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    Elementary School Enrichment
    These lessons provide topical enrichment in a wide range of mathematics.  The goal is to help young students
    see the breadth and diversity of mathematical thought.  They are aimed at 4th and 5th grade accelerated
    students.  They were originally created for use in Colorado Springs School District 11 with the support of the
    Department of Mathematical Sciences at the United States Air Force Academy.  There are 70 lessons grouped
    into 12 different units, none of which require any specialized background for student or teacher.  The design is for
    each lesson to take 15-25 minutes of student time and be appropriate for independent work (such as during
    center time in a classroom).  These lessons are appropriate for homeschool and classroom use.  Solutions and
    teacher guides are provided.  They are provided here for you to use and/or modify.  If you use the lessons,
    please email me to let me know!



    Ancient Mathematics (8 lessons)
    (Egyptian pdf files: students  teachers  answers  worksheet   worksheet answers)
    (Egyptian MS Word files: students  teachers  answers   worksheet   worksheet answers )
    (Maya pdf files: students  teachers  answers )( MS Word files: students  teachers  answers )
    Learn about Egyptian mathematics (base 10 but without a symbol for 0) and Maya mathematics (base 20).  
    Students will use these number systems to perform basic addition and subtraction and to reconsider what carrying
    and regrouping mean in our number system.  There are 4 lessons each on Egyptian and Maya mathematics, and
    students could work through one of the number systems without doing the other.

    Baseball Statistics (4 lessons)  (pdf files: students  teachers  answers )
    (MS Word files: students  teachers  answers )
    Practice multiplication and division to figure out batter stats (batting average and slugging percentage) and
    pitcher stats (earned run average and WHIP).
    Additional materials needed:  Calculator (optional)

    Fibonacci Numbers (10 lessons)
    (pdf files: students  master  teachers  answers ) (MS Word files: students  master  teachers  answers )
    (4 Lesson Worksheet version  pdf files: students  master  answers ) (MS Word files: students  master  answers )
    These lessons emphasize finding and creating patterns of numbers. Included is discussion of the golden ratio and
    of tilings of an n x 1 rectangle as they relate to Fibonacci numbers.
    Additional materials needed:  Graph paper, boxes and cans from home, calculator (optional)

    Games of Skill (9 lessons)
    (pdf files: students  teachers  answers ) (MS Word files: students  teachers  answers )
    (Towers of Hanoi  pdf files: instructions  base ) (MS Word files: instructions  base )
    In these lessons, students will work in pairs to play several games of skills.  Some are numerical and some are
    geometric.  Students will analyze winning and losing positions of the games.

    Graphs and Networks (7 lessons)
    (pdf files: students  teachers  answers )(MS Word files: students  teachers  answers )
    Graphs and networks are the basis for the solution of many real-life problems.  In these lessons, students learn
    the basics of graphs, including the Bridges of Koenigsburg and traveling salesman problems.

    Iteration (6 lessons) (pdf files: students  teachers  answers )(MS Word files: students  teachers  answers )
    In these lessons, students will explore patterns where the answer to one step is the starting point for the next
    step.  They start with a simple integer pattern, then explore the famous Sierpinski triangle and Koch snowflake,
    and finally develop their own patterns.
    Additional materials needed:  Triangle graph (light, dark), scissors, tape

    Mobius Bands (4 lessons)
    (pdf files: students  teachers  answers ) (MS Word files: students  teachers  answers )
    (Worksheet version  pdf files: students  answers ) (MS Word files: students  answers )
    This lesson is a very hands-on lesson that will challenge students’ notions of what it means for an object to have 2
    sides.  Students will create and cut Mobius bands and predict what will happen for other related objects.
    Additional materials needed:  Scissors, tape, and paper (adding machine tape is really good but optional)

    Pick’s Theorem (4 lessons) (pdf files: students  teachers  answers )(MS Word files: students  teachers  answers )
    This is a unit where students discover a result about the area of lattice polygons.  As a college educator, I did not
    know the result of Pick’s theorem and find it interesting and surprising.
    Additional materials needed:  Geoboard or a geoboard applet (such as this one or this one)

    Polygonal numbers (6 lessons) (pdf files: students  teachers  answers )(MS Word files: students  teachers  
    answers )
    Students will examine number patterns that arise from polygonal numbers.  The emphasis is on exploring patterns
    and making predictions about triangular and square numbers.

    Statistics in the library (6 lessons)
    (pdf files: students  teachers  answers )(MS Word files: students  teachers  answers )
    In this lesson, students learn one way to get a random sample of books in a school library.  They then use the
    sample to make estimates about the number of books in the library, the percentage of books that are nonfiction,
    and the percentage of books that have one-word titles.
    Additional materials needed:  A 6-sided die and access to a school library.  (A public library is probably too big for
    the plan in this unit, but the children’s section of a public library may work.)

    Tangram puzzles (4 lessons)
    (pdf files: students  teachers  master  worksheet  answers )
    (MS Word files: students  teachers  master  worksheet  answers )
    Students use the classic tangram puzzle to create shapes.  They also find the area of the tangram pieces.
    Additional materials needed:  Tangram puzzle pieces or the accompanying classroom master.