Capture-Recapture

Imagine that a city employee is given the task of counting the number of fish in a city pond in a park. The “capture-recapture” method may be used to approximate the number of fish in the pond. The employee could capture a number of fish, say 20, and tag them and release them back into the pond. Waiting until the fish have a chance to become mixed with the other fish in the pond, the employee can capture more fish. If the number of fish captured is 25 and 4 of them are tagged, we can use proportional reasoning to estimate the number of fish in the pond.

Average Athletics

One of the measures of central tendency is the mean/average. Many do not know much about the average other than it is calculated by "adding up all of the numbers and dividing by the number of numbers". This activity is designed to help students get a conceptual understanding of what an average is and not just how to calculate a numerical value.

SRS vs. Convenience Sample in the Gettysburg Address

Students have an interesting view of what a random sample looks like. They often feel that just closing their eyes and picking “haphazardly” will be enough to achieve randomness. This lesson should remove this misconception. Students will be allowed to pick words with their personal definition of random and then forced to pick a true simple random sample and compare the results.

Roll a Distribution

The purpose of this lesson is to allow the students to discover that data collected in seemingly similar settings will yield distributions that are shaped differently. Students will roll a single die 30 times counting the number of face up spots on the die and recording the result each time as a histogram or a histogram. Students will be asked to describe the shape of the distribution. Combining work with several students will yield more consistent results.

Who’s the Best Home Run Hitter of All time?

This lesson requires students to use side-by-side box plots to make a claim as to who is the "best home run hitter of all time" for major league baseball.

Why do we need MAD?

Students will wonder why we need to have a value that describes the spread of the data beyond the range. If we give them three sets of data that have the same mean, median, and range and yet are clearly differently shaped then perhaps they will see that the MAD has some use.

The Forest Problem

Students want to know why they would ever use a sampling method other than a simple random sample. This lesson visually illustrates the effect of using a simple random sample (SRS) vs. a stratified random sample. Students will create a SRS from a population of apple trees and use the mean of the SRS to estimate the mean yield of the trees. Students will then create a stratified random sample from the same population to again estimate the yield of the trees. The use of the stratified random sample is to control for a known source of variation in the yield of the crop, a nearby forest.

Sampling Reese’s Pieces

This activity uses simulation to help students understand sampling variability and reason about whether a particular sample result is unusual, given a particular hypothesis. By using first candies, a web applet, then a calculator, and varying sample size, students learn that larger samples give more stable and better estimates of a population parameter and develop an appreciation for factors affecting sampling variability.

Valentine Marbles

For this task, Minitab software was used to generate 100 random samples of size 16 from a population where the probability of obtaining a success in one draw is 33.6% (Bernoulli). Given that multiple samples of the same size have been generated, students should note that there can be quite a bit of variability among the estimates from random samples and that on average, the center of the distribution of such estimates is at the actual population value and most of the estimates themselves tend to cluster around the actual population value. Although formal inference is not covered in Grade 7 standards, students may develop a sense that the results of the 100 simulations tell them what sample proportions would be expected for a sample of size 16 from a population with about successes.

Flintstone's Writing Project - Sampling

This writing project was written as a letter from Fred Flintstone to the students asking for their advice on proper sampling techniques that requires their mathematical “expertise”. This clearly defines the target audience for the paper and gives the students an idea of the mathematical background that they should assume of the reader. The plot lines in the project is a little bit goofy, although not imprecise, which helps relax the students and gives them the opportunity to be creative when writing their papers.

Yellow Starburst - Dan Meyer Three Act Task

This lesson is designed to introduce students to probability using Dan Meyer's three-act-task, Yellow Starburst. After viewing a brief introductory video clip, students are asked to determine how many Starburst packs have exactly one yellow Starburst and how many packs will have exactly two yellow Starbursts.

College Success - Comparing Two Populations

In this task, students are able to conjecture about the differences in the two groups from a strictly visual perspective and then support their comparisons with appropriate measures of center and variability. This will reinforce that much can be gleaned simply from visual comparison of appropriate graphs, particularly those of similar scale. Students are also encouraged to consider how certain measurements and observation values from one group compare in the context of the other group. 

