Course Title: Math Grade Level: Fourth Math - Fourth Page 1 2.1 Numbers, Number Systems and Number Relationships: A. Use expanded notation to represent whole numbers or decimals. B. Apply number theory concepts to rename a number quantity. C. Demonstrate that mathematical operations can represent a variety of problem situations. D. Use models to represent fractions and decimals. E. Explain the concepts of prime and composite numbers. F. Use simple concepts of negative numbers such as on a number line, in counting, and temperature. A. Use expanded notation to represent whole numbers. B. Use whole numbers and fractions to rename a number quantity. C. Recognize that mathematical operations can represent a variety of problem situations. D. Use drawings, diagrams, or models to show the concept of fractions and decimals as part of a whole. E. Identify a negative number on a number line, in counting and temperature. F. Use and apply number theory concepts (factors and multiples) to represent numbers in various ways. Math Journal, Math Boxes, Name-Collection Boxes, Unit Review (Unit Checking Progress), Class Checklists, Number Story Math Logs, Teacher Observations, Math Masters A. Everyday Math Lessons 2.3, 2.4, 2.9, 5.8, 5.9 ADD 2.7 AND 2.10 B. Everyday Math Lessons 2.2, 7.8 C. Number Story Math Log (p 472), Everyday Math Lessons 3.7, 3.12 D. Everyday Math Lessons 4,1, 4.2, 4.4, 4.10, 7.1, 7.2, 7.3, 7.5, 7.6, 7.7, 7.9, 9.1, 9.2 ADD 7.13 E. Everyday Math Lessons 10.6, 11.6 F. Name-Collection Boxes, Everyday Math Lessons 3.1, 3.2, 3.3, 3.4 Everyday Math Activities: Games, Number Story Math Log, Name- Collection Boxes (MM p 16), Study Links, Math Masters, Projects, Mental Math and Reflexes, Student Reference Book, Math Messages
Page 2 2.2 Computation and Estimation: A. Create and solve word problems involving addition, subtraction, multiplication and division of whole numbers. B. Develop and apply algorithms to solve word problems that involve addition, subtraction, and/or multiplication with decimals with and without regrouping, fractions and mixed numbers, that include like and unlike denominators. C. Demonstrate the ability to round numbers. D. Determine through estimations the reasonableness of answers to problems involving addition, subtraction, multiplication and division of whole numbers. E. Demonstrate skills for using fraction calculators to verify conjectures, confirm computations, and explore complex problems solving situations. F. Apply estimation strategies to a variety of problems including time and money. G. Explain multiplication and division algorithms. A. Solve word problems involving addition, subtraction, multiplication and division of whole numbers. B. Develop and apply algorithms to solve word problems that involve addition, subtraction, multiplication and division. A. Everyday Math Lessons 3.7, 6.1, 6.3, 9.8, 9.9 B. Everyday Math Lessons 3.7, 6.l, 6.3, 9.8, 9.9 C. Round numbers to a given place. C. Everyday Math Lesson 5.10 D. Use estimation to determine the reasonableness of answers to problems involving addition, subtraction, multiplication, division, time, and money to whole numbers. E. Demonstrate skills for using fraction calculators. F. Use multiplication and division algorithms with regrouping. G. Select a method for computation and explain why it is appropriate. Math Boxes, Math Journal, Math Masters, Checklists, Teacher Observations, Number Story Math Log D. Everyday Math Lessons 3.6, 5.3, 5.4, 5.12 E. Everyday Math Lessons 2.4, 9.3, 9.4, 9.5, 9.7 ADD 9.10 F. Everyday Math Lessons 5.1, 5.2, 5.5, 5.6, 5.7, 6.2 G. Everyday Math Lessons 5.1, 5.2, 5.5, 5.6, 5.7, 6.2 Everyday Math Activities: Games, Study links, Projects, Sample Math Work (MM p 473), Number Story Math Log, Mental Math and Reflexes, Student Reference Book, Math Messages
