6.SP.5 - About the Math, Learning Targets, and Increasing Rigor
Grade 5 AGL Statistics and Probability
6.SP.5
Full Standard
Summarize numerical data sets in relation to their context, such as by:
- Reporting the number of observations.
- Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
- 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.
- 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.
Learning Targets (I can)
- Analyze data and determine the number of participants/observations.
- Describe what was investigated and how it was measured.
- I can find the median, mean, and interquartile ranges for a given set of data.
- Describe the overall shape of the data and how it might be influenced by quantitative measures of center (i.e. Describe the impact of an outlier on a median, mean, or range).
- Determine when median, mean, or range is a good choice for describing a data set or situation.
- Analyze the overall shape of data collected.
About the Math
Developing understanding of statistical thinking:
Building on and reinforcing their understanding of number, students begin to develop their ability to think statistically. Students recognize that a data distribution may not have a definite center and that different ways to measure center yield different values. The median measures center in the sense that it is roughly the middle value. The mean measures center in the sense that it is the value that each data point would take on if the total of the data values were redistributed equally, and also in the sense that it is a balance point. Students recognize that a measure of variability (interquartile range or mean absolute deviation) can also be useful for summarizing data because two very different sets of data can have the same mean and median yet be distinguished by their variability. Students learn to describe and summarize numerical data sets, identifying clusters, peaks, gaps, and symmetry, considering the context in which the data were collected. (CCSC Grade 6 p.38)
In learning Grade 6 mathematics, students build on the knowledge and experiences in data analysis developed in earlier grades. (See K-3 Categorical Data Progression and Grades 2-5 Measurement Progression.) They develop a deeper understanding of variability and more precise descriptions of data distributions, using numerical measures of center and spread, and terms such as cluster, peak, gap, symmetry, skew, and outlier. They begin to use histograms and box plots to represent and analyze data distributions. As in earlier grades, students view statistical reasoning as a four-step investigative process:
- Formulate questions that can be answered with data.
- Design and use a plan to collect relevant data.
- Analyze the data with appropriate methods.
- Interpret results and draw valid conclusions from the data that relate to the questions posed.
Such investigations involve making sense of practical problems by turning them into statistical investigations (MP1); moving from context to abstraction and back to context (MP2); repeating the process of statistical reasoning in a variety of contexts (MP8). (CCSC writing team p. 2 (December 2011) www.commoncoretools.wordpress.com Links to an external site.) Essential vocabulary for this standard includes: data, probability, statistical question, statistical variation, statistics, and variability. Visit the online dictionary Links to an external site., visual math dictionary Links to an external site. for vocabulary support.
Progression of Standard within Grade 6 (5 AGL)
This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.
Quarter 1 | Quarter 2 | Quarter 3 | Quarter 4 |
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Progression of this Standard Across Grades
This progression is informed by the Achieve the Core Coherence Map Links to an external site.. Information is not the complete standard.
Grade 5 | HS |
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TASKS
These tasks can be used with small group or whole group instruction.
- Create a set of data in which the mean is greater than the median. What does this tell you about the data?
- How do you calculate the upper and lower quartile of a set of data. Use an example in your explanation.
- Make a data set representing the ages of students with the following statistical measures: Sample Size: 12 students, Range/Spread: 8 years, Median Age: 12.5 years, and Mode: 10 years. Will everyone's data set look the same? Why or why not?
- What is an outlier and how does it affect the median and mode of a data set?
- Is the mean or median more affected by outliers? Use examples to support your answer.
SLIDE-BASED TASKS
These links are HCPSS created instructional tasks. These tasks are provided in Google slides. These tasks should be used for inspiration and resources, but instruction should start with students having the opportunity to engage with the math first (often involving physical and/or visual models) followed by discussion and explicit instruction to ensure student understanding.
Module 13 • Data and Statistics
Interpret Data:
- Lesson 6.8.11: Links to an external site. Deviation from the Mean
- Lesson 6.8.12: Links to an external site. Using Mean & MAD to Compare
- Desmos- MAD: What's My Number? Links to an external site.
- Desmos - Variability: Human Stopwatch Links to an external site.
- Lesson 6.8.15: Links to an external site. Quartiles and Interquartile Range
- Desmos: Strength In Numbers Links to an external site.
(Links to an external
Additional Tasks
These links provide instructional ideas connected to this standard.
- Lesson 8.14 - Comparing Mean and Median Links to an external site. (Illustrative Math Open Up Resources)
- Lesson 8.16 - Box Plots Links to an external site. (Illustrative Math Open Up Resources)
- Lesson 8.17 - Using Box Plots Links to an external site.(Illustrative Math Open Up Resources)
- Lesson 8.18 - Using Data to Solve Problems Links to an external site. (Illustrative Math Open Up Resources)
- Puzzle Times Links to an external site. (Links to an external site.) (I Links to an external site.llustrative Math)
- Electoral College (Links to an external site.) ( Links to an external site.Illustrative Math)
Tasks From Print Resources
These publications have been provided for each school. They are typically stored in team closets or the media center. Check with your team leader if you cannot find them.
Book Thumbnail | Book Title | Grade | Pages |
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Teaching Student-Centered Mathematics |
6-8 |
Leveling the Bars, Activity 15.6, Page 343 |
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Teaching Student-Centered Mathematics |
5-8 |
The Mean of Means, Activity11.4, Page 314 |
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Centers
These print resources can be used during independent or center time. These resources could also be used as lesson seeds.
- Team Salaries vs Team Wins Links to an external site. (Yummymath, print resources)
- Season 12 American idol Links to an external site.(Yummymath, print resources)
- Typical Superbowl Scores 2013 Links to an external site. (Yummymath, print resources)
- NFL Home Field Advantage? Links to an external site. (Yummymath, print resources)
- Monopoly, Are You Game? Links to an external site. (Yummymath, print resources)
INDEPENDENT PRACTICE/HOMEWORK/ASSESSMENT
These resource sheets can be used for independent practice, homework, or assessment. They are intended to reinforce procedures and concepts. They should not be used as a source of direct instruction or whole-group practice.
- Line Plots and Dot Plots Links to an external site.
- Histograms a Links to an external site.
- Histograms b Links to an external site.
- Histograms c Links to an external site.
- Box Plots a Links to an external site.
- Box Plots b Links to an external site.
- Box Plots c Links to an external site.
- Find Mean, Median, and Outliers of a Set of Data Links to an external site.
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Learning Targets
- Analyze data and determine the number of participants/observations.
- Describe what was investigated and how it was measured.
- I can find the median, mean, and interquartile ranges for a given set of data.
- Describe the overall shape of the data and how it might be influenced by quantitative measures of center (i.e. Describe the impact of an outlier on a median, mean, or range).
- Determine when median, mean, or range is a good choice for describing a data set or situation.
- Analyze the overall shape of data collected.
Learning targets identify what students should be able to do. This rubric can be applied to tasks and observations for assessment and/or grading.
Rubric for Tasks Links to an external site.
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Links to an external site. license. Content in this course can be considered under this license unless otherwise noted.