Translating Problems into Equations and Solutions

Slides:

Advertisements

Similar presentations

Using Inverse Operations

Advertisements

Mr Barton’s Maths Notes

§ 1.5 Problem Solving and Using Formulas.

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 1 1 Section 2.5 An Introduction to Problem Solving Copyright © 2013, 2009, 2006 Pearson Education,

Warmup 8/12/10 Write and solve an equation for each problem. You do not have to copy the problem. 1.The perimeter of a rectangle is 48. If the length is.

4.4 Optimization Finding Optimum Values. A Classic Problem You have 40 feet of fence to enclose a rectangular garden. What is the maximum area that you.

3.2 Solving by Substitution and Elimination 3.3 Application.

EXAMPLE 2 Use a ratio to find a dimension SOLUTION Painting You are planning to paint a mural on a rectangular wall. You know that the perimeter of the.

Systems of Equations & Inequalities

7.2, 7.3 Solving by Substitution and Elimination

4.7 Quadratic Equations and Problem Solving BobsMathClass.Com Copyright © 2010 All Rights Reserved. 1 General Strategy for Problem Solving Understand the.

Any questions on the Section 5.7 homework?

– ALGEBRA I – Unit 1 – Section 2 Consecutive

Problem Solving Kristie Ferrentino EDU 314 Dr. Pane Ninth Grade (Algebra I) Kristie Ferrentino EDU 314 Dr. Pane Ninth Grade (Algebra I)

Perimeter Is the sum of the lengths of the sides. When solving a perimeter problem, it is helpful to draw and label a figure to model the region.

Math 021. A literal equation is any equation that contains two or more variables. A literal equation can be thought of as a formula. It is useful in some.

Chapter 1 Equations, Inequalities, and Mathematical Models 1.3 Formulas and Applications.

Simultaneous Equations. Aims for this topic: You will know what simultaneous equations are You will be able to solve simultaneous equations using graphs.

Slide Copyright © 2012 Pearson Education, Inc.

Introduction to Perimeter, Circumference and Area

Module 4 Lesson 14 Find areas by decomposing into rectangles or completing composite figures to form rectangles.

Solving systems of equations with 2 variables

1/29/13. Find the slope of the line through each pair of points. 1. (1, 5) and (3, 9) 2. (–6, 4) and (6, –2) Solve each equation x + 5 x + 6 x =

Example Suppose a firework is launched with an upward velocity of about 80 ft/sec from a height of 224 feet. Its height in feet, h(t), after t seconds.

§ 1.5 Problem Solving and Using Formulas. Blitzer, Algebra for College Students, 6e – Slide #2 Section 1.5 Solving Word Problems Strategy for Solving.

Lesson Plan - APP Algebra Mental and Oral Starter Pupils to complete a ‘Heard the Word’ grid and compare it to grid they completed at the start of the.

Rectangles. Rectangles and Algebra To solve questions involving geometric shapes first draw a picture use formulas or common sense. A rectangle's perimeter.

SOLVING SYSTEMS ALGEBRAICALLY SECTION 3-2. SOLVING BY SUBSTITUTION 1) 3x + 4y = 12 STEP 1 : SOLVE ONE EQUATION FOR ONE OF THE VARIABLES 2) 2x + y = 10.

5.8 Applications: Beginning Algebra. 6.7 Applications: 1. To apply the Strategy for Problem Solving to applications whose solutions depend on solving.

Lesson 9-3 Example Solve. GEOMETRY The perimeter of a trapezoid is the sum of the length of its sides. One side length is 16 inches. One side length.

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 5.3.

EXAMPLE 2 Use a ratio to find a dimension SOLUTION Painting You are planning to paint a mural on a rectangular wall. You know that the perimeter of the.

Please close your laptops and turn off and put away your cell phones, and get out your note-taking materials.

12/12/ : Using Formulas Expectation: You will be able to use the formulas for area and perimeter of a rectangle to calculate (with correct units)

5.6 Applications of Quadratic Equations. Applications of Quadratic Equations. We can now use factoring to solve quadratic equations that arise in application.

Dear Power point User, This power point will be best viewed as a slideshow. At the top of the page click on slideshow, then click from the beginning.

Math 71 Chapter 1. Use the order of operations to simplify each expression. What is your first step? and/or

You are Master of the Word. Be sure to read the directions in each problem.

Translating & Solving Word Problems. Some Hints:  W e are going to cover several different types of word problems in this unit.  One of the keys to.

Solving a System of 3 Equations with 3 Unknowns. Breakdown Step 1 Labeling Step 2 Reduce to a 2 by 2 Step 3 Substitute Back In Step 4 Check Solution.

§ 3.3 Problem Solving in Geometry. Geometry Blitzer, Introductory Algebra, 5e – Slide #2 Section 3.3 Geometry is about the space you live in and the shapes.

Multiplication Equations Unit 2.7 Pages / / / / / Warm Up Problems Solve the following.

Copyright © Cengage Learning. All rights reserved. 1 Equations, Inequalities, and Mathematical Modeling.

Chapter 6 Section 1 - Slide 1 Copyright © 2009 Pearson Education, Inc. Chapter 6 Section 1 - Slide 1 1. Algebra 2. Functions.

3.4 – Geometric problems – 5 step approach (p200)

Copyright 2013, 2010, 2007, 2005, Pearson, Education, Inc.

Putting Your Translation Skills To Work

Applications of Linear Equations

Word Problems Involving Triangle.

Steps to solving a word problem

Introduction to Perimeter, Circumference and Area

Perimeter and Area Word Problems (Using One Variable) Taught by the Bestest of all the besterest who are not bestless, Mr. Peter Richard.