Page 3 2.3 Measurement and Estimation: A. Select and use appropriate instruments and units for measuring quantities such as perimeter, volume, area, weight, time and temperature. B. Select and use standard tools to measure the size of figures with specified accuracy, including length, width, perimeter, and area. C. Estimate, refine, and verify specified measurements of objects. D. Convert linear measurements within the same system. A. Use appropriate instruments and units for measuring quantities such as perimeter, volume, area, weight, time and temperature. B. Use standard tools to measure the size of figures with specified accuracy, including length, width, perimeter, and area. C. Estimate, refine, and verify specified measurements of objects. D. Convert linear measurements within the same system (e.g. US customary and metric units). A. Everyday Math Lessons 4.6, 4.7, 4.8, 4.9, 6.6, 8.2, 8.3, 10.6, 11.1, 11.7 ADD 4.11, 11.5, 11.8 B. Everyday Math Lessons 4.6, 4.7, 4.8, 4.9, 6.6, 8.2, 8.3, 10.6, 11.1, 11.7 ADD 4.11 C. Everyday Math Lessons 4.6, 4.7, 4.8, 4.9, 6.6, 8.2, 8.3, 10.6, 11.1, 11.7 ADD 4.11 D. Everyday Math Lessons 4.7, 4.9 E. Add and subtract measurements. E. Add and subtract measurements. E. Everyday Math Lessons 5.3, 7.4 F. Solve problems involving time. F. Everyday Math Lessons 4.5, 5.3, 6.6 Math Journal, Math Boxes, Unit Review (Unit Checking Progress), Class Checklists, Teacher Observations, Name-Collection Boxes, Math Masters, Number Story Math Logs Everyday Math Activities: Games, Projects, Study Links, Math Masters, Name-Collection Boxes, Mental Math and Reflexes
Page 4 2.4 Mathematical Reasoning and Connections: A. Compare quantities and magnitudes of numbers. B. Use models, number facts, properties and relationships to check and verify predictions and explain reasoning. C. Draw inductive and deductive conclusions within mathematical contexts. D. Distinguish between relevant and irrelevant information in a mathematical problem. E. Interpret statements made with precise language of logic (i.e. all, every, none, some, or many). F. Use statistics to quantify issues in social studies. A. Compare quantities and magnitudes of numbers. B. Use models, number facts, properties and relationships to check and verify predictions and explain reasoning. C. Using data draw inductive and deductive conclusions within mathematical contexts. D. Distinguish between relevant and irrelevant information in a mathematical problem. E. Interpret statements made with precise language of logic (i.e. all, every, none, some, or many). F. Use statistics to quantify issues in any content. Math Journal, Math Boxes, Math Masters, Checklist, Teacher Observation, Number Story Math Log (p 472) A. Everyday Math Lesson 5.4 B. Everyday Math Lesson 8.2 ADD TO C BELOW 2.10 C. Everyday Math Lessons 2.5, 2.8, 5.ll, 9.7 D. Everyday Math Lesson 3.7 E. Everyday Math Lesson 3.ll F. Everyday Math Lessons 2.5, 2.6, 3.5, 5.3, 5.4, 12.6 Everyday Math Activities: Math Messages, Student Reference Book, Study Links, Projects, Mental Math and Reflexes, Math Masters, Number-Story Log (MM p 422), Situation Diagrams (MM p 40), Logic Grid (MM p 47), Math Journal p 120
Page 5 2.5 Mathematical Problem Solving and Communication: A. Develop a plan to analyze a problem, identify the information needed to solve the problem, carry out the plan, check whether an answer makes sense and explain how the problem was solved. B. Use appropriate mathematical terms, vocabulary, language symbols and graphs to clearly and logically explain solutions to problems. C. Show ideas in a variety of ways, including words, numbers, symbols, pictures, charts, graphs, tables, diagrams and models. D. Connect, extend, and generalize problem solutions to other concepts, problems and circumstances in mathematics. E. Select, use, and justify the methods, materials and strategies used to solve problems. F. Use appropriate problem solving strategies such as solving a simpler problem or