Lakewood City Schools Mathematics Course of Study Fifth Grade

Lakewood City Schools Mathematics Course of Study Fifth Grade Welcome to Fifth Grade Mathematics. Below is an outline of four major components of the program you will be using this year. I. Lakewood City Schools Course of Study Arranged by mandated Academic Content Standards Each Standard is coordinated with 5 7 Benchmarks and Grade 6 Level Indicators Lakewood City Schools Mathematics Course of Study is aligned with the Ohio Department of Education s Academic Mathematics Content Standards II. III. IV. Pacing & Sequencing Chart A functional and fluid document meant to be utilized by teachers Grade Level Indicators reference Content Standards defined in the Lakewood City Schools Course of Study Suggested time frame included for pacing units Lesson modifications meant to assist teacher with planning Inclusion of teacher notes encouraged as lessons are implemented Everyday Mathematics Teacher s Manual Provides a comprehensive overview Introductory pages at the beginning of each lesson include essential strategies and information Instructional strategies offered throughout the lesson Structured in 3 parts: 1) Teaching the Lesson (main objective) 2) Ongoing Learning and Practice (extending skill) 3) Options for Individualizing (remedial or enrichment activities) Everyday Mathematics Content by Strand Pacing Chart Everyday Mathematics Teacher Reference Manual Includes useful suggestions for implementation of Everyday Mathematics Provides ideas for organizing curriculum, students and materials Easily accessible source of reliable mathematical knowledge Essential to understanding Everyday Mathematics program Can enhance personal comfort level of mathematical knowledge These tools will assist you and your students as you work toward mathematical proficiency. Revised: 9/7/2004 5 1

Lakewood City Schools Mathematics Course of Study Fifth Grade Mathematical Processes Students use mathematical processes and knowledge to solve problems. Students apply problem solving and decision making techniques, and communicate mathematical ideas. NOTE: Mathematical processes are used in all content areas and should be incorporated within instruction and assessment of the content specific standards and benchmarks. 5 7 Benchmarks Grade Level Indicators A. Clarify problem solving situation and identify potential solution processes; e.g., consider different strategies and approaches to a problem, restate problem from various perspectives. B. Apply and adapt problem solving strategies to solve a variety of problems, including unfamiliar and non routine problem situations. C. Use more than one strategy to solve a problem, and recognize there are advantages associated with various methods. By the end of Grade 5, the student will: 1. Pose problems and identify the information needed to solve problems. a. Construct, explain, justify, and apply a variety of problem solving strategies (e.g., guess and check, make an organized list, etc.) b. Use an organized approach and appropriate strategies, including calculators, to solve multi step problems. c. Interpret results in the context of the problem being solved. d. Interpret remainder: (dropping the remainder, using whole number part of answer, rounding up.) e. Recognize whether an estimate or an exact solution is appropriate for a given problem situation. D. Recognize whether an estimate or an exact solution is appropriate for a given problem situation. E. Use deductive thinking to construct informal arguments to support reasoning and to justify solutions to problems. F. Use inductive thinking to generalize a pattern of observations for particular cases, make conjectures, and provide supporting arguments for conjectures. G. Relate mathematical ideas to one another and to other content areas; e.g., use area models for adding fractions, interpret graphs in reading, 2. Communicate and represent mathematical ideas using explanations, both written and verbal, and tools such as manipulatives, calculators, and computers. 3. Create representations (such as physical models) to organize, record, and communicate mathematical ideas. Revised: 9/7/2004 5 2

science and social studies. H. Use representations to organize and communicate mathematical thinking and problem solutions. I. Select, apply, and translate among mathematical representations to solve problems; e.g., representing a number as a fraction, decimal or percent as appropriate for a problem. 4. Use mathematical reasoning to critique problems and their solutions. a. Make and investigate mathematical problems based on incomplete evidence and the formulate conclusions. b. Determine if a mathematical solution is reasonable by providing an explanation based on models, number relationships, and logic. J. Communicate mathematical thinking to others and analyze the mathematical thinking and strategies of others. K. Recognize and use mathematical language and symbols when reading, writing and conversing with others. Revised: 9/7/2004 5 3

Lakewood City Schools Mathematics Course of Study Fifth Grade Standard 1 Number, Number Sense and Operations Students demonstrate number sense including an understanding of number systems and operations, and how they relate to one another. Students compute fluently and make reasonable estimates using paper and pencil, technology supported and mental methods. SMART Essential Focuses: Students should know how to compute fluently with whole numbers using all four operations, and how to relate equivalent forms of commonly used fractions, decimals, and percents. 5 7 Benchmarks Grade Level Indicators Corresponding Everyday Mathematics Units A. Represent and compare numbers less than 0 through familiar applications and extending the number line. B. Compare, order and convert among fractions, decimals and percents. C. Develop meaning for percents including percents greater than 100 and less than 1. D. Use models and pictures to relate concepts of ratio, proportion and percent. By the end of Grade 5, the student will: Number and Number Systems 1. Use models and visual representation to develop the concept of ratio as part to part and part to whole, and the concept of percent as part to whole. (B, D) 2. Use various forms of one to demonstrate the equivalence of fractions; e.g., 18/24 = 9/12 x 2/2 = 3/4 x 6/6. (B) 3. Identify and generate equivalent forms of fractions, decimals and percents. (B) 4. Round decimals to a given place value and round fractions (including mixed numbers) to the nearest half. Units 5, 8, 12 Unit 5 Units 5 & 12 Unit 5 E. Use order of operations, including use of parenthesis and exponents to solve multi step problems, and verify and interpret the results. 5. Recognize and identify perfect squares and their roots. (G) Unit 1 Letters in Bold correspond to related benchmark Revised: 9/7/2004 5 4

