Sixth Grade Mathematics Lesson Plan Guidebook 2024-2025

YHALE- 6 th Grade Mathematics Lesson Plan Guidebook 2024-2025

2024-2025 Sixth Grade Mathematics YHALE SIXTH GRADE MATHEMATICS LESSON PLAN GUIDEBOOK | 2024-2025 Unit 1: Exploring Real-Life Phenomena through Statistics August 5th – August 30th – 4 weeks Grade 6 Comprehensive Grade Level Overview Guide Unit 1 Exploring Real-Life Phenomena through Statistics Guide Standards: 6.NR.2: Apply operations with whole numbers, fractions and decimals within relevant applications. • 6.NR.2.1 Describe and interpret the center of the distribution by the equal share value (mean). • 6.NR.2.2 Summarize categorical and quantitative (numerical) data sets in relation to the context: display the distributions of quantitative (numerical) data in plots on a number line, including dot plots, histograms, and box plots and display the distribution of categorical data using bar graphs. • 6.NR.2.3 Interpret numerical data to answer a statistical investigative question created. Describe the distribution of a quantitative (numerical) variable collected, including its center, variability, and overall shape. • 6.NR.2.4 Design simple experiments and collect data. Use data gathered from realistic scenarios and simulations to determine quantitative measures of center (median and/or mean) and variability (interquartile range and range). Use these quantities to draw conclusions about the data, compare different numerical data sets, and make predictions. • 6.NR.2.5 Relate the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. • 6.NR.2.6 Describe the impact that inserting or deleting a data point has on the mean and the median of a data set. Create data displays using a dot plot or box plot to examine this impact. Unit 1 Vocabulary K-12 Math Glossary Lesson 1 (1-2 days) Lesson 2 (1-2 days) Lesson 3 (1-2 days) Lesson 4 (1-2 days) Box Plot Categorical Data Distribution Dot Plot Frequency Histogram Interquartile Range Maximum Value Mean Measures of Center Measures of Spread Media Minimum Value Mode Numerical Data Outlier Range Statistical question Statistics Symmetrical or Nonsymmetrical Variability Objective: TLW describe and interpret the mean of sets of data. Lesson: Finding the Mean Standards: • 6.NR.2.1 I Can Statements: • I can determine the balance point of a given data set. • I can use the mean to analyze and interpret data collected from student generated questions. Finding the Mean Student Reproducibles Objective: TLW explore how box plots can be used to organize and represent data and a new measure of center, median. Lesson: How Long is a Minute? Standards: • 6.NR.2.2 • 6.NR.2.3 I Can Statements: • I can display data using boxplots. • I can calculate measures of center for a data set. (median) • I can calculate measures of variation for a data set. (range, interquartile range) How Long is a Minute Student Reproducibles Objective: TLW represent and interpret data in a box plot. Lesson: Where’s Waldo Standards: • 6.NR.2.1 • 6.NR.2.2 • 6.NR.2.3 • 6.NR.2.4 I Can Statements: • I can create a boxplot. • I can describe the center and variation from a boxplot. Where’s Waldo Student Reproducibles Objective: TLW analyze a survey to decide how many candy bars students typically eat in a week. Lesson: Candy Bars Standards: • 6.NR.2.2 • 6.NR.2.3 I Can Statements: • I can summarize categorical and quantitative (numerical) data sets in relation to the context of the problem. • I can create graphs, charts and/or tables to analyze data. Candy Bars Student Reproducibles

2024-2025 Sixth Grade Mathematics YHALE SIXTH GRADE MATHEMATICS LESSON PLAN GUIDEBOOK | 2024-2025 Unit 1: Exploring Real-Life Phenomena through Statistics August 5th – August 30th – 4 weeks Grade 6 Comprehensive Grade Level Overview Guide Unit 1 Exploring Real-Life Phenomena through Statistics Guide Standards: 6.NR.2: Apply operations with whole numbers, fractions and decimals within relevant applications. • 6.NR.2.1 Describe and interpret the center of the distribution by the equal share value (mean). • 6.NR.2.2 Summarize categorical and quantitative (numerical) data sets in relation to the context: display the distributions of quantitative (numerical) data in plots on a number line, including dot plots, histograms, and box plots and display the distribution of categorical data using bar graphs. • 6.NR.2.3 Interpret numerical data to answer a statistical investigative question created. Describe the distribution of a quantitative (numerical) variable collected, including its center, variability, and overall shape. • 6.NR.2.4 Design simple experiments and collect data. Use data gathered from realistic scenarios and simulations to determine quantitative measures of center (median and/or mean) and variability (interquartile range and range). Use these quantities to draw conclusions about the data, compare different numerical data sets, and make predictions. • 6.NR.2.5 Relate the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. • 6.NR.2.6 Describe the impact that inserting or deleting a data point has on the mean and the median of a data set. Create data displays using a dot plot or box plot to examine this impact. Unit 1 Vocabulary K-12 Math Glossary Lesson 5 (1-2 days) Lesson 6 (1-2 days) Lesson 7 (2-3 days) Lesson 8 (1-2 days) Box Plot Categorical Data Distribution Dot Plot Frequency Histogram Interquartile Range Maximum Value Mean Measures of Center Measures of Spread Media Minimum Value Mode Numerical Data Outlier Range Statistical question Statistics Symmetrical or Nonsymmetrical Variability Objective: TLW analyze historical baseball statistics to make inferences and answer questions about the data. Lesson: Who Was the Greatest Yankee Home Run Hitter? Standards: • 6.NR.2.1 • 6.NR.2.2 • 6.NR.2.3 • 6.NR.2.5 • 6.NR.2.6 I Can Statements: • I can determine the balance point of a given data set. • I can use the mean to analyze and interpret data collected from student generated questions. Student Reproducibles Blackline Master Histogram Creator Objective: TLW explore statistical and nonstatistical questions through creating their own questions, sorting questions into statistical and non-statistical questions, and then rewriting non statistical questions into statistical questions. Lesson: What is a Statistical Question? Standards: • 6.NR.2.3 I Can Statements • I can create statistical questions. • I can determine the difference between statistical and nonstatistical questions Student Reproducibles Blackline Masters Objective: The teacher will be able to assess how well students are able to: ● Calculate the mean, median, and range from a frequency chart. ● Use a frequency chart to describe a possible data set, given information on the mean, median, and range. Lesson: Mean, Median, Mode and Range Standards: • 6.NR.2.3 • 6.NR.2.4 • 6.NR.2.5 I Can Statements: • I can determine the measure of center from a set of data. • I can determine the variability of a set of data. • I can use a frequency chart to determine the measures of center and variability of a set of data. Student Reproducibles Objective: TLW Lesson: Suzi’s Company Standards: • 6.NR.2.3 • 6.NR.2.4 • 6.NR.2.5 • 6.NR.2.6 I Can Statements: • I can calculate mean and median. • I can explain the difference in mean and median. • I can compare mean and median and determine which is best in a given situation. Student Reproducibles

2024-2025 Sixth Grade Mathematics YHALE SIXTH GRADE MATHEMATICS LESSON PLAN GUIDEBOOK | 2024-2025 Unit 1: Exploring Real-Life Phenomena through Statistics August 5th – August 30th – 4 weeks Grade 6 Comprehensive Grade Level Overview Guide Unit 1 Exploring Real-Life Phenomena through Statistics Guide Standards: 6.NR.2: Apply operations with whole numbers, fractions and decimals within relevant applications. • 6.NR.2.1 Describe and interpret the center of the distribution by the equal share value (mean). • 6.NR.2.2 Summarize categorical and quantitative (numerical) data sets in relation to the context: display the distributions of quantitative (numerical) data in plots on a number line, including dot plots, histograms, and box plots and display the distribution of categorical data using bar graphs. • 6.NR.2.3 Interpret numerical data to answer a statistical investigative question created. Describe the distribution of a quantitative (numerical) variable collected, including its center, variability, and overall shape. • 6.NR.2.4 Design simple experiments and collect data. Use data gathered from realistic scenarios and simulations to determine quantitative measures of center (median and/or mean) and variability (interquartile range and range). Use these quantities to draw conclusions about the data, compare different numerical data sets, and make predictions. • 6.NR.2.5 Relate the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. • 6.NR.2.6 Describe the impact that inserting or deleting a data point has on the mean and the median of a data set. Create data displays using a dot plot or box plot to examine this impact. Unit 1 Vocabulary K-12 Math Glossary Lesson 9 (2-3 days) Lesson 10 (1-2 days) Lesson 11 (2-3 days) Lesson 12 (2-3 days) Box Plot Categorical Data Distribution Dot Plot Frequency Histogram Interquartile Range Maximum Value Mean Measures of Center Measures of Spread Media Minimum Value Mode Numerical Data Outlier Range Statistical question Statistics Symmetrical or Nonsymmetrical Variability TLW conceptually explore mean absolute variation as a form of variability. Lesson: Mean as Fair Share Standards: • 6.NR.2.3 • 6.NR.2.4 • 6.NR.2.5 I Can Statements: • I can determine the distance of each data point in a distribution from the mean. • I can calculate the sum of the distances from mean in a data distribution. • I can explore the relationship of mean absolute deviation and variability. Student Reproducibles TLW build their understanding that Mean Absolute Deviation (MAD) is used to measure variance. Lesson: Modified Got MAD Skills Standards: • 6.NR.2.3 • 6.NR.2.4 I Can Statements: • I can determine the distance of each data point in a distribution from the mean. • I can calculate the sum of the distances from mean in a data distribution. • I can explore the relationship of mean absolute deviation and variability. Got MAD Skills Desmos Activity Student Reproducibles TLW explore the meaning of box plots in the context of school finance. Lesson: Cost of Learning Standards: • 6.NR.2.3 • 6.NR.2.4 • 6.NR.2.5 • 6.NR.2.6 I Can Statements: • I can write a statistical question. • I can compare boxplots. Student Reproducibles: TLW analyze fat and calorie content in popular fast-food items. Lesson: Order Up! Fast Food Frenzy Standards: • 6.NR.2.2 • 6.NR.2.3 • 6.NR.2.4 • 6.NR.2.5 • 6.NR.2.6 I Can Statements: • I can determine and choose the best measure of center and variation to describe data. • I can write a statistical question and gather data to answer that question. • I can create and compare boxplots. Student Reproducibles