Sochi Olympics - Junior High Math Contest

This is the 2013 Chandler-Gilbert Community College Junior High Math Contest Team Project. You may use all or just parts of it as it contains lots of different math topics including: The idea of AVERAGE The idea of AVERAGE SPEED and GRAPHS of LINEAR FUNCTIONS The idea of CREATING and INTERPRETING BOX and WHISKER PLOTS  The idea of SLOPE The idea of ANGLE The idea of PERCENT Look at the project and decide what parts your students are ready to tackle...and HAVE FUN!

Sampling Techniques - Jelly Blubbers

This activity introduces the Simple Random Sample (SRS) to students, and shows why this process helps to get an unbiased sample statistic. Relying on our perceptions can often be deceiving. In this exercisestudents are asked to determine the average length of a jellyblubber (a hypothetically recently discovered marine species) using a variety of techniques. The student will learn that a Simple Random Sample (SRS) is the most accurate method of determining this parameter, and that intuition can be deceptive. 

Pennies From Heaven

The focus of this activity is to describe the shape of a distribution and to describe the center and spread. Students use data they collect (penny ages) to describe the distribution by its SOCS (Shape, Outlier, Center, Spread). 

Is Manute, minute?

A powerpoint presentation that can be used to introduce the topic of scatterplots and lines-of-best fit using a fun context. 

Straighten up and Fly Right!

The purpose of this lesson is to allow the students gather data in a fun way and answer a statistical question through analysis of the data.  Students will fly paper airplanes and analyze the data to determine which style of plane flies longer.

Talking Two-Way Tables

When analysis of categorical data is concerned with more than one variable, a two-way table (also known as a contingency table) can be used. These tables provide a foundation for statistical inference, where statistical tests question the relationship between the variables based on the data observed. This activity begins to explore statistical inference and testing. 

Titanic - Two Way Tables

Two way tables help us in so many ways...association and probability are just two! This PP is classroom ready to use with your 8th grade or high school students. 

Titanic & Two-Way Tables (Illustrative Mathematics)

This is the first task in the series of three, which ask related questions, but use different levels of scaffolding. Also, the third task uses a more detailed version of the data table. The emphasis is on developing their understanding of conditional probability.

Theoretical vs Empirical Probability-Dice Activity

M & M Variablility

California Adventures- Central Tendency and Variation

Tree Diagrams and Compound Probabilities

Goal: The goal of this activity is for students to understand how to find probabilities of compound events by drawing tree diagrams and listing out sample spaces. Depending on the grade level, with or without replacement events can also be used and illustrated. Materials Needed: Each person in the group will need a copy of the worksheet.

Central Tendency and Measures of Dispersion

Goal: The goal of this activity is to allow students the ability to practice data collection and find measures of central tendency and dispersion. Wrap up questions will also allow for an insight into how each of these calculations are related to one another. Materials needed: 12 small bags of M & M’s (they can be the fun size or regular packs), calculator and the M & M worksheet and answer sheet.

Ice Cream and Temperature-Correlation Activity

Goal: The goal of this activity is for students to graph the data on a scatterplot and discuss the relationship they see between ice cream and temperature. 

Outlier Activity

Goal: The goal of this activity is for students to interpret measures of central tendency when an outlier is present. They will also be able to identify which value is an outlier and create a boxplot as well.

Inferences about two populations

Goal: The goal of this activity is for students to compare to samples from two different populations. They will make inferences based on what they find from their dot plot.

Contingency Table Activity

Goal: The goal of this activity is to read a table and gather data from it and use it to create a contingency table. Students will then be asked a series of questions discussing what they see when they create a contingency table and what are some of the benefits with using one.

Understanding probability using a deck of cards

This activity is to familiarize your students with a standard deck of cards. Have your students get into groups of 2 or 3 and walk them through the beginning part. You can chose to have your students simplify each probability as a fraction or round to the thousandths place. Hopefully the students will see that all of the probabilities they find will always be between 0 and 1 inclusive.

Creating a Probability Model

Goal: The goal of this activity is for students to grasp the understanding of how to put together a probability model for the rolling of a single die and also the sum of the rolls of two dice.

Estimating the Mean

Goal: The goal of this activity is for students to randomly draw words from an excerpt to estimate the mean length word count of the entire document. 

Creating a histogram using temperatures

Goal: The goal of the current activity is to have students read data from a map of the U.S., create a frequency table, answer questions and create a frequency histrogram.

Scatter Plot Activity

Goal: The goal of this activity is for students to see different types of correlation and recognize the patterns associated with each type of correlation. They will then have to create their own scatter plot based on directions given.