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MADISON COUNTY PUBLIC SCHOOLS District Curriculum Map for Mathematics: Grade 6 Unit Description Unit: 7 Title: Statistics Suggested Length: 4 Weeks Big Idea(s) Enduring Understandings Develop an understanding of statistical thinking. What enduring understandings are essential for application to new situations within or beyond this content? Enduring Skills Rubric measures competency of the following skills: Relations & Functions Mathematical relationships can be represented and analyzed using words, tables, graphs, and equations. Data Collections An appropriately selected sample can be used to describe and make predictions about a population. The size of a sample determines how close data from the sample mirrors the population. Data Representation Each type of graph is most appropriate for certain types of data. Data Distribution The best descriptor of the center of a numerical data set (i.e., mean, median, mode) is determined by the nature of the data and the question to be answered. Outliers affect the mean, median, and mode in different ways. Data interpretation is enhanced by numerical measures telling how data are distributed. Essential Question(s) What questions will provoke and sustain student engagement while focusing learning? Curriculum and Instruction What is the best way to organize a set of data? What kinds of graphs will best represent a given set of data? How can I describe the center of a set of data? How can I describe the spread of a set of data? How can I use data to compare different groups? How do I choose and create appropriate graphs to represent data? What conclusions can be drawn from data? 2015-2016 Page 1 of 8 MADISON COUNTY PUBLIC SCHOOLS District Curriculum Map for Mathematics: Grade 6 Standards How can I recognize when a question is statistical and when it is not? What is the difference in a measure of center and a measure of variation? Standards for Mathematical Practice 1. Make sense of problems and persevere in solving them. Students will make sense of the data distributions by interpreting the measures of center and variability in the context of the situations they represent. 2. Reason abstractly and quantitatively. Students reason about the appropriate measures of center or variability to represent a data distribution. 3. Construct viable arguments and critique the reasoning of others. Students construct arguments regarding which measures of center or variability they would use to represent a particular data distribution. They may critique other students’ choices when considering how outliers are handled in each situation. 4. Model with mathematics. They use measures of center and variability and data displays (i.e. box plots and histograms) to draw inferences about and make comparisons between data sets. Students need many opportunities to connect and explain the connections between the different representations. Students collect data regarding real-world contexts and create models to display and interpret the data. 5. Use appropriate tools strategically. Students consider available tools (including estimation and technology) when answering questions about data or representing data distributions. They decide when certain tools might be helpful. For instance, students in grade 6 may decide to represent similar data sets using dot plots with the same scale to visually compare the center and variability of the data. 6. Attend to precision. Students use appropriate terminology when referring data displays and statistical measures. 7. Look for and make use of structure. Students examine the structure of data representations by examining intervals, units, and scale in box plots, line plots, histograms and dot plots. 8. Look for and express regularity in repeated reasoning. Students recognize typical situations in which outliers skew data. They can explain patterns in the way data is interpreted in the various representations they study throughout this unit. Standards for Mathematical Content 6.SP.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How Curriculum and Instruction 2015-2016 Page 2 of 8 MADISON COUNTY PUBLIC SCHOOLS District Curriculum Map for Mathematics: Grade 6 old are the students in my school?” is a statistical question because one anticipates variability in students’ ages. 6.SP.2 Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. 6.SP.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. 6.SP.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots. 6.SP.5 Summarize numerical data sets in relation to their context, such as by: a. Reporting the number of observations. b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. Supporting Standard(s) 6.NS.1 Which related standards will be incorporated to support and enhance the enduring standards? 6.NS.2 Curriculum and Instruction Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? Fluently divide multi-digit numbers using the standard algorithm. 2015-2016 Page 3 of 8 MADISON COUNTY PUBLIC SCHOOLS District Curriculum Map for Mathematics: Grade 6 Instructional Outcomes What must students learn and be able to do by the end of the unit? 6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. 