2024-2025 Sixth Grade Mathematics YHALE SIXTH GRADE MATHEMATICS LESSON PLAN GUIDEBOOK | 2024-2025 Unit 1: Exploring Real-Life Phenomena through Statistics August 5th – August 30th – 4 weeks Grade 6 Comprehensive Grade Level Overview Guide Unit 1 Exploring Real-Life Phenomena through Statistics Guide Standards: 6.NR.2: Apply operations with whole numbers, fractions and decimals within relevant applications. • 6.NR.2.1 Describe and interpret the center of the distribution by the equal share value (mean). • 6.NR.2.2 Summarize categorical and quantitative (numerical) data sets in relation to the context: display the distributions of quantitative (numerical) data in plots on a number line, including dot plots, histograms, and box plots and display the distribution of categorical data using bar graphs. • 6.NR.2.3 Interpret numerical data to answer a statistical investigative question created. Describe the distribution of a quantitative (numerical) variable collected, including its center, variability, and overall shape. • 6.NR.2.4 Design simple experiments and collect data. Use data gathered from realistic scenarios and simulations to determine quantitative measures of center (median and/or mean) and variability (interquartile range and range). Use these quantities to draw conclusions about the data, compare different numerical data sets, and make predictions. • 6.NR.2.5 Relate the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. • 6.NR.2.6 Describe the impact that inserting or deleting a data point has on the mean and the median of a data set. Create data displays using a dot plot or box plot to examine this impact. Unit 1 Vocabulary K-12 Math Glossary Additional lessons and resources for this unit Review Day Assessment Day Box Plot Categorical Data Distribution Dot Plot Frequency Histogram Interquartile Range Maximum Value Mean Measures of Center Measures of Spread Media Minimum Value Mode Numerical Data Outlier Range Statistical question Statistics Symmetrical or Nonsymmetrical Variability Unit 1 Standards List Exploring Real-life Phenomena through Statistics Note Taking Guide Lesson 1 Overview Lesson 2 Measures of Center Lesson 2 Measures of Variability Lesson 3 Graphics Representations of Data Lesson 4 Analyzing Graphs Lesson 5 Exploring Real-life Phenomena through Statistics Review Interdisciplinary Connections Review Unit 1 concepts & skills Unit 1 Assessment- August 29th

2024-2025 Sixth Grade Mathematics YHALE SIXTH GRADE MATHEMATICS LESSON PLAN GUIDEBOOK | 2024-2025 Unit 2: Making Relevant Connections through Number System Fluency September 3rd - October 1st – 6 weeks Grade 6 Comprehensive Grade Level Overview Guide Unit 2 Making Relevant Connections through Number System Fluency Guide Standards: 6.NR.1: Solve real-life, mathematical problems involving operations with whole numbers, fractions, and decimal numbers. • 6.NR.1.1 Fluently add and subtract any combination of fractions to solve problems. • 6.NR.1.2 Multiply and divide any combination of whole numbers, fractions, and mixed numbers using a student-selected strategy. Interpret products and quotients of fractions and solve word problems. • 6.NR.1.3 Perform operations with multi-digit decimal numbers fluently using models and student selected strategies. 6.NR.2: Apply operations with whole numbers, fractions and decimals within relevant applications. • 6.NR.2.1 Describe and interpret the center of the distribution by the equal share value (mean). • 6.NR.2.3 Interpret numerical data to answer a statistical investigative question created. Describe the distribution of a quantitative (numerical) variable collected, including its center, variability, and overall shape. • 6.NR.2.4 Design simple experiments and collect data. Use data gathered from realistic scenarios and simulations to determine quantitative measures of center (median and/or mean) and variability (interquartile range and range). Use these quantities to draw conclusions about the data, compare different numerical data sets, and make predictions. Unit 2 Vocabulary K-12 Math Glossary Lesson 1 (1-2 days) Lesson 2 (1-2 days) Lesson 3 (2-3 days) Lesson 4 (1-2 days) Difference Dividend Divisor Factor Mean Measurement Model of Division Median Multiple Partitive Model of Divisions Product Quotient Reciprocal Skewed data Subtrahend Sum Objective: TLW solve problems that involve adding and subtracting any combination of fractions and unlike denominators. Lesson: Estimation Fractions Standards: • 6.NR.1.1 I Can Statements: • I can solve problems by adding and subtracting any combination of fractions with unlike denominators. Student Reproducibles Objective: TLW build upon their understanding of multiplying a fraction a whole number to multiplying any combination of whole numbers, fractions, and mixed numbers. Lesson: Multiplying Fractions Standards: • 6.NR.1.2 I Can Statements: • I can use diagrams to represent the multiplication of fractions. • I can determine a fractional amount of whole numbers, fractions, and mixed numbers. Student Reproducibles Grid Squares Objective: TLW explore dividing fractions by representing various expressions and looking for patterns in repeated reasoning. Lesson: Exploring the Division of Fractions Standards: • 6.NR.1.2 I Can Statements: • I can apply what I know about division of whole numbers to divide fractions by fractions. • I can use various strategies to divide fractions. Student Reproducibles Objective: TLW represent and solve fraction division tasks in problem-based contexts. Lesson: Modeling with Fraction Division Standards: • 6.NR.1.2 I Can Statements: • I can represent fraction division using manipulatives and drawings. • I can explain the meaning of problems involving division of fractions. Student Reproducibles

2024-2025 Sixth Grade Mathematics YHALE SIXTH GRADE MATHEMATICS LESSON PLAN GUIDEBOOK | 2024-2025 Unit 2: Making Relevant Connections through Number System Fluency September 3rd - October 1st – 6 weeks Grade 6 Comprehensive Grade Level Overview Guide Unit 2 Making Relevant Connections through Number System Fluency Guide Standards: 6.NR.1: Solve real-life, mathematical problems involving operations with whole numbers, fractions, and decimal numbers. • 6.NR.1.1 Fluently add and subtract any combination of fractions to solve problems. • 6.NR.1.2 Multiply and divide any combination of whole numbers, fractions, and mixed numbers using a student-selected strategy. Interpret products and quotients of fractions and solve word problems. • 6.NR.1.3 Perform operations with multi-digit decimal numbers fluently using models and student selected strategies. 6.NR.2: Apply operations with whole numbers, fractions and decimals within relevant applications. • 6.NR.2.1 Describe and interpret the center of the distribution by the equal share value (mean). • 6.NR.2.3 Interpret numerical data to answer a statistical investigative question created. Describe the distribution of a quantitative (numerical) variable collected, including its center, variability, and overall shape. • 6.NR.2.4 Design simple experiments and collect data. Use data gathered from realistic scenarios and simulations to determine quantitative measures of center (median and/or mean) and variability (interquartile range and range). Use these quantities to draw conclusions about the data, compare different numerical data sets, and make predictions. Unit 2 Vocabulary K-12 Math Glossary Lesson 5 (1-2 days) Lesson 6 (1-2 days) Lesson 7 (1-2 days) Lesson 8 (1-2 days) Difference Dividend Divisor Factor Mean Measurement Model of Division Median Multiple Partitive Model of Divisions Product Quotient Reciprocal Skewed data Subtrahend Sum Objective: TLW use real-world situations to represent the meaning of fraction division Lesson: No Matter How You Slice It! Standards: • 6.NR.1.2 I Can Statements: • I can interpret and compute quotients of fractions. • I can utilize real-world situations to show the meaning of fraction division. Student Reproducibles Introduction Video Objective: TLW use number sense to reason about adding and subtracting decimals. Lesson: Estimating is the Root of FluencyAddition & Subtraction Standards: • 6.NR.1.3 I Can Statements: • I can use diagrams to represent the multiplication of fractions. • I can determine a fractional amount of whole numbers, fractions, and mixed numbers. Student Reproducibles Objective: TLW use number sense to reason about multiplying decimals. Lesson: Estimating is the Root of FluencyMultiplication Standards: • 6.NR.1.3 I Can Statements: • I can apply what I know about division of whole numbers to divide fractions by fractions. • I can use various strategies to divide fractions. Student Reproducibles Objective: TLW use number sense to reason about dividing decimals. Lesson: Estimating is the Root of FluencyDivision Standards: • 6.NR.1.3 • 6.NR.2.3 I Can Statements: • I can represent fraction division using manipulatives and drawings. • I can explain the meaning of problems involving division of fractions. Student Reproducibles

