You can’t go wrong with these four steps. They make a great template for designing good statistical activities as well as best pedagogical practices.
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Make sense of problems, persevere in solving them
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Reason abstractly and quantitatively
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Construct viable arguments and critique others’ reasoning
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Model with mathematics
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Use appropriate tools strategically
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Attend to precision
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Look for and make use of structure
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Look for and express regularity in repeated reasoning
Marzano’s 10 Coginitive Skills from CCSS:
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Generating conclusions
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Identifying common logical errors
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Presenting and supporting claims
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Navigating digital devices
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Problem solving
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Decision making
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Experimenting
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Investigating
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Identifying basic relationships between ideas
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Generating and manipulating mental images
Trick or Treat!
Fun size M&M’s and Skittles NAME___________________________
1. Question: How many MM’s are there in a Fun Size bag? Guess:_________
Graph the class distribution of guesses on the next page.
2. Actual number of M&M’s in your bag: _________
3. Make a dot plot of the class distribution of counts on the next page.
4. What is the population of interest?
5. What is a sample?
6. What is the observational unit (subject)?
7. So how many M&M’s are in a fun size bag?
8. Do you think the typical number of Skittles in a Fun Size bag is more than the typical number of M&M’s in a Fun Size bag? Explain.
9. Number of Skittles in your bag: _________
10. Make a dot plot of the class distribution of counts on the next page.
11. So how many Skittles are in a fun size bag?
12. Compare and contrast the three distributions in context. Be sure to talk about the shapes, centers, spreads and outliers.
Random Rectangles
Measuring, Plotting, Predicting NAME____________________________
1. From a sheet of 8.5 by 11” paper, make three cuts that make rectangles. Try to create rectangles that vary in size and shape.
2. Measure each rectangle’s length and width in centimeters (which is which?).
3. Compute each rectangle’s perimeter and area.
4. Write these measurements and calculations on the rectangle.
5. On the graph below, plot a point for each of your rectangles with coordinates (Length, Width).
6. Predict, then sketch the shape of the following from the class data. Explain your reasoning.
a) distribution of all the lengths
b) distribution of all the widths
c) distribution of all the perimeters
d) distribution of all the areas
e) scatterplot of lengths vs. widths (like you started on the previous page)
f) scatterplot of lengths vs. perimeter
g) scatterplot of lengths vs. area
h) scatterplot of perimeter vs. area
Census at School Survey
amstat.org/censusatschool NAME____________________________
Use Safari. Class ID: _______________ Password: ________________
The following questions require measurements. Please fill these out prior to taking the online survey.
4. How tall are you without your shoes on? Answer to the nearest centimeter. _________
5. What is the length of your right foot (without your shoe on)? Answer to the nearest centimeter.
__________
6. What is your arm span? (Open arms wide and measure distance across your back from tip of right hand middle finger to tip of left hand middle finger.) Answer to the nearest centimeter.
__________
9. How long does it usually take you to travel to school? Answer to the nearest minute.
__________
14. What is the length of your left foot (without your shoe on)? Answer to the nearest centimeter.
__________
16. What is the length of your index finger (finger next to your thumb) on your left hand? Answer to the nearest centimeter.
__________
17. What is the length of your ring finger? (located between your middle finger and little finger) on your left hand? Answer to the nearest millimeter (there are 10 millimeters in one centimeter).
__________
26. How many hours of sleep do you usually get when you have school the next day?
__________
27. How many hours of sleep do you usually get when you don’t have school the next day?
__________
Project
Group members:_____________________________________________________________
Overview: You will formulate an appropriately framed statistical question, gather data from the Census at School database, create an appropriate visual display, and justify conclusions from the data.
Steps:
1. Read the Census at School survey questions. Discuss with your group possible statistical questions that can be answered with data from the survey. Keep in mind that students from grades 4-12 have taken the survey from many states,
2. Write out 2 or 3 of your best questions and hand them in for approval.
3. Once a question is approved, decide the following for each group member: sample size, states, grade level(s), gender(s), year. EACH STUDENT MUST GATHER THEIR OWN RANDOM SAMPLE, AND EACH SAMPLE MUST BE DIFFERENT IN SOME WAY (sample size, states sampled, grade, etc.).
4. Now you’re ready to collect your random samples. Go to www.amstat.org/censusatschool and select Random Sampler. Follow the directions to download your sample. It should download as a .csv file. This can easily be opened in Excel and/or copied to Fathom for further analysis.
5. Once you have your data, you must “clean” it for possible errors. Then you can create your visual displays, calculate relevant statistics and write your final report. Be sure your conclusion can be justified from the data you collected, and that your scope of inference is correct.
6. Write your final report in Word, print and turn in. Your report should have the following:
Statistical question clearly stated
Description of your sample, method and population of interest
Relevant and accurate graph(s) and statistics
Reasonable conclusion linked to analysis (justification of your conclusion).
Self reflection: What were the 2-3 biggest lessons learned through project. What were the difficulties? What could have been done differently to improve the quality of your results?
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