Unit 6

Statistics

 

Grade 6

Math

Unit Length and Description:

 

24 days

 

In Unit 6, students develop an understanding of statistical variability and apply that understanding as they summarize, describe, and display distributions. In particular, careful attention is given to measures of center and variability.  Students will begin to use dot plots, histograms, and box plots to represent and analyze data distributions for quantitative data and use bar graphs to represent and analyze data distributions.  Students will also examine relationships among multiple representations of the same data set.  Students should examine the relationships among making a graph, computing a mean, and predicting a trend rather than viewing these as independent activities.

 

Standards:

 

Additional Cluster

Statistics and Probability

Develop understanding of statistical variability.

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 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.

Summarize and describe distributions.

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.

 

Foundational Standards

Perform operations with multi-digit whole numbers and with decimals to hundredths.

5.NBT.5

Fluently multiply multi-digit whole numbers using the standard algorithm.

5.NBT.6

Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division.  Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

5.NBT.7

Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

Represent and interpret data.

5.MD.2

Make a line plot to display a data set of measurements in fractions of a unit.  Use operations on fractions for this grade to solve problems involving information presented in line plots.  For example, given different measurements of liquid in identical beakers find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.

Apply and extend previous understandings of arithmetic to algebraic expressions.

6.EE.2

Write, read, and evaluate expressions in which letters stand for numbers.

a.    Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract 𝑦 from 5” as 5 − 𝑦.

b.    Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2(8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.

Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas 𝑉=𝑠3 and 𝐴=6𝑠2 to find the volume and surface area of a cube with sides of length .

Standards for Mathematical Practices

1.   Make sense of problems and persevere in solving them.

2.   Reason abstractly and quantitatively.

3.   Construct viable arguments and critique the reasoning of others.

4.   Model with mathematics.

5.   Use appropriate tools strategically.

6.   Attend to precision.

7.   Look for and make use of structure.

8.   Look for and express regularity in repeated reasoning.

Instructional Outcomes

·         6.SP.A.1

o   I can recognize that data has variability.

o   I can explain why a given question is/is not a statistical question.

o   I can formulate a statistical question, which includes a population of interest, a measurement of interest, and anticipates answers based on data that varies.

·         6.SP.2

o   I can 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.

o   I can informally describe measures of center for quantitative data.

o   I can describe extremes, clusters, gaps, and outliers.

o   I can describe the overall shape of the displayed data in terms of its symmetry or skew.

o   I can describe variability for quantitative or categorical data.

·         6.SP.3

o   I can use measures of center and measures of variability to describe a data set, for example, mean, median and mode.

o   I can recognize that there are measures of variances for a data set, for example, range, interquartile range, and mean absolute deviation.

o   I can recognize that measure of central tendency for a data set summarizes the data with a single number.

o   I can recognize that measures of variation for a data set describe how its values vary with a single number.

·         6.SP.4

o   I can idientify the components of dot plots, histograms, and box plots.

o   I can find the median, quartile and interquartile range of a set of data.

o   I can analyze a set of data to determine its variance.

o   I can creat a dot plot to display a set of numberical data.

o   I can create a histogram to display a set of numerical data.

o   I can create a box plot to display a set of numerical data.

·         6.SP.5

o   I can summarize numerical data sets in relation to the context.

o   I can report the number of observations in a data set or display.

o   I can describe the data being collected, including how it was measured and its units of measure.

o   I can find quantitative measures of center (median and/or mean) and variability (rang, interquartile range, and/or mean absolute deviation).

o   I can choose the appropriate measure of central tendency to represent the data.

o   I can identify outliers. 

o   I can determine the effect of outliers on quantitative measures of a set of data, for example, mean, median, mode, range, interquartile range, and mean absolute deviation.

o   I can describe an overall pattern, as well as any striking deviations, with reference to the context in which the data was gathered.

 

 

 

Enduring Understandings:

 

·         Data can be collected, organized, sorted, represented, and analyzed in a variety of ways.

·         The results of a statistical investigation can be used to support or refute an argument.

·         A statistical question should anticipate variability or more than one answer.

 

Essential Questions:

 

·         What is the best way to summarize data collected from a study?

·         How can understanding and use of measures of central tendency be useful for interpreting and drawing conclusions about data?

·         What does variability mean?

·         What is the difference between measures of center and measures of variation?

·         How do you ask a question to collect statistical data?