, ; 12-5: Relating Graphs to Events, SE/TE: 12-3: Graphing Linear Functions, ; 12-6: Quadratic and Other Nonlinear Functions,

11 Concept 3: Algebraic Representations Evaluate algebraic expressions by substituting rational values for variables. [e.g., 2(ab+ac+bc), when a = 2, b = 3/5, and c = 4] SE/TE: 1-7: Powers and Exponents, 39-43; 2-3: Simplifying Algebraic Expressions, Use variables in contextual situations. SE/TE: 1-1: Algebraic Expressions and the Order of Operations, 5-10; 2-1: Solving One-Step Equations, 61-66; 2-2: Solving Two-Step Equations, 69-72; 2-3: Simplifying Algebraic Expressions, 73-77; 2-4: Solving Multi-Step Equations, 78-82; 2-6: Solving Inequalities by Adding or Subtracting, 90-95; 2-7: Solving Inequalities by Multiplying or Dividing, ; 2-8: Solving Two-Step Inequalities, PO 5. Translate a written sentence or phrase into an algebraic equation or expression and vice versa. (e.g., three less than twice a number is 2n-3) Translate a sentence written in context into an algebraic equation involving two operations. Translate a contextual situation into an algebraic inequality. (e.g., Joe earns more than $5.00 an hour; therefore, x > 5) SE/TE: 5-3: Write an Equation, ; 6-7: Write an Equation, ; 7-5: Write an Equation, ; 12-7: Write an Equation, Generator CD-ROM, PH SuccessNet; SE/TE: 6-7: Write an Equation, ; 7-5: Write an Equation, ; 12-7: Write an Equation, SE/TE: 2-6: Solving Inequalities by Adding or Subtracting,

12 PO 6. Identify an equation or inequality that represents a contextual situation. SE/TE: 2-6: Solving Inequalities by Adding or Subtracting, 90-95; 2-7: Solving Inequalities by Multiplying or Dividing, ; 2-8: Solving Two-Step Inequalities, PO 7. PO 8. PO 9. Solve one-step equations with rational numbers as coefficients or as solutions. Solve one-step equations that model contextual situations. Solve two-step equations with rational coefficients and integer solutions. (e.g., 3x+5=11, 4x 20 = 8) SE/TE: 2-1: Solving One-Step Equations, 61-66; Chapter Preview: 302, 406 SE/TE: 2-1: Solving One-Step Equations, 61-66; Chapter Preview: 302, 406 SE/TE: 2-2: Solving Two-Step Equations, 69-72; 3-7: Solving Linear Systems by Graphing, PO 10. Graph an inequality on a number line. PO 10. Graph an inequality on a number line. SE/TE: 2-6: Solving Inequalities by Adding or Subtracting, Resource Pro CD-ROM TECH: Computer Test Generator CD-ROM; PH SuccessNet; PO 11. Solve a simple algebraic proportion. SE/TE: 5-4: Solving Proportions, ; 5-5: Similar Figures and Proportions, ; 6-3: Percents and Proportions,

13 PO 12. Solve applied problems using the Pythagorean theorem. SE/TE: 4-9: The Pythagorean Theorem, Concept 4: Analysis of Change Identify the slope of a line as the rate of change. (the ratio of rise over run) SE/TE: 3-3: Understanding Slope, STRAND 4: GEOMETRY AND MEASUREMENT Concept 1: Geometric Properties Draw a model that demonstrates basic geometric relationships such as parallelism, perpendicularity, similarity/proportionality, and congruence. Draw three-dimensional figures by applying properties of each. (e.g. parallelism, perpendicularity and congruency) Recognize the three-dimensional figure represented by a net. Represent the surface area of rectangular prisms and cylinders as the area of their net. SE/TE: 8-1: Pairs of Angles, ; 8-2: Angles and Parallel Lines, ; 8-9: Constructions, SE/TE: 9-1: Solids, ; 9-2: Drawing Views of Solids, SE/TE: 9-3: Nets and Solids, Resource Pro CD-ROM, Computer Test SE/TE: 9-4: Surface Areas of Prisms and Cylinders,