6.NS.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). I am learning to…. Curriculum and Instruction Recognize that data can have variability Recognize a statistical question (examples versus non-examples) Know that a set of data has a distribution. Describe a set of data by its center, e.g., mean and median. Describe a set of data by its spread and overall shape, e.g., by identifying data clusters, peaks, gaps, and symmetry. Recognize there are measures of central tendency for a data set, e.g., mean, median, mode. Recognize there are measures of variances for a data set, e.g., range, interquartile range, mean absolute deviation. Recognize measures of central tendency for a data set summarizes the data with a single number. Recognize measures of variation for a data set describes how its values vary with a single number. Identify the components of dot plots, histograms, and box plots. Find the median, quartile and interquartile range of a set of data. Analyze a set of data to determine its variance. Create a dot plot to display a set of numerical data. Create a histogram to display a set of numerical data Create a box plot to display a set of numerical data. Organize and display data in tables and graphs. Report the number of observations in a data set of display. Describe the data being collected, including how it was measured and its units of measurement. Calculate quantitative measures of center, e.g., mean, median, mode. Calculate quantitative measures of variance, e.g., range, interquartile range, mean absolute deviation. Identify outliers. Determine the effect of outliers on quantitative measures of a set of 2015-2016 Page 4 of 8 MADISON COUNTY PUBLIC SCHOOLS District Curriculum Map for Mathematics: Grade 6 Essential Vocabulary What vocabulary must students know to understand and communicate effectively about this content? Curriculum and Instruction data, e.g., mean, median, mode, range, interquartile range, mean absolute deviation. Choose the appropriate measure of central tendency to represent the data. Analyze the shape of the data distribution and the context in which the data were gathered to choose the appropriate measures of central tendency and variability and justify why this measure is appropriate in terms of the context. Essential Vocabulary Box Plot Cluster Distribution Dot plot Quartile (First/Lower and Third/Upper) Frequency table Gap Histogram Interquartile Range Line plot Lower extreme Maximum Mean Mean Absolute Deviation Measure of Center Measure of Variability Median Minimum Mode Outlier Range Skewed Data Spread Statistical Question Statistical Variability Statistics Upper Extreme Supporting Vocabulary Bar graph Interval Number line Plot Table 2015-2016 Page 5 of 8 MADISON COUNTY PUBLIC SCHOOLS District Curriculum Map for Mathematics: Grade 6 Resources/Activities Resources/Activities What resources could we use to best teach this unit? https://www.georgiastandards.org/CommonCore/Common%20Core%20Frameworks/CCGPS_Math_6_6thGrade_Unit6.pdf The following website is a website with lessons to address CCSS: https://www.engageny.org/resource/grade-6-mathematics http://www.insidemathematics.org/common-core-resources/mathematicalcontent-standards/standards-by-grade/6th-grade http://www.mathchimp.com/6th-grade-math-resources Newspaper and magazine graphs for analysis of the spread, shape and variation of data from the National Council of Teachers of Mathematics, Illuminations: Numerical and Categorical Data. In this unit of three lessons, students formulate and refine questions, and collect, display and analyze data. (ORC # 391, 392, 393) Data Analysis and Probability Virtual Manipulatives Grades 6-8 #5048 Students can use the appropriate applet from this page of virtual manipulatives to create graphical displays of the data set. This provides an important visual display of the data without requiring students to spend time hand-drawing the display. Classroom time can then be spent discussing the patterns and variability of the data. Guidelines for Assessment and Instruction in Statistics Education (GAISE) Report, American Statistics Association http://www.illustrativemathematics.org/6 http://commoncoretools.me/tools/ http://www.opusmath.com/common-core Students can use applets to create data displays. Examples of applets include the Box Plot Tool and Histogram Tool on NCTM’s Illuminations. Box Plot Tool - http://illuminations.nctm.org/ActivityDetail.aspx?ID=77 Histogram Tool -- http://illuminations.nctm.org/ActivityDetail.aspx?ID=78 Curriculum and Instruction 2015-2016 Page 6 of 8 MADISON COUNTY PUBLIC SCHOOLS District Curriculum Map for Mathematics: Grade 6 Remember there are other sources in your school that may not be listed on this resources list due to variation in each individual school. If you have a good resource that you would be willing to share, please let Mendy Mills know so that she can share with other math teachers. [email protected] Curriculum and Instruction 2015-2016 Page 7 of 8 Curriculum and Instruction 2015-2016 Page 8 of 8