Elementary School EnrichmentThese 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. |