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.

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

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.

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!

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.

A Pool Design Pattern

A pool desinger has lost his plans for some large, rectangular pools. He needs your help to sketch the next two pools in the pattern, and to develop a rule to determine how many tiles he'll need to create a visual model of the designs.

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

AN algorithm for subtraction

A 2nd grade student shared an algorithm for subtraction that was learned at home. This provides a great opportunity to make sense of mathematics! With a focus on place value, the algorithm can be made sense of by our students.  The PDF Pencast simply explains the algorithm...share it in class and use it as a context to make sense of math, develop number sense, focus on place value. NOTE: Adobe Reader DC (or equivalent) is needed to view the "video" aspect of this pencast PDF.

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...

Area of a house

Goal: The goal of this activity is for students to find the area of a house floor plan. They will need to use their knowledge of rectangles to identify the missing side lengths to find the correct area. This also allows students to see how area is used in a real-life application.

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.

Biking to Bernie's

Broomsticks - Multiplicative Reasoning

This is the broomsticks activity created by Ted Coe.

Cal Clulus: In Pursuit of Justice!

This project involves a movie that was written by, directed by, and starring Dr. Scott Adamson and Dr. Trey Cox. The focus of the project is making sense out of average rate of change, instantaneous rate of change, and the Mean Value Theorem. Watch this clip first with your class before doing the activity: https://www.youtube.com/watch?v=DBRwU9ubYQo After doing the activity, view the 2nd part of the video at: https://www.youtube.com/watch?v=pqy3VivFs9Y

California Adventures- Central Tendency and Variation

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? 

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.

Cat food and Recycling

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.

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. 

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. 

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.

Covariation and the Finger Tool

The intended sequence is: Sprinter Skateboarder Bungee Jumper Jump start the car

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 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 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.

Creating a Histogram using the TI 83/84 calculator

The steps to creating a histogram on the TI calculator. 

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.

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.

Definite Integral using Substitution

Derivative of Trigonometric Functions

This is a project designed for a Calculus 1 course.

Developing and Solving Equations Unit

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.

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.

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.

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.

Equations and Expressions Module

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. 

Explorations with Unit Rates, Slope, Equations of a Line and an Intro to Systems of Equations

Handouts to walk students through exploring unit rates, slope, equation of a line, x and y intercepts and an intro to systems of equations.

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.

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...

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!

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.

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.

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.

Geometric Sequences

This lesson utilizes the softward Smart Notebook to introduce students to geometric sequences and related vocabulary, as well as how to find the nth term of a geometric sequence. Several practice problems are included.

Growth Factors

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

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.

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

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?