Discrete Mathematics Teacher Resources

Find Discrete Mathematics lesson plans and worksheets
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Coloring Discrete Structures

For Teachers 6th - 9th
What's the least number of colors needed to color a U.S. map? The lesson begins by having pupils view a video clip on continuous and discrete phenomenon, then launches into an activity reminiscent of Zeno's paradox. A separate video and...
4:38
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How the Königsberg Bridge Problem Changed Mathematics

For Students 9th - Higher Ed
There is one bridge too many. A video presents the history of the Konigsberg Bridge problem. To solve the problem, Euler invented a new branch of mathematics—and graph theory was born. Using this new branch of mathematics, mathematicians...
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Choose Your Best Way

For Teachers 6th - 12th Standards
Classic graph theory problems of the traveling salesman and bridges of Konigsburg get the school treatment in this multi-age, multi-level activity. Learners distill a local map down to a few key locations, and then detail characteristics...
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NUMB3RS Activity: The Konigsberg Bridge Problem

For Teachers 9th - 12th
Students explore the concept of graph theory. In this graph theory lesson, students discuss a problem on a NUMB3RS episode about the 7 bridges of Konigsberg. Students discuss and apply Euler's two theorems on graph theory about odd...
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Lesson 10: Graphs

For Teachers 10th - 11th
Students explore graph theory.  In this geometry instructional activity,  graphs are used to solve problems in a variety of domains.  In this instructional activity the term graph refers to a collection of vertices and edges used to...
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Networks

For Students 6th - 8th Standards
Ever wonder how the Internet works? The lesson teaches scholars the basics of graph theory and how it applies to the Internet. They perform simulations to see how information is sent on the Internet.
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Graph Creator

For Students 6th - 12th
Discover the right path to learn about graph theory. Scholars use an interactive to create graphs by placing vertices and edges. They determine if their graphs have Euler or Hamiltonian paths.
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Traveling Networks

For Teachers 4th - 8th
Show your class the path to understanding graph theory. Scholars learn about basic graph theory using an activity based on the Bridges of Konigberg problem. They draw networks on the playground and decide whether it is possible to travel...
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Choose Your Best Way

For Teachers 6th - 12th
Find the best path through town. The lesson teaches future computer programmers about networks and paths in graph theory. They develop a network of their towns to determine the most efficient path to visit each of their homes.
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Connect the Dots

For Teachers 9th - 12th
Have you ever wondered how delivery companies figure out the shortest route for delivering packages? This lesson is an exploration of Euler Circuits by studying his work with the Konigsberg Bridge and five-room house problem. It contains...
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Application of Graph Theory

For Teachers 9th - 11th
Students investigate different online tutorials as they study graphing. In this graphing instructional activity, students apply the concept of graphs cross curricular and use it to make predictions. They define the purpose and theories...
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Eulerian Paths and Circuits

For Teachers 9th - Higher Ed
Young scholars explore the concept of euler paths and circuits. In this euler paths and circuits instructional activity, students discuss the bridges of Königsberg problem. Young scholars discuss how to determine if an euler circuit...
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Ants and Graphs

For Teachers 8th
Eighth graders investigate ant interactions in terms of graph theory.  In this ant interactions in terms of graph theory lesson, 8th graders tally the number of times 8 ants interact in a petri dish.  Students make a graph of the ants...
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Paths and Circuits

For Teachers K - 8th
Students complete math puzzles. In this graph theory lesson, students look at an image and attempt to trace it without picking up their pencil or retracing their line. They see to count the nodes to find where to begin tracing. 
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Complex Networks and Graphs

For Students 7th - 10th Standards
Show your class how engineers use graphs to understand large and complex systems. The resource provides the beginnings of graph theory by introducing the class to set theory, graphs, and degree distributions of a graph. 
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More Games on Graphs

For Teachers 8th - 11th
Learners investigate various games employing graphs as game boards.  In this game theory lesson, students problem solve through the use of graphs.  The lesson is a list of both indoor and outdoor games to encourage learners to think...
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Math Applications

For Students Higher Ed
In this math applications worksheet, students solve one word problem that has two parts to it. First, they determine the expected value of a ticket for a prize. Then, student determine the fair price for the ticket purchased and explain...
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Graph Theory

For Teachers 10th - Higher Ed
Students explore the concept of graph theory. In this graph theory lesson, students participate in hands-on activities that enforce graph theory. Students manipulate graph applets on the internet. Students create a graphical model of...
4:18
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Can You Solve the River Crossing Riddle?

