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:

  1. Reporting the number of observations.
  2. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
  3. 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.
  4. 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.

Progression Throughout Year
Quarter 1 Quarter 2 Quarter 3 Quarter 4
 
  • 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.

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.

Progression Across Grades
Grade 5 HS
  • Make line plots with fractions. Solve problems with information presented in line plots. ( 5.MD.2 )
  • Evaluate reports based on data (HS.S-ID.B.6)
  • Interpret differences in shape, center, and spread in the context of the data sets (HS.S-ID.A.3)
  • Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages (HS.S-ID.A.4)

 

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