F. Apply number system properties when performing computations. G. Apply and explain the use of prime factorizations, common factors, and common multiples in problem situations. H. Use and analyze the steps in standard and non standard algorithms for computing with fractions, decimals and integers. I. Use a variety of strategies, including proportional reasoning, to estimate, compute, solve and explain solutions to problems involving integers, fractions, decimals and percents. Meaning of Operations 6. Represent and compare numbers less than 0 by extending the number line and using familiar applications; e.g., temperature, owing money. (A) 7. Use commutative, associative, distributive, identity and inverse properties to simplify and perform computations. (F) 8. Identify and use relationships between operations to solve problems. (E) 9. Use order of operations, including use of parentheses, to simplify numerical expressions. (E) 10. Justify why fractions need common denominators to be added or subtracted. (H) 11. Explain how place value is related to addition and subtraction of decimals; e.g., 0.2 + 0.14; the two tenths is added to the one tenth because they are both tenths. (H) Computation and Estimation 12. Use physical models, points of reference, and equivalent forms to add and subtract commonly used fractions with like and unlike denominators and decimals. 13. Estimate the results of computations involving whole numbers, fractions and decimals, using a variety of strategies. Unit 7 Unit 2 & 4 Units 2, 4, 7 Unit 7 Unit 6 Unit 2 Unit 5, 6, 8 Units 2 & 4 Letters in Bold correspond to related benchmark. Revised: 9/7/2004 5 5

Lakewood City Schools Mathematics Course of Study Fifth Grade Standard 2 Measurement Students estimate and measure to a required degree of accuracy and precision by selecting and using appropriate units, tools and technologies. SMART Essential Focus: Students should know how to define and determine area. 5 7 Benchmarks Grade Level Indicators Corresponding Everyday Mathematics Units A. Select appropriate units to measure angles, circumference, surface area, mass and volume, using: U.S. customary units; e.g., degrees, square feet, pounds, and other units as appropriate; metric units; e.g., square meters, kilograms and other units as appropriate. By the end of Grade 5, the student will: Measurement Units 1. Identify and select appropriate units to measure angles; i.e., degrees. (A) 2. Identify paths between points on a grid or coordinate plane and compare the lengths of the paths; e.g., shortest path, paths of equal length. (E) Unit 9 B. Convert units of length, area, volume, mass and time within the same measurement system. C. Identify appropriate tools and apply appropriate techniques for measuring angles, perimeter or circumference and area of triangles, quadrilaterals, circles and composite shapes, and surface area and volume of prisms and cylinders. 3. Demonstrate and describe the differences between covering the faces (surface area) and filling the interior (volume) of threedimensional objects. (F, G) 4. Demonstrate understanding of the differences among linear units, square units and cubic units. (F, G) Units 9 and 11 Units 9 and 11 Letters in Bold correspond to related benchmark. Revised: 9/7/2004 5 6

D. Select a tool and measure accurately to a specified level of precision. E. Use problem solving techniques and technology as needed to solve problems involving length, weight, perimeter, area, volume, time and temperature. F. Analyze and explain what happens to area and perimeter or surface area and volume when the dimensions of an object are changed. G. Understand and demonstrate the independence of perimeter and area for two dimensional shapes and of surface area and volume for three dimensional shapes. Use Measurement Techniques and Tools 5. Make conversions within the same measurement system while performing computations. (B) 6. Use strategies to develop formulas for determining perimeter and area of triangles, rectangles and parallelograms, and volume of rectangular prisms. (C, E) 7. Use benchmark angles (e.g.; 45, 90, 120 ) to estimate the measure of angles, and use a tool to measure and draw angles. (C) Units 9 and 11 Units 9 and 11 Unit 3 Letters in Bold correspond to related benchmark. Revised: 9/7/2004 5 7

Lakewood City Schools Mathematics Course of Study Fifth Grade Standard 3 Geometry and Spatial Sense Students identify, classify, compare and analyze characteristics, properties and relationships of one, two, and three dimensional geometric figures and objects. Students use spatial reasoning, properties of geometric objects and transformations to analyze mathematical situations and solve problems. SMART Essential Focuses: Students should know how to identify and determine relationships among the radius, diameter, center, and circumference of a circle, and how to describe and classify fundamental relationships among shapes. 5 7 Benchmarks Grade Level Indicators Corresponding Everyday Mathematics Units A. Identify and label angle parts and the regions defined within the plane where the angle resides. B. Draw circles, and identify and determine the relationships among the radius, diameter, center and circumference. C. Specify locations and plot ordered pairs on a coordinate plane. D. Identify, describe and classify types of line pairs, angles, twodimensional figures and threedimensional objects using their properties. E. Use proportions to express relationships among corresponding parts of similar figures. By the end of Grade 5, the student will: Characteristics and Properties 1. Draw circles, and identify and determine relationships among the radius, diameter, center and circumference; e.g., radius is half the diameter, the ratio of the circumference of a circle to its diameter is an approximation of π. (B) 2. Use standard language to describe line, segment, ray, angle, skew, parallel and perpendicular. (A, D) 3. Label vertex, rays, interior and exterior for an angle. (A) 4. Describe and use properties of congruent figures to solve problems. (F, J) 5. Use physical models to determine the sum of the interior angles of triangles and quadrilaterals. (D, G) Unit 10 Units 3 and 9 Unit 3 Unit 3 Unit 3 Letters in Bold correspond to related benchmark. Revised: 9/7/2004 5 8

