## A Weekly Curriculum for 3rd-5th Graders

Click the buttons below to view each week's lesson overview and materials.

**If you're a student who is currently taking the Math Adventures course,** you'll have a lot more fun and get to discover many more mathematical phenomena firsthand if you wait until class time each week to work on the worksheet and look at the slides. We want you to get most out of the class as possible!

**If you're an educator,** feel free to use these guides to plan lessons for your students. For more information or answer keys, contact Joy Cheng.

Learn about polygons and polyhedra, and build the five Platonic solids out of toothpicks and marshmallows! Then, find patterns in the numbers of faces, vertices, and edges in various polyhedra to come up with Euler's formula. The first step to mathematical discovery is recognizing patterns!

### Each Student Needs:

- Pencil
- Worksheet
- Toothpicks (90 to make all Platonic solids)
- Marshmallows (50 to make all Platonic solids)
- Stale marshmallows work best, especially for the dodecahedron!
- Paper pyramids (optional and can be shared)
- 3-sided base
- 4-sided base
- 5-sided base
- 6-sided base

### Lecture Slides:

Dive into the famous real-world problem of the Seven Bridges of Königsberg and learn how Leonhard Euler used graph theory solve it! Discover the different components of a graph as well as Euler paths, Euler circuits, and chromatic numbers. Think back to Week 1 and find out how graphs relate to polyhedra!

### Each Student Needs:

- Pencil
- Worksheet
- Crayons/colored pencils

### Lecture Slides:

Discover some awesome topological properties of Möbius strips by doing various experiments with paper, scissors, and tape. The results may blow your mind! Fun fact: the Math Adventures logo is a Möbius strip.

### Each Student Needs:

- Pencil
- Worksheet
- Scissors
- Tape
- Eight long, rectangular paper strips (cut from two sheets of Letter- or Legal-size paper)
- Cut each sheet of paper into four equal-sized strips. The longer the strips the better! If you happen to have Legal-size paper at home, you can cut strips that are each 2⅛ x 14 in. Letter-size paper works great also; cut strips that are each 2⅛ x 11 in.
- One slightly wider strip on both sides of which you should draw the ⅓ and ⅔ lines

### Lecture Slides:

### Additional Enrichment Links:

Learn about the origins of the Fibonacci sequence and how it appears in nature! Then, explore the ratios of different shapes and patterns in nature to discover phi and the golden ratio. What is so special about the golden rectangle?

### Each Student Needs:

- Pencil
- Worksheet
- Ruler (cm)
- Four-function calculator

### Lecture Slides:

### Additional Enrichment Links:

Discover a world of number systems beyond base 10! Find out how other number systems are used in computers and how computers make sure that the data they receive has not been corrupted during transmission.

### Each Student Needs:

- Pencil
- Worksheet

### Lecture Slides:

### Additional Enrichment Links:

How do we tessellate shapes to tile or decorate floors, walls, ceilings, and windows? Find out which shapes can be used to make regular and semi-regular tessellations. Also, discover some patterns that can be folded up to create different polyhedra!

### Each Student Needs:

- Pencil
- Worksheet
- Polygon Cutouts
- Scissors

### Lecture Slides:

Explore the paradox of Hilbert's Hotel, and experiment with adding finite and infinite numbers of elements to infinite sets! Are all infinities the same size, or are some infinities larger than others? Follow the footsteps of Georg Cantor and compare the sizes of different infinities.

### Each Student Needs:

- Pencil
- Worksheet

### Lecture Slides:

### Additional Enrichment Links:

Create your own paper flexagons and learn about their topological properties! Did you know that some flexagons are topologically equivalent to Möbius strips?

### Each Student Needs:

- Pencil
- Worksheet
- Flexagon Templates
- Flexagon Folding Instructions (you won't need these if you're taking the Math Adventures course)
- Scissors
- Glue stick/double-sided tape