1 / 12

Week 2--Glad you came back!

Week 2--Glad you came back!. Please take out your homework. Staple it if necessary. Your homework and exploration should be turned in separately. Make sure your name is on it. Write who helped you on any problems. Agenda for today!. Exploration 1.4 (Darts) discussion. Collect homework

saki
Download Presentation

Week 2--Glad you came back!

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. Week 2--Glad you came back! Please take out your homework. Staple it if necessary. Your homework and exploration should be turned in separately. Make sure your name is on it. Write who helped you on any problems.

  2. Agenda for today! • Exploration 1.4 (Darts) discussion. • Collect homework • More with problem solving and patterns • Assign homework for week • Number systems--Egyptian, Babylonian, Mayan, and Roman

  3. Exploration 1.4 Darts • Discuss strategies you would use to find a solution to the assigned darts problem.

  4. Problem Solving Strategies

  5. Problem Solving Strategies • Guess and check • Work backwards • Solve a simpler problem • Draw a picture • Solve a similar problem • Make a table • Draw a diagram • Make a graph • Find a pattern • Write an equation • Find a counter-example • Estimate • Solve by induction • Act it out • Organized List (Proof by exhaustion) • Other?

  6. Patterns… the beginnings of reasoning • 1 + 2 2 terms sum = 3 • 1 + 2 + 3 3 terms sum = 6 • 1 + 2 + 3 + 4 4 terms sum = 10 • 1 + 2 + 3 + 4 + 5 5 terms sum = 15 • 1 + 2 + 3 + … + n n terms sum = ?

  7. More Patterns • Find the next term in the sequence. Describe the pattern in a sentence. J, F, M, A, M, J, … 1, 3, 6, 10, 15, … 25, 5, 1, 0.2, 0.04, …1, 11, 21, 1211, 111221, 312211, … 1, 2, 4, 8, 16, … 1, 1, 2, 3, 5, 8, …1, 0, -1, 0, 1, 0, -1, …

  8. More Patterns • Try to figure out the next number in the sequence--explain how you got it in words that a 3rd grader would understand. • 1, 3, 6, 10, … • 1, 4, 9, 16, … • 2, 4, 8, 16, … • 1, 1, 2, 3, 5, 8, …

  9. Principles and Standards of School Mathematics (NCTM, 2000) • Website: http://www.nctm.org/standards/ • Five process standards: problem solving reasoning and proof communication connections representations

  10. Reasoning and Proof • if x = 10 and y = 10, then 2 • 10 + 5 • 10 = 70 this is too small. • If x = 12 and y = 8, then 2 • 12 + 5 • 8 = 64 making y smaller decreases the amount of money raised. Since my first guess was y = 10, I will try y > 10 for my next guess. • If x = 6 and y = 14, then 2 • 6 + 5 • 14 = 82. Still too small. I will try y > 14 next. • If x = 5 and y = 15, then 2 • 5 + 5 • 15 = 85! • Five $2 tickets and fifteen $5 tickets = $85 and 5 + 15 = 20.

  11. Homework For class Friday: • in textbook, begin reading Section 2.3 (no farther than p. 111) • Due Friday:in textbook, p. 54-57 # 11, 12, 30a, True or False and explain • (1) sum of 3 consecutive numbers is divisible by 3 • (2) sum of 4 consecutive numbers is divisible by 4

More Related