Mathematics Lesson Planning Guide IP4 | Fifth Grade Instructional Period 4 Overview Content Strand 1: Number and Operations G.E.S.D. suggestion: distributed practice Concepts 1, 2 and 3 Strand 2: Data Analysis, Probability, and Discrete Math Concept 1: Data Analysis PO1. Collect, record, organize, and display data using multi-bar graphs or double line graphs. PO2. Formulate and answer questions by interpreting and analyzing displays of data, including multi-bar graphs or double line graphs. PO3. Use mean, median, mode, and range to analyze and describe the distribution of a given data set. Concept 2: Probability PO1. Describe the theoretical probability of events and represent the probability as a fraction, decimal, or percent. PO2. Explore probability when performing experiments by • predicting the outcome, • recording the data, • comparing outcomes of the experiment to predictions, and • comparing the results of multiple repetitions of the experiment. G.E.S.D. suggestion: distributed practice Concepts 3, and 4 Strand 3: Patterns, Algebra, and Functions Concept 4: Analysis of Change PO1. Describe patterns of change including constant rate and increasing or decreasing rate. G.E.S.D. suggestion: distributed practice Concepts 1 and 3 Process Strand 5: Structure and Logic Concept 2: Logic, Reasoning, Problem Solving, and Proof PO1. Analyze a problem situation to determine the question(s) to be answered. PO2. Identify relevant, missing, and extraneous information related to the solution to a problem. PO3. Select and use one or more strategies to efficiently solve the problem and justify the selection. PO4. Determine whether a problem to be solved is similar to previously solved problems, and identify possible strategies for solving the problem. PO5. Represent a problem situation using any combination of words, numbers, pictures, physical objects, or symbols. PO6. Summarize mathematical information, explain reasoning, and draw conclusions. PO7. Analyze and evaluate whether a solution is reasonable, is mathematically correct, and answers the question. Mathematical Practices MP1. Make sense of problems and persevere in solving them. MP2. Reason abstractly and quantitatively. MP3. Construct viable arguments and critique the reasoning of others. MP4. Model with mathematics. MP5. Use appropriate tools strategically. MP6. Attend to precision. MP7. Look for and make use of structure. MP8. Look for and express regularity in repeated reasoning. Strand 4: Geometry and Measurement G.E.S.D. suggestion: distributed practice Concepts 1 and 4. Strand 5: Structure and Logic Concept 2: Logic, Reasoning, Problem Solving, and Proof PO8: Make and test conjectures based on data or information collected from explorations and experiments. 1 of 10 Glendale Elementary School District | June 2011 Mathematics Lesson Planning Guide IP4 | Fifth Grade Instructional Period 4 Topic: Data Analysis & Graphing Strand 2: Data Analysis, Probability, and Discrete Math Concept 1: Data Analysis In Grade 5, students apply their understanding of whole numbers, fractions, and decimals as they construct, analyze, and describe data. Students apply this understanding of data in other core content areas and in their lives. Essential Questions: In which ways do we analyze data? How can graphs be used to misrepresent information? How do you determine the most appropriate way to display data? What does the data tell you? What predictions can you make based on the data? How do sets of data compare? Big Ideas: Data can be collected, organized, sorted, represented and interpreted in a variety of ways in order to answer questions about our world. Performance Objective S2C1PO1. Collect, record, organize, and display data using multi-bar graphs or double line graphs. Connections: S2C1PO2, Science: S1C2PO5,S1C4PO2, Social Studies:S4C1PO6 Process Integration Mathematical Practices S5C2PO5. Represent a problem situation using any combination of words, numbers, pictures, physical objects, or symbols. MP.1. Make sense of problems and persevere in solving them. MP.4. Model with mathematics. Explanations and Examples Resources *5-2 p. 264 “National Park Visitors” – add another year to force a multiple bar graph SFAW 5-1 *5-5 p. 278 “Favorite Music Store” – add another store to force a multiple bar graph Collecting Data from a Survey *5-8 p. 290 “Temperatures in Orlando” – add Phoenix or another city to force a double 5-2 line graph Bar Graphs* 5-3 *5-9 pp. 292-293 – combine data from two lines graphs to create a double line graph Line Graphs or have students brainstorm other variables that would force a double line graph. 