drawing a picture or diagram. A. Develop a plan to analyze a problem, identify the information needed to solve the problem, carry out the plan, check whether an answer makes sense and explain how the problem was solved. B. Use appropriate mathematical terms, vocabulary, language symbols and graphs to clearly and logically explain solutions to problems. C. Show ideas in a variety of ways, including words, numbers, symbols, pictures, charts, graphs, tables, diagrams and models. D. Connect, extend, and generalize problem solutions to other concepts, problems and circumstances in mathematics. E. Select, use, and justify the methods, materials and strategies used to solve problems. F. Use appropriate problem solving strategies such as solving a simpler problem or drawing a picture or diagram to solve a more complex problem. Math Journal, Math Boxes, Math Masters, Checklist, Teacher Observation, Number Story Math Log (p 472) A. Everyday Math Lessons 2.1, 2.8, 3.7, 4.3, 5.3, 5.11, 6.4 B. Everyday Math Lessons 2.1, 2.8, 3.7, 4.3, 5.3, 5.11, 6.4 C. Everyday Math Lessons 2.1, 2.8, 3.7, 4.3, 5.3, 5.11, 6.4 D. Everyday Math Lessons 2.1, 2.8, 3.7, 4.3, 5.3, 5.11, 6.4 E. Everyday Math Lessons 2.1, 2.8, 3.7, 4.3, 5.3, 5.11, 6.4 F. Everyday Math Lessons 2.1, 2.8, 3.7, 4.3, 5.3, 5.11, 6.4 Everyday Math Activities: World Tour Project, Study Links, Math Masters, Math Messages, Mental Math and Reflexes, Student Reference Book
Page 6 2.6 Statistics and Data Analysis: A. Organize and display data using pictures, A. Organize and display data using pictures, A. Everyday Math Lessons 2.8, 9.4, 12.2 tallies, tables, charts, bar graphs, and circle graphs. tallies, tables, charts, bar graphs, and circle graphs. B. Describe data sets using mean, median, B. Describe data sets using mean, median, B. Everyday Math Lesson 2.5 mode and range. mode and range. C. Sort data using Venn diagrams. C. Sort data using comparison diagrams. C. Everyday Math Lesson 1.3 D. Predict the likely number of times a condition will occur based on the analyzed data. E. Construct and defend simple conclusions based on data. D. Predict the likely number of times a condition will occur based on the analyzed data. E. Construct and defend simple conclusions based on data. Math Journal, Math Boxes, Math Masters, Checklist, Teacher Observation D. Everyday Math Lesson 7.10 E. Everyday Math Lessons 2.8, 9.4, 12.2 Everyday Math Activities: Evaluating My Math Class (MM p 468), Study Links, Math Masters, Projects, Games, Mental Math and Reflexes, Math Messages, Student Reference Book
Page 7 2.7 Probability and Predictions: A. Perform simulations with concrete devices (dice, spinner, etc.) to predict the chance of an event occurring. B. Determine the fairness of the design of a spinner. C. Express probabilities as fractions and decimals. D. Compare predictions based on theoretical probability and experimental results. E. Calculate the probability of a simple event. F. Determine patterns generated as a result of an experiment G. Determine the probability of an event involving "and", "or" or "not". H. Predict and determine why some outcomes are certain, more likely, less likely, equally likely or impossible. I. Find all possible combinations and arrangements involving a limited number of variables. J. Make a tree diagram and list the elements in the sample space. A. Perform simulations with concrete devices A. Everyday Math Lessons 2.5, 5.4 (dice, spinner, etc.) to predict the chance of an event occurring. B. Determine the fairness of the design of a B. Everyday Math Lesson 7.11 spinner. C. Express probabilities as fractions. C. Everyday Math Lesson 7.12 D. Compare predictions based on theoretical D. Everyday Math Lesson 7.11 probability and experimental results. E. Calculate the probability of a simple E. Everyday Math Lesson 9.6 event. F. Determine patterns generated as a result F. Everyday Math