F. Describe and use the concepts of congruence, similarity and symmetry to solve problems. G. Describe and use properties of triangles to solve problems involving angle measures and side lengths of right triangles. H. Predict and describe results (size, position, orientation) of transformations of twodimensional figures. I. Identify and draw threedimensional objects from different views (top, side, front and perspective). J. Apply properties of equality and proportionality to solve problems involving congruent or similar figures; e.g., create a scale drawing. Spatial Relationships 6. Extend understanding of coordinate system to include points whose x or y values may be negative numbers. (C) Visualization and Geometric Models 7. Understand that the measure of an angle is determined by the degree of rotation of an angle side rather than the length of either side. (D) 8. Predict what three dimensional object will result from folding a two dimensional net, then confirm the prediction by folding the net. (I) Unit 9 Unit 3 Unit 11 Letters in Bold correspond to related benchmark. Revised: 9/7/2004 5 9

Lakewood City Schools Mathematics Course of Study Fifth Grade Standard 4 Patterns, Functions and Algebra Standard Students use patterns, relations and functions to model, represent and analyze problem situations that involve variable quantities. Students analyze, model and solve problems using various representations such as tables, graphs and equations. SMART Essential Focus: Students should know how to use symbolic algebra to represent and explain mathematical relationships. 5 7 Benchmarks Grade Level Indicators Corresponding Everyday Mathematics Units A. Describe, extend and determine the rule for patterns and relationships occurring in numeric patterns, computation, geometry, graphs and other applications. By the end of Grade 5, the student will: Use Patterns, Relations and Functions 1. Justify a general rule for a pattern or a function by using physical materials, visual representations, words, tables or graphs. (A) Unit 10 B. Represent, analyze and generalize a variety of patterns and functions with tables, graphs, words and symbolic rules. C. Use variables to create and solve equations and inequalities representing problem situations. D. Use symbolic algebra to represent and explain mathematical relationships. E. Use rules and variables to describe patterns, functions and other relationships. 2. Use calculators or computers to develop patterns, and generalize them using tables and graphs. (A) Use Algebraic Representation 3. Use variables as unknown quantities in general rules when describing patterns and other relationships. (B, E, G) 4. Create and interpret the meaning of equations and inequalities representing problem situations. (C) 5. Model problems with physical materials and visual representations, and use models, graphs and tables to draw conclusions and make predictions. (F, K) Unit 7 Unit 10 Unit 10 Unit 10 Letters in Bold correspond to related benchmark. Revised: 9/7/2004 5 10

F. Use representations, such as tables, graphs and equations, to model situations and to solve problems, especially those that involve linear relationships. G. Write, simplify and evaluate algebraic expressions. H. Solve linear equations and inequalities symbolically, graphically and numerically. I. Explain how inverse operations are used to solve linear equations. J. Use formulas in problem solving situations. K. Graph linear equations and inequalities. L. Analyze functional relationships, and explain how a change in one quantity results in a change in the other. M. Approximate and interpret rates of change from graphical and numerical data. Analyze Change 6. Describe how the quantitative change in a variable affects the value of a related variable; e.g., describe how the rate of growth varies over time, based upon data in a table or graph. (L) Unit 10 Letters in Bold correspond to related benchmark. Revised: 9/7/2004 5 11

Lakewood City Schools Mathematics Course of Study Fifth Grade Standard 5 Data Analysis and Probability Students pose questions and collect, organize, represent, interpret and analyze data to answer those questions. Students develop and evaluate inferences, predictions and arguments that are based on data. SMART Essential Focuses: Students should know how to use a sample to project the information for a larger populations and know that probabilities range from 0 to 1 inclusive. 5 7 Benchmarks Grade Level Indicators Corresponding Everyday Mathematics Units A. Read, create and use line graphs, histograms, circle graphs, box andwhisker plots, stem and leaf plots, and other representations when appropriate. B. Interpret data by looking for patterns and relationships, draw and justify conclusions, and answer related questions. By the end of Grade 5, the student will: Data Collection 1. Read, construct and interpret frequency tables, circle graphs and line graphs. (A) 2. Select and use a graph that is appropriate for the type of data to be displayed; e.g., numerical vs. categorical data, discrete vs. continuous data. (E) 3. Read and interpret increasingly complex displays of data, such as double bar graphs. (D) Units 1, 6, 10 and 12 Units 10 and 12 Units 6, 10 and 12 C. Evaluate interpretations and conclusions as additional data are collected, modify conclusions and predictions, and justify new findings. D. Compare increasingly complex displays of data, such as multiple sets of data on the same graph. 4. Determine appropriate data to be collected to answer questions posed by students or teacher, collect and display data, and clearly communicate findings. (E) 5. Modify initial conclusions, propose and justify new interpretations and predictions as additional data are collected. (C) Statistical Methods 6. Determine and use the range, mean, median and mode, and explain what each does and does not indicate about the set of data. (F) Units 2, 6 and 12 Unit 12 Unit 12 Letters in Bold correspond to related benchmark. Revised: 9/7/2004 5 12

E. Collect, organize, display and interpret data for a specific purpose or need. F. Determine and use the range, mean, median and mode to analyze and compare data, and explain what each indicates about the data. G. Evaluate conjectures and predictions based upon data presented in tables and graphs, and identify misuses of statistical data and displays. H. Find all possible outcomes of simple experiments or problem situations, using methods such as lists, arrays and tree diagrams. I. Describe the probability of an event using ratios, including fractional notation. J. Compare experimental and theoretical results for a variety of simple experiments. K. Make and justify predictions based on experimental and theoretical probabilities. Probability 7. List and explain all possible outcomes in a given situation. (H) 8. Identify the probability of events within a simple experiment, such as three chances out of eight. (I) 9. Use 0, 1 and ratios between 0 and 1 to represent the probability of outcomes for an event, and associate the ratio with the likelihood of the outcome. (I) 10. Compare what should happen (theoretical/expected results) with what did happen (experimental/actual results) in a simple experiment. (J) 11. Make predictions based on experimental and theoretical probabilities. (K) Unit 12 Units 2 and 12 Units 2 and 12 Units 2 and 12 Units 2 and 12 Letters in Bold correspond to related benchmark. Revised: 9/7/2004 5 13

