K12 Education
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SOCR Educational Materials - SOCR K-12 Educational Materials
Overview
The SOCR K-12 educational resources are developed to provide specific guideance, hands-on activities, demonstrations and learning materials specifically for technology-enhanced elementary, midle and high school probability and statistics education.
General Curriculum Outline
There are large variations in the probability and statistics curricula based on age, geographic location, culture, economic, social and visionary settings. This curricular outline includes many of the commonly discussed topics, terminologies, properties and protocols for data-driven probability modeling and statistical analysis.
Calculating probabilities of events and compare theoretical and experimental probability
Use basic concepts of probability to determine the likelihood of an event and compare the results of various experiments
Statistics are often used in sports. For example, if you watch professional tennis players on television, the sports channels like to show the probability of a first serve landing inside the service box.
Say, for instance, that Roger Federer’s percentage of first serves in the service box is 90% (and that he serves that percentage consistently). What does this mean?
Use the coin sample experiment. Set n = 1 (since he only has one chance to get his first serve in) and p = 0.9 (the probability that his service will be in the service box). Stop the experiment after 10 trials. Count the number of 1’s, which represent serves in. Repeat this experiment several times.
Around what number of 1’s does the experiment get each time? What does this predict about the number of serves Roger Federer will most likely serve into the box when he is only allowed 10 tries?
Display and compare data to make predictions and formulate conclusions
Graphs are very helpful in presenting data instead of simply showing numbers. For example, a graph is very useful in displaying the music content of an iPod.
Two graphs that work well are the histogram and the pie chart.
Graph the following data using the SOCR charts.
- Genre Number of songs
- Jazz 17
- Pop 44
- Indie Rock 23
- Easy Listening 37
- Hip Hop, R&B 56
Now try applying this to the previous section about probabilities. How many times will the iPod play a certain genre if it is on random for 100 songs? The iPod is not keeping track of what it plays and so songs can be played twice ( sampling with replacement.
Your pie chart already gives you an idea of the probability of each genre. The bigger the area of a certain genre the greater the chance it will be played.
Using the SOCR spinner experiment, perform an experiment that will answer the question above. Set n = 5 since you have 5 genres. Click on the small spinner icon to change the probabilities of each section to the appropriate probability. For example, jazz would be 17/177 = 0.0960. Be sure that these probabilities add up to 1! Then set the experiment to stop 100.
Fill in the chart below.
- Genre Number of times played Proportion
- Jazz
- Pop
- Indie Rock
- Easy Listening
- Hip Hop, R&B
After solving for each genre’s probability, what do they predict about the number of songs that will be played from each genre if the iPod is running only 100 songs?
How well does the experiment’s data agree with the math?
Fundamental Counting Principle
You are going to buy new school supplies for school. There are five different things that are on your shopping list: a three ring binder, pencils, color pencils, a calculator, and folders.
For each of these items you have the following choices:
- Three Ring Binder: with pockets, without pockets, or clear cover
- Pencils: mechanical or regular
- Color Pencils: Crayola, Rose Art, or Bic
- Calculator: TI-83, regular, solar powered
- Folders: plastic, paper with prongs, paper without prongs
- How many different ways can you choose your school supplies? Use the fundamental counting principle.
Measures of Variation
Standardized test scores are often reported in relation to all the test scores of other students. For example, when your test score is in the 95 percentile that means that you have a test score that is higher than 95% of the other students who took the test.
Say the test scores are the following: 85 88 90 92 76 57 88 91 74 72 98 100 97 88 96
- There are three basic aspects of the data that will help you evaluate each student’s performance:
- Range: The range is the difference between the highest test score and the lowest test score. What is the range for this set of test scores?
- Quartiles: The quartiles split the data into four equal (hence “quartiles”) sections after the data values have been arranged from least to greatest. The quartiles mark the 25th (Q1), 50th (Q2), and 75th (Q3) percentile. Find the three quartiles for the test scores. Also, what is another term for the second quartile?
- Inter-quartile Range: The IQR is the middle 50% of the data. This means taking the difference between the 75th percentile (Q3) and the 25th percentile (Q1). What is the IQR for this set of test scores?
Charts and Plots
Box and whisker plots are a very useful way of displaying data that involves the range, quartiles and IQR. Using SOCR Charts, enter in the data for the test scores to see if your answers are correct and view how the data looks in this type of graph. (Go to SOCR Charts, click on Miscellaneous, then Box and Whisker Chart Demo 2).
Calculating probabilities of events and compare theoretical and experimental probability
Sampling without replacement example: Door prize drawings - You and your parents attend a banquet at school. The school decides to have door prizes to make the event more fun. 35 students and parents are present and each of them are given a raffle ticket. Only one ticket is drawn at a time and once a ticket has won a prize, it can no longer be selected. What is the chance that your ticket or your parents' tickets are drawn?
Bivariate Data
Graph the following using SOCR charts and look at the correlations.
- Use the scatter plot to plot the data. Then use the line of best fit to estimate the data.
[Two data sets will be given: number of worms eaten -> fish weight (positive correlation example); number of cavities a student has -> student's test scores (no correlation example)]
- Using the equation from the line of best fit, how many pounds would
you expect a fish to gain if it eats x number of worms?
Apply basic concepts of probability (permutations, combinations,conditional probabilities)
Stringing beads on a string example - [permutation and combination equations explained and written here]
- 1. permutation deals with order: how many different ways can you order the beads if you have 3 blue, 4 green, 2 yellow, and 2 red beads?
- 2. combination deals with grouping: how many ways can you group the beads if you still have the same number of each?
