problem solving in math

PROBLEM SOLVINGYeah, this is for real.

RULES 1. Be attentive. 2. Compute.3. CP's/calculators are not allowed.4. Listen.5. Enjoy.

GEORGE POLYA'S PROBLEM SOLVING TECHNIQUES Understand the problem.Device a plan. Carry out the plan.Look back.

PATTERNSNEED FOR DIAGRAMNEED FOR SIMPLER PROBLEM

TRUE TO ONE, TRUE TO ALL

BASIC TECHNIQUES (eg

fractions)

WORK BACKWARDS

BUILD CONJECTURES

WHAT IS THE PATTERN? -2 1 11 41 61 30-3 1 9 23 15 0-5 1 6 5 0 1 1 0

WHAT IS THE PATTERN?

x, y, 2x, 5y, 4x, 9y, 8x, 13y, 16x, 17y, 32x, 21y

WHAT IS THE PATTERN?

10, 21, 31, 52, 83, 135, 218, 353, 571, 924

EXERCISE I If A is the first two-digit term of a series and adding B (any two-digit number) to the first term to determine the next, what

must be the sum of the first ten terms?

1. A2. B3. A + B4. A + 2B5. 2A + 3B6. 3A + 5B

7. 5A + 8B 8. 8A + 13B9. 13A + 21B10. 21A + 34B SUM = 55A + 88B = 11(5A +

8B)

1. A = 322. B = 15 3. A + B4. A + 2B5. 2A + 3B6. 3A + 5B

7. 5A + 8B 8. 8A + 13B9. 13A + 21B10. 21A + 34B

EXERCISE II

1. 322. 15 3. 474. 625. 1096. 171

7. 2808. 4519. 73110. 1182

Find the SUM in 10 seconds.

SUM = 3080

EXERCISE IIIDivide 987 654 321 by 5 WITHOUT using calculator. The usual way of long division IS NOT ALLOWED.

EXERCISE IV (BY GROUP)Find the area of a triangle whose vertices are at (-1,4), (1,2) and (3,6). Show your illustration and complete solution.

EXERCISE V (BY GROUP)What is the product when (x + y) raised to 6 is expanded using binomial theorem? Show all pertinent solutions.

DISCUSSIONWhat is Binomial Theorem?

EXERCISE V.5 (FOLLOW UP)What is the numerical coefficient of the third to the last term of the binomial expansion of

EXERCISE VI (BY GROUP) If another square is drawn inside a square whose vertices of the smaller touch the sides of the small, what is the difference of their areas?

EXERCISE VIIA, B and C have no common factor greater than 1. Alog200 5 + Blog200 2 = C, find A, B, and C.

EXERCISE VIII (BY PAIR)Six digit numbers will be selected from the numbers 1,2,3,4,….10. If the second to the smallest digit is 3, how many arrangements are possible?

EXERCISE IX (BY GROUP)Show all ways to find the area of the figure without actual measurements.

EXERCISE XSimplify .

EXERCISE XIWhat is the value of k in

+ 2kx – 15 = 0 if the sum of the roots is -2?

EXERCISE XII

Solve for n in = and • = .

EXERCISE XIII (BY GROUP) How big is the

area of the black region compared to that of the

orange square?

EXERCISE IXWhat is the sum of the

sequence 1, , ………..?

EXERCISE XXEvaluate

THANK YOU!