2024-2025 Sixth Grade Mathematics YHALE SIXTH GRADE MATHEMATICS LESSON PLAN GUIDEBOOK | 2024-2025 Unit 2: Making Relevant Connections through Number System Fluency September 3rd - October 1st – 6 weeks Grade 6 Comprehensive Grade Level Overview Guide Unit 2 Making Relevant Connections through Number System Fluency Guide Standards: 6.NR.1: Solve real-life, mathematical problems involving operations with whole numbers, fractions, and decimal numbers. • 6.NR.1.1 Fluently add and subtract any combination of fractions to solve problems. • 6.NR.1.2 Multiply and divide any combination of whole numbers, fractions, and mixed numbers using a student-selected strategy. Interpret products and quotients of fractions and solve word problems. • 6.NR.1.3 Perform operations with multi-digit decimal numbers fluently using models and student selected strategies. 6.NR.2: Apply operations with whole numbers, fractions and decimals within relevant applications. • 6.NR.2.1 Describe and interpret the center of the distribution by the equal share value (mean). • 6.NR.2.3 Interpret numerical data to answer a statistical investigative question created. Describe the distribution of a quantitative (numerical) variable collected, including its center, variability, and overall shape. • 6.NR.2.4 Design simple experiments and collect data. Use data gathered from realistic scenarios and simulations to determine quantitative measures of center (median and/or mean) and variability (interquartile range and range). Use these quantities to draw conclusions about the data, compare different numerical data sets, and make predictions. Unit 2 Vocabulary K-12 Math Glossary Lesson 9 (1-2 days) Review & Assessment Quarterly Assessment Additional Resources for this Unit Difference Dividend Divisor Factor Mean Measurement Model of Division Median Multiple Partitive Model of Divisions Product Quotient Reciprocal Skewed data Subtrahend Sum Objective: TLW complete tasks to build fluency with the addition of fractions while finding mean and median. Lesson: What is the Average? Standards: • 6.NR.1.3 • 6.NR.2.1 • 6.NR.2.3 • 6.NR.2.4 I Can Statements: • I can apply my fractional understanding in statistical situations. • I can interpret data to answer a statistical question. • I can find the mean and median of a set of fractional data. • I can describe the distribution of a set of fractional data. Student Reproducibles Review Day- TBA Optional Assessment Day • Unit 2 Assessment • Performance Task Review- October 2nd - 7 th First Quarter Assessment- October 8th • Unit 1 • Unit 2 Review Results- October 9th Interdisciplinary Connections Unit 2 Standards List Making Relevant Connections through Number System Fluency Note Taking Guide Lesson 1 Overview Lesson 2 GCF & LCM Lesson 3 Distributive Property Lesson 4 Operations with Fractions Lesson 5 Decimal Fluency Unit Review

2024-2025 Sixth Grade Mathematics YHALE SIXTH GRADE MATHEMATICS LESSON PLAN GUIDEBOOK | 2024-2025 Unit 3: Investigating Rate, Ratio, and Proportional Reasoning October 15th – November 15th – 5 weeks Grade 6 Comprehensive Grade Level Overview Guide Unit 3 Investigating Rate, Ratio, & Proportional Reasoning Guide Standards: 6.NR.4: Solve a variety of contextual problems involving ratios, unit rate, equivalent ratios, percentages, and conversions within measurement systems using proportional reasoning. • 6.NR.4.1 Explain the concept of a ratio, represent ratios, and use ratio language to describe a relationship between two quantities. • 6.NR.4.2 Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. • 6.NR.4.3 Solve problems involving proportions using a variety of student selected strategies. • 6.NR.4.4 Describe the concept of rates and unit rate in the context of a ratio relationship. • 6.NR.4.5 Solve unit rate problems including those involving unit pricing and constant speed. • 6.NR.4.6 Calculate a percent of a quantity as a rate per 100 and solve real-life problems given a percent. • 6.NR.4.7 Use ratios to convert within measurement systems (customary and metric) to solve real-life problems. Unit 3 Vocabulary K-12 Math Glossary Lesson 1 (1-2 days) Lesson 2 (1-2 days) Lesson 3 (1-2 days) Lesson 4 (1-2 days) Percent Ration Proportion Rational number Quantity Rate Tape diagram Unit rate Objective: TLW explore the concept of a ratio and how to use them in real-world scenarios. Lesson: Recipe for Ratios Standards: • 6.NR.4.1 • 6.NR.4.2 • 6.NR.4.3 I Can Statements: • I can explain the concept of a ration, represent ratios, and use ratio language to describe a relationship between two quantities. • I can make tables of equivalent ratio relating to quantities with whole-number measurements, find missing values in the tables, plot the pairs of values on the coordinate plane, and use tables to compare ratios. • I can solve problems involving proportions using a variety of student-selected strategies. Student Reproducibles Objective: TLW reason about special ratios called rates and use unit rates to solve rate problems within real-world scenarios. Lesson: Talking Rates Standards: • 6.NR.4.4 • 6.NR.4.5 • 6.NR.4.7 I Can Statements: • I can describe rates and unit rates in terms of the context. • I can solve problems involving rates and unit rates. • I can make generalizations about changes in rates (e.g., what changes always result in a rate decrease?). Student Reproducibles Objective: TLW discover a proportional relationship between the length and width of a rectangle and extrapolate that relationship to other units of measure. Lesson: Constant Dimensions Standards: • 6.NR.4.1 • 6.NR.4.2 I Can Statements: • I can use equivalent ratios to determine unknown dimensions. • I can draw conclusions about the relationship of two dimensions based on collected data. • I can plot pairs of values on the coordinate plane. Student Reproducibles Objective: TLW apply the concept of ratio and proportion to determine the length of the Statue of Liberty’s torch-bearing arm. Lesson: How Many Noses are in Your Arm? Standards: • 6.NR.4.1 • 6.NR.4.3 • 6.NR.4.7 I Can Statements: • I can use proportional reasoning to find the missing value of equivalent measurements. • I can determine the multiplicative relationship between ratios. • I can convert measurement units using proportional reasoning. Student Reproducibles

2024-2025 Sixth Grade Mathematics YHALE SIXTH GRADE MATHEMATICS LESSON PLAN GUIDEBOOK | 2024-2025 Unit 3: Investigating Rate, Ratio, and Proportional Reasoning October 15th – November 15th – 5 weeks Grade 6 Comprehensive Grade Level Overview Guide Unit 3 Investigating Rate, Ratio, & Proportional Reasoning Guide Standards: 6.NR.4: Solve a variety of contextual problems involving ratios, unit rate, equivalent ratios, percentages, and conversions within measurement systems using proportional reasoning. • 6.NR.4.1 Explain the concept of a ratio, represent ratios, and use ratio language to describe a relationship between two quantities. • 6.NR.4.2 Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. • 6.NR.4.3 Solve problems involving proportions using a variety of student selected strategies. • 6.NR.4.4 Describe the concept of rates and unit rate in the context of a ratio relationship. • 6.NR.4.5 Solve unit rate problems including those involving unit pricing and constant speed. • 6.NR.4.6 Calculate a percent of a quantity as a rate per 100 and solve real-life problems given a percent. • 6.NR.4.7 Use ratios to convert within measurement systems (customary and metric) to solve real-life problems. Unit 3 Vocabulary K-12 Math Glossary Lesson 5 (1-2 days) Lesson 6 (1-2 days) Lesson 7 (1-2 days) Lesson 8 (2-3 days) Percent Ration Proportion Rational number Quantity Rate Tape diagram Unit rate Objective: TLW use proportional reasoning to determine the amount of specific ingredients used in a snack recipe. Lesson: Snack Mix Standards: • 6.NR.4.1 • 6.NR.4.3 • 6.NR.4.4 • 6.NR.4.5 I Can Statements: • I can solve a proportion for a missing value. • I can determine what missing information I need in order to answer a mathematical question. • I can use proportional reasoning to solve rate problems. Student Reproducibles Snack Mix 3 Act Task Objective: TLW shoot “free throws” while analyzing and making conjectures about rate increase and decreases and write percents as rates out of 100. Lesson: Percentage Shots Standards: • 6.NR.4.2 • 6.NR.4.3 • 6.NR.4.5 • 6.NR.4.6 I Can Statements: • I can use ratio and rate reasoning to solve real-world and mathematical problems. • I can find a percent of a quantity as a rate per 100. • Given a percent, I can solve problems involving finding the whole given a part and the part given the whole. Student Reproducibles Objective: TLW use proportional reasoning to predict the number of basketball shots that will be made in a given amount of time. Lesson: Arcade Basketball Insanity Standards: • 6.NR.4.1 • 6.NR.4.3 • 6.NR.4.4 • 6.NR.4.5 I Can Statements: • I can use proportional reasoning to solve problems. • I can determine the missing values within a proportion. Student Reproducibles Objective: TLW apply concepts of decimals, percentages, and moon phases to develop mathematical spreadsheet models that will allow them to predict the moon phase on future dates. Lesson: In a Phase Standards: • 6.NR.1.2 • 6.NR.4.6 I Can Statements: • I can represent fraction division using manipulatives and drawings. • I can explain the meaning of problems involving division of fractions. (No Student Reproducibles)

