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.

Biking to Bernie's

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. 

Division of Fractions

This is a series of 4 activities designed to help students to focus on the idea of division from a proportional reasoning perspective.

Nana's Lemonade - Dan Meyer Three Act Task

In a brief video, students are confronted with the situation of a person squeezing a lemon slice into a small cup of water. Then a "big gulp" cup is placed next to the smaller, lemon filled cup. By asking the question, "How many lemon wedges do you need to add for the same lemony taste?" students will begin to experiment and mathematically determine the answer.

Shooting Hoops! - Dan Meyer Three Act Task

In this lesson, students learn to graph quadratic equations, translate between the vertex, standard, and factored forms, and recognize the impact of changing the parameters of a quadratic equation.

What is my portion of the bill?

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. 

Sharing Pencils

Sarah and Michelle are working on a class project using colored pencils. Given some information about the number of pencils that Sarah and Michelle had when they started, and how some sharing of pencils has taken place, students must employ proportional reasoning skills to determine how many colored pencils the girls now possess.

Steeper, Faster, Division, and Slope

What does "steeper" mean? What does "faster" mean? And how do these ideas connect to the idea of linear functions? This 3-part series explores these questions and helps students to understand why we divide when computing slope and what proportional correspondence has to do with it all!

Here Fishy, Fishy!

Yolanda and Zachary each have some fish. Zachary gives Yolanda some of his fish, and now he has twice as many fish as she does. Students must utilize given information and apply proportional reasoning skills in order to figure out how many fish Zach gave Yolanda.

Paper-folding - Exponential Growth/Percentage Change

In this activity students are posed a simple question, "How tall will a paper be if it is folded 50 times?" and it is used as a fun way to introduce them to the concepts of growth factors, and percentage change. 

Is the Sine a Circular Function? How about a Star Sine?

Students are often challenged by seeing the conncection between the unit circle and the graph of the sine and cosine functions. This activity is designed to take students out of their comfort zone to experience what the "sine" function would look like if it were based upon other geometric figures. 

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.

Knee surgery & Muscle weakness