Lessons 6.5, 7.12 of an experiment. G. Determine the probability of an event G. Everyday Math Lessons 7.11, 7.12, 8.3 involving "and", "or" or "not". H. Predict why some outcomes are certain, H. Everyday Math Lessons 7.11, 7.12, 8.3 more likely, less likely, equally likely or impossible. I. Find all possible combinations and I. Everyday Math Lessons 7.11, 7.12 arrangements involving a limited number of variables. J. Use a tree diagram to answer questions. J. Everyday Math Lesson 1.4 Math Journals, Math Boxes, Math Masters, Checklist, Teacher Observation Everyday Math Activities: Study Links, Math Masters, Mental Math and Reflexes, Project 3 (p 891), Games, World Tour Project, Math Messages, Student Reference Book
Page 8 2.8 Algebra and Functions: A. Recognize, reproduce, extend, create and describe patterns, sequences and relationships verbally, numerically, symbolically and graphically, using a variety of materials. B. Connect patterns to geometric relations and basic number skills. C. Form rules based on patterns (e.g., an equation that relates pairs in a sequence). D. Use concrete objects and combinations of symbols and numbers to create expressions that model mathematical situations. E. Explain the use of combinations of symbols and numbers in expressions, equations, and inequalities. F. Describe a realistic situation using information given in equations, inequalities, fables or graphs. G. Select and use appropriate strategies, including concrete materials, to solve number sentences and explain the method of solution. A. Recognize, reproduce, extend, create and describe patterns, sequences and relationships verbally, numerically, symbolically and graphically, using a variety of materials. B. Connect patterns to geometric relations and basic number skills. C. Form rules based on patterns (e.g., an equation that relates pairs in a sequence). D. Use concrete objects and combinations of symbols and numbers to create expressions that model mathematical situations. E. Use combinations of symbols and numbers in expressions, equations, and inequalities. F. Describe a realistic situation using information given in equations, inequalities, fables or graphs. G. Select and use appropriate strategies, including concrete materials, to solve number sentences and explain the method of solution. A. Everyday Math Lessons 3.8, 3.9, 3.10, 10.5 B. Everyday Math Lessons 6.6, 6.7, 10.3, 10.4 ADD 6.11 C. Everyday Math Lessons 6.5, 12.1, 12.2 D. Everyday Math Lesson 8.8 E. Everyday Math Lessons 3.8, 3.9, 3.10 F. Everyday Math Lessons 12.4, 12.5 G. Everyday Math Lessons 3.7, 3.8, 3.9, 3.10
H. Locate and identify points on a coordinate system. I. Generate functions from tables of data and relate data to corresponding graphs and functions. H. Locate and identify points on a coordinate system. I. Generate functions from tables of data and relate data to corresponding graphs and functions. Math Journal, Math Boxes, Math Masters, Checklist, Teacher Observations, What's My Rule, Masters Rate Table (p 190), Everyday Math Lesson 12.7 Math - Fourth Page 9 H. Everyday Math Lessons 6.5, 6.6, 6.9, 6.10 I. Everyday Math Lessons 7.12, 12.1, 12.3, 12.4, 12.5 ADD 12.7 Everyday Math Activities: Games, Student Reference Book, Math Messages, Mental Math and Reflexes, Study Links Projects 4 & 5, What's My Rule?, World Tour, Rate Tables (MM p. 190), Fact Triangles
