Creating an Exponential Model - The Salary Problem

This video is a short demonstration of how a constant percent change can be represented using an exponential function. The context is an individual is given a salary and gets a 5% annual raise.

Exploring the Function Definition and Notation

This worksheet will allow students to explore the function topic by answering questions about the definition, working with the notation, finding domain and range and performing some basic compositions.

Modeling with Exponential Functions

A worksheet involving exponential modeling.

Growth Factors

This short video describes where a growth factor comes from and how to use it for a percent increase.

Transforming a Sine Function

This applet allows the user to transform the coefficients of a sine function and see how it changes the resulting graph.

Definite Integral using Substitution

Inside Mathematics Educator Resource Site

Inside Mathematics is a professional resource for educators passionate about improving students' mathematics learning and performance. This site features classroom examples of innovative teaching methods and insights into student learning, tools for mathematics instruction that teachers can use immediately, and video tours of the ideas and materials on the site.

Mathematics Vision Project Website

MVP provides curricular materials aligned with the Common Core State Standards for secondary mathematics. These items are free to download and remix.

Wile E. Coyote - Modeling with Quadratic Functions (Writing project)

This is a creative writing project (dealing with Wile E. Coyote and the Road Runner) dealing with modeling falling bodies with quadratics and solving quadratic equations. An optional aspect is to have students estimate the instantaneous rate of change.

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.

A Bug's Life - Estimating Area of Irregular Polygons

This is a creative writing project that includes a rubric for scoring student's work. It works well as a team project. The focus of the project is on solving a contextual problems involving area of a two-dimensional object composed of triangles, quadrilaterals, and polygons.

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.

Powers of Ten - Number Sense

Students (and adults) have a difficult time trying to grasp very large (and very small) numbers. This activity uses an interesting context (astronomical objects0 to stimulate their interest in modeling enormous distances in a way that can help them understand relative distances. Students naturally arrive at the need for a different kind of number scale than linear and arrive at a "power of ten" (logarithmic) scale. The lesson includes an extension for advanced students ready to begin to investigate logarithms.

Proportional Relationships of Triangles - An Activity

This is a two-part activity and will most likely take two 50 - 55 minute class periods – one day per part. Part I (Day one) is a hands-on activity that allows students to work together on computers to discover the proportional relationship between a pair of similar right triangles. Ideally, you will have a class set of computers or a computer lab you could use for this lesson. If you don't have access to these resources you can run a demonstration on one computer and project it for the class and have students come up to manipulate the triangles.

Directed Distance - An Introduction to "Graph"

This annotated lesson can be used to introduce directed distance and the concept of graph. It can be used as the very first experience students have with graphs, as a review, and/or as an introduction to “circular” coordinates (you can choose to never refer to them as polar coordinates). It is highly interactive and connects the concepts of “new” graphing systems to rectangular coordinates. Initially, there is a brief history given and review of the Cartesian rectangular coordinate system.

Sugar Packets - Dan Meyer Three Act Task

The question is simple: How many sugar packets are in a soda bottle? The lesson hooks students immediately with the initial video clip of a man sitting in a restaurant downing packets of sugar one-after-another! The mathematics involved is proportional reasoning.

Number Systems - Place Value

Exploring different number bases may not only help you if you are needing in some particular application (like computers or electronics), but also in helping you make sense of the number system with which you are most familiar – the base 10 number system.

25 billion apps - Dan Meyer Three Act Task

The question is simple: When should you start bombarding the App Store with purchases if you want to win a $10,000 App Store Gift card? The lesson hooks students immediately with the initial video clip of a “live” counter of current downloads showing the number approaching 25,000,000,000. The mathematics deals with modeling a linear relationship between two quantities

Rule Time: Salute to Sports!

The purpose of this module is to help students learn important applied mathematical concepts regarding exponential and logistic functions. Students will also learn how to graph and interpret exponential (and logistic, if desired) functions. The unique element of this lesson is the use of video to generate interest in the students and motivate the content through interactive technology, humor, and cooperative learning. Students are encouraged to work together and help each other “make sense” of the activities. You will need these video clips: Part 1 - https://www.youtube.com/watch?v=xUavijWEwaQ Part 2 (after the problem situation is resolved) - https://www.youtube.com/watch?v=GfGj7Ik7Zao

Dimensional Analysis: Using the Idea of Identity Multiplication

Reflecting over my years of teaching, I have found that students are challenged by what would seem to be an easy question – “How do we convert from one unit of measure to another?” When confronted with this type of question, I have come to recognize that many students fall back on relying on a procedure that they try to recall.

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.

Number Sense: Getting a Feel for "BIG" numbers

Good number sense is fundamental for success in estimation, approximation, and problem solving. We need to develop a sense of large numbers because newspaper and television news reports contain many references to large quantities. This activity has students working with large numbers to understand their relative magnitudes.

Pythagorean Theorem Investigation: It's As Easy As… a, b, c

Oftentimes, the Pythagorean Theorem is taught from the standpoint of, "Here is the formula, let's practice finding the lengths of the sides of triangles!" without helping students understand or develop the relationships between the sides on their own. This activity helps students experience those relationships using multiple approaches, prove why the theorem is true, and practice using it. 

Proving the Pythagorean Theorem with Geogebra

The Pythagorean theorem is one of the most important concepts in all of mathematics. This activity uses Geogebra to help students see why the relationship between the sides of a right triangle are as they are. 

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. 

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. 

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?

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. 

Number Systems - Binary, Decimal, and Other systems

Students can struggle mightily with understanding place value as they begin to add and subtract numbers and "carry" and "borrrow". This short activity can be a great way to help students understand the concept of place value.

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. 

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.

Histograms vs. Bar Graphs

Using data from the Internet, students summarize information about party affiliation and ages at inauguration of Presidents of the United States in frequency tables and graphs.  This leads to a discussion about categorical data (party affiliations) vs. numerical data (inauguration ages) and histograms vs bar graphs. This activity is from NCTM Illuminations at http://illuminations.nctm.org/Lesson.aspx?id=2983

Creating a Collaborative Classroom Culture: Team Building Activities

A website with many team building activites to assist in building a collaborative classroom culture. Go to: https://getrealmath.wordpress.com/team-building-activities/ and download as many as you want! 

Creating a box plot on the TI 84 Calculator

Steps for entering data into lists and creating a box (box and whisker) plot. 

Creating a Histogram using the TI 83/84 calculator

The steps to creating a histogram on the TI calculator. 

Coin Counting - Dan Meyer Three Act-Task

Systems of equations can be a difficult concept for students to understand. This activity is a useful tool for introducing the concept in a concrete way that will help them make sense of the ideas and procedures for solving a system of linear equations.