2024-2025 Sixth Grade Mathematics YHALE SIXTH GRADE MATHEMATICS LESSON PLAN GUIDEBOOK | 2024-2025 Unit 3: Investigating Rate, Ratio, and Proportional Reasoning October 15th – November 15th – 5 weeks Grade 6 Comprehensive Grade Level Overview Guide Unit 3 Investigating Rate, Ratio, & Proportional Reasoning Guide Standards: 6.NR.4: Solve a variety of contextual problems involving ratios, unit rate, equivalent ratios, percentages, and conversions within measurement systems using proportional reasoning. • 6.NR.4.1 Explain the concept of a ratio, represent ratios, and use ratio language to describe a relationship between two quantities. • 6.NR.4.2 Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. • 6.NR.4.3 Solve problems involving proportions using a variety of student selected strategies. • 6.NR.4.4 Describe the concept of rates and unit rate in the context of a ratio relationship. • 6.NR.4.5 Solve unit rate problems including those involving unit pricing and constant speed. • 6.NR.4.6 Calculate a percent of a quantity as a rate per 100 and solve real-life problems given a percent. • 6.NR.4.7 Use ratios to convert within measurement systems (customary and metric) to solve real-life problems. Unit 3 Vocabulary K-12 Math Glossary Lesson 9 (1-2 days) Lesson 10 (1-2 days) Review & Assessment Additional Resources for this Unit Percent Ration Proportion Rational number Quantity Rate Tape diagram Unit rate Objective: TLW reason about rates and ratios to determine and justify a solution to an open-ended problem. Lesson: Traveling to School Standards: • 6.NR.4.1 • 6.NR.4.2 • 6.NR.4.3 • 6.NR.4.4 • 6.NR.4.5 I Can Statements: • I can reason about rates and ratios to determine and justify a solution to an open-ended problem. • I can solve a real-world modeling problem. Student Reproducibles Sharing Costs Equitably: Traveling to School Objective: TLW demonstrate their understanding of rate, ratio, and proportional reasoning, and apply various strategies to solve real-life problems. Lesson: The Rocky Mountain Vacation Trip Problem Standards: • 6.NR.4.1 • 6.NR.4.2 • 6.NR.4.4 • 6.NR.4.5 I Can Statements: • I can make tables of equivalent ratios relating quantities with wholenumber measurements, find missing values in the tables, plot the pairs of values on the coordinate plane, and use tables to compare ratios. • I can solve problems involving proportions using a variety of student-selected strategies. • I can describe the concept of rates and unit rate in the context of a ratio relationship. • I can solve unit rate problems including those involving unit pricing and constant speed. Student Reproducibles Review- November 12th – 13th Assessment Day- November 14th Review Results- November 15th Interdisciplinary Resources Unit 3 Standards List Investigating Rate, Ratio, and Proportional Reasoning Note Taking Guide Lesson 1 Overview Lesson 2 Ratios, Rates, and Unit Rates Lesson 3 Proportional Reasoning using Equivalent Fractions Lesson 4 Percent Word Problems Lesson 5 Fractions, Decimals, and Percents Lesson 6 Using Ratios to Convert Within Measurement Systems Lesson Lesson 7 Investigating Rate, Ratio, and Proportional Reasoning Review

2024-2025 Sixth Grade Mathematics YHALE SIXTH GRADE MATHEMATICS LESSON PLAN GUIDEBOOK | 2024-2025 Unit 4: Building a Conceptual Understanding of Expressions November 18th – December 20th – 4 weeks Grade 6 Comprehensive Grade Level Overview Guide Unit4 Building a Conceptual Understanding of Expressions Standards: 6.PAR.6: Identify, write, evaluate, and interpret numerical and algebraic expressions as mathematical models to explain authentic situations. • 6.PAR.6.1 Write and evaluate numerical expressions involving rational bases and whole-number exponents. • 6.PAR.6.2 Determine the greatest common factors and least common multiples using a variety of strategies to make sense of applicable problems. • 6.PAR.6.3 Write and read expressions that represent operations with numbers and variables in realistic situations. • 6.PAR.6.4 Evaluate expressions when given values for the variables, including expressions that arise in everyday situations. • 6.PAR.6.5 Apply the properties of operations to identify and generate equivalent expressions. Unit 4 Vocabulary K-12 Math Glossary Lesson 1 (1-2 days) Lesson 2 (1-2 days) Lesson 3 (1-2 days) Lesson 4 (1-2 days) Algebraic Expressions Associative Property of Addition Associative Property of Multiplication Coefficient Commutative Property of Addition Commutative Property of Multiplication Constant Distributive Property Exponent Expression Like Terms Order of Operations Term Variable Objective: TLW explore exponent notation as a shorthand recording of repeated multiplication of a number times itself. Lesson: Exponent Notation Standards: • 6.PAR.6.1 I Can Statements: • I can write numerical expressions in expanded notation and exponent notation. • I can evaluate expressions involving whole-number exponents. Student Reproducibles Objective: TLW use the order of operations to evaluate exponential expressions for equivalence. Students will also discover the necessity of following the order of operations. Lesson: Does Order Matter? Standards: • 6.PAR.6.1 • 6.PAR.6.5 I Can Statements: • I can generate equivalent numerical expressions. • I can use the order of operations to evaluate expressions involving whole-number exponents. Student Reproducibles • Basic (four-function) calculators • Scientific calculators Objective: TLW demonstrate an understanding of multiples and least common multiples. Lesson: Hourglass Mathematics Standards: • 6.PAR.6.1 • 6.PAR.6.2 I Can Statements: • I can solve problems using common multiples. • I can solve problems using common factors and multiples Student Reproducibles Objective: TLW engage in purposeful practice of greatest common factors and least common multiples. Lesson: Gearing Up for Practice Standards: • 6.PAR.6.2 I Can Statements: • I can solve problems using common factors and multiples. • I can demonstrate reasoning when I apply given clues to find a number and create rules for their number. Student Reproducibles

2024-2025 Sixth Grade Mathematics YHALE SIXTH GRADE MATHEMATICS LESSON PLAN GUIDEBOOK | 2024-2025 Unit 4: Building a Conceptual Understanding of Expressions November 18th – December 20th – 4 weeks Grade 6 Comprehensive Grade Level Overview Guide Unit4 Building a Conceptual Understanding of Expressions Standards: 6.PAR.6: Identify, write, evaluate, and interpret numerical and algebraic expressions as mathematical models to explain authentic situations. • 6.PAR.6.1 Write and evaluate numerical expressions involving rational bases and whole-number exponents. • 6.PAR.6.2 Determine the greatest common factors and least common multiples using a variety of strategies to make sense of applicable problems. • 6.PAR.6.3 Write and read expressions that represent operations with numbers and variables in realistic situations. • 6.PAR.6.4 Evaluate expressions when given values for the variables, including expressions that arise in everyday situations. • 6.PAR.6.5 Apply the properties of operations to identify and generate equivalent expressions. Unit 3 Vocabulary K-12 Math Glossary Lesson 5 (1-2 days) Lesson 6 (1-2 days) Lesson 7 (1-2 days) Lesson 8 (1-2 days) Algebraic Expressions Associative Property of Addition Associative Property of Multiplication Coefficient Commutative Property of Addition Commutative Property of Multiplication Constant Distributive Property Exponent Expression Like Terms Order of Operations Term Variable Objective: TLW generalize about sets of equations based on properties of operations. Lesson: Properties and Order of Operations Standards: • 6.PAR.6.2 • 6.PAR.6.5 I Can Statements: • I can evaluate numerical expressions using properties of operations. • I can generate equivalent expressions. Student Reproducibles Objective: TLW first construct expressions with numbers to determine the number of tiles that border a pool. They will use those numerical expressions to help them write an expression with variables. Lesson: Pool Border Problem Standards: • 6.PAR.6.1 • 6.PAR.6.3 • 6.PAR.6.4 • 6.PAR.6.5 I Can Statements: • I can write and evaluate numerical expressions involving rational bases and whole-number exponents. • I can identify and generate equivalent expressions using the Distributive Property. Student Reproducibles Objective: TLW decode the algebra of “magic” using algebraic reasoning to break down the steps of the “tricks”. Lesson: The Algebra of Magic Standards: • 6.PAR.6.3 • 6.PAR.6.4 • 6.PAR.6.5 I Can Statements: • I can write algebraic expressions to explain a contextual situation. • I can make simple conjectures and generalizations. • I can use properties of operations to determine whether algebraic expressions are equivalent. • I can use algebra to make sense of contexts. Student Reproducibles Objective: TLW translate between verbal and symbolic algebraic expressions and equations. Lesson: Writing Expressions Standards: • 6.PAR.6.3 • 6.PAR.6.4 I Can Statements: • I can use tools to represent algebraic expressions in context. • I can write algebraic expressions using verbal description. • I can evaluate algebraic expressions. Student Reproducibles