Recommendations for the Teacher: Key Information about 5 th Grade Everyday Mathematics Program Familiarize yourself with the content standards for 5 th grade mathematics found on pages 146 149 in the blue Ohio Department of Education Academic Content Standards book for Mathematics and refer to the Course of Study pages 5 1 5 15 in this document that connect each standard with the units in the Everyday Mathematics Program. Prior to beginning a new unit, study the unit overview pages of the Everyday Mathematics Teacher s Lesson Guide to understand which learning goals are Beginning, Developing, or Secure. Use this information to assist in determining the amount of time spent on individual lessons and in the modification of assessment. Familiarize yourself with the games and the related topics (highlighted in pink boxes). Further explanation of the games can be found in the Student Reference Book. Further explanation of the related topics can be found in the Teacher s Reference Manual. Thorough preparation of daily lessons is required for the teaching of Everyday Mathematics. To help prepare your lessons, study and work through all aspects of the individual lessons. Refer to the Teacher s Reference Manual and other professionals for additional support. Display vocabulary to encourage the use of mathematical language throughout the day (e.g., Line up perpendicular to the north wall. Sit along the perimeter of the gym. Turn your chair 90º to the east. ) Due to time constraints, the American Tour lessons may be incorporated into other subject areas (e.g. social studies) or omitted. The 8 projects listed at the end of both of the Teacher s Lesson Guides may be used for optional enrichment. Calculator activities throughout the Everyday Mathematics Program may be modified depending on the types of calculators available to the students. Revised: 9/7/2004 5 14

Fifth Grade Pacing & Sequencing Chart for Everyday Mathematics Program Key: NNS & O = Number, Number Sense & Operations Standard M = Measurement Standard G & SS = Geometry & Spatial Sense Standard PF & A = Patterns, Functions &Algebra Standard DA & P = Data Analysis & Probability Standard MP = Mathematical Processes *Note: # of Weeks suggested based on a minimum of 60 minutes daily Unit # Title of Content Standards Grade Level Indicators Everyday Mathematics NNS & O: 5. Recognize and identify perfect squares 1.7, 1.8, 1.9 and their roots. 7. Use commutative, associative, 1.2 distributive, identity and inverse properties to simplify and perform computations. Lesson & Assessment Planning # of Weeks Modifications Teacher Suggestions 3 Weeks Incorporate frequent review for practice of basic computation throughout the year (games, etc.). Omit teaching divisibility rules for 3, 6, 9. Teach with conceptual meaning only, not rule memorization. Emphasize number sense, computation, and guess & check as strategies for determining divisibility. Adjust Math Boxes & Assessments. Perhaps challenge some students (GT) to discover & explain rationale for divisibility rules of 3, 6, 9. 1. Number Theory Assessment Verbs: construct, explain, justify and apply use interpret recognize communicate and represent create representations make and investigate determine solution Revised: 9/7/2004 5 15

Assessment Verbs: (continued) generate extend understand predict create and interpret model read, construct and interpret modify list and explain compare collect apply the concept represent and compare identify relationships explain use physical models estimate compute order combinations explain and reflect apply select demonstrate and describe draw Revised: 9/7/2004 5 16

Unit # Title of Everyday Mathematics 2. Estimation & Computation Content Standards Grade Level Indicators NNS & O: 3. Identify and generate equivalent forms of fractions, decimals and percents. 4. Round decimals to a given place value and round fractions (including mixed numbers) to the nearest half. 7. Use commutative, associative, distributive, identity and inverse properties to simplify and perform computations. 8. Identify and use relationships between operations to solve problems. 11. Explain how place value is related to addition and subtraction of decimals; e.g., 0.2 + 0.14; the two tenths is added to the one tenth because they are both tenths. 12. Use physical models, points of reference, and equivalent forms to add and subtract commonly used fractions with like and unlike denominators and decimals. 13. Estimate the results of computations involving whole numbers, fractions and decimals, using a variety of strategies. M: 5. Make conversions within the same measurement system while performing computations. PF & A: 4. Create and interpret the meaning of equations and inequalities representing problem situations. 2.6 2.7 2.8, 2.9, 2.10 2.2, 2.3, 2.4 2.2, 2.3 2.2, 2.3 2.1, 2.7, 2.8, 2.9, 2.10 2.1 2.4 Lesson & Assessment Planning # of Weeks Modifications Teacher Suggestions 4 Weeks Display Probability Meter and use it throughout year to make relevant connections to everyday situations, i.e., What is the probability of snow falling on Lakewood tomorrow? Emphasize Partial Products Method for whole number multiplication. This method is an important application of the distributive property, which is essential for development of number sense and algebraic sense. Interchange frequently the words of and times for the multiplication sign (2/3 x 15 = 2/3 of 15). Revised: 9/7/2004 5 17

DA & P: 2. Select and use a graph that is appropriate for the type of data to be displayed; e.g., numerical vs. categorical data, discrete vs. continuous data. 4. Determine appropriate data to be collected to answer questions posed by students or teacher, collect and display data, and clearly communicate findings. 5. Modify initial conclusions, propose and justify new interpretations and predictions as additional data are collected. 6. Determine and use the range, mean, median and mode, and explain what each does and does not indicate about the set of data. 8. Identify the probability of events within a simple experiment, such as three chances out of eight. 9. Use 0, 1 and ratios between 0 and 1 to represent the probability of outcomes for an event, and associate the ratio with the likelihood of the outcome. 10. Compare what should happen (theoretical/expected results) with what did happen (experimental/actual results) in a simple experiment. 11. Make predictions based on experimental and theoretical probabilities. 2.5, 2.6 2.5, 2.10 2.1, 2.5, 2.10 2.5, 2.6 2.6 2.6 2.6 2.6 Revised: 9/7/2004 5 18

