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.

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.

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.

System of Inequalities

Students create a system of inequalities given certain real-life conditions and then find solutions of their system that would fit their scenario.

Quadratic - Fence Problem

This is an activity designed to introduce a lot of concepts tied to quadratic functions. A piece of advice, make sure each group uses TWO pieces of pipe cleaners.

To Rent or Not to Rent....

An real world intro activity to solving systems of equations using a graph.

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.

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.

Preheating the Oven

Students use rate of change ideas to predict how long it will take for an oven to preheat to 400 degrees. The youtube video may be used to bring drama to the lesson! A link to the video is here and also in the documents. https://www.youtube.com/watch?v=I2ooIWFAcII&list=UUiPlxONW80Z8rGpu3lSLwjg

How Big or How Little?

This activity is designed to have students think about what it means to “keep it in proportion” – a very common phrase, but what does it mean?

Rule Time: Salute to Speed

You will need these video clips: Part 1 - https://www.youtube.com/watch?v=-XLkMx58Mb8 Part 2 (after the problem situation is resolved) - https://www.youtube.com/watch?v=BQ28I3TLcRI Outtakes if you want - https://www.youtube.com/watch?v=ObBiRjepgxA

Survivor - Mathematics!

Students will apply their understanding of linear and quadratic functions to solve a Survivor challenge!

Rule Time: Salute to Brakes

This project involves a movie that was written by, directed by, and starring Scott Adamson and Trey Cox. The focus of the project is making sense of the idea of quadratic functions from a rate of change perspective. First, watch Part 1 with your class. https://www.youtube.com/watch?v=b2huVGJXnH8 Then watch Part 2 after the problem has been resolved. https://www.youtube.com/watch?v=KStlLsmURcw

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.

Adding Integers

This is a series of lessons focused on: Making Zero (Sea of Zeros idea) Adding integers using chips and a checking account analogy It contains three activities and homework: Part 1 - Making Zero Part 2 - Adding integers with the Chip Model Part 3 - Adding inetgers with the Checking Account Analogy Homework To see a related video, go to: http://vimeo.com/71450580

Subtracting Integers

This is a series of lessons fouced on Making sense of integer subtraction using number lines, patterns, and the chip model It contains two activities and homework Part 1 - Number lines and Patterns Part 2 - Chip Model Homework To see a related video, go to: http://vimeo.com/71450580

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.

What does division mean and how do you do it?

This activity focuses on the idea of divsion and challenges students to make sense of what division means and helps students to make sense of the traditional algorithm of "long division."

Now THAT'S Some Gas Mileage!

This activity involves working with percentages and is connected with the ACCR Standards at the sixth and seventh grade levels.

Spreading Rumors!

Welcome to Rumor Middle School! News at Rumor Middle School travels quickly! Use the information presented in the problem to determine how many kids will know a rumor an hour and ten minutes after the first person shared it.  Then, find what time it will be when over 4,000 students know the rumor! Stick with it! Use multiple strategies, and be ready to share and defend your work!

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. 

A Motorcycle Transaction

Myles purchases two motorcycles without his mother's permission. She makes him sell them. You will determine if he made a profit or a loss in this buying and selling transaction. Concepts: percent to decimal conversion, finding the percent of a number, and calculating the percent of change.

Thinking About Exponents

The idea of negative exponents and zero as an exponent is a problem that persists with students into a college calculus class. What is, for example, 2-4 and why? This activity is designed to help students to make sense of exponents from a real-world context.  By the way, I plan to follow this up with an extension including rational exponents like 21/2.

Piggy Bank Ca$h!

Meredith has LOTS of one dollar bills in her piggy bank, and she discovers something special when she stacks the bills in piles of 5, 6, and 8 bills. Find a pattern to answer some questions about what will happen if she stacks the bills in piles of 9. 

A Coin Conundrum!

Figure out how many nickels and how many quarters Jamie has if you also know the total value of the coins. Then, take the problem to a whole new level by mixing in several dimes. Now THIS is a real coin conundrum!

An AREA Riddle

Knowing the perimeter of a certain rectangle, see if you can figure out what the area of the rectangle might be. Then, discover what happens to the area when the perimeter of the rectangle doubles...

Fantastic Fruit!

Algebra at its finest! The weights of several different fruits are being compared in this problem. Use the given information to state the weight of various fruits in terms of the other fruit...

Can We SWIM Yet?

The Johnson family is SO excited to go swimming in their new pool! Which of the three hoses should they use to fill it the most quickly? How long will it take to fill if they use all three of the hoses? 

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. 

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!

Mathematics and Advertising

This activity is from the 2011 CGCC Junior High Math Contest Team Project. You may pick and choose which parts of the project to use or use it all! Percent increase/decrease and Area of circles The Counting Principle Pythagorean Theorem and Ratios

Sunsplash

This is a series of activities from the 2007 CGCC Excellence in Math Junior High Contest Team Project.  You can pick and choose which parts of the project you want to use or do them all! Volume and converting of units Circumference and average speed Understanding average speed Readiing and interpreting line graphs Volume of a cylinder and rates

Solving Systems of Linear Equations

This is a lesson to introduce the idea of solving systems of equations using graphical methods and substitution.  The goal is to help students to make sense of the meaning of the solution to a system and to make sense of what it means to substitute.

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.