2024-2025 Sixth Grade Mathematics YHALE SIXTH GRADE MATHEMATICS LESSON PLAN GUIDEBOOK | 2024-2025 Unit 4: Building a Conceptual Understanding of Expressions November 18th – December 20th – 4 weeks Grade 6 Comprehensive Grade Level Overview Guide Unit4 Building a Conceptual Understanding of Expressions Standards: 6.PAR.6: Identify, write, evaluate, and interpret numerical and algebraic expressions as mathematical models to explain authentic situations. • 6.PAR.6.1 Write and evaluate numerical expressions involving rational bases and whole-number exponents. • 6.PAR.6.2 Determine the greatest common factors and least common multiples using a variety of strategies to make sense of applicable problems. • 6.PAR.6.3 Write and read expressions that represent operations with numbers and variables in realistic situations. • 6.PAR.6.4 Evaluate expressions when given values for the variables, including expressions that arise in everyday situations. • 6.PAR.6.5 Apply the properties of operations to identify and generate equivalent expressions. Unit 3 Vocabulary K-12 Math Glossary Lesson 9 (1-2 days) Review Assessment Additional Resources Algebraic Expressions Associative Property of Addition Associative Property of Multiplication Coefficient Commutative Property of Addition Commutative Property of Multiplication Constant Distributive Property Exponent Expression Like Terms Order of Operations Term Variable Objective: TLW represent algebraic expressions to explore the concepts of combining like terms and generating equivalent expressions. Lesson: What Makes Them Equivalent? Standards: • 6.PAR.6.1 • 6.PAR.6.2 • 6.PAR.6.3 • 6.PAR.6.4 • 6.PAR.6.5 I Can Statements: • I can identify and generate equivalent expressions by applying the properties of numbers. • I can demonstrate equivalent expressions using manipulatives, such as Algebra tiles. Student Reproducibles Review Unit 4 concepts & skills Unit 4 Assessment- TBA Quarterly Assessment-December- TBA Interdisciplinary Connections Unit 4 Standards List Building a Conceptual Understanding of Expressions Note Taking Guide Lesson 1 Overview Lesson 2 Exponents Lesson 3 Properties Lesson 4 Writing & Evaluating Expressions Lesson 5 Equivalent Expressions Lesson 6 Review

2024-2025 Sixth Grade Mathematics YHALE SIXTH GRADE MATHEMATICS LESSON PLAN GUIDEBOOK | 2024-2025 Unit 5: Exploring Real-life Phenomena through One-Step Equations & Inequalities January 7th – January 24th – 3 weeks Grade 6 Comprehensive Grade Level Overview Guide Unit 5 Exploring Real-life Phenomena through One-Step Equations & Inequalities Guide Standards: 6.PAR.7: Write and solve one-step equations and inequalities as mathematical models to explain authentic, realistic situations. • 6.PAR.7.1 Solve one-step equations and inequalities involving variables when values for the variables are given. Determine whether an equation and inequality involving a variable is true or false for a given value of the variable. • 6.PAR.7.2 Write one-step equations and inequalities to represent and solve problems; explain that a variable can represent an unknown number of any number in a specified set. • 6.PAR.7.3 Solve problems by writing and solving equations of the form x ± p = q, px = q and for cases in which p, q and x are all nonnegative rational numbers. • 6.PAR.7.4: Recognize and generate inequalities of the form x > c, x > c, x < c, or x < c to explain situations that have infinitely many solutions; represent solutions of such inequalities on a number line. Unit 5 Vocabulary K-12 Math Glossary Lesson 1 (1-2 days) Lesson 2 (1-2 days) Lesson 3 (1-2 days) Lesson 4 (1-2 days) Addition Property of Equality Constant of Proportionality Dependent Variable Direct Proportion (Direct Variation) Division Property of Equality Equation Independent Variable Inequality Inverse Operation Multiplication Property of Equality Proportion Solution Substitution Subtraction Property of Equality Term Variable Objective: TLW solve one-step equations involving variables when values for the variables are given and determine whether an equation involving a variable is true or false for a given value of the variable. Lesson: Two Truths and a Lie Standards: • 6.PAR.7.1 • 6.PAR.7.2 I Can Statements: • I can use solve equations using a value given for the variable. • I can determine when an equation is true or false. Student Reproducibles Objective: TLW solve one-step equations involving whole numbers and rational numbers using mobiles. Lesson: Solve me Mobiles Standards: • 6.PAR.7.2 • 6.PAR.7.3 I Can Statements: • I can use equality to solve for an unknown quantity. • I can solve equations involving whole numbers and rational numbers. Student Reproducibles Objective: TLW use the balance method to write and solve one-step equations. It is designed as a learning task. Students will also learn why conventions are an integral part of mathematics. Lesson: Set It Up Standards: • 6.PAR.7.2 • 6.PAR.7.3 I Can Statements: • I can use a visual model, such as a balance or tape diagram to represent solving an equation. • I can explain and apply the addition and subtraction properties of equality. Student Reproducibles Blackline Masters Objective: TLW generalize a formula, based on identifying a pattern, for expressing the perimeter of a figure built with toothpicks. Lesson: Building with Toothpicks Standards: • 6.PAR.7.2 • 6.PAR.7.3 I Can Statements: • I can explain how variables can be used to describe patterns. • I can write and solve a one-step equation based on a context. Student Reproducibles

2024-2025 Sixth Grade Mathematics YHALE SIXTH GRADE MATHEMATICS LESSON PLAN GUIDEBOOK | 2024-2025 Unit 5: Exploring Real-life Phenomena through One-Step Equations & Inequalities January 7th – January 24th – 3 weeks Grade 6 Comprehensive Grade Level Overview Guide Unit 5 Exploring Real-life Phenomena through One-Step Equations & Inequalities Guide Standards: 6.PAR.7: Write and solve one-step equations and inequalities as mathematical models to explain authentic, realistic situations. • 6.PAR.7.1 Solve one-step equations and inequalities involving variables when values for the variables are given. Determine whether an equation and inequality involving a variable is true or false for a given value of the variable. • 6.PAR.7.2 Write one-step equations and inequalities to represent and solve problems; explain that a variable can represent an unknown number of any number in a specified set. • 6.PAR.7.3 Solve problems by writing and solving equations of the form x ± p = q, px = q and for cases in which p, q and x are all nonnegative rational numbers. • 6.PAR.7.4: Recognize and generate inequalities of the form x > c, x > c, x < c, or x < c to explain situations that have infinitely many solutions; represent solutions of such inequalities on a number line. Unit 5 Vocabulary K-12 Math Glossary Lesson 5 (1-2 days) Lesson 6 (1-2 days) Lesson 7 (1-2 days) Lesson 8 (1-2 days) Addition Property of Equality Constant of Proportionality Dependent Variable Direct Proportion (Direct Variation) Division Property of Equality Equation Independent Variable Inequality Inverse Operation Multiplication Property of Equality Proportion Solution Substitution Subtraction Property of Equality Term Variable Objective: TLW use different representations to analyze the relationship between two quantities and to solve realworld problems. Lesson: Writing Equations Standards: • 6.PAR.7.2 • 6.PAR.7.3 I Can Statements: • I can explain how variables can be used to describe patterns. • I can write and solve a one-step equation based on a context. Student Reproducibles Objective: TLW make sense of equations that express the relationship between two real-world variables, as well as explore the meaning of variables in contextualized equations. Lesson: Interpreting Equations Standards: • 6.PAR.7.2 • 6.PAR.7.3 I Can Statements: • I can connect algebraic equations to real-life situations. Student Reproducibles Lesson Guide Objective: TLW write and solve one-step inequalities and graph them on the number line. Lesson: Representations of Inequalities Standards: • 6.PAR.7.1 • 6.PAR.7.2 • 6.PAR.7.4 I Can Statements: • I can use my prior knowledge of equations to check to see if a value is a solution for inequality. • I can verify that if a given value makes an inequality true, it is a solution. Student Reproducibles Objective: TLW write and solve one-step inequalities and graph them on the number line. Lesson: Inequalities Problems Standards: • 6.PAR.7.1 • 6.PAR.7.2 • 6.PAR.7.4 I Can Statements: • I can write and solve inequalities. • I can create representations of inequalities. • I can graph inequalities on number lines. Student Reproducibles