Unit # Title of Everyday Mathematics 3. Geometry Explorations & American Tour Content Standards Grade Level Indicators NNS & O: 3. Identify and generate equivalent forms of fractions, decimals and percents. 7. Use commutative, associative, distributive, identity and inverse properties to simplify and perform computations. 13. Estimate the results of computations involving whole numbers, fractions and decimals, using a variety of strategies. M: 1. Identify and select appropriate units to measure angles; i.e., degrees. 7. Use benchmark angles (e.g.; 45, 90, 120 ) to estimate the measure of angles, and use a tool to measure and draw angles. G & SS: 1. Draw circles, and identify and determine relationships among the radius, diameter, center and circumference; e.g., radius is half the diameter, the ratio of the circumference of a circle to its diameter is an approximation of π. 2. Use standard language to describe line, segment, ray, angle, skew, parallel and perpendicular. 3. Label vertex, rays, interior and exterior for an angle. 4. Describe and use properties of congruent figures to solve problems. 3.1 3.7 3.1, 3.7 3.3, 3.4 3.3, 3.4, 3.6, 3.8, 3.9 3.10 3.3, 3.5, 3.10 3.3, 3.5 3.6 Lesson & Assessment Planning 3 4 Weeks # of Weeks Modifications Teacher Suggestions Lesson 3.5 use term opposite angles (avoid term vertical angles ). Emphasize use of measurement sense, estimation and measuring with protractor to determine angle measures (as opposed to memorization of angle relationship rules). Revised: 9/7/2004 5 19

5. Use physical models to determine the sum of the interior angles of triangles and quadrilaterals. 7. Understand that the measure of an angle is determined by the degree of rotation of an angle side rather than the length of either side. PF & A: 4. Create and interpret the meaning of equations and inequalities representing problem situations. 5. Model problems with physical materials and visual representations, and use models, graphs and tables to draw conclusions and make predictions. DA & P: 1. Read, construct and interpret frequency tables, circle graphs and lien graphs. 6. Determine and use the range, mean, median and mode, and explain what each does and does not indicate about the set of data. 3.3, 3.8, 3.9 3.3, 3.4 3.3 3.9 3.4, 3.9 3.4, 3.9 Revised: 9/7/2004 5 20

Unit # Title of Everyday Mathematics 4. Division Content Standards Grade Level Indicators NNS & O: 4. Round decimals to a given place value and round fractions (including mixed numbers) the nearest half. 8. Identify and use relationships between operations to solve problems. 13. Estimate the results of computations involving whole numbers, fractions and decimals, using a variety of strategies. M: 1. Identify and select appropriate units to measure angles; i.e., degrees. 2. Identify paths between points on a grid or coordinate plane and compare the lengths of the paths; e.g., shortest path, paths of equal length. 5. Make conversions within the same measurement system while performing computations. 7. Use benchmark angles (e.g.; 45, 90, 120 ) to estimate the measure of angles, and use a tool to measure and draw angles. PF & A: 3. Use variables as unknown quantities in general rules when describing patterns and other relationships. 4. Create and interpret the meaning of equations and inequalities representing problem situations. 4.6 4.4, 4.5 4.3 4.3 4.3, 4.6 4.3 4.6 4.6 Lesson & Assessment Planning # of Weeks Modifications Teacher Suggestions 2 Weeks Partial Quotients Algorithm provides important conceptual development of division. This low stress strategy is introduced in Grade 4 and is the only division algorithm taught in the Everyday Mathematics program. This method is an important application of the distributive property. Revised: 9/7/2004 5 21

DA & P: 3. Read and interpret increasingly complex displays of data, such as double bar graphs. 4.2 Revised: 9/7/2004 5 22

Unit # Title of Everyday Mathematics 5. Fractions, Decimals, Percents Content Standards Grade Level Indicators NNS & O: 1. Use models and visual representation to develop the concept of ratio as part topart and part to whole, and the concept of percent as part to whole. 2. Use various forms of one to demonstrate the equivalence of fractions; e.g., 18/24 = 9/12 x 2/2 = 3/4 x 6/6. 3. Identify and generate equivalent forms of fractions decimals and percents. 4. Round decimals to a given place value and round fractions (including mixed numbers) to the nearest half. 10. Justify why fractions need common denominators to be added or subtracted. 12. Use physical models, points of reference, and equivalent forms to add and subtract commonly used fractions with like and unlike denominators and decimals. 13. Estimate the results of computations involving whole numbers, fractions and decimals, using a variety of strategies. PF & A: 4. Create and interpret the meaning of equations and inequalities representing problem situations. DA & P: 1. Read, construct and interpret frequency tables, circle graphs and line graphs. 3. Read and interpret increasingly complex displays of data, such as double bar graphs. 5.1, 5.2, 5.8 5.2, 5.3, 5.4 Lesson & Assessment Planning 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.8, 5.11, 5.12 5.5, 5.6, 5.7, 5.8 5.3 5.3 5.5 5.3 5.9, 5.10, 5.11 5.10, 5.12 # of Weeks Modifications Teacher Suggestions 4 Weeks Use Everyday Math Journal (pages 140 141) (rounding decimals) for optional enrichment. To develop the meaning of fractions, refer to the segment that separates the numerator and denominator as the dividing bar. Revised: 9/7/2004 5 23