5-5 Making a Graph* Problem Solving Workbook p. 68 – Have students combine data sets to create a 5-8 double line graph. Choosing an Appropriate Graph* **Explore student generated topics that would require a double line graph or multiple 5-9 bar graphs. Writing to Compare* MP.1. Make sense of problems and persevere in solving them. Students solve problems by applying their understanding of operations with whole numbers, decimals, and fractions including mixed numbers. They solve problems related to volume and measurement conversions. Students seek the meaning of a problem and look for efficient ways to represent and solve it. They may check their thinking by asking themselves, “What is the most efficient way to solve the problem?”, “Does this make sense?”, and “Can I solve the problem in a different way?”. *GESD suggestion: with modifications. See explanations and examples.* ATM pp. 105 TSCM 2 MP.4. Model with mathematics. Students experiment with representing problem pp. 320-323, 329-335 situations in multiple ways including numbers, words (mathematical language), 2 of 10 Assessment SFAW Diagnostic checkpoint pp. 281 Chapter Test pp. 314-315 IC Fly, Fly Away (on CD) ** Cafeteria Lunches (on CD) ** Heating Up-Cooling Down (on CD) ** **Modify to force a double graph.** IR Typical Family Size (on CD) ** Create a Graph (1) (on CD)** **Modify to force a double graph.** IPS The Awesome Amusement Park 1 (on CD) ** Glendale Elementary School District | June 2011 Mathematics Lesson Planning Guide IP4 | Fifth Grade drawing pictures, using objects, making a chart, list, or graph, creating equations, etc. Students need opportunities to connect the different representations and explain the connections. They should be able to use all of these representations as needed. Fifth graders should evaluate their results in the context of the situation and whether the results make sense. They also evaluate the utility of models to determine which models are most useful and efficient to solve problems. S2C1PO2. Formulate and S5C2PO2. Identify Students are expected to estimate and make computations using a data set. SFAW answer questions by relevant, missing, and 5-6 interpreting and analyzing extraneous information Example: Mean, Median, and Mode displays of data, including related to the solution to What is the median number of siblings that students in this class have? multi-bar graphs or double a problem. What is the mode of the data? What is the mean number of siblings? What MBL line graphs. is the range of the number of siblings? What do the mean; median, mode, Tikki Tikki Tembo Connections: S5C2PO6. Summarize and range of the number of siblings tell you about the students in the class? Math: S1C1PO5, S1C3PO1, mathematical TSCM2 (see graph below) S2C1PO1, S2C1PO3, information, explain pp.323, 331-332 S3C4PO1, S5C2PO9, reasoning, and draw Science: S1C1PO1, conclusions. S1C1PO2, S1C3PO1, MP.1. Make sense of Social Studies: S4C6PO2, problems and S4C6PO3 persevere in solving them. MP.1. Make sense of problems and persevere in solving them. Students solve problems by applying their understanding of operations with whole numbers, MP.2. Reason decimals, and fractions including mixed numbers. They solve problems related abstractly and to volume and measurement conversions. Students seek the meaning of a quantitatively. problem and look for efficient ways to represent and solve it. They may check MP.3. Construct viable their thinking by asking themselves, “What is the most efficient way to solve arguments and critique the problem?”, “Does this make sense?”, and “Can I solve the problem in a the reasoning of different way?”. others. MP.5. Use appropriate MP.2. Reason abstractly and quantitatively. Fifth graders should recognize that a number represents a specific quantity. They connect quantities to written tools strategically. symbols and create a logical representation of the problem at hand, considering both the appropriate units involved and the meaning of quantities. MP.6. Attend to They extend this understanding from whole numbers to their work with precision. fractions and decimals. Students write simple expressions that record calculations with numbers and represent or round numbers using place value MP.7. Look for and make use of structure. concepts. 3 of 10 **Modify to force a double graph.** SFAW Diagnostic checkpoint pp. 295 Chapter Test pp. 314-315 IPS Drink Favorites (on CD) Weather Watchers (on CD) MP.3. Construct viable arguments and critique the reasoning of others. In fifth grade, students may construct arguments using concrete referents, such as objects, pictures, and drawings. They explain calculations based upon models Glendale Elementary School District | June 2011 Mathematics Lesson Planning Guide IP4 | Fifth Grade and properties of operations and rules that generate patterns. They demonstrate and explain the relationship between volume and multiplication. They refine their mathematical communication skills as they participate in mathematical discussions involving questions like “How did you get that?” and “Why is that true?” They explain their thinking to others and respond to others’ thinking. MP.5. Use appropriate tools