Course Title: Math Grade Level: Sixth
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1 Course Title: Math Grade Level: Sixth 8TH GRADE STATE STANDARDS STUDENT PERFORMANCE STRATEGIES, ACTIVITIES, AND RESOURCES 2.1 Numbers, Number Systems and Number Relationships: A. Represent and use numbers in equivalent forms (integers, fractions, decimals, percents, exponents, scientific notation and square roots). B. Simplify numerical expressions involving exponents, scientific notation and using order of operations. C. Distinguish between and order rational and irrational numbers. D. Apply ratio and proportion to mathematical problem situations involving distance, rate, time and similar triangles. E. Simplify and expand algebraic expressions using exponential forms. F. Use the number line model to demonstrate integers and their applications. G. Use the inverse relationships between addition, subtraction, The student will be able to: A. Use expanded notation to represent whole numbers and decimals. B. Represent and use numbers in equivalent forms (integers, fractions, decimals, percents, and exponents). C. Simplify numerical expressions involving exponents. D. Distinguish between and order whole numbers, decimals, and fractions. E. Identify and explain the concepts of prime and composite numbers. F. Use the number line model to demonstrate negative numbers and their applications. G. Use the inverse relationships between addition, subtraction, multiplication, and A. Everyday Mathematics Lessons 2.4, 2.6, 2.7, 2.8, 2.9 B. Everyday Mathematics Lessons 1.3, 2.5, 2.6, 2.7, 2.8, 2.9, 2.12, 3.1, 3.2, 3.3, 3.4, 4.1, 4.8, 6.5, 8.8 C. Everyday Mathematics Lessons 2.6, 2.7, 2.8, 6.5 D. Everyday Mathematics Lessons 4.2, 4.8, 4.9 E. Everyday Mathematics Lessons 1.1 F. Everyday Mathematics Lesson 6.3, 6.5, 6.12 G. Everyday Mathematics Lessons 6.3, 6.4
2 multiplication, division, and exponentiation and root extraction to determine unknown quantities in equations. PROCEDURES FOR ASSESSMENT: division to determine unknown quantities in equations. Tests, Quizzes, Teacher Observations, Rubrics, Math Journals, Checklists, Unit Review (Checking Progress), Math Boxes, Slate Assessment, Math Logs Every Day Counts: Aug/Sept, Oct, Nov, Dec, Jan, Feb, Mar, Apr
3 8TH GRADE STATE STANDARDS STUDENT PERFORMANCE STRATEGIES, ACTIVITIES, AND RESOURCES 2.2 Computation and Estimation: A. Complete calculations by applying the order of operations. B. Add, subtract, multiply and divide different kinds and forms of rational numbers including integers, decimal fractions, percents and proper and improper fractions. C. Solve word problems using ratio and proportion. D. Estimate the value of irrational numbers. The student will be able to: A. Create and solve word problems involving addition, subtraction, multiplication and division of whole numbers and decimals. B. Develop and apply algorithms to solve word problems that involve addition, subtraction, multiplication and/or division with decimals, fractions and mixed numbers, that include like and unlike denominators. C. Determine through estimates the reasonableness of answers to problems involving addition, subtraction, multiplication and division of whole numbers and decimals. D. Solve complex problems using fraction calculators. A. Everyday Mathematics Lessons 2.1, 2.2, 2.3, 2.4, 2.10, 2.11 B. Everyday Mathematics Lessons 2.1, 2.7, 2.8, 2.10, 2.11, 3.3, 3.7, 3.8, 6.1, 6.4 C. Everyday Mathematics Lessons 2.2, 2.10, 2.11, 3.3 D. Everyday Mathematics Lessons 6.1, 6.5, 9.10, 9.12 E. Estimate amount of tips and discounts using ratios, proportions and percents. E. Apply estimation strategies to a variety of problems including time, money, and percents. E. Everyday Mathematics Lessons 1.8, 4.8, 4.9, 4.10, 4.11, 8.6, 8.7, 8.8 F. Determine appropriateness of F. Complete calculations of whole F. Everyday Mathematics Lessons