2024-2025 Sixth Grade Mathematics YHALE SIXTH GRADE MATHEMATICS LESSON PLAN GUIDEBOOK | 2024-2025 Unit 5: Exploring Real-life Phenomena through One-Step Equations & Inequalities January 7th – January 24th – 3 weeks Grade 6 Comprehensive Grade Level Overview Guide Unit 5 Exploring Real-life Phenomena through One-Step Equations & Inequalities Guide Standards: 6.PAR.7: Write and solve one-step equations and inequalities as mathematical models to explain authentic, realistic situations. • 6.PAR.7.1 Solve one-step equations and inequalities involving variables when values for the variables are given. Determine whether an equation and inequality involving a variable is true or false for a given value of the variable. • 6.PAR.7.2 Write one-step equations and inequalities to represent and solve problems; explain that a variable can represent an unknown number of any number in a specified set. • 6.PAR.7.3 Solve problems by writing and solving equations of the form x ± p = q, px = q and for cases in which p, q and x are all nonnegative rational numbers. • 6.PAR.7.4: Recognize and generate inequalities of the form x > c, x > c, x < c, or x < c to explain situations that have infinitely many solutions; represent solutions of such inequalities on a number line. Unit 5 Vocabulary K-12 Math Glossary Lesson 9 (1-2 days) Lesson 10 (1-2 days) Review-Assess-Review Additional Resources for this Unit Addition Property of Equality Constant of Proportionality Dependent Variable Direct Proportion (Direct Variation) Division Property of Equality Equation Independent Variable Inequality Inverse Operation Multiplication Property of Equality Proportion Solution Substitution Subtraction Property of Equality Term Variable Objective: TLW represent inequalities algebraically and in words, while substituting values into inequality statements in order to test their validity. Lesson: Evaluating Statements About Number Operations Standards: • 6.PAR.7.1 • 6.PAR.7.2 • 6.PAR.7.3 • 6.PAR.7.4 I Can Statements: • I can explain how the properties of number operations work. • I can substitute integers, fractions, decimals, and negative numbers into inequality statements in order to test their validity. • I can represent inequalities algebraically and in words. Student Reproducibles Lesson Guide Objective: TLW demonstrate their understanding of direct proportions as applied to the context of newspaper “want ads”. Students will demonstrate algebraic thinking using newspaper “Want Ads”. Lesson: Want Ads Standards: • 6.PAR.7.1 • 6.PAR.7.2 • 6.PAR.7.3 • 6.PAR.7.4 I Can Statements: • I can describe and define a direct proportion. • I can write an equation in the form of y=kx to represent a direct proportion. • I can graph a direct proportion. • I can solve equations and inequalities representing real-life situations for given values. Student Reproducibles Review Unit 5 concepts and skills Assessment Day- January 23rd Review assessment results- January 24th Interdisciplinary Connections Unit 5 Standards List Unit 5 Exploring Real-life Phenomena through One-Step Equations & Equalities Note Taking Guide Lesson 1 Overview Lesson 2 Equations and Their Solutions Lesson 3 Solving Equations by Adding or Subtracting Lesson 4 Solving Equations by Multiplying or Dividing Lesson 5 Inequalities Lesson 6 Direct Variation Lesson 7 Graphing with Variation Lesson 8 Review

2024-2025 Sixth Grade Mathematics YHALE SIXTH GRADE MATHEMATICS LESSON PLAN GUIDEBOOK | 2024-2025 Unit 6: Exploring Area & Volume January 27th - February 21st – 4 weeks Grade 6 Comprehensive Grade Level Overview Guide Unit 6 Exploring Area and Volume Guide Standards: 6.GSR.5: Solve relevant problems involving area, surface area, and volume • 6.GSR.5.1 Explore area as a measurable attribute of triangles, quadrilaterals, and other polygons conceptually by composing or decomposing into rectangles, triangles, and other shapes. Find the area of these geometric figures to solve problems. • 6.GSR.5.2 Given the net of three-dimensional figures with rectangular and triangular faces, determine the surface area of these figures. • 6.GSR.5.3 Calculate the volume of right rectangular prisms with fractional edge lengths by applying the formula, V = (area of base) x (height). Unit 6 Vocabulary K-12 Math Glossary Lesson 1 (1-2 days) Lesson 2 (2-3 days) Lesson 3 (2-3 days) Lesson 4 (1-2 days) 2-Dimensional Square Dimension Kite Lateral Faces Prism Rectangles Face Surface Area Volume 3-Dimensional Edge Net Rectangular Prism Trapezoid Area Equilateral Triangle Parallelogram Rhombus Triangles Bases of Prism Decomposing Polygon Right Triangle Triangular Prism Composing Fractional edge length Polyhedron Right rectangular prism Vertices Cubic Units Isosceles Triangle Quadrilaterals Scalene Triangle Volume of a Prism Objective: TLW first measure the area of polygons without using formulas and then make sense of the formulas by reasoning about the models. Lesson: Formulating Thoughts of Area Standards: • 6.GSR.5.1 I Can Statements: • I can describe how the areas of geometric figures are related to each other. • I can explain how I can figure the area of a shape without a formula for that shape. • I can relate the discovery of a shape’s area to the computation of the formula for that shape using the formula. Student Reproducibles Objective: TLW follow a path from concrete exploration to an abstract understanding of triangle area, surface area, and volume. Students will explore the areas of triangles and make connections to the surface area. Lesson: Building from Area to Surface Area Standards: • 6.GSR.5.1 • 6.GSR.5.2 I Can Statements: • I can use one figure to determine the area of another. • I can find the area of irregular shapes by decomposing them into rectangles, and triangles. Student Reproducibles Objective: TLW identify 2D nets and 3D figures and calculate surface area using nets and formulas. Lesson: Finding Surface Area Standards: • 6.GSR.5.2 I Can Statements: • I can use manipulatives and nets to compute the surface areas of rectangular and triangular prisms. Student Reproducibles Blackline Master Objective: TLW solve a multi-step problem involving a rectangular prism with noninteger edge lengths. Lesson: Banana Bread Standards: • 6.GSR.5.3 I Can Statements: • I can compare the volumes of two rectangular prisms. • I can estimate comparisons of volumes for prisms with fractional edge lengths. Student Reproducibles

2024-2025 Sixth Grade Mathematics YHALE SIXTH GRADE MATHEMATICS LESSON PLAN GUIDEBOOK | 2024-2025 Unit 6: Exploring Area & Volume January 27th - February 21st – 4 weeks Grade 6 Comprehensive Grade Level Overview Guide Unit 6 Exploring Area and Volume Guide Standards: 6.GSR.5: Solve relevant problems involving area, surface area, and volume • 6.GSR.5.1 Explore area as a measurable attribute of triangles, quadrilaterals, and other polygons conceptually by composing or decomposing into rectangles, triangles, and other shapes. Find the area of these geometric figures to solve problems. • 6.GSR.5.2 Given the net of three-dimensional figures with rectangular and triangular faces, determine the surface area of these figures. • 6.GSR.5.3 Calculate the volume of right rectangular prisms with fractional edge lengths by applying the formula, V = (area of base) x (height). Unit 6 Vocabulary K-12 Math Glossary Lesson 5 (1-2 days) Lesson 6 (2-3 days) Lesson 7 (2-3 days) Review-Assess-Review 2-Dimensional Square Dimension Kite Lateral Faces Prism Rectangles Face Surface Area Volume 3-Dimensional Edge Net Rectangular Prism Trapezoid Area Equilateral Triangle Parallelogram Rhombus Triangles Bases of Prism Decomposing Polygon Right Triangle Triangular Prism Composing Fractional edge length Polyhedron Right rectangular prism Vertices Cubic Units Isosceles Triangle Quadrilaterals Scalene Triangle Volume of a Prism Objective: TLW examine the mathematical relationship between the volume of a rectangular prism in cubic units and the number of unit cubes with fractional edge lengths (i.e., ½-inch) it takes to fill the prism. Lesson: Volume and Cubes Standards: • 6.GSR.5.3 I Can Statements: • I can use solve equations using a value given for the variable. • I can determine when an equation is true or false. Student Reproducibles Objective: TLW select appropriate mathematical methods to use for an unstructured problem and communicate their reasoning clearly. Lesson: Designing 3-D Products: Candy Cartons Standards: • 6.GSR.5.1 • 6.GSR.5.2 • 6.GSR.5.3 I Can Statements: • I can select appropriate mathematical methods to use for an unstructured problem. • I can interpret a problem situation, identifying constraints and variables and specifying assumptions. • I can work with 2- and 3- dimensional shapes to solve a problem involving capacity and surface area. • I can communicate their reasoning clearly. Student Reproducibles Lesson Guide Blackline Masters Objective: TLW design the foam packaging for Fish Tank Experts. The students will determine dimensions, describe the effects of the fractional edge lengths, and compute the minimum amount of space needed to package a 15- gallon tank. Lesson: Fist Tank Foam Packaging Design Standards: • 6.GSR.5.2 • 6.GSR.5.3 I Can Statements: • I can use manipulatives and nets to help compute the surface areas of rectangular and triangular prisms. • I can use formulas to compute the surface area of rectangular and triangular prisms. • I can use surface areas of rectangular and triangular prisms to solve problems. Student Reproducibles Review Unit 6 concepts and skills Assessment DayReview assessment results-