strategically. Fifth graders consider the available tools (including estimation) when solving a mathematical problem and decide when certain tools might be helpful. For instance, they may use unit cubes to fill a rectangular prism and then use a ruler to measure the dimensions. They use graph paper to accurately create graphs and solve problems or make predictions from real world data. MP.6. Attend to precision. Students continue to refine their mathematical communication skills by using clear and precise language in their discussions with others and in their own reasoning. Students use appropriate terminology when referring to expressions, fractions, geometric figures, and coordinate grids. They are careful about specifying units of measure and state the meaning of the symbols they choose. For instance, when figuring out the volume of a rectangular prism they record their answers in cubic units. MP.7. Look for and make use of structure. In fifth grade, students look closely to discover a pattern or structure. For instance, students use properties of operations as strategies to add, subtract, multiply and divide with whole numbers, fractions, and decimals. They examine numerical patterns and relate them to a rule or a graphical representation. S2C1PO3. Use mean, S5C2PO2. Identify Students use sets of data as well as graphical representation of data sets arising from SFAW median, mode, and range to relevant, missing, and real-world contexts. 5-6 analyze and describe the extraneous information Mean, Median, and Mode distribution of a given data related to the solution to Example: set. a problem. • What is the median number of siblings that students in this class have? What is the MBL mode of the data? What is the mean number of siblings? What is the range of the Tikki Tikki Tembo; Tiger Connections: S5C2PO6. Summarize number of siblings? What do the mean; median, mode, and range of the number of Math: Learning to Graph Math: S1C3PO1, S2C1PO2, mathematical siblings tell you about the students in the class? from a Baby Tiger Science: S1C3PO1 information, explain reasoning, and draw TSCM 2 conclusions. pp. 325-328 A.V. mean 4 of 10 SFAW Diagnostic checkpoint pp. 295 Chapter Test pp. 314-315 SFAW PW pp. 65, 72 (5-6) IR Typical Family Size (on CD) IPS Scoring Baskets (on CD) Museum Visitors (on CD) Glendale Elementary School District | June 2011 Mathematics Lesson Planning Guide IP4 | Fifth Grade MP.1. Make sense of problems and persevere in solving them. MP.2. Reason abstractly and quantitatively. MP.3. Construct viable arguments and critique the reasoning of others. MP.5. Use appropriate tools strategically. MP.6. Attend to precision. MP.1. Make sense of problems and persevere in solving them. Students solve problems by applying their understanding of operations with whole numbers, decimals, and fractions including mixed numbers. They solve problems related to volume and measurement conversions. Students seek the meaning of a problem and look for efficient ways to represent and solve it. They may check their thinking by asking themselves, “What is the most efficient way to solve the problem?”, “Does this make sense?”, and “Can I solve the problem in a different way?”. MP.2. Reason abstractly and quantitatively. Fifth graders should recognize that a number represents a specific quantity. They connect quantities to written symbols and create a logical representation of the problem at hand, considering both the appropriate units involved and the meaning of quantities. They extend this understanding from whole numbers to their work with fractions and decimals. Students write simple expressions that record calculations with numbers and represent or round numbers using place value concepts MP.3. Construct viable arguments and critique the reasoning of others. In fifth grade, students may construct arguments using concrete referents, such as MP.7. Look for and objects, pictures, and drawings. They explain calculations based upon models make use of structure. and properties of operations and rules that generate patterns. They demonstrate and explain the relationship between volume and multiplication. They refine their mathematical communication skills as they participate in mathematical discussions involving questions like “How did you get that?” and “Why is that true?” They explain their thinking to others and respond to others’ thinking. MP.5. Use appropriate tools strategically. Fifth graders consider the available tools (including estimation) when solving a mathematical problem and decide when certain tools might be helpful. For instance, they may use unit cubes to fill a rectangular prism and then use a ruler to measure the dimensions. They use graph paper to accurately create graphs and solve problems or make predictions from real world data. MP.6. Attend to precision. Students continue to refine their mathematical communication skills by using clear and precise language in their discussions with others and in their own reasoning. Students use appropriate terminology when referring to expressions, fractions, geometric figures, and coordinate grids. They are careful about specifying units of measure and state the meaning of the symbols they choose. For instance, when figuring out the volume of a rectangular prism they record their answers in cubic units. 