1 / 15

Welcome to the 2 nd annual Math Contest Summer Mini-Camp!!!

Welcome to the 2 nd annual Math Contest Summer Mini-Camp!!!. Get a pocket folder a nd write your name o n it. Get a note card and m ake a “name tent” Feel free to sit where you want (we’ll be moving around seats in just a bit). Schedule for the week. Monday : Geometry

jackie
Download Presentation

Welcome to the 2 nd annual Math Contest Summer Mini-Camp!!!

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Welcome to the 2nd annual Math Contest Summer Mini-Camp!!! • Get a pocket folder and write your name on it. • Get a note card and make a “name tent” • Feel free to sit where you want (we’ll be moving around seats in just a bit)

  2. Schedule for the week • Monday: Geometry • Tuesday: Counting and Algebra • Wednesday: Primes and Number Theory • Each day we’ll play some math/logic games, and have a snack sometime around 10:45. • Each day, if we have time we’ll end with a little team math competition, just for fun.

  3. Groundrules • Do your best at all times, whether the activity is a worksheet, a game, a contest, or anything else. • Keep all your materials (notes, worksheets, etc) and refer back to them whenever you want. • Participate, and listen to each other. • If we don’t have time to thoroughly answer your questions, don’t give up! (talk to me afterwards, or send me an email) • Try to minimize your “break time.”

  4. Major Math Contests • MathCounts • The AMC 8 and AMC 10 • Colorado Math League • The Purple Comet

  5. Math Contest Topics (a quick overview) • Arithmetic • Algebra • Geometry • Number Theory • Counting • Probability and Statistics • “Other”

  6. Why we do math contests • Discuss • “How Would You Move Mount Fuji” video

  7. Icebreaker “Naughts and Crosses” • 3 in a row = 1 point • 4 in a row = 2 points • 5 in a row = 3 points

  8. 1st Problem Set!! • This first problem set is from the 2008 AMC 8 (25 questions, no calculator). • Yes, THREE out of the last FIVE questions are geometry questions . . . that’s why we’re ONLY going to focus on geometry today.

  9. Geometry Essentials • Area/volume formulas • Basic Algebra 1 (equations, binomials) • Similar triangles • Diagonals of polygons • Interior angles of polygons • The Pythagorean Theorem!! For higher-level contests: • Special Right Triangles: • 45, 45, 90 • 30, 60, 90 • What it means when figures are “tangent”

  10. Area/Volume Formulas Area: • Triangles, rectangles, parallelograms, squares, circles, and trapezoids. • (optional) Equilateral Triangles: A = Volume: • Prisms and Cylinders: V = Bh (B is the area of the base) • Pyramids and Cones: V = (Bh)/3 (Again, B is the area of the base)

  11. Basic Algebra 1 Solving equations 2x + 4 = -5(x + 2) 2x + 4 = -5x – 10Distribute +5x +5xAdd 5x to both sides 7x + 4 = -10 -4 -4Subtract 4 from both sides 7x = -14 x = -2 Divide by 7 on both sides

  12. The Pythagorean Theorem • In right triangles, if a and b are the legs, and c is the hypotenuse, then a2+ b2 = c2 • Often, you have to work to find the hidden right triangles in diagrams. • Example: “If a bird flew directly from A to B, how far would it travel?” (all angles are right angles) A 3mi 8mi 3mi B

  13. Similarity/Diagonals/Angles • Similar Triangles • Look for ways to prove triangles similar, then use proportions to solve for missing sides If DE and BC are parallel, find the length of DE A 4cm Do we need those two angle measures? Which triangles are similar? How do you know? 50o D E 2cm 50o B C 6cm

  14. BONUS Geometry: Special Right Triangles • 45,45,90 • Sides in ratio of 1: • 30,60,90 • As easy as “1,2,3”!! 60o 2 6 1 90o 30o 90o 45o

  15. MORE Bonus: What it means to be “tangent” • When things are tangent, they touch at exactly one point • When lines are tangent to circles, right angles are formed  • When circles are tangent to each other, their centers connect in a line (and the shared tangent line is perpendicular to the radii) 90o 90o

More Related