2.1 Using Problem Solving Strategies and Models

Slides:

Advertisements

Similar presentations

EXAMPLE 2 Look for a pattern Paramotoring A paramotor is a parachute propelled by a fan-like motor. The table shows the height h of a paramotorist t minutes.

Advertisements

This word equation is called a verbal model. U SING A P ROBLEM S OLVING P LAN The verbal model is then used to write a mathematical statement, which is.

EXAMPLE 2 Look for a pattern Paramotoring A paramotor is a parachute propelled by a fan-like motor. The table shows the height h of a paramotorist t minutes.

EXAMPLE 5 Write and solve an equation

1.5 Use Problem Solving Strategies and Models Word Problems, YAY!

1.5 Problem Solving Using Algebraic Models Algebra 2 Mrs. Spitz Fall 2008.

Solving Multiplication and Division Equations. EXAMPLE 1 Solving a Multiplication Equation Solve the equation 3x = x = 15 Check 3x = 45 3 (15)

Solve the equation. ANSWER 62.4 ANSWER 17 ANSWER 11 Warm-Up Exercises 1. = r = 25+ 9x9x g = 636 () g – 18.

Standardized Test Practice

Table of Contents Unit 1- Understand the Problem Unit 2- Gather Information Unit 3-Develop Solutions Unit 4-Implement a Solution Unit 5-Test and Evaluate.

Rewrite Formulas and Equations

A solution of a system of two equations in two variables is an ordered pair of numbers that makes both equations true. A solution to two equations (1,

EXAMPLE 1 Use a formula High-speed Train The Acela train travels between Boston and Washington, a distance of 457 miles. The trip takes 6.5 hours. What.

R ELATED R ATES. The Hoover Dam Oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the oil spill increases at a constant.

ANSWER = 12.5r 2.9x + 25 = 178 ANSWER ANSWER = 40g + 28(18 – g) 4. A balloon is released from a height of 5 feet above the ground.

EXAMPLE 1 Use a formula High-speed Train The Acela train travels between Boston and Washington, a distance of 457 miles. The trip takes 6.5 hours. What.

Transforming Formulas Chapter 4.4. What is a formula? A formula shows a relationship between two or more variables. To transform a formula, you rewrite.

Foundations of Algebra Literal Equations Practice.

4.4 Find Slope and Rate of Change

1.5 Problem Solving. Word Problems  Steps: 1. Declare your variables/verbal model 2. Write an equation 3. Solve 4. Answer questions—check answer to make.

4. ; $22, $11, $10 5. C6. F7. B An equation is a mathematical statement that two expressions are equal. A solution of an equation is a value of the variable.

The Quadratic Formula For any quadratic equation of the form The solutions are given by the formula:

Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Lesson 3.5 Solving Inequalities Using Multiplication or Division Skill Check Skill Check.

1.5 PROBLEM SOLVING USING ALGEBRAIC MODELS Algebra 2.

EXAMPLE 1 Use a formula High-speed Train The Acela train travels between Boston and Washington, a distance of 457 miles. The trip takes 6.5 hours. What.

Objectives Represent linear patterns with equations.

1.5 “Problem Solving Strategies” Examples: 1. A train travels between Boston and Washington, a distance of 457 miles. The trip takes 6.5 hours. What is.

2.1 Using Problem Solving Strategies and Models Math Midterm: March 11.

Copyright © 2014, 2010, 2006 Pearson Education, Inc. 1 Chapter 2 Linear Functions and Equations.

1.4 Setting Up Equations; Applications. Verbal Description Language of Math Mathematical Problem Solution Real Problem.

EXAMPLE 1 Use a formula High-speed Train The Acela train travels between Boston and Washington, a distance of 457 miles. The trip takes 6.5 hours. What.

KAYAKING EXAMPLE 4 Write and solve a linear system During a kayaking trip, a kayaker travels 12 miles upstream (against the current) and 12 miles downstream.

2.3 Direct Variation. A linear function in the form of y=kx where k is the constant of variation.

To Start: 20 Points!! -2(4x + 3y – 4z – 11) 12(11) + 12(14) + 12(24) – 12(9) Use front-end estimation: Estimate the quotient: 29.5 ÷ x.