14 PO 5. Draw regular polygons with appropriate labels. SE/TE: 8-6: Angles and Polygons, PO 6. PO 7. Identify the properties of angles created by a transversal intersecting two parallel lines (e.g., corresponding angles are congruent). Recognize the relationship between inscribed angles and intercepted arcs. SE/TE: 8-2: Angles and Parallel Lines, ; 8-6: Angles and Polygons, SE/TE: 8-8: Circumferences and Areas of Circles, PO 8. Identify tangents and secants of a circle. SE/TE: 8-8: Circumferences and Areas of Circles, PO 9. Determine whether three given lengths can form a triangle. SE/TE: 8-5: Classifying Triangles and Quadrilaterals, PO 10. Identify corresponding angles of similar polygons as congruent and sides as proportional SE/TE: 5-5: Similar Figures and Proportions, ; 8-3: Congruent Polygons, Concept 2: Transformation of Shapes 14

15 Identify the planar geometric figure that is the result of a given rigid transformation. SE/TE: 3-8: Translations, ; 3-9: Reflections and Symmetry, ; 3-10: Rotations, Model a simple transformation on a coordinate grid. (e.g. translate right four units and down two units) SE/TE: 5-6: Similarity Transformations, Concept 3: Coordinate Geometry Use a table of values to graph a linear equation Determine the midpoint given two points on a number line. Determine the distance between two points on a number line. SE/TE: 3-2: Graphing Equations With Two Variables, ; 3-3: Understanding Slope, ; 3-4: Using the y-intercept, ; 3-6: Using Graphs of Equations, SE/TE: 8-9: Constructions, SE/TE: 1-4: Adding and Subtracting Integers, 22-26; 2-6: Solving Inequalities by Adding or Subtracting, Concept 4: Measurement Units of Measure - Geometric Objects Solve problems for the area of a trapezoid. SE/TE: 8-7: Areas of Polygons,

16 Solve problems involving the volume of rectangular prisms and cylinders. SE/TE: 9-6: Volumes of Prisms and Cylinders, PO 5. PO 6. PO 7. Calculate the surface area of rectangular prisms or cylinders. Identify rectangular prisms and cylinders having the same volume. Find the sum of the interior and exterior angles of a polygon. Solve problems using ratios and proportions given the scale factor. Calculate the length of a side given two similar triangles. SE/TE: 9-4: Surface Areas of Prisms and Cylinders, SE/TE: 9-6: Volumes of Prisms and Cylinders, SE/TE: 8-6: Angles and Polygons, SE/TE: 5-7: Scale Models and Maps, ; 5-8: Similarity and Indirect Measurement, SE/TE: 5-5: Similar Figures and Proportions, STRAND 5: STRUCTURE AND LOGIC Concept 1: Algorithms and Algorithmic Thinking Describe how to use a proportion to solve a problem in context. SE/TE: 5-4: Solving Proportions, ; 5-5: Similar Figures and Proportions, ; 6-3: Percents and Proportions, Resource Pro CD-ROM 16

17 Describe how to use a proportion to solve a problem in context. TECH: Computer Test Generator CD-ROM; PH SuccessNet; Analyze algorithms. SE/TE: 1-4: Adding and Subtracting Integers, 22-26; 1-5: Multiplying and Dividing Integers, 28-32; 4-4: Adding and Subtracting Rational Numbers, ; 4-5: Multiplying and Dividing Rational Numbers, ; 6-3: Percents and Proportions, ; 6-4: Percents and Equations, ; 6-5: Percent of Change, ; 6-6: Markup and Discount, ; 6-8: Simple and Compound Interest, ; 7-2: Exponents and Multiplication, ; 7-3: Exponents and Division, Concept 2: Logic, Reasoning, Arguments and Mathematical Proof Solve a logic problem given the necessary information. Identify simple valid arguments using if then statements. (e.g., All squares are rectangles. If quadrilateral ABCD is a rectangle, is it a square?) Model a contextual situation using a flow chart. Verify the Pythagorean theorem using an area dissection argument. SE/TE: 10-8: Draw a Diagram and Use Logical Reasoning, SE/TE: 10-8: Draw a Diagram and Use Logical Reasoning, SE/TE: related material: 10-8: Draw a Diagram and Use Logical Reasoning, SE/TE: related material: 4-9: The Pythagorean Theorem,

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