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May 20th

May 20th

Discrete Mathematics

Overview:
Our lessons are designed in such a way that you can pick one lesson that fits in
with your curriculum. These lessons also work well when you can not avoid a
substitute teacher in your room. The lessons are self guided and will al low for
classroom
discussion at a later time.

The lessons are designed to have students investigate Graph Theory , Counting
Principles, Venn Diagrams, Least Common and Greatest Common Multiples ,
Greedy and Nearest Neighbor Graphs.

We hope you enjoy the selections we put together and they enhance your classes.

Lessons:
1. Greatest Common Factor and Least Common Multiples
2. Number Puzzle
3. Take a Picture
4. Counting Methods
5. Gold Lotto
6. The Colorful Houses of Tourist Town
7. Ice Cream Stands
8. Ice Cream Algorithms
9. More Ice Cream

GCF & LCM

Goals
• Find a pattern to use using a Venn diagram to find the GCF and
LCM

Materials
•handout “GCF & LCM Recording Sheet”
Standards:

 7 IV. DATA ANALYSIS, STATISTICS AND PROBABILITY A. Data and Statistics Re present data and use various measures associated with data to draw conclusions and identify trends. 7 IV. DATA ANALYSIS, STATISTICS AND PROBABILITY B. Probability Calculate and express probabilities numerically and apply probability concepts to solve real-world and mathematical problems . 7 I. MATHEMATICAL REASONING Apply skills of mathematical representation, communication and reasoning throughout the remaining four content strands.

Activity
Distribute copies of handout and have students complete the following tasks presented
on it:
1. Group students together in pairs.
2. Have students connect to website:
3. From website, students click on Factor Tree.
4. Have students solve 10 different problems and record their results on their handout.
5. Student record a pattern or rule they can use to find the GCF & LCM from a Venn
diagram.

Write a rule to find the GCF & LCM using a Venn Diagram:

Number Puzzle

Goal
To assess students-
•Ability to solve problems.
• To find patterns to help solve problems

Materials
Computers
Handout
Standards:

 7 I. MATHEMATICAL REASONING Apply skills of mathematical representation, communication and reasoning throughout the remaining four content strands. 7 II. NUMBER SENSE, COMPUTATION AND OPERATIONS A. Number Sense Use positive and negative rational numbers, represented in a variety of ways, to quantify information and to solve real-world and mathematical problems. 7 IV. DATA ANALYSIS, STATISTICS AND PROBABILITY A. DATA AND STATISTICS REPRESENT DATA AND USE VARIOUS MEASURES ASSOCIATED WITH DATA TO DRAW CONCLUSIONS AND IDENTIFY TRENDS.

Activity
The students should work with a partner. They are to go to the website and do the
following;
1. Get with a partner
2. Pass out handout
3. Go to website
Click on “Number Puzzle”
4. Play the game and record each game.
5. Develop and write out their strategy they can use to help them win each game.
6. Test their strategy and record results

Number Puzzle Data Sheet Take a Picture

Goal
To assess students-
•Ability to make and use tables and/or graphs
• To learn and understand counting methods
Standards:

 7 IV. DATA ANALYSIS, STATISTICS AND PROBABILITY A. Data and Statistics Represent data and use various measures associated with data to draw conclusions and identify trends. 7 IV. DATA ANALYSIS, STATISTICS AND PROBABILITY B. PROBABILITY CALCULATE AND EXPRESS PROBABILITIES NUMERICALLY AND APPLY PROBABILITY CONCEPTS TO SOLVE REAL-WORLD AND MATHEMATICAL PROBLEMS.

Materials
Paper
Color pencils (optional)

Activity
The students should work with a partner. They are to as sume that they are at a party
with 9 other friends (total of 10 including themselves) and they want to get a picture of
themselves and one other person but they want a picture of two with everyone . Each student
1. Make a graph to represent how many pictures need to be taken.
2. Decide how many pictures total are taken, not including duplicates.
3. Repeat steps 1 and 2, but for 3, 4, 5 and 6 people in each picture.
4. Record there results in some organized method so they can present it to the entire
class.
5. Write a rule or method they would use to determine total possibilities if there
were nth number of people at the party.
6. Share results with entire class.

Extension
Have students determine how many possibilities for seating charts in their classroom ,
since some are never satisfied with the seating chart the teacher makes for the class. This
could lead into classroom management and behavior for your
class.

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