4 overestimating or underestimating in computation. G. Identify the difference between exact value and approximations and determine which is appropriate for a given situation. H. Check the reasonableness of an answer. numbers by applying the order of operations. G. Add, subtract, multiply and divide proper and improper fractions and mixed numbers. H. Explore word problems using ratio and proportions. 6.6, 6.7 G. Everyday Mathematics Lessons 4.3, 4.4, 4.5, 4.6, 4.7, 4.8, 6.1, 6.2 H. Everyday Mathematics Lessons 8.1, 8.2, 8.3, 8.6, 8.7, 8.9, 8.11, 8.12, 8.13
5 PROCEDURES FOR ASSESSMENT: I. Determine appropriateness of overestimating or underestimating in computation. J. Identify the difference between exact value and approximations and determine which is appropriate for a given situation. K. Check the reasonableness of an answer. Tests, Quizzes, Teacher Observations, Rubrics, Math Journals, Checklists, Unit Review (Checking Progress), Math Boxes, Slate Assessment, Math Logs I. Everyday Mathematics Lessons 2.2, 4.10 J. Everyday Mathematics Lesson 3.4 K. Everyday Mathematics Lessons 2.2, 3.3 Every Day Counts: Aug/Sept, Oct, Nov, Dec, Jan, Feb, Mar, Apr
6 8TH GRADE STATE STANDARDS STUDENT PERFORMANCE STRATEGIES, ACTIVITIES, AND RESOURCES 2.3 Measurement and Estimation: A. Develop formulas and procedures for determining measurements (e.g. area, volume, distance, etc.). B. Solve rate problems (e.g. rate x time = distance, principal x interest rate = interest, etc.) C. Measure angles in degrees and determine relations of angles. The student will be able to: A. Use formulas and procedures for A. Everyday Mathematics Lessons calculating customary and metric 1.9, 3.6, 3.8, 9.8, 9.9, 9.11, 9.14 measurements (e.g. area, volume, distance, etc.) B. Explore the meaning of rates. B. Everyday Mathematics Lesson 1.7, 3.5, 8.1 C. Measure angles in degrees and determine relations of angles. C. Everyday Mathematics Lessons 5.2, 5.5 D. Estimate, use and describe measures of distance, rate, perimeter, area, volume, capacity, weight, mass and angles. E. Describe how a change in linear dimension of an object affects its perimeter, area, and volume. F. Use scale measurements to interpret maps or drawings. G. Create and use scale models. D. Estimate, use and verify measures of distance, perimeter, area, volume and angles. E. Use measurements to interpret maps or drawings. PROCEDURES FOR Tests, Quizzes, Teacher D. Everyday Mathematics Lessons 1.9, 3.6, 3.8, 5.2, 9.9 E. Everyday Mathematics Lesson 8.9 Every Day Counts: Aug/Sept, Oct, Nov, Mar, Apr, May/June
7 ASSESSMENT: Observations, Rubrics, Math Journals, Checklists, Unit Review (Checking Progress), Math Boxes, Slate Assessment, Math Logs
8 8TH GRADE STATE STANDARDS STUDENT PERFORMANCE STRATEGIES, ACTIVITIES, AND RESOURCES 2.4 Mathematical Reasoning and Connections: A. Make conjectures based on logical reasoning and test conjectures by using counter-examples. B. Combine numeric relationships to arrive at a conclusion. C. Use if...then statements to construct simple valid arguments. D. Construct, use, and explain algorithmic procedures for computing and estimating with whole numbers, fractions, decimals and integers. E. Distinguish between inductive and deductive reasoning. F. Use measurements and statistics in family and consumer science. The student will be able to: A. Make conjectures based on logical reasoning. B. Use models, number facts, properties, and relationships to arrive at a conclusion. C. Use inductive and deductive reasoning within mathematical contexts to construct simple valid arguments. D. Distinguish between relevant and irrelevant information to construct, use, and explain algorithmic procedures for computing with whole numbers, fractions, and decimals. E. Interpret and use statements made with precise language of logic to distinguish between inductive and deductive reasoning. F. Use measurement and statistics to quantify issues in any content. A. Everyday Mathematics Lesson 5.2 B. Everyday Mathematics Lesson 3.2, 9.1, 9.2 C. Everyday Mathematics Lesson 6.7 D. Everyday Mathematics Lessons 2.10, 2.11 E. Everyday Mathematics Lesson 6.8 F. Everyday Mathematics Lessons 1.2, 1.3, 1.4, 1.5, 1.11, 5.3 Every Day Counts: Dec, Apr, May/June
9 PROCEDURES FOR ASSESSMENT: Tests, Quizzes, Teacher Observations, Rubrics, Math Journals, Checklists, Unit Review (Checking Progress), Math Boxes, Slate Assessment, Math Logs