5 of 10 Glendale Elementary School District | June 2011 Mathematics Lesson Planning Guide IP4 | Fifth Grade MP.7. Look for and make use of structure. In fifth grade, students look closely to discover a pattern or structure. For instance, students use properties of operations as strategies to add, subtract, multiply and divide with whole numbers, fractions, and decimals. They examine numerical patterns and relate them to a rule or a graphical representation. Topic: Probability and Discrete Mathematics Strand 2: Data Analysis, Probability, and Discrete Math Concept 2: Probability In Grade 5, students extend their knowledge of fractions to be able to state the theoretical probability of an event as a fraction, decimal, or percent. They predict, record, and compare results in actual experiments. Students begin to understand how probability is determined and make predictions related to probability . Essential Questions: When does probability help us make a decision? What makes an event certain or impossible? What combinations are possible? How do you know you have all possible combinations? What is a vertex-edge graph? How can vertex-edge graphs help you solve problems? How do vertex-edge graphs lead to more optimized solutions? Big Ideas: Possible outcomes and combinations can be determined in a systematic way. Discrete math is the mathematics for optimizing finite systems. S2C2PO1. Describe the theoretical probability of events and represent the probability as a fraction, decimal, or percent. Connections: S1C1PO1, S1C1PO5, S1C3PO1, S2C2PO2, S2C3PO2 S5C2PO5. Represent a problem situation using any combination of words, numbers, pictures, physical objects, or symbols. S5C2PO7. Analyze and evaluate whether a solution is reasonable, is mathematically correct, and answers the question. A.V. event experiment repetition theoretical probability MP.1. Make sense of problems and persevere in solving them. MP.4. Model with mathematics. MP.5. Use appropriate 6 of 10 Example: SFAW SFAW • A bag contains 4 green marbles, 6 red marbles, and 10 blue marbles. If one marble 5-12 Diagnostic checkpoint pp. is drawn randomly from the bag, what is the probability it will be red? What is the Expressing Probability as 309 probability that it will not be red? a Fraction Chapter Test pp. 314-315 Problem Solving pp. 71 MP.1. Make sense of problems and persevere in solving them. Students solve problems ATM by applying their understanding of operations with whole numbers, decimals, and pp. 85-103, 310-321 SFAW PW fractions including mixed numbers. They solve problems related to volume and pp. 71 measurement conversions. Students seek the meaning of a problem and look for BNA efficient ways to represent and solve it. They may check their thinking by asking Investigations 1, Sessions INV ASB themselves, “What is the most efficient way to solve the problem?”, “Does this make 1-2 pp. 57-58 sense?”, and “Can I solve the problem in a different way?”. MP.4. Model with mathematics. Students experiment with representing problem situations in multiple ways including numbers, words (mathematical language), drawing pictures, using objects, making a chart, list, or graph, creating equations, etc. Students need opportunities to connect the different representations and explain the connections. They should be able to use all of these representations as needed. Fifth graders should evaluate their results in the context of the situation and whether the results make sense. They also evaluate the utility of models to determine which models are most useful and efficient to solve problems. MBL Martha Blah Blah IC Even Odd Product Game (on CD) TSCM 2 4.15 Theoretical Probabilities pp. 349-351 MP.5. Use appropriate tools strategically. Fifth graders consider the available tools (including estimation) when solving a mathematical problem and decide when certain tools might be helpful. For instance, they may use unit cubes to fill a rectangular prism and then use a ruler to measure the dimensions. They use graph paper to accurately create graphs and solve problems or make predictions from real world data. MP.8. Look for and express regularity in repeated reasoning. Fifth graders use repeated Glendale Elementary School District | June 2011 Mathematics Lesson Planning Guide IP4 | Fifth Grade tools strategically. 