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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The Golden Rectangle Lesson 1(Two Class Periods)
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.
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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
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
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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
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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? What are the Platonic Solids?
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. Build an icosahedron.
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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