For Students 6th - 8th
Getting three wildebeest across a river should be no problem— but what happens when you add three lions to the mix? Watch a video that features a classic river-crossing puzzle with a crocodile twist. Viewers listen as the narrator...
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Data Analysis, Probability, and Discrete Mathematics

For Teachers 4th
Fourth graders analyze the data in a bar graph, pictograph, line graph, and a chart/table and draw conclusions based on the data. They discuss each type of graph, write questions for each graph, and analyze the data as a class.
11:05
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The Map of Mathematics

For Students 9th - Higher Ed
How does all this math fit together? The resource creates a graphical view of the extent of mathematics. The map shows the pure and applied sides of studying mathematics and breaks them down into their many disciplines.
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A Tour of Jaffa

For Teachers 8th - 10th Standards
Use the age-old Traveling Salesman Problem to introduce Hamilton circuits to your young travelers. Individuals then plan an efficient route to visit all the places they want to go.
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Red Dots, Blue Dots

For Students 11th - 12th
Count the connections between dots. Young mathematicians come up with a method to determine the number of connections between pairs of dots. The assessment leads the class to determine the connections they can make when groups are...
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Leadership Program in Discrete Mathematics

For Teachers 6th - 8th
Middle schoolers, using Pascal's triangle, find the number of items given each day in the song, "The 12 Days of Christmas."
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The Poor Cartographer—Graph Coloring

For Teachers 2nd - 12th
Color the town red. Demonstrate the concept of graph theory with a task that involves determining the least number of colors needed to color a map so that neighboring countries are not represented by the same color. Pupils make...
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The Incredible Yuma Bat and Clapper Rail - Discrete Mathematics -- Systematic Listing and Counting

For Teachers 6th
Sixth graders are introduced to the wonderful world of Bats and Clapper Rails. They comprehend and demonstrate the systematic listing and counting of possible outcomes. Students systematically list and count each bat and clapper rail...
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Data Analysis, Probability, and Discrete Mathematics: Lesson 4

For Teachers 8th
Eighth graders investigate the concepts of probability while performing data analysis. They apply statistical methods in order to measure or predict some possible outcomes. The information is collected and graphed, 8th graders analyze...
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Matrices and Graphs (Graph Theory)

For Teachers 9th - 10th
Students use Internet links that are either accessed directly or in a TrackStar. They answer questions in the TrackStar about finite graphing, digraphs, and matrices.
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NUMB3RS Activity: Driving with Dijkstra

For Teachers 9th - 12th
Students investigate graph theory.  In this secondary mathematics lesson, students explore Dijkstra’s algorithm which is used to analyze optimal outcomes.  Students examine a graph to determine the vertex that will result in the shortest...
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Leadership Program in Discrete Mathematics

For Teachers 3rd - 4th
Learners find the total cost of the items in the song, "The 12 Days of Christmas."
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One-way Functions – The WiFi Hotspot Problem

For Teachers 9th - 12th
Pupils attempt to solve the Wireless Hotspot Problem and learn why it is considered a computationally hard problem in the ninth lesson of the series on 12. They also learn about one-way functions and how the Wireless Hotspot Problem is...
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Hard Problems – Traveling Salesperson Problem

For Teachers 9th - 12th
Even computers find this to be a hard problem. In the eighth installment of a 12-part unit, young computer scientists learn about the traveling salesperson problem. They formulate algorithms to solve the problem and find out why it is...
11:47
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Proving Pick's Theorem

For Students 10th - Higher Ed
Pick up a resource on Pick's Theorem. Individuals watch a video explaining how to find the area of a polygon drawn on a lattice using Pick's Theorem. The film also shows a proof of the theorem using the Euler characteristic and algebra.
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Combinations and Permutations

For Teachers 9th
Ninth graders explore combinations and permutations. In this discrete mathematics instructional activity, 9th graders examine hypothetical situations to gain an understanding of the difference between a combination and a permutation. ...
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Pre-K Mathematics

For Teachers Pre-K - 1st Standards
Kick-start children's education with this pre-school math unit. Offering 31 different hands-on learning activities that develop young mathematicians' pattern and shape recognition, basic number sense, and much more, this is a must-have...
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The Landfill Loafers Meet the Wise Buys

For Teachers 2nd - 5th
Students discover recyclable materials and the proper disposal of those items through Internet research. Working in groups of four, they search the Internet for uses of recyclable materials. After research is complete, they participate...
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Math in Fashion

For Teachers 6th - 10th Standards
How do fashion and math relate? Using interactive websites and video clips, learners apply proportional reasoning to the fashion industry. They look for patterns and linear relationships, apply unit rate concepts to garment materials...
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Tax Examination

For Students 11th - Higher Ed Standards
What are your chances of being audited by the IRS? An engaging problem scenario asks pupils to examine the likelihood of being audited compared to factors such as receiving a refund or claiming a home office. The final product of the...
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Boogie Boards