5.MP.8. Look for and express regularity in repeated reasoning S2C2PO2. Explore S5C2-05. Represent a probability when performing problem situation using experiments by any combination of • predicting the outcome words, numbers, • recording the data pictures, physical • comparing outcomes of the objects, or symbols. experiment to predictions and S5C2-08. Make and test • comparing the results of conjectures based on multiple repetitions of the data or information experiment. collected from explorations and Connections: S2C2PO1 experiments. reasoning to understand algorithms and make generalizations about patterns. Students connect place value and their prior work with operations to understand algorithms to fluently multiply multi-digit numbers and perform all operations with decimals to hundredths. Students explore operations with fractions with visual models and begin to formulate generalizations Students should have opportunities to perform experiments using spinners, number cubes, or other objects. BNA Sessions 3-7 pp. 16 – 45 INV ASB pp. 58 MP.1. Make sense of problems and persevere in solving them. Students solve problems by applying their understanding of operations with whole numbers, decimals, and fractions including mixed numbers. They solve problems related to volume and measurement conversions. Students seek the meaning of a problem and look for efficient ways to represent and solve it. They may check their thinking by asking themselves, “What is the most efficient way to solve the problem?”, “Does this make sense?”, and “Can I solve the problem in a different way?”. SFAW 5-10 Predicting Outcomes SFAW PS pp. 69 TSCM 2 pp. 345-348, 356-357 IR Data Analysis pp. 111-114 MP.3. Construct viable arguments and critique the reasoning of others. In fifth grade, students may construct arguments using concrete referents, such as MP.1. Make sense of objects, pictures, and drawings. They explain calculations based upon models problems and and properties of operations and rules that generate patterns. They persevere in solving demonstrate and explain the relationship between volume and multiplication. them. They refine their mathematical communication skills as they participate in mathematical discussions involving questions like “How did you get that?” and MP.3. Construct viable “Why is that true?” They explain their thinking to others and respond to others’ arguments and critique thinking. the reasoning of others. MP.4. Model with mathematics. Students experiment with representing problem situations in multiple ways including numbers, words (mathematical language), MP.4. Model with drawing pictures, using objects, making a chart, list, or graph, creating mathematics. equations, etc. Students need opportunities to connect the different MP.5. Use appropriate representations and explain the connections. They should be able to use all of tools strategically. these representations as needed. Fifth graders should evaluate their results in the context of the situation and whether the results make sense. They also MP.7. Look for and evaluate the utility of models to determine which models are most useful and make use of structure efficient to solve problems. MP.5. Use appropriate tools strategically. Fifth graders consider the available tools (including estimation) when solving a mathematical problem and decide when certain tools might be helpful. For instance, they may use unit cubes to fill a rectangular prism and then use a ruler to measure the dimensions. They use graph paper to accurately create 7 of 10 Glendale Elementary School District | June 2011 Mathematics Lesson Planning Guide IP4 | Fifth Grade graphs and solve problems or make predictions from real world data. MP.7. Look for and make use of structure. In fifth grade, students look closely to discover a pattern or structure. For instance, students use properties of operations as strategies to add, subtract, multiply and divide with whole numbers, fractions, and decimals. They examine numerical patterns and relate the to a rule or a graphical representation. Topic: Reasoning Through Patterns, Algebra, and Functions Strand 3: Patterns, Algebra, and Functions Concept 4: Analysis of Change In Grade 5, students will build on their knowledge of change over time and extend this to include describing patterns of change as constant, increasing, or decreasing. Essential Questions: What patterns are in our number system? How can understanding patterns help us to make predictions and make sense of mathematical situations? How can the appearance of a graph represent change? Why do we use variables? Big Ideas: Mathematical situations can be represented in a variety of ways. Relationships between numbers can be expressed using algebraic equations. Logical patterns exist and can be generalized with both words and symbols. S3C4PO1. Describe patterns of change including constant rate and increasing or decreasing rate. Connections: S1C1PO5, S1C3PO1, S2C1PO2, S3C1PO1, S5C2PO10, Science: S1C3PO1 S5C2PO2. Identify Example: relevant, missing, and • Describe the change in speed