4. Determine appropriate data to be collected to answer questions posed by students or teacher, collect and display data, and clearly communicate findings. 5. Modify initial conclusions, propose and justify new interpretations and predictions as additional data are collected. 7. List and explain all possible outcomes in a given situation. 9. Use 0, 1 and ratios between 0 and 1 to represent the probability of outcomes for an event, and associate the ratio with the likelihood of the outcome. 10. Compare what should happen (theoretical/expected results) with what did happen (experimental/actual results) in a simple experiment. 11. Make predictions based on experimental and theoretical probabilities. 5.9 5.9, 5.12 5.10 5.10 5.10 5.10 Revised: 9/7/2004 5 24

Unit # Title of Everyday Mathematics 6. Using Data: Addition & Subtraction of Fractions Content Standards Grade Level Indicators NNS & O: 1. Use models and visual representation to develop the concept of ratio as part topart and part to whole, and the concept of percent as part to whole. 2. Use various forms of one to demonstrate the equivalence of fractions; e.g., 18/24 = 9/12 x 2/2 = 3/4 x 6/6. 3. Identify and generate equivalent forms of fractions decimals and percents. 4. Round decimals to a given place value and round fractions (including mixed numbers) to the nearest half. 10. Justify why fractions need common denominators to be added or subtracted. 12. Use physical models, points of reference, and equivalent forms to ad and subtract commonly used fractions with like and unlike denominators and decimals. M: 5. Make conversions within the same measurement system while performing computations. 7. Use benchmark angles (e.g.; 45, 90, 120 ) to estimate the measure of angles, and use a tool to measure and draw angles. PF & A: 5. Model problems with physical materials and visual representations, and use models, graphs and tables to draw conclusions and make predictions. 6.1, 6.5 6.9, 6.10 6.5, 6.6, 6.8, 6.9, 6.10 6.4 6.8, 6.9, 6.10 6.8, 6.9, 6.10 6.2, 6.3, 6.4, 6.9 Lesson & Assessment Planning 6.1, 6.3, 6.4, 6.5, 6.6, 6.7, 6.10 # of Weeks Modifications Teacher Suggestions 3 Weeks Use Lesson 6.8 (slide rule) for optional enrichment. Revised: 9/7/2004 5 25

DA & P: 1. Read, construct and interpret frequency tables, circle graphs and line graphs. 2. Select and use a graph that is appropriate for the type of data to be displayed; e.g., numerical vs. categorical data, discrete vs. continuous data. 3. Read and interpret increasingly complex displays of data, such as double bar graphs. 4. Determine appropriate data to be collected to answer questions posed by students or teacher, collect and display data, and clearly communicate findings. 5. Modify initial conclusions, propose and justify new interpretations and predictions as additional data are collected. 6. Determine and use the range, mean, median and mode, and explain what each does and does not indicate about the set of data. 7. List and explain all possible outcomes in a given situation. 8. Identify the probability of events within a simple experiment, such as three chances out of eight. 9. Use 0, 1 and ratios between 0 and 1 to represent the probability of outcomes for an event, and associate the ratio with the likelihood of the outcome. 10. Compare what should happen (theoretical/expected results) with what did happen (experimental/actual results) in a simple experiment. 11. Make predictions based on experimental and theoretical probabilities. 6.1, 6.5, 6.6 6.1, 6.4, 6.6 6.3, 6.4, 6.6, 6.7, 6.10 6.1, 6.5 6.1, 6.5 6.1, 6.3, 6.4, 6.6, 6.10 6.5 6.2, 6.3, 6.5 6.5, 6.6 6.2, 6.3, 6.4, 6.5, 6.6 6.2, 6.3, 6.5, 6.6 Revised: 9/7/2004 5 26

Unit # Title of Everyday Mathematics 7. Exponents & Negative Numbers Content Standards Grade Level Indicators NNS & O: 2. Use various forms of one to demonstrate the equivalence of fractions; e.g., 18/24 = 9/12 x 2/2 = 3/4 x 6/6. 3. Identify and generate equivalent forms of fractions decimals and percents. 5. Recognize and identify perfect squares and their roots 6. Represent and compare numbers less than 0 by extending the number line and using familiar applications; e.g., temperature, owing money. 7. Use commutative, associative, distributive, identity and inverse properties to simplify and perform computations. 8. Identify and use relationships between operations to solve problems. 9. Use order of operations, including use of parentheses, to simplify numerical expressions. 12. Use physical models, points of reference, and equivalent forms to add and subtract commonly used fractions with like and unlike denominators and decimals. 7.9 7.6, 7.7, 7.8, 7.9, 7.10 7.5 7.4, 7.5, 7.6 7.1 Lesson & Assessment Planning # of Weeks Modifications Teacher Suggestions 3 Weeks Use Lessons 7.9 (slide rule) and 7.10 (calculator) for optional enrichment. Revised: 9/7/2004 5 27

G & SS: 2. Use standard language to describe line, segment, ray, angle, skew, parallel and perpendicular. 6. Extend understanding of coordinate system to include points whose x or y values may be negative numbers. PF & A: 2. Use calculators or computers to develop patterns, and generalize them using tables and graphs. 3. Use variables as unknown quantities in general rules when describing patterns and other relationships. 4. Create and interpret the meaning of equations and inequalities representing problem situations. DA & P: 3. Read and interpret increasingly complex displays of data, such as double bar graphs. 7. List and explain all possible outcomes in a given situation. 7.9 7.10 7.2 7.2, 7.4 7.5 7.1 Revised: 9/7/2004 5 28

