Advanced Math

Area of Triangles Fun

Activator: What is the formula for the area of a square? a triangle? Show visually why they work.

Mini Lesson: Introduce Area of Triangles of 1 square units through nine square units, using standard geoboards.

Student Engagement: Complete Activity above

Wrap-up: Which were the most difficult to figure out?

Extensions: Simply Geometry (p 6 AGMATH) & 5 circles in a square: Find the radius of the smaller circle

Triangle in Circle (Harvard Group) Activity & County Concerns Activity

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Enigma

Activator: Do you know what the Enigma Machine was?

Mini Lesson: Watch Numberphile Enigma Discuss.

Student Engagement:

Read about the Navajo Code Talkers

Code Breaking Game

http://www.sheppardsoftware.com/braingames/codebreaking/codebreaking.htm

Wrap-up:

What strategies helped you solve the code?

Extensions:

Watch the followup video to the one above: it's about the flaw in the machine.

Research the Enigma Machine (http://www.telegraph.co.uk/sponsored/culture/the-imitation-game/11158548/The-evolution-of-the-Enigma-machine.html)

Fridays: Complete unfinished work, Puzzle of the Week, Future City, Purple Comet Math Work, Work on STEM website

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**(Two Class Periods)**

The Golden Rectangle Lesson 1

The Golden Rectangle Lesson 1

**Objective:**To look at beauty in mathematics and learn about some famous mathematical patterns.

**Activator:**Look at this sequence: 1,1,2,3,5,8.... Can you continue the pattern? Discuss the Fibonacci Sequence.

**Mini Lesson:**Watch Donald Duck in Mathemagic Land

**Student Engagement:**Draw a Golden Rectangle and a Golden Spiral

**Wrap-up:**What did you learn from this lesson?

**Fibonacci Numbers**

**Extension:**How the Fibonacci Sequence and the Golden Rectangle are related.__________________________________________________________________________________

The Golden Ratio Lesson 2

**Objective: To learn about the Golden Ratio**

**Activator: A closer look at the Golden Ratio**

**Mini Lesson: Introduce the art project**

**Student Engagement: Golden Ratio Art Project**

**extension:**

**Watch this video about the Parthenon from PBS**

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**The Handshake Problem**

**Objective:**To analyze patterns in math and to try to create formulas to describe patterns.

**Activator:**Building with Toothpicks problem

**Mini Lesson:**

Introduce Handshake Problem: If there are 10 people in a room, and every person shakes everybody's hand once, how many handshakes are there? What if there are

*n*people in the room?

**Student Engagement:**

Students spend some time working alone on the problem.

Students spend some time working together on the problem.

**Wrap-up:**

Discuss Answer

**Extension**

Find a quick way to add up all the numbers between 1 and 100

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Pythagoras

Pythagoras

**Objective:**To learn about Pythagoras, The Pythagoreans and the Pythagorean Theorem

**Activator:**Draw three or more nets for a cube.

**Mini Lesson:**

- Introduce the Pythagorean Theorem
- Share Common Pythagorean Triplets and Similar Triangles
- Visual proof of the Pythagorean Theorem (using plastic squares)
- Another proof and history
- A few practice problems: 1.) a=2, b=5, c=?, 2.) a=1, b=1, c=?, 3.) a=12, b=9, c=?, 4.) a=4, b=?, c= 10

**Student Engagement:**The Spider and Fly Problem

**Wrap-up:**Discuss the problem

Astronomy and Large Numbers

**________________________________________________________________________________________**Astronomy and Large Numbers

**Objective:**Students will be able to multiply very large numbers. Students will be able to use ratios to solve problems.

**Activator:**What is Astronomy? Why is the mathematics of circles important in the study of astronomy?

**Mini Lesson:**As a class, read through Chapter 1 of Ed Zacarro's Challenge Math: Astronomy and Large Numbers.

**Student Engagement:**Complete problems #1-4 on page 12

**Wrap-up:**Write down one thing that you learned about very big numbers and astronomy on your wrap-up sheet.

**Extensions:**Astronomy Level 1, 2 and 3 problems

The Origin of Pi

**_______________________________________________________________________________________________**The Origin of Pi

**Objectives:**Students will be able to explain the origin of Pi. Students will understand that Pi is the ratio of the Circumference of a circle divided by its diameter.

**Activator:**List some things you think of when you hear the word circle.

**Mini Lesson:**How to measure the circumference of a circle. Introduce Vocab: Circumference, diameter, origin,

**Student Engagement:**Hands-on activity with circles.

**Wrap-up:**How to calculate Pi, with pies! How did your accuracy compare with the video?

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Platonic Solids Lesson 3 (and some other fun stuff!)

Activator: How many platonic solids are there? Why?

Mini Lesson: Origami Puzzle Intro. Quick Discussion of Platonic Solids

Student Engagement: Work on Platonic Solids Sheet. Try origami puzzles when done.

Wrap-up: Some math questions

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Objective: To gain a deep understanding of polygons, polyhedrons and the platonic solids.

Platonic Solids Lesson 2

Activator: Platonic Solid Rock

Mini Lesson: Fill in the Platonic Solid Chart. Learn how to find the Interior Angles of a Regular Polygon.

Student Engagement: Complete Platonic Solids Work individually

Wrap-up: Collect work!

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Objective: To gain a deep understanding of polygons, polyhedrons and the platonic solids.

Platonic Solid Lesson 1

**Activator:**What is a polygon? What is a polyhedron?

**Mini Lesson:**Watch Numberphile: Platonic Solids

Discuss Platonic Solids (Face, Edge, Vertex)

**Student Engagement:**Look at the Platonic Solids. Fill in chart. Look for patterns.

**Wrap-up:**Discuss Pattern

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Friday Catch Up

Activator: What do you have to complete?

Mini Lesson: Solution to Problem of the Week

Student Engagement: 1st: Complete incomplete work from the week

Then: Work on Future City, My website, Purple Comet Math Problems

Wrap-up: Turn in weekly work.

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