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.

Growth Factors

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

Problem Solving Template

Problem solving template used in my classroom. In PDF and Word formats. Created by members of Cohort 1 in Collaboration with Dr. Vicich.

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.

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.

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.

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.

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?

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

Rational Number Project - Initial Fraction Ideas

This is a series of lessons from the Rational Number Project (http://www.cehd.umn.edu/ci/rationalnumberproject/default.html) including teacher notes, activities ready to be copied. The Rational Number Project (RNP) is a cooperative research and development project funded by the National Science Foundation. Project personnel have been investigating children’s learning of fractions, ratios, decimals and proportionality since 1979. This book of fraction lessons is the product of several years of working with children in classrooms as we tried to understand how to organize instruction so students develop a deep, conceptual understanding of fractions. You may pick and choose the lessons that you would like to try and do not need to complete them all in order.

Fraction Operations and Initial Decimal Ideas

This is a series of lessons from the Rational Number Project (http://www.cehd.umn.edu/ci/rationalnumberproject/rnp2.html) including teacher notes, activities ready to be copied. The Rational Number Project (RNP) is a cooperative research and development project funded by the National Science Foundation. Project personnel have been investigating children’s learning of fractions, ratios, decimals and proportionality since 1979. This book of fraction lessons is the product of several years of working with children in classrooms as we tried to understand how to organize instruction so students develop a deep, conceptual understanding of fractions. You may pick and choose the lessons that you would like to try and do not need to complete them all in order.

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!

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. 

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...

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? 

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!

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

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.

Fractions and Free Throws

Do we always add fractions by first finding a common denominator, etc.? Or, could it make sense to add two fractions by adding the numerators and denominators? This activity explores these questions.

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.

What is my portion of the bill?

Earth Day Math

This powerpoint presentation for Earth Day Mathematics Lesson touches on many mathematical concepts such as volume, estimation, mean (average), measurement, and unit conversion. Students work in cooperative groups to find the approximate volume of rubber that a small business has 'rescued' from a local landfill. Alternate application ideas provided.

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). 

2015 Excellence in Mathematics Contest

This is the Team Project from the 2015 Junior High Excellence in Mathematics Contest at Chandler-Gilbert Community College. It involves lots of open ended problems from many mathematical areas: Find the weight of a snowman (geometry, proportional reasoning) Find how long it takes ice to form on a lake (rate of change, awkward units) Questions about the amount of mining done in Northern Minnesota (proportional reasoning, conversions) You can use just one part or all parts depending on the audience and the purpose.

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.

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.

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.

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. 

Shipping Routes - Dan Meyer Three Act Task

The questions are simple: As two ships leave port at the same time but at different speeds, we wonder if they will ever meet again? And if so, how long will that take? The lesson hooks students immediately with the initial video clip of two simulated ships leaving port and separating from one another as they travel at slower rates. 

How Many Houses?

Carpenters and apprentices are busy building houses... Students are asked to answer four questions regarding the relationships between the number of workers and how many houses can be built during a specific number of days.

Find the Fraction!

Students will certainly need to persevere while applying their prior knowledge about variables, expressions, and equations to solve the fraction problem posed in this activity!

How Many Chickens?

Farmer Frank raises chickens and pigs. Students are asked to use specific given information to determine how many of Farmer Frank's animals are chickens. This problem will require students to persevere as they apply prior knowledge of fractions, ratios, and percents to algebra concepts such as solving a system of equations.

Broomsticks - Multiplicative Reasoning

This is the broomsticks activity created by Ted Coe.

M & M Variablility

NEW and IMPROVED Division of Fractions

A NEW and IMROVED division of fractions activity designed to develop the...do I have to say it..."Keep Change Flip"...algorithm.  Includes student pages, teacher pages (with answers and description of the intended thinking) and a Smartpen pencast where I provide an overview/example of the intended thinking. Note that the pencast document comes in the form of a PDF - check out this for details as you need a PDF reader like Adobe Acrobat X in order to view the pencast. -http://www.livescribe.com/en-us/faq/online_help/Maps/Connect_Desktop/c_viewing-and-playing-a-pencast-pdf.html