Unit # Title of Everyday Mathematics 8. Fractions & Ratios Content Standards Grade Level Indicators NNS & O: 1. Use models and visual representation to develop the concept of ratio as part topart and part to whole, and the concept of percent as part to whole. 2. Use various forms of one to demonstrate the equivalence of fractions; e.g., 18/24 = 9/12 x 2/2 = 3/4 x 6/6. 3. Identify and generate equivalent forms of fractions decimals and percents. 7. Use commutative, associative, distributive, identity and inverse properties to simplify and perform computations. 8. Identify and use relationships between operations to solve problems. 9. Use order of operations, including use of parentheses, to simplify numerical expressions. 10. Justify why fractions need common denominators to be added or subtracted. 12. Use physical models, points of reference, and equivalent forms to add and subtract commonly used fractions with like and unlike denominators and decimals. 13. Estimate the results of computations involving whole numbers, fractions and decimals, using a variety of strategies. 8.1 8.1, 8.4, 8.8, 8.12 Lesson & Assessment Planning 8.1, 8.3, 8.4, 8.8, 8.10, 8.12 8.8 8.8 8.7 8.1, 8.3 8.1, 8.2, 8.3 8.5, 8.10, 8.11 # of Weeks Modifications Teacher Suggestions 3.5 Weeks Use Everyday mathematics Journal p. 261 (calculator) for optional enrichment. Revised: 9/7/2004 5 29

PF & A: 1. Justify a general rule for a pattern or a function by using physical materials, visual representations, words, tables or graphs. DA & P: 3. Read and interpret increasingly complex displays of data, such as double bar graphs. 4. Determine appropriate data to be collected to answer questions posed by students or teacher, collect and display data, and clearly communicate findings. 8.3, 8.6 8.11 8.11 Revised: 9/7/2004 5 30

Unit # Title of Everyday Mathematics 9. Coordinates, Area, Volume, Capacity Content Standards Grade Level Indicators NNS & O: 2. Use various forms of one to demonstrate the equivalence of fractions; e.g., 18/24 = 9/12 x 2/2 = 3/4 x 6/6. 3. Identify and generate equivalent forms of fractions decimals and percents. 6. Represent and compare numbers less than 0 by extending the number line and using familiar applications; e.g., temperature, owing money. 9. Use order of operations, including use of parentheses, to simplify numerical expressions. 13. Estimate the results of computations involving whole numbers, fractions and decimals, using a variety of strategies. M: 2. Identify paths between points on a grid or coordinate plane and compare the lengths of the paths; e.g., shortest path, paths of equal length. 3. Demonstrate and describe the differences between covering the faces (surface area) and filling the interior (volume) of threedimensional objects. 4. Demonstrate understanding of the differences among linear units, square units and cubic units. 5. Make conversions within the same measurement system while performing computations. 9.8 9.5, 9.8 9.3 9.7 9.6 9.5, 9.8, 9.9 Lesson & Assessment Planning 9.4, 9.5, 9.6, 9.8, 9.9, 9.10 9.10 # of Weeks Modifications Teacher Suggestions 2.5 Weeks Use Lesson 9.7 (Earth s water surface) for optional enrichment. To avoid confusion between b and B when using formulas to determine area or volume, use the language length of base for b and area of base for B. Revised: 9/7/2004 5 31

6. Use strategies to develop formulas for determining perimeter and area of triangles, rectangles and parallelograms, and volume of rectangular prisms. G &SS: 2. Use standard language to describe line, segment, ray, angle, skew, parallel and perpendicular. 6. Extend understanding of coordinate system to include points whose x or y values may be negative numbers. PF & A: 1. Justify a general rule for a pattern or a function by using physical materials, visual representations, words, tables or graphs. 3. Use variables as unknown quantities in general rules when describing patterns and other relationships. 5. Model problems with physical materials and visual representations, and use models, graphs and tables to draw conclusions and make predictions. DA & P: 2. Select and use a graph that is appropriate for the type of data to be displayed; e.g., numerical vs. categorical data, discrete vs. continuous data. 3. Read and interpret increasingly complex displays of data, such as double bar graphs. 4. Determine appropriate data to be collected to answer questions posed by students or teacher, collect and display data, and clearly communicate findings. 5. Modify initial conclusions, propose and justify new interpretations and predictions as additional data are collected. 7. List and explain all possible outcomes in a given situation. 9.4, 9.5, 9.6, 9.8, 9.9, 9.10 9.1, 9.2, 9.3, 9.9 9.4, 9.5, 9.6 9.6 9.4, 9.5, 9.6 9.1, 9.7 9.1 9.7 9.7, 9.10 9.10 Revised: 9/7/2004 5 32

Unit # Title of Everyday Mathematics 10. Algebra Concepts & Skills Content Standards Grade Level Indicators NNS & O: 3. Identify and generate equivalent forms of fractions, decimals and percents. 13. Estimate the results of computations involving whole numbers, fractions and decimals, using a variety of strategies. M: 6. Use strategies to develop formulas for determining perimeter and area of triangles, rectangles and parallelograms, and volume of rectangular prisms. G & SS: 1. Draw circles, and identify and determine relationships among the radius, diameter, center and circumference; e.g., radius is half the diameter, the ratio of the circumference of a circle to its diameter is an approximation of π. PF & A: 1. Justify a general rule for a pattern or a function by using physical materials, visual representations, words, tables or graphs. 2. Use calculators or computers to develop patterns, and generalize them using tables and graphs. 3. Use variables as unknown quantities in general rules when describing patterns and other relationships. 4. Create and interpret the meaning of equations and inequalities representing problem situations. 10.8, 10.9 10.4, 10.6 10.4, 10.9 10.8, 10.9 10.3, 10.4, 10.6, 10.9 10.4, 10.6, 10.9 Lesson & Assessment Planning 10.1, 10.2, 10.3, 10.4, 10.6, 10.9 10.1, 10.2, 10.3, 10.4, 10.6, 10.7, 10.9 # of Weeks Modifications Teacher Suggestions 3 Weeks Avoid teaching formulas for determining area and circumference of circles. Provide students opportunities to determine relationships among the radius, diameter, center, and circumference, by using a variety of tools (i.e., string, tape measure, ruler, compass, etc.) Revised: 9/7/2004 5 33