4-3 Solving Multiplication Equations Standard : PFA Indicator: P9 (same as 4-2)

4.4 Absolute Value 11/14/12. Absolute Value: The distance of a number from 0 on a number line. Written as l x l Ex. |5| (distance of 5 from 0) = 5 Ex.

Solve Linear Systems by Substitution Students will solve systems of linear equations by substitution. Students will do assigned homework. Students will.

1.1 Using Problem Solving Strategies and Models Goal : Solve problems using verbal models Note Taking Guide Pg. 1.

ALGEBRA II: CHAPTER 1 SECTION 5: USE PROBLEM SOLVING STRATEGIES AND MODELS OBJ: SOLVE PROBLEMS USING VERBAL MODELS.

2.1 Rates, Ratios, and Proportions EQ: How can I use units to understand problems and guide the solution of proportions?

LESSON 2–4 Solving Equations with the Variable on Each Side.

Notes Over 3.2 Solve the equation. Notes Over 3.2 Solve the equation.

WRITE AN ALGEBRAIC MODEL.

1.5 Translating Words into Mathematical Symbols

Do Now 1. Solve 2x+3>x+5 2. Solve - c - 11>23

Finding Perimeter and Area

3.3 Rate of Change and Slope

Five-Minute Check (over Lesson 3–2) Mathematical Practices Then/Now

3-3 Slope as Rate of Change

Warm Up Lesson Presentation Lesson Quiz

To Start: 20 Points!! -2(4x + 3y – 4z – 11) 12(11) + 12(14) + 12(24) – 12(9) Use front-end estimation: Estimate the quotient: 29.5 ÷ 4.83.

4.4 Find Slope and Rate of Change

The sum of six and a number The sum of six and a number 6 + x 6 + x

9.6: Solving Polynomials when a > 1

0.4 Solving Linear Inequalities

Lesson 8-6 Solving Systems of Linear Equations by Graphing

3-3 Slope as Rate of Change

Use Problem Solving Strategies and Models

Speed, Distance, Time Calculations

Use Problem Solving Strategies and Models

Convert the measurements.

Speed, Distance, Time Calculations

Example 1: Solving Equations Containing One Radical

1.1 Using Problem Solving Strategies and Models

Problem Solving Strategies and Models

5-Minute Check Solve each equation. Check your solution. x/3 =

2.1 Using Problem Solving Strategies and Models

Use Graphs of Functions

Algebra 1 Notes Lesson 7-5 Graphing Systems of Inequalities

Presentation transcript:

2.1 Using Problem Solving Strategies and Models Goal : Solve problems using verbal models Pg. 24

Vocabulary Verbal Model Distance Formula Writing an equation in words before you write it in mathematical symbols Distance Formula Distance = rate · time

Example #1, (Use a formula) A bus travels at an average rate of 50 miles per hour. The distance between Atlanta and Miami is 663 miles. How long would it take for the bus to travel from Atlanta to Miami? Solution Use the distance formula for distance traveled as a verbal model. = · ________ = ________ · t An equation for this situation is _____ = _____t. _____ = _____t (Write the equation) _____ ≈ t (Divide each side by _____) Distance (miles) Rate (mi/h) Time (hours)

Continued The amount of time it would take to travel from Atlanta to Miami is about ______ hours. Use unit analysis to check your answer _____ miles ≈ _____ miles · _____ hours hours

Checkpoint In Example 1, how fast is the buss traveling if it takes 22 hours to travel from San Francisco to Colorado Springs, a distance of 1335 miles? ≈ 60.7 miles per hour

Example #2, (Look for a pattern) The table shows the height (h) of a jet airplane (t) minutes after beginning its descent. Find the height of the airplane after 9 minutes. Solution The height decreases by 3000 feet per minute. You can use this equation to write a verbal model for the height. Time (min), t 1 2 3 4 Height (ft), h 35,000 32,000 29,000 26,000 23,000

Solution Height = Initial Height – Rate of Descent · Time This is a Linear Equation So, the height after 9 minutes is h = ________ - _________(___) = ________ feet

Class Work and Homework Pg. 26, 1 – 17 all