6.SP.3 - About the Math, Learning Targets, and Increasing Rigor

Full Standard

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.

Learning Targets (I can)

• Find the mean for a set of data.
• Find the median for a set of data.
• Describe the distribution of data by looking at the shape of the data.

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. or 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.

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.

TASKS

These tasks can be used with small group or whole group instruction.

• Safeway sells 5 different kinds of orange juice in gallon containers. The mean price of a gallon of orange juice is $3.29. No two prices are the same. List 5 possible reasonable prices for the orange juice.
• The following data shows the number of pins knocked down in each frame of a bowling game: 7, 8, 10, 6, 8, 8, 9, and ?. The mean of the data is 8. What is the value of the ? in the data set? Then, the bowler plays another frame and the mean goes down to 7.67. What score did the bowler get on that next frame?
• Adam and Lauren have just bought a pet rabbit. The owner of the pet store told them that the median lifespan of the rabbit is seven years. What could a data set for the lifespan of fifteen rabbits look like?
• Best Buy sells 3 different types of printers. The mean price for the printers at Best Buy is $150. What are the possible prices for the 3 printers?

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.

Additional Tasks 

  These links provide instructional ideas connected to this standard. 

• Lesson 8.13 - The Median of a Data Set Links to an external site.(Illustrative Math Open Up Resources) 
• Bar Charts Links to an external site. (Inside Mathematics Lesson)
• SP3 Lesson Collection Download SP3 Lesson Collection (HCPSS Lesson Collection)

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. 

Print Resources

Book Thumbnail	Book Title	Grade	Pages
	Teaching Student-Centered Mathematics	6-8	The Mean Foot, Activity 15.7, Page 344 Finding the Balance Point, Activity 15.8, Page 345
	Teaching Student-Centered Mathematics	5-8	The Mean of Means, Activity11.4, Page 314 Equal Means, Activity 11.6, Page 317 Toying with the Measures, Activity 11.7, Page 317 Bus Time, Activity 11.8, Page 317

Centers

  These print resources can be used during independent or center time. These resources could also be used as lesson seeds.

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.

• Central Tendencies a Links to an external site.
• Central Tendencies b Links to an external site.
• Distribution of Data Links to an external site.
• Find Median, Mean, and Range of a Set of Data Links to an external site.
• Find Median, Mean, and Range of a Set of Data_2 Links to an external site.
• Find Median, Mean, Range, and Outliers of a Set of Data Links to an external site.
• Reason About Mean of a Set of Data Links to an external site.
• Reason About Mean and Median of a Set of Data Links to an external site.

Learning Targets

• Find the mean for a set of data.
• Find the median for a set of data.
• Describe the distribution of data by looking at the shape of the data.

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.