5. Model problems with physical materials and visual representations, and use models, graphs and tables to draw conclusions and make predictions. 6. Describe how the quantitative change in a variable affects the value of a related variable; e.g., describe how the rate of growth varies over time, based upon data in a table or graph. DA & P: 1. Read, construct and interpret frequency tables, circle graphs and line graphs. 2. Select and use a graph that is appropriate for the type of data to be displayed; e.g., numerical vs. categorical data, discrete vs. continuous data. 3. Read and interpret increasingly complex displays of data, such as double bar graphs. 4. Determine appropriate data to be collected to answer questions posed by students or teacher, collect and display data, and clearly communicate findings. 6. Determine and use the range, mean, median and mode, and explain what each does and does not indicate about the set of data. 10.1, 10.2, 10.4, 10.6 10.5, 10.6 10.4, 10.6 10.5, 10.7 10.5, 10.7, 10.8 10.4 Revised: 9/7/2004 5 34

Unit # Title of Everyday Mathematics 12. Probability, Ratios & Rates Content Standards Grade Level Indicators NNS & O: 1. Use models and visual representation to develop the concept of ratio as part topart and part to whole, and the concept of percent as part to whole. 2. Use various forms of one to demonstrate the equivalence of fractions; e.g., 18/24 = 9/12 x 2/2 = 3/4 x 6/6. 3. Identify and generate equivalent forms of fractions, decimals and percents. 9. Use order of operations, including use of parentheses, to simplify numerical expressions. M: 5. Make conversions within the same measurement system while performing computations. PF & A: 3. Use variables as unknown quantities in general rules when describing patterns and other relationships. 4. Create and interpret the meaning of equations and inequalities representing problem situations. 5. Model problems with physical materials and visual representations, and use models, graphs and tables to draw conclusions and make predictions. Lesson & Assessment Planning 12.1, 12.3, 12.4, 12.5, 12.8 12.1, 12.2, 12.5 12.2, 12.8 12.4 12.6 12.5 12.5 12.5 # of Weeks Modifications Teacher Suggestions 3 Weeks Note sequence switch: Do Unit 12 before Unit 11. Revised: 9/7/2004 5 35

DA & P: 1. Read, construct and interpret frequency tables, circle graphs and line graphs. 2. Select and use a graph that is appropriate for the type of data to be displayed; e.g., numerical vs. categorical data, discrete vs. continuous data. 3. Read and interpret increasingly complex displays of data, such as double bar graphs. 4. Determine appropriate data to be collected to answer questions posed by students or teacher, collect and display data, and clearly communicate findings. 5. Modify initial conclusions, propose and justify new interpretations and predictions as additional data are collected. 6. Determine and use the range, mean, median and mode, and explain what each does and does not indicate about the set of data. 7. List and explain all possible outcomes in a given situation. 8. Identify the probability of events within a simple experiment, such as three chances out of eight. 9. Use 0, 1 and ratios between 0 and 1 to represent the probability of outcomes for an event, and associate the ratio with the likelihood of the outcome. 10. Compare what should happen (theoretical/expected results) with what did happen (experimental/actual results in a simple experiment. 11. Make predictions based on experimental and theoretical probabilities. 12.7 12.7 12.3, 12.7 12.6, 12.7 12.6, 12.7 12.7 12.2 12.2 12.2 12.6 12.6 Revised: 9/7/2004 5 36

Unit # Title of Everyday Mathematics 11. Volume Content Standards Grade Level Indicators NNS & O: 1. Use models and visual representation to develop the concept of ratio as part topart and part to whole, and the concept of percent as part to whole. 2. Use various forms of one to demonstrate the equivalence of fractions; e.g., 18/24 = 9/12 x 2/2 = 3/4 x 6/6. 3. Identify and generate equivalent forms of fractions decimals and percents. 9. Use order of operations, including use of parentheses, to simplify numerical expressions. 12. Use physical models, points of reference, and equivalent forms to add and subtract commonly used fractions with like and unlike denominators and decimals. M: 3. Demonstrate and describe the differences between covering the face (surface area) and filling the interior (volume) of threedimensional objects. 4. Demonstrate understanding of the differences among linear units, square units and cubic units. 5. Make conversions within the same measurement system while performing computations. 6. Use strategies to develop formulas for determining perimeter and area of triangles, rectangles and parallelograms, and volume of rectangular prisms. 11.5 11.5 11.6 11.5 11.7 11.6 11.4, 11.6, 11.7 Lesson & Assessment Planning # of Weeks Modifications Teacher Suggestions 2 Weeks Note sequence switch: Do Unit 12 before Unit 11. Revised: 9/7/2004 5 37

G & SS: 1. Draw circles, and identify and determine relationships among the radius, diameter, center and circumference; e.g., radius is half the diameter, the ratio of the circumference of a circle to its diameter is an approximation of π. 8. Predict what three dimensional object will result from folding a two dimensional net, then confirm the prediction by folding the net. PF & A: 3. Use variables as unknown quantities in general rules when describing patterns and other relationships. 4. Create and interpret the meaning of equations and inequalities representing problem situations. DA & P: 3. Read and interpret increasingly complex displays of data, such as double bar graphs. 7. List and explain all possible outcomes in a given situation. 8. Identify the probability of events within a simple experiment, such as three chances out of eight. 9. Use 0, 1 and ratios between 0 and 1 to represent the probability of outcomes for an event, and associate the ratio with the likelihood of the outcome. 11.1 11.1 11.3 11.3 Revised: 9/7/2004 5 38