Page 10 5TH GRADE STATE STANDARDS STUDENT PERFORMANCE STRATEGIES, AC 2.9 Geometry: A. Give formal definitions of geometric A. Explore, classify, and identify geometric A. Everyday Math Lessons Unit I figures. figures. B. Classify and compare triangles and B. Classify triangles and quadrilaterals. B. Everyday Math Lessons 1.3, 1.4, 1.5, 1.8 quadrilaterals according to sides or angles. C. Identify and measure circles, their C. Identify and measure circles, their C. Everyday Math Lessons 1.6, 1.7 diameters and radii. diameters and radii. D. Describe in words how geometric shapes D. Describe in words how geometric shapes D. Everyday Math Lessons 1.7, 11.3 are constructed. are constructed. E. Construct two and three dimensional E. Construct two and three dimensional E. Everyday Math Messons 1.4, 8.1, 11.3, 11.4 shapes and figures using manipulatives, geoboards, and computer software. shapes and figures using manipulatives, and geoboards. F. Find familiar solids in the environment F. Find familiar solids in the environment F. Everyday Math Lesson 11.2 and describe them. and describe them. G. Create an original tesselation. G. Create an original tesselation. G. Everyday Math Lesson 10.5 H. Describe the relationship between the perimeter and area of triangles, quadrilaterals and circles. I. Represent and use the concepts of line, point, and plane. J. Define the basic properties of squares, pyramids, parallelograms, quadrilaterals, trapezoids, polygons, rectangles, rhombi, circles, triangles, cubes, prisms, spheres, and cylinders. K. Analyze simple transformations of geometric figures and rotations of line segments. H. Describe the relationship between the perimeter and area of triangles and quadrilaterals. I. Represent and use the concepts of line and point. J. Define the basic properties of squares, pyramids, parallelograms, quadrilaterals, trapezoids, polygons, rectangles, rhombi, circles, triangles, cubes, prisms, spheres, and cylinders. K. Use simple transformations of geometric figures and rotations of line segments. H. Everyday Math Lessons 8.5, 8.6, 8.7 ADD 8.9 I. Everyday Math Lesson 1.2 J. Everyday Math Lessons 1.3, 1.5, 1.6, 1.7 ADD 1.9 K. Everyday Math Lesson 10.5
L. Identify properties of geometric figures (i.e. parallel, perpendicular, similar, congruent, symmetrical). L. Identify properties of geometric figures (i.e. parallel, perpendicular, similar, congruent, symmetrical). Math Journal, Math Boxes, Math Masters, Checklist, Teacher Observations Math - Fourth Page 11 L. Everyday Math Lessons 10.1, 10.2, 10.3, 10.4 ADD 10.7 Everyday Math Activities: Student Reference Book, Math Messages, Mental Math and Reflexes, Study Links, Games, Projects 4 and 7
Page 12 2.10 Trigonometry: A. Identify and compare parts of right A. Identify and compare parts of right triangle including right angles, acute angles, triangles including right angles, acute hypotenuse, and legs. angles, hypotenuse, legs and obtuse angles. B. Create right triangles on a geoboard. B. Create right triangles using a variety of materials. Math Journal, Math Boxes, Math Masters, Unit Review (Unit Checking Progress), Class Checklist, Teacher Observations A. Everyday Math Lessons 6.6, 6.8 B. Everyday Math Lesson 1.3 Everyday Math Activities: Student Reference Book, Math Messages, Mental Math and Reflexes, Games, Study Links
Page 13 2.11 Concepts of Calculus: A. Make comparisons of numbers such as A. Make comparisons of numbers such as A. Everyday Math Lessons 3.8, 3.9, 3.10 more, less, same, least, most, greater than and less than. more, less, same, least, most, greater than and less than. B. Identify least and greatest values B. Identify least and greatest values B. Everyday Math Lessons 2.6, 2.8, 9.4 represented in bar and circle graphs. represented in bar, circle, and line graphs. C. Identify maximum and minimum. C. Identify maximum and minimum. C. Everyday Math Lesson 2.5 D. Describe the relationship between rates of change and time. E. Estimate areas and volumes as the sums of areas of tiles and volumes of cubes. D. Explore rates of change. D. Everyday Math Lessons 12.1, 12.2 E. Estimate areas and volumes as the sums of areas of tiles and volumes of cubes. Math Journal, Math Boxes, Math Masters, Checklist, Teacher Observations E. Everyday Math Lessons 8.3, 8.4, 11.4, 11.5 Everyday Math Activities: Student Reference Book, Math Messages, Mental Math and Reflexes, Study Links, Games