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Content Area: Math Grade/Course: 8 Strand: Numbers and Operations Standard 1: Numbers and Operations: NUMBER SENSE: Understand numbers, ways of representing numbers, relationships among numbers, and number systems Topic: Numbers and Number Systems PAGE(S) WHERE TAUGHT (If submission is not a Benchmark text, cite appropriate resource(s)) MA.8.1.1 Identify situations SE:/TE: Looking for represented by square Pythagoras: 19, 22-25, 34roots and cube roots 39, 46-58, 59-62, 71-74 TE: Looking for Pythagoras: 40a-40j, 52j, 63b, 70r TECH: www.phschool.com Used at school? Alignment to benchmark map 2 (square roots) 3 (cube roots) MA.8.1.2 Compare and order rational numbers and square roots SE:/TE: Looking for Pythagoras: 7, 19, 22-25, 34-39, 46-58, 59-62, 71-74 Say It With Symbols: 5-8 Clever Counting: 37-40, 41-45 TE: Looking for Pythagoras: 40a-40j, 52j, 63b, 70r Say It With Symbols: 4b, 19a-19f Clever Counting: 1e, 36j, 46a-46f TECH: www.phschool.com 2 MA.8.1.3 Use ratios and proportions to represent the relationship between two quantities SE:/TE: Samples and Populations: 5-23 3 TE: Samples and Populations: 4b, 23a-23o TECH: www.phschool.com Strand: Numbers and Operations Supplement Standard 2: Numbers and Operations: OPERATION SENSE: Understand the meaning of operations and how they relate to each other Topic: Operations Benchmark MA.8.2.1 Apply the order of operations when calculating with rational numbers PAGE(S) WHERE TAUGHT (If submission is not a text, cite appropriate resource(s)) SE:/TE: Say It With Symbols: 5-11, 12-18 Used at school? Alignment to benchmark map Supplement 1 TE: Say It With Symbols: 1b, 4b, 19a-19h TECH: www.phschool.com MA.8.2.2 Demonstrate the inverse relationship between square numbers and square roots, and cubes and cubed roots SE:/TE: Looking for Pythagoras: 19, 22-25, 3439, 46-58, 59-62, 71-74 Thinking With Mathematical Models: 36, 56, 60 Kaleidoscopes, Hubcaps, and Mirrors: 62 2 (square numbers and square roots) 3 (cubes and cubed roots) TE: Looking for Pythagoras: 40a-40j, 52j, 63b, 70r Thinking With Mathematical Models: 1a, 136 Kaleidoscopes, Hubcaps, and Mirrors: 1g, 70h70k TECH: www.phschool.com Strand: Numbers and Operations Standard 3: Numbers and Operations: COMPUTATION STRATEGIES: Use computational tools and strategies fluently and, when appropriate, use estimation Topic: Computational Fluency Benchmark MA.8.3.1 Add, subtract, multiply, and divide numbers with whole number exponents SE:/TE: Say It With Symbols: 5-7, 8-9, 34-35, 73 Clever Counting: 27-31 2 TE: Say It With Symbols: 4b, 19a-19c, 19d19h, 52a52c, 52k-52m, 148 Clever Counting: 1b-1e, 26f-26g, 36d-36f TECH: www.phschool.com Topic: Estimation Benchmark MA.8.3.2 Estimate a reasonable range (i.e., upper and lower limit) for the solution to a problem PAGE(S) WHERE TAUGHT (If submission is not a text, cite appropriate resource(s)) SE:/TE: Looking for Pythagoras: 60 Samples and Populations: 4, 6, 7-11, 17, 39, 47, 50, 51, 57 TE: Looking for Pythagoras: 63b Samples and Populations: 4b, 23e-23n, 23o Used at school? Alignment to benchmark map Supplement 2 TECH: www.phschool.com Strand: Measurement Standard 4: Measurement: FLUENCY WITH MEASUREMENT: Understand attributes, units, and systems of units in measurement; and develop and use techniques, tools, and formulas for measuring Topic: Measurement Attributes and Units Benchmark MA.8.4.1 Select and use appropriate units to measure the surface area and volume of solids SE:/TE: Say It With Symbols: 16, 17, 23-25, 65-66, 67-69 TE: Say It With Symbols: 33h-33j, 64v, 70a70f TECH: www.phschool.com Topic: Measurement Tools and Techniques Benchmark 3 MA.8.4.2 Express rates of change as a ratio of two different measures, where units are included in the ratio, and use the derived rate to solve problems SE:/TE: Growing, Growing, Growing: 33-37, 47-52 Looking for Pythagoras: 8-10, 12-15, 27-33, 34-39, 41-45, 46-51 TE: Growing, Growing, Growing: 30h, 44a44g, 44h, 60c-60i Looking for Pythagoras: 1c-1d, 4b, 40a-40j TECH: www.phschool.com 3 Topic: Measurement Formulas Benchmark MA.8.4.3 Use ratios and proportions to solve measurement problems MA.8.4.4 Use formulas to determine the surface area and volume of selected prisms, cylinders, and pyramids PAGE(S) WHERE TAUGHT (If