Lesson #2 - Augsburg College

More documents

Recommendations

Info

Geometry: A Shapely Approach to Math From this diagram, we know that the area of the large, tilted square is c 2 . Next we will move around two of the four triangles in this illustration to prove our theorem. It may be helpful for your students to cut out the two triangles with arrows in them and the small square in the center because the next step is to shift each of these triangles down to their new locations, outlined with dotted lines. Now if we look at this same figure, we can see that the area of the red square is a^2 and the area of the blue square is b^2. We already know that the area of the largest square with side length c is c^2. And the red square and blue square include exactly all four triangles from the original illustration, and the small square in the center, which is exactly what the large square of area c^2 includes: four triangles and the small square. Therefore their areas are equal, so we see that c 2 = a 2 + b 2 , and we have proven the Pythagorean Theorem! 42
Geometry: A Shapely Approach to Math To conclude the lesson, ask your students to recall their earlier definition of a proof. Have the activities they just completed changed this definition? If so, then how? If they had to explain a proof to someone who knows nothing about mathematics, what would they say? Further Reading: • http://en.wikipedia.org/wiki/Pythagorean_theorem • http://www.cut-the-knot.org/pythagoras/index.shtml 43
Page 2 and 3: CHALLENGE MATH FOR 5TH GRADERS, FIR
Page 4 and 5: 4 Table of Contents An Introduction
Page 7 and 8: An Introduction Hi and Welcome! Hi!
Page 9 and 10: Gender and Multiculturalism in Math
Page 11 and 12: this year. For less competitive rec
Page 13 and 14: The name of this lesson’s unit go
Page 15 and 16: 1. Read a lesson before you teach i
Page 17 and 18: Lesson #1: Introduction to Triangle
Page 19 and 20: Geometry: A Shapely Approach to Mat
Page 21 and 22: Notes: Geometry: A Shapely Approach
Page 23 and 24: • • • • Geometry: A Shapely
Page 29 and 30: Supplement 1: Pre-made Triangles Ge
Page 35 and 36: Lesson #5: Pythagorean Triples Appr
Page 37 and 38: Here are some more examples of how
Page 39 and 40: Lesson #6: Pythagorean Proofs Appro
Page 41: Geometry: A Shapely Approach to Mat
Page 45 and 46: Lesson Objectives: • Learn how to
Page 51 and 52: Lesson #8: Combinations Approximate
Page 53 and 54: Notes: Probability: What are the Ch
Page 55 and 56: Probability: What are the Chances?!
Page 57 and 58: Notes: Probability: What are the Ch
Page 59 and 60: Further Reading: • http://en.wiki
Page 61 and 62: Lesson #11: Coins, Dice, and Playin
Page 65 and 66: Lesson #12: The Monty Hall Problem
Page 69 and 70: Estimation and Approximation 69
Page 71 and 72: Estimation and Approximation slight
Page 73 and 74: Estimation and Approximation Lesson
Page 75 and 76: Estimation and Approximation How ca
Page 77 and 78: Combinatorics: How Many Ways Can Yo
Page 81 and 82: Notes: Combinatorics: How Many Ways
Page 85 and 86: Lesson #17: Cracking the Postal Cod
Page 87 and 88: Supplement 1 Combinatorics: How Man
Page 89 and 90: Lesson #18: The Catalan Numbers App
Page 91 and 92: Supplement 1: Parents’ Guide Comb
Page 93 and 94:
Supplement 1: Parents’ Guide Comb
Page 95 and 96:
Again and Again and Again... 95
Page 97 and 98:
Again and Again and Again... Iterat
Page 99 and 100:
Again and Again and Again... So how
Page 101 and 102:
Again and Again and Again... You ma
Page 103 and 104:
Notes: Again and Again and Again...
Page 105 and 106:
Again and Again and Again... number
Page 107 and 108:
ship. The most famous example of a
Page 109 and 110:
Supplement 2: Grids and Initial Con
Page 111 and 112:
Algebra: Solve for X 111
Page 113 and 114:
Algebra: Solve for X Each of these
Page 115 and 116:
Algebra: Solve for X same thing as
Page 117 and 118:
Algebra: Solve for X Lesson #22: So
Page 119 and 120:
Part 3: Square Roots and Exponents
Page 121 and 122:
Supplement 1: Addition and Subtract
Page 123 and 124:
Supplement 3: Square Roots and Expo
Page 125 and 126:
Supplement 5: Teacher Answer Key 1)
Page 127 and 128:
Lesson #23: Puzzle Worksheets Appro
Page 129 and 130:
Supplement 2: Solution Sheet 1 2 3
Page 131 and 132:
Supplement 4: Worksheet 2 Algebra P
Page 133 and 134:
Page 135 and 136:
Page 137 and 138:
Notes: Algebra: Solve for X 137
Page 139 and 140:
Lesson Objectives: • Understand p
Page 141 and 142:
Graphing: Plot the Points say that
Page 143 and 144:
Notes: Graphing: Plot the Points 14
Page 145 and 146:
Part 2: Graph It Further Reading:
Page 147 and 148:
Page 149 and 150:
Graphing: Plot the Points For an ad
Page 151 and 152:
Page 153 and 154:
Graphing: Plot the Points your stud
Page 155 and 156:
Supplement 1: Graph Paper Graphing:
Page 157 and 158:
Lesson #28: Manipulating Graphs App
Page 159 and 160:
f(x) = -x 2 f(x) = -x 3 Notice that
Page 161 and 162:
Page 163 and 164:
Lesson #29: Set Basics Approximate
Page 165 and 166:
Part 2: Tying the sets together Fur
Page 167 and 168:
Lesson #30: Infinite Sets and Greek
Page 169 and 170:
Notes: An Introduction to Sets 169
Page 171 and 172:
The Story of the HOTEL AD INFINITUM
Page 173 and 174:
An Introduction to Sets Well, in on
Page 175 and 176:
Fun with Numbers 175
Page 177 and 178:
Part 2: Multiplication Further Read
Page 179 and 180:
Lesson #33: Introduction to Sequenc
Page 181 and 182:
Fun with Numbers Ask the question:
Page 183 and 184:
Lesson Objectives: • Find pattern
Page 185 and 186:
Fun with Numbers draw a number line
Page 187 and 188:
Lesson #35: Fun with the Fibonacci
Page 189 and 190:
Part 2: The Golden Rectangle Fun wi
Page 191 and 192:
Further Reading: • http://www.mcs
Page 193 and 194:
Supplement 2: Golden Rectangle Fun
Page 195 and 196:
Notes: Fun with Numbers 195
Page 197 and 198:
Fun with Numbers What do you notice
Page 199 and 200:
Supplement 2: Da Vinci’s Vitruvia
Page 201 and 202:
Lesson #37: Prime Numbers and the U
Page 203 and 204:
Fun with Numbers Once each group ha
Page 205 and 206:
Supplement 1: 399 x 399 Ulam Spiral
Page 207 and 208:
Different Bases: Beyond Base 10 207
Page 209 and 210:
Part 1: Draw a computer Different B
Page 211 and 212:
Notes: Different Bases: Beyond Base
Page 213 and 214:
Different Bases: Beyond Base 10 bas
Page 215 and 216:
Lesson #40: Exploding Dots Approxim
Page 217 and 218:
3 6 = 279 3 5 = 243 3 4 = 81 3 3 =
Page 219 and 220:
Supplement 1 How can you count the
Page 221 and 222:
Lesson #41: Jeopardy Approximate le
Page 223 and 224:
Notes: Different Bases: Beyond Base
Page 225 and 226:
Lesson #42: The Four Color Theorem
Page 227 and 228:
Connecting Dots and Coloring Graphs
Page 229 and 230:
7. Use that third color to fill in
Page 231 and 232:
Supplement 1: U.S. Map Connecting D
Page 233 and 234:
Supplement 3: More Maps Connecting
Page 235 and 236:
Notes: Connecting Dots and Coloring
Page 237 and 238:
Page 239 and 240:
Page 241 and 242:
Page 243 and 244:
Page 245 and 246:
Page 247 and 248:
Lesson #45: Playdough and Mobius St
Page 249 and 250:
Further Reading: • http://en.wiki
Page 251 and 252:
Lesson #46: Euler Number Approximat
Page 253 and 254:
Topology: Coffee Cups and Doughnuts
Page 255 and 256:
Supplement 1 (cont’d): Cut-outs T
Page 257 and 258:
Thinking Puzzles 257
Page 259 and 260:
Thinking Puzzles ber, and you can i
Page 261 and 262:
Notes: Thinking Puzzles 261
Page 263 and 264:
Thinking Puzzles Yet the 8 is in th
Page 265 and 266:
Lesson #49: Secret Code Approximate
Page 267 and 268:
Thinking Puzzles Depending on how f
Page 269 and 270:
Thinking Puzzles Lesson #50: Playin
Page 271 and 272:
Supplement 1: Student Worksheet Log
Page 273 and 274:
Space Fillers and Mathematical Game
Page 275 and 276:
3-D Tic-Tac-Toe Space Fillers and M
Page 277 and 278:
Crypto Space Fillers and Mathematic
Page 279 and 280:
Actue Used to describe an angle les
Page 281 and 282:
Circle A two-dimensional figure cre
Page 283 and 284:
Eulerian path A graph has an Euleri
Page 285 and 286:
Glossary Infinite sequence An infin
Page 287 and 288:
Glossary Phi (Pronounced ‘fee’
Page 289 and 290:
though both contain the exact same
Page 291:
With replacement In probability, wh
show all

Lesson #2 - Augsburg College

Create successful ePaper yourself

Delete template?

Save as template?