Solving Equations from Word Problems

Use the substitution method to find all solutions of the system of equations {image} Choose the answer from the following: (10, 2) (2, 10) (5, - 2) ( -

3.2 Solving by Substitution and Elimination 3.3 Application

Solving Word Problems Objective: Students will be able to write and solve equations based on real world situations.

Solving Linear Equations Unit Test Review Game

Objective: Solve Applied Problems involving Quadratic Equations

In all things of nature there is something of the marvelous.

Writing Equations and Inequalities

Bell Ringer: Simplify:

Problem Solving and Using Formulas

one of the equations for one of its variables Example: -x + y = 1

Algebra 1 Section 12.3.

Chapter 6 Section 6.

Simultaneous Equations

Area = l(w) 38 = 2(3x + 4) 38 = 6x = 6x = x CHECK: 38 = 2(3(5) + 4) 38 = 2(15 + 4) 38 = 2(19) 38 = 38 √

Chapter 3 Section 6 Applications.

Using Equations to Solve Word Problems

Discuss: Is student 1 correct? How do you know? “The missing lengths

Presentation transcript:

Translating Problems into Equations and Solutions – ALGEBRA I – Unit 1 – Section 2 Translating Problems into Equations and Solutions Solving word problems can be one of the trickiest processes in Algebra. The key lies in having a solid approach and plan to attacking word problems.

Translating Problems into Equations and Solutions – ALGEBRA I – Unit 1 – Section 2 Translating Problems into Equations and Solutions We will be using a FIVE-STEP approach for solving word problems in this class… 1 3 5 2 4

This step involves several things: FIVE-STEP Problem Solving Plan STEP #1 – GET ORGANIZED Figure out what you know. Figure out what you DON’T know. Draw a sketch (if necessary). This step involves several things: Getting organized is the key to success. Take the time to sort through the information and develop a game plan.

FIVE-STEP Problem Solving Plan – PICK A VARIABLE Choose a letter that makes sense to you. Pick something that reminds you of what you are solving for. For instance, “t” may stand for time. Write any “unknowns” in terms of your variable.

FIVE-STEP Problem Solving Plan – WRITE AN EQUATION Remember that if you write one equation and want to be able to solve it, you can only have one variable in it. GOOD EXAMPLE: w + w + 6 = 20 BAD EXAMPLE: w + l = 20

I think that this step is pretty self explanatory. FIVE-STEP Problem Solving Plan STEP #4 – SOLVE THE EQUATION I think that this step is pretty self explanatory. Until we officially start solving equations, you will be given possible answers to guess and test with.

There are several things to do: FIVE-STEP Problem Solving Plan STEP #5 – CHECK YOUR ANSWER There are several things to do: Check your math and labels. Make sure that you are answering the question. Make sure your answers make sense in the context of the problem.

Let’s recap. The five steps are: Problem Solving Plan ORGANIZE VARIABLE EQUATION SOLVE CHECK Let’s recap. The five steps are:

Example Problem ORGANIZE A rectangle is 5 inches longer than it is wide. What are the dimensions of the rectangle if the perimeter is 38 inches? (Choices for w: 5, 7, or 8) ORGANIZE What do you know? What don’t you know? Draw a sketch Perimeter = 38 in Length is 5 inches more that the width Add all sides to get the perimeter Length Width length width p = 38 in

Example Problem VARIABLE Width = w Length = w + 5 A rectangle is 5 inches longer than it is wide. What are the dimensions of the rectangle if the perimeter is 38 inches? (Choices for w: 5, 7, or 8) VARIABLE w + 5 Since the two unknowns are length and width, make one of them your variable and write the other one in terms of that variable. Edit your sketch as you go… w p = 38 in Width = w Length = w + 5

w + w + 5 + w + w + 5 = 38 Example Problem EQUATION A rectangle is 5 inches longer than it is wide. What are the dimensions of the rectangle if the perimeter is 38 inches? (Choices for w: 5, 7, or 8) EQUATION w + 5 Write the equation that will allow you to solve for the variable. w p = 38 in w + w + 5 + w + w + 5 = 38

w = 7 inches Example Problem SOLVE A rectangle is 5 inches longer than it is wide. What are the dimensions of the rectangle if the perimeter is 38 inches? (Choices for w: 5, 7, or 8) SOLVE w + 5 If you can solve the equation algebraically, the go ahead. Otherwise, guess and test with the possible choices. w p = 38 in w = 7 inches

w = 7 inches l = 12 inches Example Problem CHECK A rectangle is 5 inches longer than it is wide. What are the dimensions of the rectangle if the perimeter is 38 inches? (Choices for w: 5, 7, or 8) CHECK w + 5 The question is asking for the dimensions. Thus, we need to know the width AND length. w p = 38 in w = 7 inches l = 12 inches

w = 7 inches l = 12 inches Example Problem CHECK A rectangle is 5 inches longer than it is wide. What are the dimensions of the rectangle if the perimeter is 38 inches? (Choices for w: 5, 7, or 8) CHECK w + 5 Do the answers make sense? Do the sides of the rectangle add up to 38 inches? If yes, then we are done! w p = 38 in w = 7 inches l = 12 inches

Try This Problem… Use the problem solving plan to solve the following problem. Be sure to show your work. Possible answers for the shorter piece have been provided. Suppose that a 2'×4' piece of lumber is originally 16 feet long, but it is cut into two pieces. The longer piece is three times as long as the shorter piece. How long is each piece? (Possible answers for short piece: 4, 5, or 6) **The answers can be found at the end of the PowerPoint.

ALGEBRA IS FUN AND EASY! **Answers: 1) 4 feet and 12 feet