submission is not a text, cite appropriate resource(s)) SE:/TE: Growing, Growing, Growing: 16, 30, 44, 60 TE: Growing, Growing, Growing: 1k, 4b, 16j, 30h, 44h TECH: www.phschool.com Used at school? SE:/TE: Say It With Symbols: 16, 23-25, 6566, 67-69 Alignment to benchmark map Supplement 3 3 TE: Say It With Symbols: 33h-33j, 64v, 70a70f TECH: www.phschool.com Strand: Geometry and Spatial Sense Standard 5: Geometry and Spatial Sense: PROPERTIES AND RELATIONSHIPS: Analyze properties of objects and relationships among the properties Topic: Geometric Shapes and Their Properties and Relationships Benchmark MA.8.5.1 Apply the Pythagorean theorem to solve problems involving right triangles PAGE(S) WHERE TAUGHT (If submission is not a text, cite appropriate resource(s)) SE:/TE: Looking for Pythagoras: 4, 27-33, 3439, 41-45, 46-51 Used at school? Alignment to benchmark map Supplement 2 TE: Looking for Pythagoras: 1d-1e, 26n, 40a40j, 40p, 52a-52h, 158 TECH: www.phschool.com Strand: Geometry and Spatial Sense Standard 6: Geometry and Spatial Sense: TRANSFORMATIONS AND SYMMETRY: Use transformations and symmetry to analyze mathematical situations Topic: Transformation Benchmark MA.8.6.1 Perform a transformation (reflection, rotation, translation) when given a figure and necessary parameters SE:/TE: Kaleidoscopes, Hubcaps and Mirrors: 1114, 15-22, 24-33, 34-40, 42-49, 50-57, 5963, 64-69 2 TE: Kaleidoscopes, Hubcaps and Mirrors: 1a1g, 4b, 23i-23k, 23p, 41a41o, 41v, 58p, 70a70k, 203 TECH: www.phschool.com MA.8.6.2 Describe the size, position, and orientation of shapes under transformations and compositions of transformations SE:/TE: Kaleidoscopes, Hubcaps and Mirrors: 1114, 15-22, 24-33, 34-40, 42-49, 50-57, 5963, 64-69 TE: Kaleidoscopes, Hubcaps and Mirrors: 1a1g, 4b, 23i-23k, 23p, 41a41o, 41v, 58p, 70a70k, 203 TECH: www.phschool.com 2 Strand: Geometry and Spatial Sense Standard 7: Geometry and Spatial Sense: VISUAL AND SPATIAL SENSE: Use visualization and spatial reasoning to solve problems both within and outside of mathematics Topic: Visualization and Spatial Reasoning Benchmark PAGE(S) WHERE TAUGHT (If submission is not a text, cite appropriate resource(s)) MA.8.7.1 Use twodimensional representations of pyramids, prisms, and cylinders to solve problems involving these figures Strand: Geometry and Spatial Sense Used at school? Alignment to benchmark map Supplement 3 Standard 8: Geometry and Spatial Sense: REPRESENTATIONAL SYSTEMS: Select and use different representational systems, including coordinate geometry Topic: Coordinate Geometry Benchmark MA.8.8.1 Use coordinate 2 geometry to represent transformations in the coordinate plane Strand: Patterns, Functions, and Algebra Standard 9: Patterns, Functions, and Algebra: PATTERNS AND FUNCTIONAL RELATIONSHIPS: Understand various types of patterns and functional relationships Topic: Patterns Benchmark MA.8.9.1 Represent a variety of patterns (including recursive patterns) with tables, graphs (including graphing technology when available), words, and when possible, symbolic rules Topic: Functions 1 Benchmark MA.8.9.2 Use linear relationships with two variables to solve problems PAGE(S) WHERE TAUGHT (If submission is not a text, cite appropriate resource(s)) SE:/TE: Growing, Growing, Growing: 17-20 Thinking With Mathematical Models: 4, 5-14, 15-24, 61 TE: Growing, Growing, Growing: 1d Thinking With Mathematical Models: 1a-1c, 25a-25j, 136 TECH: www.phschool.com Used at school? Alignment to benchmark map Supplement 1 Topic: Functions Benchmark MA.8.9.3 Identify functions 1 as linear or nonlinear and contrast their properties from tables, graphs (including graphing technology when available), or equations Strand: Patterns, Functions, and Algebra Standard 10: Patterns, Functions, and Algebra: SYMBOLIC REPRESENTATION: Use symbolic forms to represent, model, and analyze mathematical situations Topic: Numeric and Algebraic Representations Benchmark MA.8.10.1 Translate among tables, graphs (including graphing technology when available), and equations involving linear relationships MA.8.10.2 Solve linear equations and inequalities with two variables using algebraic methods, 1 1 manipulatives, or models MA.8.10.3 Use tables and graphs to represent and compare linear relationships Topic: Rates of Change Benchmark 1 PAGE(S) WHERE