Chapter 2: Problem Solving1 Chapter 2 Problem Solving.

Slides:

Advertisements

Similar presentations

Bellwork 30 x 4 x 6 x y.

Advertisements

HOW TO SOLVE IT Alain Fournier (stolen from George Polya) Computer Science Department University of British Columbia.

By William Huang. Solve Problems by writing and solving equations (Math Textbook)

8.5 Proving Triangles Similar

Clicker Question 1 The function f (x ) is graphed on the board. If the derivative function f '(x ) were graphed, where would it intersect the x – axis?

Special Right Triangles Chapter 7.4. Special Right Triangles triangles triangles.

Geometry Warm ups.

Demo Disc “Teach A Level Maths” Vol. 1: AS Core Modules © Christine Crisp.

Bellringer Solve for x. 1. x=4 2. x=7 3. x=8 4. x=10.

© Where quality comes first! PowerPointmaths.com © 2004 all rights reserved.

Other types of Equations Polynomial Equations. Factoring Solve.

Today – Friday, March 15, 2013  Warm Up: Solving missing sides of right triangles or angles of right triangles  Review Solutions to Angles of Elevation.

4 Steps to Problem Solving.. UNDERSTANDING THE PROBLEM Can you state the problem in your own words? What are you trying to find or do? What are the unknowns?

Copyright © Cengage Learning. All rights reserved.

WARM-UP. 8.6 PRACTICE SOLUTIONS(14-33 EVEN) CLEAR UP A FEW THINGS.

Answers to homework problems – page 8

About 2,500 years ago, a Greek mathematician named Pythagorus discovered a special relationship between the sides of right triangles.

5.1 Special Right Triangles. What you should already know… Right triangles have one 90 o angle The longest side is called the HYPOTENUSE  It is directly.

Section 7.2 – The Quadratic Formula. The solutions to are The Quadratic Formula

30°, 60°, and 90° - Special Rule The hypotenuse is always twice as long as the side opposite the 30° angle. 30° 60° a b c C = 2a.

 The tangent theorem states that if two segments are tangent to a circle and intersect one another, the length from where the segments touch the circle.

Be Creative Learning to be creative.. What is Creativity? Newly developed idea or… Newly derived connection between ideas.

Triangle Congruence by ASA and AAS Chapter 4 Section 3.

Quiz 5-5 Solve for the missing angle and sides of Triangle ABC where B = 25º, b = 15, C = 107º Triangle ABC where B = 25º, b = 15, C = 107º 1. A = ? 2.

Lesson 9.6 Families of Right Triangles Objective: After studying this lesson you will be able to recognize groups of whole numbers know as Pythagorean.

6.6 Solving Radical Equations. Principle of power: If a = b then a n = b n for any n Question: Is it also true that if a n = b n then a = b? Explain in.

This is a right triangle: We call it a right triangle because it contains a right angle.

Proportions. State of the Classes Chapter 4 Test2 nd 9 week average

First, recall the Cartesian Plane:

Lesson 6.4 Prove Triangles Similar by AA. Objective Use the AA similarity postulate.

Math – Rational Equations 1. A rational equation is an equation that has one or more rational expressions in it. To solve, we start by multiplying.

Pythagorean Theorem Chapter 3 – 5. What’s a, b, & c? a & b are the two sides that form the 90° angle a & b are also known as “legs” of a right triangle.

11.4 Pythagorean Theorem Definitions Pythagorean Theorem

4.7 – Square Roots and The Pythagorean Theorem Day 2.

Homework  WB p.3-4 #36-54 (evens or odds). Chapter 1 Review.

Solving an equation with one unknown From arithmetic to algebra Modifying equations in algebra.

World 1-1 Pythagoras’ Theorem. When adding the areas of the two smaller squares, a2a2 Using math we say c 2 =a 2 +b 2 b2b2 c2c2 their sum will ALWAYS.

1. Factor 2. Factor 3.What would the value of c that makes a perfect square. Then write as a perfect square. M3U8D3 Warm Up (x+4) 2 (x-7) 2 c = 36 (x+6)

Perimeter, Circumference, and Area 1.7 This presentation was created following the Fair Use Guidelines for Educational Multimedia. Certain materials are.

Pythagorean Theorem Converse Special Triangles. Pythagorean Theorem What do you remember? Right Triangles Hypotenuse – longest side Legs – two shorter.

Find the area of a circle with the given measure.

Warm Up Solve by graphing (in your calculator) 1) 2)

Solving equations with variable on both sides Part 1.