2024-2025 Sixth Grade Mathematics YHALE SIXTH GRADE MATHEMATICS LESSON PLAN GUIDEBOOK | 2024-2025 Unit 6: Exploring Area & Volume January 27th - February 21st – 4 weeks Grade 6 Comprehensive Grade Level Overview Guide Unit 6 Exploring Area and Volume Guide Standards: 6.GSR.5: Solve relevant problems involving area, surface area, and volume • 6.GSR.5.1 Explore area as a measurable attribute of triangles, quadrilaterals, and other polygons conceptually by composing or decomposing into rectangles, triangles, and other shapes. Find the area of these geometric figures to solve problems. • 6.GSR.5.2 Given the net of three-dimensional figures with rectangular and triangular faces, determine the surface area of these figures. • 6.GSR.5.3 Calculate the volume of right rectangular prisms with fractional edge lengths by applying the formula, V = (area of base) x (height). Unit 6 Vocabulary K-12 Math Glossary Additional Resources for this Unit 2-Dimensional Square Dimension Kite Lateral Faces Prism Rectangles Face Surface Area Volume 3-Dimensional Edge Net Rectangular Prism Trapezoid Area Equilateral Triangle Parallelogram Rhombus Triangles Bases of Prism Decomposing Polygon Right Triangle Triangular Prism Composing Fractional edge length Polyhedron Right rectangular prism Vertices Cubic Units Isosceles Triangle Quadrilaterals Scalene Triangle Volume of a Prism Interdisciplinary Connections Unit 6 Standards List Exploring Area & Volume Note Taking Guide Lesson 1 Overview Lesson 2 Areas of Rectangles and Parallelograms Lesson 3 Volume of Prisms Lesson 4 Surface Area Lesson 5 Review

2024-2025 Sixth Grade Mathematics YHALE SIXTH GRADE MATHEMATICS LESSON PLAN GUIDEBOOK | 2024-2025 Unit 7: Rational Exploration: Numbers and Their Opposites February 24th - March 7th – 2 weeks Grade 6 Comprehensive Grade Level Overview Guide Unit 7 Rational Exploration: Numbers and Their Opposites Guide Standards: 6.NR.2: Apply operations with whole numbers, fractions and decimals within relevant applications. • 6.NR.2.3 Interpret numerical data to answer a statistical investigative question created. Describe the distribution of a quantitative (numerical) variable collected, including its center, variability, and overall shape. • 6.NR.2.4 Design simple experiments and collect data. Use data gathered from realistic scenarios and simulations to determine quantitative measures of center (median and/or mean) and variability (interquartile range and range). Use these quantities to draw conclusions about the data, compare different numerical data sets, and make predictions. 6.NR.3: Solve a variety of problems involving whole numbers and their opposites; model rational numbers on a number line to describe problems presented in relevant, mathematical situations. • 6.NR.3.1 Identify and compare integers and explain the meaning of zero based on multiple authentic situations. • 6.NR.3.2 Order and plot integers on a number line and use distance from zero to discover the connection between integers and their opposites. • 6.NR.3.3 Recognize and explain that opposite signs of integers indicate locations on opposite sides of zero on the number line; recognize and explain that the opposite of the opposite of a number is the number itself. • 6.NR.3.4 Write, interpret, and explain statements of order for rational numbers in authentic, mathematical situations. Compare rational numbers, including integers, using equality and inequality symbols. • 6.NR.3.5 Explain the absolute value of a rational number as its distance from zero on the number line; interpret absolute value as distance for a positive or negative quantity in a relevant situation. • 6.NR.3.6 Distinguish comparisons of absolute value from statements about order Unit 7 Vocabulary K-12 Math Glossary Lesson 1 (2-3 days) Lesson 2 (1-2 days) Lesson 3 (1-2 days) Lesson 4 (2-3 days) Absolute Value Distance Inequality Integers Magnitude Negative Numbers Opposite Positive Numbers Rational Number Sign Objective: TLW plot and order integers and rational numbers on the number line, and work with opposites. Lesson: What’s Your Sign? Standards: • 6.NR.3.1 • 6.NR.3.2 • 6.NR.3.3 • 6.NR.3.4 • 6.NR.3.5 I Can Statements: • I can use positive and negative numbers to represent quantities in real-world contexts. • I can explain how opposites are shown on a number line. • I can use number lines to find the distances between points and compare/order rational numbers. Student Reproducibles Objective: TLW engage in an interactive Geogebra lesson plotting rational numbers. Lesson: Representing Rational Numbers on The Number Line Standards: • 6.NR.3.1 • 6.NR.3.2 • 6.NR.3.3 • 6.NR.3.5 I Can Statements: • I can explain why it is useful for me to know the absolute value of a number. • I can describe opposites and determine the characteristics they have on the number line. • I can compare and order rational numbers. Student Reproducibles Objective: TLW distinguish between absolute value and order. Lesson: Absolute Value and Ordering Standards: • 6.NR.3.1 • 6.NR.3.2 • 6.NR.3.3 • 6.NR.3.4 I Can Statements: • I can use a visual model, such as a balance or tape diagram to represent solving an equation. • I can explain and apply the addition and subtraction properties of equality. Student Reproducibles Objective: TLW plot points on number lines - vertical and horizontal - and will use absolute value to determine the distance between two points. Lesson: Symbols of Inequalities- Part 1 Standards: • 6.NR.3.4 6.NR.3.6 I Can Statements: • I can explain when negative numbers are used and why they are important. • I can explain what absolute value is, and why it is useful to know the absolute value of a number. • I can write inequalities using the > and < symbols. • I can use vertical and horizontal number lines to solve problems. • I can compare and order rational numbers. Student Reproducibles

2024-2025 Sixth Grade Mathematics YHALE SIXTH GRADE MATHEMATICS LESSON PLAN GUIDEBOOK | 2024-2025 Unit 7: Rational Exploration: Numbers and Their Opposites February 24th - March 7th – 2 weeks Grade 6 Comprehensive Grade Level Overview Guide Unit 7 Rational Exploration: Numbers and Their Opposites Guide Standards: 6.NR.2: Apply operations with whole numbers, fractions and decimals within relevant applications. • 6.NR.2.3 Interpret numerical data to answer a statistical investigative question created. Describe the distribution of a quantitative (numerical) variable collected, including its center, variability, and overall shape. • 6.NR.2.4 Design simple experiments and collect data. Use data gathered from realistic scenarios and simulations to determine quantitative measures of center (median and/or mean) and variability (interquartile range and range). Use these quantities to draw conclusions about the data, compare different numerical data sets, and make predictions. 6.NR.3: Solve a variety of problems involving whole numbers and their opposites; model rational numbers on a number line to describe problems presented in relevant, mathematical situations. • 6.NR.3.1 Identify and compare integers and explain the meaning of zero based on multiple authentic situations. • 6.NR.3.2 Order and plot integers on a number line and use distance from zero to discover the connection between integers and their opposites. • 6.NR.3.3 Recognize and explain that opposite signs of integers indicate locations on opposite sides of zero on the number line; recognize and explain that the opposite of the opposite of a number is the number itself. • 6.NR.3.4 Write, interpret, and explain statements of order for rational numbers in authentic, mathematical situations. Compare rational numbers, including integers, using equality and inequality symbols. • 6.NR.3.5 Explain the absolute value of a rational number as its distance from zero on the number line; interpret absolute value as distance for a positive or negative quantity in a relevant situation. • 6.NR.3.6 Distinguish comparisons of absolute value from statements about order Unit 7 Vocabulary K-12 Math Glossary Lesson 5 (1-2 days) Review-Assess-Review Additional Resources for this Unit Absolute Value Distance Inequality Integers Magnitude Negative Numbers Opposite Positive Numbers Rational Number Sign Objective: TLW extend the process of calculating MAD by considering absolute value in analyzing the data. Lesson: Modified Got MAD Skills Revisited Standards: • 6.NR.2.3 • 6.NR.2.4 • 6.NR.3.2 • 6.NR.3.5 I Can Statements: • I can use solve equations using a value given for the variable. • I can determine when an equation is true or false. Student Reproducibles Review Unit 7 concepts and skills Assessment DayReview assessment resultsInterdisciplinary Connections Unit 7 Standards List Rational Explorations: Numbers and their Opposites Note Taking Guide Lesson 1 Overview Lesson 2 Representing Numbers on a Number Line Lesson 3 Absolute Value Lesson 4 Opposites Lesson 5 Review