over time shown by the graph. extraneous information related to the solution to a problem. PC Investigation 2: Describing Changing Speeds pp. 28-32 Graph Stories pp. 96-97 S5C2PO5. Represent a problem situation using any combination of words, numbers, pictures, physical objects, or symbols. TSCM 2 pp. 297-302 MP.1. Make sense of problems and persevere in solving them. MP.4. Model with mathematics. INV ASB pp. 30-32 IR All About Graphs (on CD) MP.1. Make sense of problems and persevere in solving them. Students solve problems by applying their understanding of operations with whole numbers, decimals, and fractions including mixed numbers. They solve problems related to volume and measurement conversions. Students seek the meaning of a problem and look for efficient ways to represent and solve it. They may check their thinking by asking themselves, “What is the most efficient way to solve the problem?”, “Does this make sense?”, and “Can I solve the problem in a different way?”. MP.4. Model with mathematics. Students experiment with representing problem situations in multiple ways including numbers, words (mathematical language), drawing pictures, using objects, making a chart, list, or graph, creating 8 of 10 Glendale Elementary School District | June 2011 Mathematics Lesson Planning Guide IP4 | Fifth Grade equations, etc. Students need opportunities to connect the different representations and explain the connections. They should be able to use all of these representations as needed. Fifth graders should evaluate their results in the context of the situation and whether the results make sense. They also evaluate the utility of models to determine which models are most useful and efficient to solve problems. Topic: Problem Solving Strand 5: Structure and Logic Concept 1: Algorithms and Algorithmic Thinking In Grade 5, students extend their work analyzing common algorithms for calculation with fractions and decimals, explaining why the procedures work on the basis of properties of operations and place value. They also use their understanding of geometric properties to develop algorithms for calculating area and perimeter of polygons. Essential Questions: How and why do algorithms work? On which foundations are algorithms developed? What are the similarities and differences between common algorithms and alternative strategies? When do I use an algorithm? Big Ideas: An algorithm is an abstract procedure for solving a problem. Algorithms are effective only when they are understood. Common algorithms are grounded in the fact that math is logical and sensible. S5C2PO8. Make and test conjectures based on data or information collected from explorations and experiments. ATM pp. 85-103 IC Even Odd Product Game 9 (on CD) **Note: This game corresponds to probability standards.** 9 of 10 Glendale Elementary School District | June 2011 Mathematics Lesson Planning Guide IP4 | Fifth Grade Key for Resources Adopted Text Code Resource Title SFAW SFAW PW SFAW PS ATN (Grade 7) BNYK BNA CC MB MT5 NTP PC PP Scott Foresman Addison Wesley Mathematics Scott Foresman Addison Wesley Mathematics Practice Workbook Scott Foresman Addison Wesley Mathematics Problem Solving Workbook Connected Math: Accentuate the Negative Investigations: Building on Numbers You Know Investigations: Between Never and Always Investigations: Containers and Cubes Investigations: Measurement Benchmarks Investigations: Mathematical Thinking at Grade 5 Investigations: Name That Portion Investigations: Patterns of Change Investigations: Picturing Polygons Code Assessment Title INV ASB SFAW PW SFAW SRTP Investigations Assessment Sourcebook Scott Foresman Addison Wesley Practice Workbook Scott Foresman Addison Wesley Spiral Review and Test Prep Book Additional Resources (Ask Achievement Advisor) Code Assessment Title ATM CP:PS5 HOE LED LEM LIF MBL4-6 NTDM TSCM 2 TSCM 3 IC 3-5 IPS 3-5 IR 3-5 IRP 3-5 10 of 10 About Teaching Mathematics Creative Publications: Problem Solver Hands-On Equations Kit Teaching Arithmetic: Lessons for Extending Division: Grades 4-5 Teaching Arithmetic: Lessons for Extending Multiplication: Grades 4-5 Teaching Arithmetic: Lessons for Introducing Fractions: Grades 4-5 Marilyn Burns Classroom Math Library Grades 4-6 Navigating Through Discrete Mathematics Teaching Student-Centered Mathematics Volume 2: Grades 3-5 Teaching Student-Centered Mathematics Volume 3: Grades 5-8 The Math Process Standards Series: Introduction to Connections Grades 3-5 The Math Process Standards Series: Introduction to Problem Solving Grades 3-5 The Math Process Standards Series: Introduction to Representation Grades 3-5 The Math Process Standards Series: Introduction to Reasoning & Proof Grades 3-5 **Used as a resource and/or assessment **Used as a resource and/or assessment **Used as a resource and/or assessment **Used as a resource and/or assessment Glendale Elementary School District | June 2011