TAUGHT (If submission is not a text, cite appropriate resource(s)) Used at school? MA.8.10.4 Use the slope of a line to describe a constant rate of change Strand: Data Analysis, Statistics, and Probability Alignment to benchmark map Supplement 1 Standard 11: Data Analysis, Statistics, and Probability: FLUENCY WITH DATA: Pose questions and collect, organize, and represent data to answer those questions Topic: Data Collection and Representation Benchmark MA.8.11.1 Design a study that compares two samples, collect data, and select the appropriate representation (e.g., double bar graph, back-toback stem and leaf plot, parallel box and whisker plots, scatter plot) to compare the sets of data SE:/TE: Samples and Populations: 4, 5-25, 2728, 39, 41-42, 47, 49-54, 57 4 TE: Samples and Populations: 1e-1g, 4b, 23e23n, 23o, 36a-36h, 62a62f, 148 TECH: www.phschool.com Topic: Data Collection and Representation Benchmark PAGE(S) WHERE TAUGHT (If submission is not a text, cite appropriate resource(s)) MA.8.11.2 Judge the Used at school? Alignment to benchmark map 4 Supplement validity of data based on the data collection method Strand: Data Analysis, Statistics, and Probability Standard 12: Data Analysis, Statistics, and Probability: STATISTICS: Interpret data using methods of exploratory data analysis Topic: Data Interpretation Benchmark MA.8.12.1 Recognize situations appropriate for scatter plots 4 Topic: Data Interpretation Benchmark MA.8.12.2 Analyze different representations of the same data to describe how representations can be used to skew a person's interpretation of the data Strand: Data Analysis, Statistics, and Probability 4 Standard 13: Data Analysis, Statistics, and Probability: DATA ANALYSIS: Develop and evaluate inferences, predictions, and arguments that are based on data Topic: Predictions and Inferences Benchmark MA.8.13.1 Make conjectures about possible relationships between two characteristics of a sample based on interpretations of scatter plots 4 Strand: Data Analysis, Statistics, and Probability Standard 14: Data Analysis, Statistics, and Probability: PROBABILITY: Understand and apply basic notions of chance and probability Topic: Probability Benchmark MA.8.14.1 Judge the validity of conjectures that are based on experiments or simulations PAGE(S) WHERE TAUGHT (If submission is not a text, cite appropriate resource(s)) SE:/TE: Samples and Populations: 4, 13-14, 4142 Used at school? Alignment to benchmark map Supplement 4 TE: Samples and Populations: 1g-1i, 4b, 23n23o, 36f, 48f-48h TECH: www.phschool.com Major Understandings by Quarter (HI Benchmark Maps) First Quarter: Wes’ suggested books: Thinking with Mathematical Models – Inv. 1 and 2 (and supplement) Situations can be represented in different ways for different purposes Understanding patterns can lead to educated predictions or solutions Data sometimes behaves in predictable patterns (linear) Second Quarter: Looking for Pythagoras + Kaleidescopes, Hubcaps, and Mirrors – Inv 1 and 2 (and supplement) Measurements may be taken directly, or derived from other measurements Numbers and situations can be represented in many ways for different purposes The position, location, and orientation of shapes can be manipulated through reflection, rotation, and translation Transformations can be precisely duplicated with a specific set of directions Third Quarter: Filling and Wrapping + Comparing and Scaling (and supplement) Numbers and situations can be represented in many ways for different purposes Measurements may be taken directly, or derived from other measurements Rations help to compare quantities Known measurements can be used to determine other proportional measurements Fourth Quarter: Samples and Populations and (supplement) Data helps people to understand situations and make informed decisions Sometimes, certain representations can be fashioned to be misleading Probabilities give us an idea of what we expect should happen in the long run Curriculum Focal Points for Grade 8: Algebra: Analyzing and representing linear functions and solving linear equations and systems of linear equations Geometry and Measurement: Analyzing two- and three- dimensional space and figures by using distance and angle Data Analysis and Number and Operations and Algebra: Analyzing and summarizing data sets