For Students 10th - Higher Ed Standards
Solve a complex business puzzle by building a linear programming model. An engaging project-based learning problem has classes examining transportation costs and manufacturing limitations from several plants. Ultimately, they use their...
1 In 1 Collection
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Mathematical Treasure Hunt

For Teachers 3rd - 8th Standards
The hunt is on! Young mathematicians follow clues and complete a series of ten math puzzles as they try to crack Dr. Integer's code and find the location of his hidden treasure.
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Graphs and Data

For Teachers 7th - 10th
Students investigate poverty using graphs. In this algebra lesson, students collect data on the effects of poverty and use different rules to analyze the data. They graph and use the trapezoid rule to interpret the data.
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An Introduction to Arithmetic and Geometric Sequences

For Teachers 4th - 8th Standards
Help your class look for patterns as they create their own arithmetic and geometric sequences. Engage learners with an introductory discussion on sequences and use the applet to let them explore how sequences are formed. Teachers might...
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Grid Frame Mapping

For Teachers 3rd - 8th
Learners map and describe a small area of the schoolyard.
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Four Color Map

For Teachers 3rd - 7th
Students explore geometry by completing a color puzzle. In this shape identification lesson plan, students utilize deductive reasoning to complete a Google SketchUp puzzle with trapezoid, triangles and rectangular shapes. Students...
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Where Is The Juice?

For Teachers 9th - 12th
Students are introduced to the component's of Ohm's Law. In groups, they practice their problem solving skills by reviewing problems solved earlier. They participate in activities that help them gather information on the importance of...
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Iterating the Function and Complex Numbers

For Teachers 7th - 10th
Students identify the end behavior of polynomial graphs. In this algebra lesson, students factor and solve quadratic and complex equations. They factor out negative roots and identify the real and imaginary parts of an equation.
4:51
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Can You Solve the Prisoner Boxes Riddle?

For Students 7th - 12th
Viewers must save the day for their favorite band by helping them find their instruments or the long-anticipated concert will be canceled. The show must go on, so get busy solving this riddle.
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An Introduction to Sequences

For Teachers 4th
Fourth graders are introduced to arithmetic and geometric sequences. In this mathematics activity, 4th graders produce a variety of sequences by varying the starting number, multiplier, and the add-on number.
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Get the Picture!

For Teachers 9th - 12th
Astronomers practice downloading data from a high-energy satellite and translate the data into colored or shaded pixels. As a hands-on activity, they use pennies to simulate high-energy satellite data and they convert their penny...
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Math in Video Games

For Teachers 7th - 10th
Relate math to video games by investigating the making of video games and where in the game math is used to make the game work. Learners will work on communication and problem solving strategies in this engaging lesson.
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Math in Music

For Teachers 7th - 10th
How does music relate to math? Learners will discover review pattern, relationships, equivalence, rates and proportions as it relates to music. This is a very rigours and relevant activity. Many extension ideas are given as well.
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Algorithms Detour - Minimum Spanning Tree

For Teachers 9th - 12th
This optional lesson introduces the class to the idea of a minimum spanning tree. The activity focuses on determining an algorithm that will find the most efficient path in a network to transfer data. 
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Iterating Linear Functions

For Teachers 7th - 9th
Young scholars use a spreadsheet to investigate data. For this algebra lesson, students collect and graph data on a coordinate plane. They explain properties of a linear equation both algebraically and orally.
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Wiggling With Math

For Teachers 6th - 8th
Students identify and graph averages. Groups of students observe the length of time it takes for a lizard to re-grow its tail. After collecting the data over a 12-month period, students find the median, mode and range of the data. ...
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Paint My Counties: Map Coloring the Counties of Arizona

For Teachers 4th
Fourth graders identify the counties of Arizona. For this social studies lesson, 4th graders color a county map of Arizona using the fewest number of colors possible. Students write a persuasive paragraph.
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The Capacity of Planets

For Teachers 10th
Tenth graders change numbers written in standard form to scientific notation. In this scientific notation lesson, 10th graders use given diameters and distances from the sun for each planet in our solar system. After rewriting each of...
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Ocean Temperature

For Teachers 1st - 3rd
Students investigate the effects of salt and the sun on the ocean water temperatures. In small groups they make predictions, then take the temperature of water that are fresh, salty, shady, and sunny, and combinations of the four. ...
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Tic-Tac-Toe

For Teachers 10th - 11th
Students investigate finite mathematics using a flow chart. In this algebra lesson, students investigate logic and strategies using flowcharts. Students compete against each other using different approaches to playing the game.
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Planarity and Bagels

For Teachers 8th
Eighth graders investigate planar and non-planar graphs. For this algebra lesson, 8th graders discuss conjectures as they apply to both rules of solving equations graphed in a coordinate plane. They discuss ideas, agree and disagree, and...
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Coloring Interval Graphs