10 8TH GRADE STATE STANDARDS STUDENT PERFORMANCE STRATEGIES, ACTIVITIES, AND RESOURCES 2.5 Mathematical Problem Solving and Communication: A. Invent, select, use, and justify the appropriate methods, materials and strategies used to solve problems. B. Verify and interpret results using precise mathematical language, notation, and representations, including numerical tables and equations, simple algebraic equations and formulas, charts, graphs and diagrams. C. Justify strategies and defend approaches used and conclusions reached. D. Determine pertinent information in problem situations, and whether any further information is needed for solution. The student will be able to: A. Select, use, and justify the appropriate methods, materials, and strategies used to solve problems. B. Use appropriate mathematical terms, vocabulary, language symbols, graphs, numerical tables, charts, and diagrams to clearly and logically explain solutions to problems. C. Explain strategies and defend approaches used and conclusions reached in problem solving. D. Determine pertinent information in problem situations and whether any further information is needed. E. Connect, extend, and generalize problem solutions to other concepts, problems and circumstances in mathematics using appropriate problem solving strategies. A. Everyday Mathematics Lessons 6.5, 6.6, 9.10 B. Everyday Mathematics Lessons 1.5, 1.6, 1.7, 1.8, 3.5, 3.9, 3.11, 4.10, 5.3, 9.7 C. Everyday Mathematics Lessons 1.8, 3.5, 3.11 D. Everyday Mathematics Art and Design Activities, Lesson 9.9 E. Everyday Mathematics Art and Design Activities, Lessons 8.5, 8.8, 8.9, 9.8, 9.9
11 PROCEDURES FOR ASSESSMENT: Tests, Quizzes, Teacher Observations, Rubrics, Math Journals, Checklists, Unit Review (Checking Progress), Math Boxes, Slate Assessment, Math Logs Every Day Counts: Nov, Dec, Jan, Feb, Mar, Apr
12 8TH GRADE STATE STANDARDS STUDENT PERFORMANCE STRATEGIES, ACTIVITIES, AND RESOURCES 2.6 Statistics and Data Analysis: A. Compare and contrast different plots of data using values of mean, median, mode, quartiles and range. B. Explain effects on reliability of sampling procedures and of missing or incorrect information. C. Fit a line to the scatter plot of two quantities and describe any correlation of the variables. D. Design and carry out a random sampling procedure. E. Analyze and display data in stemand-leaf and box-and-whisker plots. F. Use scientific and graphing calculators and computer spreadsheets to organize and analyze data. G. Determine the validity of the sampling method described in studies published in local or national newspapers. The student will be able to: A. Compare different sets of data using values of mean, median, mode, and range. B. Organize and display data using tallies, tables, charts, graphs, and stem and leaf plots. C. Analyze and display data using comparison diagrams. D. Use probability to make predictions. E. Analyze and defend simple conclusions based on data. A. Everyday Mathematics Lesson 1.2, 1.3, 1.4, 1.5, 1.9, 1.11 B. Everyday Mathematics Lessons 1.5, 1.6, 1.7, 1.8, 1.9, 1.10, 1.11, 4.10, 5.3, 8.7 C. Everyday Mathematics Lesson 7.6 D. Everyday Mathematics Lessons 7.1, 7.2, 7.3 E. Everyday Mathematics Lessons 1.10, 1.11, 3.9, 4.10 Every Day Counts: Aug/Sept, Oct, Nov, Dec, Jan, Feb, Mar, Apr, May/June
13 PROCEDURES FOR ASSESSMENT: Tests, Quizzes, Teacher Observations, Rubrics, Math Journals, Checklists, Unit Review (Checking Progress), Math Boxes, Slate Assessment, Math Logs
