ITQ Day One: Wednesday Feb 19: 4-6pm Room 5 of Sierra Vista School:

Coach: JacqueddaValadez :

ITQ Grant facilitator: Darcy White:

Statistics

Time / Subject / Notes / References/Materials
4:00 / Paperwork / Fill in sign-in sheet / Agenda / Copies of Sign in
4:05 / Book Topics and standards / Emphasize interquartile range and variability / Handout
4:15 / Exploration / Using the hundred grids to find percentage
Count and record number
Other ideas: blinking, clicking, water drops on a penny / Skittles and M&Ms
4:40 / Comparing single graphs / Have everyone display the graphs that they have made. Make sure there is a histogram, a frequency table, and stem and leaf plot. / Chart Paper
Markers
Rulers
4:50 / Comparing double graphs / Have everyone construct a double bar and double stem and leaf / Chart paper
Markers
Rulers
5:00 / Box Plot / Essential Questions:
What is the best manner for displaying my information? What are the advantages and disadvantages of each graph?
What one number best represents the number of Skittles in a package?
What one number best represents the number of M&Ms in a package?
How can I determine how precise the data is (How spread out)?
Measure of central tendency help. / Protractors
Paper
Calculators
Markers
5:40 / Variability
Interquartile Range / Construct Box Plots and discuss the quartiles. / Proportion Problems

Statistics at the 5th and 6th Grades

Textbook: / Roosevelt Curriculum Maps
Graphs:
  • Circle Graphs
  • Picture Graph
  • Frequency Table
  • Histograms
  • Bar graphs and double bar graph
  • Line graphs
  • Stem and Leaf
  • Scattergram (Scatter Plot)
  • Enrichment: Box Plot
Concepts
  • Mean
  • Median
  • Mode
  • Range
  • Variability
  • Misleading graphs
/ Graphs
  • Box
  • Stem and Leaf
  • Histogram
  • Frequency Chart
Concepts
  • Mean
  • Median
  • Mode
  • Variability
  • Mean Absolute Deviation
  • Quartile
  • Interquartile Range

Arizona Standards

6.SP.A.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.A.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.A.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.B.4. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

6.SP.B.5. 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.

The following Mathematical Practices were with each of the standards above.

6.MP.2. Reason abstractly and quantitatively.

6.MP.4.Model with mathematics.

6.MP.5. Use appropriate tools strategically.

6.MP.6. Attend to precision.

6.MP.7. Look for and make use of structure.

Exploration with Skittles and M&Ms

Open the bag of Skittles and record the number of Skittles and the colors of the Skittles on the recording sheet.

Do the same for your M&Ms bag.

Your results:

Red / Orange / Yellow / Green / Purple / Brown / Blue / total
Skittles
M&Ms

Results from the class for the total:

Total number of Skittles in each bag:

Total number of M&Ms in each bag:

What graphs could we use to show the total number of Skittles in each pack?

Draw a graph to represent the amount of pieces that class found.

As you look at the ones that are displayed, what information is visible or hidden by the method that was chosen by your classmates?

What graphs could we use to compare the number of Skittles compared to the number of M&Ms in each pack?

Draw a graph that compares the two and be ready to share it.

As you look at the ones that are displayed, what information is visible or hidden by the method that was chosen by your classmates?

In what ways can we represent the number of each color found in a pack?

Variability

Which company was more precise in how many pieces were packed in a bag?

How would one measure that?

Vocabulary:

Range

Interquartile Range

Mean Absolute Variation