For Teachers 7th - 9th
Students investigate planning an activity and getting it done on time. In this algebra instructional activity, students define vocabulary words related quadratic equations, including the vertex and intervals. They figure a good way to...
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Analyzing Birds and Planes

For Teachers 8th - 11th
Learners find a variety of topics and subjects in this lesson. In the math section of this lesson, students graph linear equations and analyze their data. They solve one and two step equations to find the variable.
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Know the System

For Teachers 8th - 11th
Students identify the different systems of equations. In this algebra instructional activity, students solve systems of equations using graphing, elimination and substitution. They use the Ti to graph their systems.
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Opportunity Cost

For Teachers 5th
Fifth graders build upon knowledge and skills that allow them to understand the concept of opportunity cost.  In this mathematical economics lesson, 5th graders define opportunity cost, and analyze situation where economical choices must...
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Investing

For Teachers 8th - 10th
Pupils collect data on investments and draw conclusions. In this algebra lesson, students analyze exponential graphs as they relate to money. They discuss the cause of an account balance being high or low.
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Shell Sort; Serving up Seafood

For Teachers 2nd - 3rd
Pupils complete various small group activities to classify items and determine the types of combinations that can be made with these items. In the second lesson, students create menus for a restaurant to help them gain money sense and...
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Sorting

For Teachers K
Students sort a variety of manipulatives and use a software program that provides more sorting practice.
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Party Of Six

For Teachers 8th - 12th
Learners engage in a lesson that is about the concept of finding the solution to a problem by using inductive reasoning from statistics and then branching into the skills of patterning. They read and solve a word problem while taking...
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Exploring Pascal's Triangle and Other Recursive Patterns

For Teachers 3rd - 5th
Learners explore patterns in everyday life and in the mathematic world. They create various concrete examples of patterns and verbally describe these patterns to a fellow student.
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Pascal's Triangle

For Teachers 6th - 8th
In this math worksheet, middle schoolers read the discussion about the importance of games. They create a game as directed. They also read the rules for the Pascal Triangle.
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Chaos

For Teachers 9th - 12th
Students explore the concept of probability. In this probability lesson, students use a applet that demonstrates chaos and probability of spread for a forest fire. Students also play applets about the Game of Life and Rabbits and Wolves,...
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Moving Straight Ahead

For Teachers 6th - 9th
Students analyze the relationship between speed, time and distance. In this math lesson, students plan a school trip. Students determine the efficiency and cost effectiveness of a trip.
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Friendship Quilt

For Teachers 3rd
Third graders name different kinds of shapes and then discuss what they know about them an what they would like to learn using a K-W-L chart whole group. They listen to the book, THE GREEDY TRIANGLE and then retell it to the class. They...
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An Introduction to the Natural Logarithm (ln)

For Teachers 10th - 12th
Students explore the dose response principle, an introduction to what the "natural log" (ln) is and how it behaves. They create and analyze a dose response graph.
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Is Organic Food Worth the Extra Cost?

For Teachers 9th - 12th
Students calculate the amount of pesticide residue in selected foods for two pesticides and determine if these levels are safe. They read an article about a research study looking for metabolites of these pesticides in children. Finally,...
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More of Carrie's Cubes

For Teachers 7th - 9th
Students solve a word problem that explores the shape of a cube and ways that part of it can be colored. They discuss the problem and analyze a Rubik's cube, explore the problem using a graph, and discuss the solutions as a class.
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Conic Sections and Locii

For Teachers 9th - 11th
Learners differentiate between ellipse and hyperbola. In this algebra lesson, students graph and solve elliptical equations. They use the cabri program to create the different conics and move them around.
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Architecture And Math

For Teachers 7th - 8th
Young scholars investigate the ties that architecture and math have in common. They focus on works of architecture in the world that is considered of great significance. Students use the internet to find building images from around the...
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Enumeration

For Teachers 8th - 11th
In this calculus lesson, students review counting using the principles of Enumeration. They use random selections to count and convert word problems and count. There are 21 problems with an answer key.
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Compound Locus

For Teachers 7th - 10th
Students investigate circles and compound locus. In this geometry instructional activity, students identify the distance from a point to a line. They use Cabri software to create lines and circles.
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Graphing With RXTE

For Teachers 9th - 12th
Learners use data from the Rossi X-ray Tiiming Explorer (RXTE) satellite to analyze and graph.
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Episode Hot Shot

For Teachers 9th - 12th
Pupils engage in a study of using geometry to solve a word problem about statistical analysis. They collect information and make inferences about when encounters were made with victims to a crime. Then key vocabulary is defined and the...
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Thanksgiving Pie Graph

For Teachers 5th
Fifth graders apply previously studied concepts in collecting, organizing and interpreting data, and show data results using a pie graph as the tool for interpreting and reaching a conclusion.

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Discrete Mathematics