Flying Frogs

6 and 7.SP.1 Develop and Broaden statistical reasoning by using the GAISE model:

a. Formulate Questions: Recognize and formulate a statistical question as one that anticipates variability and can be answered with quantitative data. 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 of the variability in students’ ages. (GAISE Model, step 1)

b. Collect Data: Design and use a plan to collect appropriate data to answer a statistical question. (GAISE Model, step 2)

c. Analyze Data: Select appropriate graphical methods and numerical measures to analyze data by displaying variability within a group, comparing individual to individual, and comparing individual to group. (GAISE Model, step 3)

d. Interpret Results: Draw logical conclusions from the data based on the original question.(GAISE Model, step 4)

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.

6.SP.4 Display numerical data in plots on a number line, including dot plotsG (line plots), histograms, and box plotsG. (GAISE Model, step 3)

6.SP.5 Summarize numerical data sets in relation to their context.

a. Report the number of observations.

c. Find the quantitative measures of center for a numerical data set and recognize that this value summarizes the data set with a single number. Interpret mean as an equal or fair share. Find measures of variability as well as informally describe the shape and the presence of clusters, gaps, peaks, and outliers in a distribution.

d. Choose the measures of center and variability, based on the shape of the data distribution and the context in which the data were gathered.

7.SP.3 Describe and analyze distributions.

a. Summarize quantitative data sets in relation to their context by using mean absolute deviationG (MAD), interpreting mean as a balance point.

S.ID.1 Represent data with plots on the real number line (dot plotsG, histograms, and box plots) in the context of real-world applications using the GAISE model.★

S.ID.2 In the context of real-world applications by using the GAISE model, use statistics appropriate to the shape of the data distribution to compare center (median and mean) and spread (mean absolute deviationG, interquartile rangeG, and standard deviation) of two or more different data sets. ★

S.ID.3 In the context of real-world applications by using the GAISE model, interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

Looking at the frog in front of you, what questions do you have?

Will the frogs always fly the same distance?

Distance.

  1. Fling your frog and record the distance it travels in feet.
  1. Who in your group had the farthest fling?

The shortest?

The middle?

How would you compare your fling with the rest of your group?

  1. Make a dot plot (line graph) of your groups’ flings.
  1. What are some things you see in your graph?

Let’s see who in your group can fling the furthest…

Fling your frog 10 times and record the distance it flew in feet. Make a dot plot (line graph) of your flings.

  1. Using one number, how far can you fling your frog?

How does that compare to your group?

  1. Who in your group could fling your frog the furthest?
  1. If you had to estimate how far your next fling would be, what would you say?

How confident would you be in your estimate?

  1. Who was the most consistent frog flinger? How can you tell?

Teaching Notes

Looking at the frog in front of you, what questions do you have?

Goal: This starts a discussion about what makes a question a statistical question.

Will the frogs always fly the same distance?

Of course not. For older kids, discuss the variables that influence the distance the frogs will fly. For younger kids, start a discussion about variability.

  1. Fling your frog and record the distance it travels in feet.

I have an 80ft measuring tape that I roll out and let kids estimate their distances.

  1. Who in your group had the farthest fling? The shortest? The middle? How would you compare your fling with the rest of your group?

Goal: In grade 6, they should be making individual to group and individual to individual comparisons.

  1. Make a dot plot (line graph) of your groups’ flings.

This can be an instruction focus for grades 6 & 7 and statistical tool for older students.

  1. What are some things you see in your graph?

Shape, center, & variability

Let’s see who in your group can fling the furthest…

Fling your frog 10 times and record the distance it flew in feet. Make a dot plot (line graph) of your flings.

For grades 7 and high school, comparing group to group is now possible.

  1. Using one number, how far can you fling your frog? How does that compare to your group?

For all levels, measure of center are about summarizes the typical values of a data set and for older students, there is comparing to other students.

  1. Who in your group could fling your frog the furthest?

I try to use this as a discussion question by emphasizing how it is different from question 2. This is asking about a summary not a specific value.

  1. If you had to estimate how far your next fling would be, what would you say? How confident would you be in your estimate?

Goal: The very beginning of making conclusions from a data set. The word confident is used intentionally.

  1. Who was the most consistent frog flinger? How can you tell?

For younger students, this is a jumping off point to discuss measuring variability. For older students, I would ask them to quantify using IQR or MAD.

Presenter Note: Discussion is imperative and should be done, even if it means not completing the activity.

Discussion Questions

How could this lesson be modified to address Levels A, B, and C of the GAISE model? Use pages 14-15 of the GAISE model to guide your discussion.

Level A / Level B / Level C
Formulate Questions
Collect Data
Analyze Data
Interpret Results

How could you modify this activity for your classroom?

*If you have time, read the other information on the pages of the GAISE model pertinent to your activity.