2024-2025 Sixth Grade Mathematics YHALE SIXTH GRADE MATHEMATICS LESSON PLAN GUIDEBOOK | 2024-2025 Unit 8: Graphing Rational Numbers March 10th -March 21st – 2 weeks Grade 6 Comprehensive Grade Level Overview Guide Unit 8 Graphing Rational Numbers Standards: 6.PAR.8: Graph rational numbers as points on the coordinate plane to represent and solve contextual, mathematical problems; draw polygons using the coordinates for their vertices and find the length of a side of a polygon. • 6.PAR.8.1 Locate and position rational numbers on a horizontal or vertical number line; find and position pairs of integers and other rational numbers on a coordinate plane. • 6.PAR.8.2 Show and explain that signs of numbers in ordered pairs indicate locations in quadrants of the coordinate plane and determine how two ordered pairs may differ based only on the signs. • 6.PAR.8.3 Solve problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same x-coordinate or the same ycoordinate. • 6.PAR.8.4 Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same x-coordinate or the same y-coordinate. Unit 8 Vocabulary K-12 Math Glossary Lesson 1 (2-3 days) Lesson 2 (1-2 days) Lesson 3 (1-2 days) Lesson 4 (1-2 days) Absolute value Magnitude Rational number Cartesian Coordinate Plane Ordered Pair x-axis Coordinates Origin x-coordinate distance polygon y-axis integers quadrant y-coordinate Objective: TLW solve real-world problems and plot points on the x-axis and y-axis. Lesson: Graphing on the Coordinate Plane Standards: • 6.PAR.8.1 • 6.PAR.8.2 • 6.PAR.8.3 • 6.PAR.8.4 I Can Statements: • I can use absolute value to help determine the distance between two points on a coordinate plane. • I can make generalizations about reflecting points across the x-axis or the y-axis. Student Reproducibles Objective: TLW plot points on coordinate grid. Lesson: Symbols of Inequalities and the Coordinate System Part 2 Standards: • 6.PAR.8.1 • 6.PAR.8.2 • 6.PAR.8.3 I Can Statements: • I can plot points on the coordinate plane in all 4-quadrants. • I can determine the distance between two-points on the coordinate plane. Student Reproducibles Objective: TLW plot points in the four quadrants of the coordinate plane and work with reflections in the coordinate plane. Lesson: Polygons on the Coordinate Plane Standards: • 6.PAR.8.1 • 6.PAR.8.2 • 6.PAR.8.3 • 6.PAR.8.4 I Can Statements: • I can use a visual model, such as a balance or tape diagram to represent solving an equation. • I can explain and apply the addition and subtraction properties of equality. Student Reproducibles Objective: TLW explore the meaning of absolute value in real-world context. Lesson: Planning a Field Trip Standards: • 6.PAR.8.1 • 6.PAR.8.2 • 6.PAR.8.3 I Can Statements: • I can use absolute value in realworld context. • I can understand why it is useful for me to know the absolute value of a number. Student Reproducibles

2024-2025 Sixth Grade Mathematics YHALE SIXTH GRADE MATHEMATICS LESSON PLAN GUIDEBOOK | 2024-2025 Unit 8: Graphing Rational Numbers March 10th -March 21st – 2 weeks Grade 6 Comprehensive Grade Level Overview Guide Unit 8 Graphing Rational Numbers Standards: 6.PAR.8: Graph rational numbers as points on the coordinate plane to represent and solve contextual, mathematical problems; draw polygons using the coordinates for their vertices and find the length of a side of a polygon. • 6.PAR.8.1 Locate and position rational numbers on a horizontal or vertical number line; find and position pairs of integers and other rational numbers on a coordinate plane. • 6.PAR.8.2 Show and explain that signs of numbers in ordered pairs indicate locations in quadrants of the coordinate plane and determine how two ordered pairs may differ based only on the signs. • 6.PAR.8.3 Solve problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same x-coordinate or the same ycoordinate. • 6.PAR.8.4 Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same x-coordinate or the same y-coordinate. Unit 8 Vocabulary K-12 Math Glossary Lesson 5 (2-3 days) Review-Assess-Review Additional Resources for this Unit Absolute value Magnitude Rational number Cartesian Coordinate Plane Ordered Pair x-axis Coordinates Origin x-coordinate distance polygon y-axis integers quadrant y-coordinate Objective: TLW plan the placement of the percussion of a marching band on a coordinate grid. Lesson: Sounds of the Band Standards: • 6.PAR.8.1 • 6.PAR.8.2 • 6.PAR.8.3 • 6.PAR.8.4 I Can Statements: • I can explain why it is useful for me to know the absolute value of a number. • I can explain why graphing on the coordinate plane is helpful. Student Reproducibles Review Unit 8 concepts and skills Assessment DayReview assessment resultsInterdisciplinary Connections Unit 8 Standards List Graphing Rational Numbers Note Taking Guide Lesson 1 Overview Lesson 2 Coordinate System Lesson 3 Practicing w/Coordinate System Lesson 4 Distances between Points Lesson 5 Polygons in the Coordinate Plane Lesson 6 Review

2024-2025 Sixth Grade Mathematics YHALE SIXTH GRADE MATHEMATICS LESSON PLAN GUIDEBOOK | 2024-2025 Math Milestones Review March 24th – April 23rd Final Exam Study Guides GMAS Math Test Dates • 6 th Grade Math End of the Student Guide • April 24th -25th

2024-2025 Sixth Grade Mathematics YHALE SIXTH GRADE MATHEMATICS LESSON PLAN GUIDEBOOK | 2024-2025 Capstone Project Information- April 28th - May 16th (Presentations May 19th – May 21st) Grade 6 Comprehensive Grade Level Overview Guide Capstone Project Information Guide All 6th Grade Math Standards Review the Capstone Project Information Guide for more details on presenting these capstone project options to students. Mathematics Game Design To demonstrate their understanding of the content taught in the grade level, students can create a mathematics game that uses the concepts and skills they have learned. Students should create game rules to accompany the game. Students should also prepare their game to share with students in a lower grade to provide them with a sneak peek about what they will be learning in the upcoming grade level. The game can be digital or a physical board game. Interdisciplinary Classroom Challenge Engage students in an Interdisciplinary Classroom challenge throughout the school year, semester, or quarter. During the final unit of study, students should create and share a presentation of the semester-long or quarter-long classroom challenge. Students should explain how the results of their challenge benefit the greater good of their school, community and/or society at-large There’s An App for That! Have students design an app that explains what they have learned over the course of the year. The students should utilize the app to explain to the upcoming class (or a younger grade level) what they will be expected to learn in that grade level. If possible, provide an opportunity for students to set up their display in the cafeteria to explain their app and have the students in younger grades come into the student-led exhibit to learn from the older students. Cereal Box Design To demonstrate their understanding of the content taught in the grade level, students can create a cereal box design that explains the concepts and skills they have learned. Students should create game rules to accompany the game. Students should also prepare their game to share with students in a lower grade. Infographic Design Challenge Have students create an infographic to explain all of the essential concepts in the grade level (at the standard level). Allow students to use maximum creativity to design their infographic. Tools such as Canva, PosterMyWall, Google Slides, and MS PowerPoint (among others) can be used to assist students with the development. Students should be encouraged to be as detailed as possible while also maintaining a high level of precision with their language and explanations. Mathematics Video Challenge Have students create an infomercial (or video) to explain all of the critical concepts in the grade level (at the standard level). Allow students to use maximum creativity to design their video or infomercial. Tools such as iMovie, Garage Band, and tablet recording (among others) can be used to assist students with the video development. Students should be encouraged to be as detailed as possible while also maintaining a high level of precision with their language and explanations. Creating a Code Challenge Students can use foundational coding knowledge to create a code to explain a specific topic from the course. To demonstrate their understanding of the content taught in the grade level, students can create a mathematics game that uses the concepts and skills they have learned. Students should create game rules to accompany the game. Students should also prepare their game to share with students in a lower grade. Engineering Design Challenge This project will require the student to construct a physical model in an effort to solve a real-life contextual problem aligned with the gradelevel standards. The physical model should be constructed using the Mathematical Modeling Framework and the Engineering Design Process. Students should be comfortable testing their model, making adjustments, and retesting their model until they get it ready for presentation. The final physical model should be presented to a larger audience where students explain the purpose, the design process, and the overall problem that the model will solve. Investigative Research An investigative research project could be assigned at some point during the school year and the student’s presentation of the research findings will serve as the culminating capstone project. Students should engage in developing a research question and creating, designing, and conducting an age-appropriate experiment to answer a statistical investigative question. Students should be expected to use their mathematical and statistical reasoning skills acquired over the year to present their research findings from the research project conducted over time by creating an organized presentation to share the results in front of a larger audience. Invention Students can engage in creating, designing, and presenting a model or invention related to a specific mathematical topic. This invention should assist the greater good of the community in some way. Students should be expected to use their mathematical reasoning skills acquired over the year. Students should present their invention or model to a wider audience during this culminating capstone experience.