14 8TH GRADE STATE STANDARDS STUDENT PERFORMANCE STRATEGIES, ACTIVITIES, AND RESOURCES 2.7 Probability and Predictions: A. Determine the number of combinations and permutations for an event. B. Present the results of an experiment using visual representations (tables, charts, and graphs). C. Analyze predictions such as election polls. D. Compare and contrast results from observations and mathematical models. E. Make valid inferences, predictions and arguments based on probability. PROCEDURES FOR ASSESSMENT: The student will be able to: A. Using concrete devices (dice, spinner, etc.) predict the chance of an event occurring. B. Compute and express probabilities as fractions and decimals. C. Investigate and compare predictions based on theoretical probability and experimental results. D. Make valid inferences and predictions based on probability. E. Devise and determine patterns generated as a result of an experiment. F. Make a tree diagram and analyze the outcome. Tests, Quizzes, Teacher Observations, Rubrics, Math Journals, Checklists, Unit Review A. Everyday Mathematics Lesson 7.1, 7.2 B. Everyday Mathematics Lesson 7.1, 7.2 C. Everyday Mathematics Lessons 7.3, 7.8 D. Everyday Mathematics Lessons 7.7, 7.8, 7.9 E. Everyday Mathematics Lesson7.1, 7.2, 7.3 F. Everyday Mathematics Lessons 7.4, 7.5, 7.6 Every Day Counts: Aug/Sept, Oct, Nov, Dec, Jan, Feb, Mar, Apr, May/June
15 (Checking Progress), Math Boxes, Slate Assessment, Math Logs
16 8TH GRADE STATE STANDARDS STUDENT PERFORMANCE STRATEGIES, ACTIVITIES, AND RESOURCES 2.8 Algebra and Functions: A. Apply simple algebraic patterns to basic number theory and to spatial relations. B. Discover, describe, and generalize patterns, including linear, exponential and simple quadratic relationships. C. Create and interpret expressions, equations, or inequalities that model problem situations. D. Use concrete objects to model algebraic concepts. E. Select and use a strategy to solve an equation or inequality, explain the solution and check the solution for accuracy. F. Solve and graph equations and inequalities using scientific and graphing calculators and computer spreadsheets. G. Represent relationships with tables, graphs in the coordinate plane, and verbal or symbolic rules. The student will be able to: A. Apply simple algebraic patterns to basic number theory. B. Discover and describe patterns including linear and exponential relationships. C. Interpret expressions, equations, or inequalities that model problem situations. D. Use concrete objects to model algebraic concepts. E. Use a strategy to solve an equation or inequality, explain the solution and check the solution for accuracy. F. Locate, identify, and plot points on a coordinate system. G. Generate functions from tables of data and create corresponding graphs. A. Everyday Mathematics Lessons 3.1, 3.2, 3.3, 9.1, 9.2 B. Everyday Mathematics Lessons 3.1, 3.2 C. Everyday Mathematics Lessons 3.3, 3.4, 6.7, 6.12, 9.1, 9.5, 9.6, 9.11 D. Everyday Mathematics Lessons 6.9, 6.10, 6.13 E. Everyday Mathematics Lessons 3.4, 3.6, 3.7, 6.8, 6.9, 6.10, 6.11, 6.12, 9.3, 9.4, 9.5, 9.8, 9.9, 9.11 F. Everyday Mathematics Lesson 5.4 G. Everyday Mathematics Lesson 3.10, 5.3
17 H. Graph a linear function from a rule or table. H. Show that an equality relationship between two quantities remains the same as long as the same change is made to both quantities. H. Everyday Mathematics Lesson 6.9, 6.10, 6.11, 9.3, 9.4, 9.5
18 I. Generate a table or graph from a function and use graphing calculators and computer spreadsheets to graph and analyze functions. J. Show that an equality relationship between two quantities remains the same as long as the same change is made to both quantities; and explain how a change in one quantity determines another quantity in a functional relationship. PROCEDURES FOR ASSESSMENT: Tests, Quizzes, Teacher Observations, Rubrics, Math Journals, Checklists, Unit Review (Checking Progress), Math Boxes, Slate Assessment, Math Logs Every Day Counts: Aug/Sept, Oct, Nov, Dec, Jan, Feb, Mar, Apr
19 8TH GRADE STATE STANDARDS STUDENT PERFORMANCE STRATEGIES, ACTIVITIES, AND RESOURCES 2.9 Geometry: A. Construct figures incorporating perpendicular and parallel lines, the perpendicular bisector of a line segment and an angle bisector using computer software. B. Draw, label, measure and list the properties of complementary, supplementary, and vertical angles. C. Classify familiar polygons as regular or irregular up to a decagon. D. Identify, name, draw and list all properties of squares, cubes, pyramids, parallelograms, quadrilaterals, trapezoids, polygons, rectangles, rhombi, circles, spheres, triangles, prisms, and cylinders. E. Construct parallel lines, draw a transversal, measure and compare