1.7 Perimeter, Area, & Circumference HMWK: pp. 55 – 57, #s 15 – 29 odd, 40 – 46 even Game Plan: Today I will be able to … Calculate area, perimeter, &

A Quick Review ► We already know two methods for calculating unknown sides in triangles. ► We are now going to learn a 3 rd, that will also allow us to.

Problemløsning: hvordan? PROGRAMMERING SOM HÅNDVÆRK V/ Wilfred Gluud I Samarbejde med: Maj 2003Copyright Wilfred Gluud Programmering How to Solve IT.

How to Solve it?. How to Solve It? Polya, G. (1957). How to solve it: A new aspect of mathematical method, 2nd ed. Princeton, NJ: Princeton University.

Thinking Mathematically Problem Solving. Polya’s Four Steps Understand the problem Devise a plan Carry out the plan and solve the problem Look back and.

Law of Sines  Use the Law of Sines to solve oblique triangles (AAS or ASA).  Use the Law of Sines to solve oblique triangles (SSA).  Find the.

PIB GEOMETRY 5-1: Properties of Parallelograms. Warm Up.

The Different Numbers. Simple Inequalities A Word Problem A movie rental company offers two subscription plans. You can pay $36 per month and rent as.

Solving Radical Equations and Inequalities Objective: Solve radical equations and inequalities.

Circle the ways that Triangles can be congruent: SSS SAS SSA AAA AAS.

SOLVING QUADRATIC EQUATIONS BY COMPLETING THE SQUARE

WARM UP Use a calculator to find the approximate value. Express your answer in degrees. (Hint: check the mode of your calculator)

Lesson 11-7 Ratios of Areas (page 456)

Areas of Triangles and Special Quadrilaterals

Radical Equations.

Chapter 4 Section 1.

Proving Triangles Similar.

Agenda Investigation 8-3 Proving Triangles are Similar Class Work

Section 7.1: Modeling with Differential Equations

Use the Pythagorean Theorem to find a Leg

13.9 Day 2 Least Squares Regression

Proving Triangles Similar.

Agenda Investigation 8-3 Proving Triangles are Similar Class Work

Segment Lengths in Circles

Example 5A: Solving Simple Rational Equations

9.4 Special Right Triangles

Module 16: Lesson 4 AA Similarity of Triangles

Presentation transcript:

Chapter 2: Problem Solving1 Chapter 2 Problem Solving

Chapter 2Problem Solving2 How To Solve It

Chapter 2Problem Solving Process3 qPhase 1: Understanding the problem qPhase 2: Devising a plan qPhase 3: Carrying out the plan qPhase 4: Looking back

Chapter 2Phase 1: Understanding the problem 4 1: Understanding the problem qWhat is the unknown? What are the data? qWhat is the condition? Is it possible to satisfy the condition? Is the condition sufficient to determine the unknown? qDraw a figure. Introduce suitable notation.

Chapter 2Phase 2: Devising a plan5 2: Devising a plan qHow you seen the problem before? Do you know a related problem? qLook at the unknown. Think of a problem having the same or similar unknown. qSplit the problem into smaller sub-problems. qIf you can’t solve it, solve a more general version, or a special case, or part of it.

Chapter 2Phase 3: Carrying out the plan6 3: Carrying out the plan qCarry out your plan of the solution. Check each step. qCan you see clearly that the step is correct? qCan you prove that it is correct?

Chapter 2Phase 4: Looking back7 4: Looking back qCan you check the result? qCan you derive the result differently? qCan you use the result, or the method, for some other problem?

Chapter 2Area of circle8 qWhat is the data? Side of square = 2a qWhat is the unknown? Area of circle, C. qWhat is the condition? If radius r is known, C can be calculated. qHow to obtain r? 2a2a

Chapter 2Area of circle9 qPythagoras’ theorem r 2 = 2 * a 2 qArea of circle C =  * r 2 =  * 2 * a 2 a a r

Chapter 2Pascal's triangle10 Pascal’s triangle n C k = n! / (k! * (n-k)!)

Chapter 2NE-paths11 NE-paths qTo find number of NE-paths between any two points. C A

Chapter 2Creative thinking12 Creative thinking Most new discoveries are suddenly-seen things that were always there. A new idea is a light that illuminates presences while simply had no form for us before the light fell on them. Susan Langer

Chapter 2Creative thinking13 Creative thinking Myths qCreativity requires genius qYou have to be odd qCreative thinking isn’t rigorous, but uses simple processes

Chapter 2Homework14 Homework Try exercises behind chapter 2.