angles formed such as alternate interior and exterior angles. F. Distinguish between similar and congruent polygons. The student will be able to: A. Describe in words how geometric shapes are constructed using geometric terms. B. Classify and compare triangles, quadrilaterals, and polygons according to sides and angles. C. Measure and construct angles, circles, diameters, and radii. D. Construct two and three dimensional shapes and figures using manipulatives, geoboards and other tools. E. Create geometric patterns, such as tesselations and sequences of shapes, and develop descriptions of the pattern. F. Explore the relationship between perimeter, area and volume of 2 and 3-dimensional figures. A. Everyday Mathematics Lessons 5.8, 5.10, 10.4 B. Everyday Mathematics Lessons 1.1, 5.1, 5.7, 5.9 C. Everyday Mathematics Lessons 5.1, 5.2, 5.11, 9.8 D. Everyday Mathematics Lessons 5.7, 5.8, 5.10, 8.10, 10.4 E. Everyday Mathematics Lessons 10.1, 10.2, 10.3 F. Everyday Mathematics Lessons 9.8, 9.9
20 G. Approximate the value of (pi) through experimentation. H. Use simple geometric figures such as triangles and squares to create, through rotation, transformational figures in three dimensions. I. Generate transformations using computer software. J. Analyze geometric patterns, such as tesselations and sequences of shapes, and develop descriptions of the patterns. K. Analyze objects to determine if they illustrate tesselations, symmetry, congruence, similarity, and scale. PROCEDURES FOR ASSESSMENT: G. Represent and use the concepts of point, line, line segment, ray, angle, and plane. H. Explore and create simple transformations of geometric figures. I. Classify geometric figures by using geometric properties (i.e. parallel, perpendicular, similar, congruent, symmetrical). Tests, Quizzes, Teacher Observations, Rubrics, Math Journals, Checklists, Unit Review (Checking Progress), Math Boxes, Slate Assessment, Math Logs G. Everyday Mathematics Lesson 5.1, 5.2, 5.8 H. Everyday Mathematics Lessons 5.5, 5.6, 10.5, 10.6, 10.7 I. Everyday Mathematics Lessons 5.6, 8.10, 9.13 Every Day Counts: Oct, Nov, Dec, Jan, Feb, Mar, Apr, May/June
21 8TH GRADE STATE STANDARDS STUDENT PERFORMANCE STRATEGIES, ACTIVITIES, AND RESOURCES 2.10 Trigonometry: A. Compute measures of sides and angles using proportions, the Pythagorean Theorem, and right triangle relationships. B. Solve problems requiring indirect measurement for lengths of sides of triangles. PROCEDURES FOR ASSESSMENT: The student will be able to: A. Compute measures of sides and angles in right triangles. B. Solve problems requiring indirect measurement for lengths of sides of triangles. Tests, Quizzes, Teacher Observations, Rubrics, Math Journals, Checklists, Unit Review (Checking Progress), Math Boxes, Slate Assessment, Math Logs A. Everyday Mathematics Lessons 5.2, 9.12 B. Everyday Mathematics Lesson 9.13 Every Day Counts: Nov, Dec, Jan, Mar
22 8TH GRADE STATE STANDARDS STUDENT PERFORMANCE STRATEGIES, ACTIVITIES, AND RESOURCES 2.11 Concepts of Calculus: A. Analyze graphs of related quantities for minimum and maximum values and justify. B. Describe concept of unit rates, ratios, and slope in the context of rate of change. C. Continue a pattern of numbers or objects that could be extended infinitely. PROCEDURES FOR ASSESSMENT: The student will be able to: A. Analyze graphs to identify minimum and maximum values. B. Apply ratio and proportion to mathematical problem solving situations involving distance, rate, and time. C. Estimate and find the relationship between the size of the unit of measurement and the areas and volumes. D. Continue a pattern of numbers or objects that could be extended infinitely. Tests, Quizzes, Teacher Observations, Rubrics, Math Journals, Checklists, Unit Review (Checking Progress), Math Boxes, Slate Assessment, Math Logs A. Everyday Mathematics Lessons 1.2, 1.6, 1.12, 5.7, Project 7 B. Everyday Mathematics Lessons 8.1, 8.2, 8.3, 8.4, 8.5, 8.11 C. Everyday Mathematics Lessons 9.8, 9.9 D. Everyday Mathematics Lesson 10.1 Every Day Counts: Dec, Jan, Feb, Apr, May/June
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