Why do some problems have one solution and other problems have more than one?

Slides:

Advertisements

Similar presentations

2.1 Solving One Step Equations

Advertisements

Rational Expressions To add or subtract rational expressions, find the least common denominator, rewrite all terms with the LCD as the new denominator,

Solving Equations with the Variable on Both Sides Objectives: to solve equations with the variable on both sides.

Solving 2 Step Equations

Solving Linear Equations

Solving Equations. Equations contain an equal sign (or inequality) and at least one variable.

Solving Equations with the Variable on Both Sides

Solve an equation with variables on both sides

Solve an equation by combining like terms

7.8 Equations Involving Radicals. Solving Equations Involving Radicals :  1. the term with a variable in the radicand on one side of the sign.  2. Raise.

Solving Equations. Equations contain an equal sign (or inequality) and at least one variable.

Solve an equation using subtraction EXAMPLE 1 Solve x + 7 = 4. x + 7 = 4x + 7 = 4 Write original equation. x + 7 – 7 = 4 – 7 Use subtraction property of.

 Start Bellwork #37  Write out the questions!  HW, red pen, book, pencil on desk.

Solving one- and two-step equations. Solving One-Step Equations using Additive Inverse Steps Given the equation x + 4 = 9 use the inverse of adding 4.

ALGEBRAIC EQUATIONS. EQUATIONS AND SOLUTIONS  A correct equation is like a balance scale.  In order to determine if a given value for a variable is.

Solving Equations Containing To solve an equation with a radical expression, you need to isolate the variable on one side of the equation. Factored out.

Graphing Systems of Equations Graph of a System Intersecting lines- intersect at one point One solution Same Line- always are on top of each other,

1.4 Solving Equations ●A variable is a letter which represents an unknown number. Any letter can be used as a variable. ●An algebraic expression contains.

3-2 Solving Equations by Using Addition and Subtraction Objective: Students will be able to solve equations by using addition and subtraction.

Solving Compound Inequalities. Compound Inequality – two inequalities connected by and or or.

SOLVING QUADRATIC EQUATIONS Unit 7. SQUARE ROOT PROPERTY IF THE QUADRATIC EQUATION DOES NOT HAVE A “X” TERM (THE B VALUE IS 0), THEN YOU SOLVE THE EQUATIONS.

The Equation Game. Why is an equation like a balance scale? 3 2x - 1 =

Evaluating Algebraic Expressions 1-7 Solving Equations by Adding or Subtracting Preparation for AF4.0 Students solve simple linear equations and inequalities.

Solve an equation by combining like terms EXAMPLE 1 8x – 3x – 10 = 20 Write original equation. 5x – 10 = 20 Combine like terms. 5x – =

Solve an equation using addition EXAMPLE 2 Solve x – 12 = 3. Horizontal format Vertical format x– 12 = 3 Write original equation. x – 12 = 3 Add 12 to.

Example 1 Solving Two-Step Equations SOLUTION a. 12x2x + 5 = Write original equation. 112x2x + – = 15 – Subtract 1 from each side. (Subtraction property.

Solving Linear Equations Substitution. Find the common solution for the system y = 3x + 1 y = x + 5 There are 4 steps to this process Step 1:Substitute.

Systems of Equations: Substitution

1.graph inequalities on a number line. 2.solve inequalities using addition and subtraction. Objective The student will be able to:

Steps for Solving Equations with Variables on Both Sides 1.Distribute when necessary. 2.Combine like terms if possible. 3.Add or subtract to get the variables.

MAT111 epw 11/1/061 ALGEBRA REVIEW Three Basic Rules.

Bell Ringer 2. Systems of Equations 4 A system of equations is a collection of two or more equations with a same set of unknowns A system of linear equations.

Multiply one equation, then add

Warm Up Solve, showing all steps. 1. n + 9 = x = – z = n = 8 x = 7 z = 16 Course Solving Two-Step Equations = 9 y = 72 y8y8.

1.7 Intro to Solving Equations Objective(s): 1.) to determine whether an equation is true, false, or open 2.)to find solutions sets of an equation 3.)to.

Solve a two-step equation by combining like terms EXAMPLE 2 Solve 7x – 4x = 21 7x – 4x = 21 Write original equation. 3x = 21 Combine like terms. Divide.

11-1 Solving Two-Step Equations Do Now Solve. 1. n + 9 = z = x = n = 8 x = 7 z = -16 = 9 y = 72 y8y8.

What is an Equation  An equation is an expression with an ‘equal’ sign and another expression.  EXAMPLE:  x + 5 = 4  2x – 6 = 13  There is a Left.

Chapter 3.2 and 3.3 – Solving One-Step Equations.

1) GOAL : Get the variable on one side of the equation. 2) You always perform the same operation to both sides of an equation.

Solving Algebraic Equations. Equality 3 = = = 7 For what value of x is: x + 4 = 7 true?

© 2010 Pearson Prentice Hall. All rights reserved Solving Equations Using Two Properties § 10.5.

Solving Linear Inequalities Chapter Solving Inequalities by Addition and Subtraction CLE ; SPI Solve problems involving linear equations.

1.4 Solving Equations.

2.3 Solving Multi-Step Equations

Solve for variable 3x = 6 7x = -21

2 Understanding Variables and Solving Equations.

6-2 Solving Systems Using Substitution

Solving Equations by Factoring and Problem Solving

Solve a system of linear equation in two variables

Do Now 1) t + 3 = – 2 2) 18 – 4v = 42.

Equations Containing Decimals

1.4 Solving Equations I’ve taught you how to solve equations the “simonized” way but here’s another way of doing the same thing!

Solving one- and two-step equations

Warm Up Solve. 1. 2x + 9x – 3x + 8 = –4 = 6x + 22 – 4x 3. + = 5

Solving Equations Finding Your Balance

Solving a System of Equations in Two Variables by the Addition Method

Solving 1-Step Integer Equations

Activating Prior Knowledge -Simplify each expression.

Solving Equations with Variables on Both Sides

Solving Equations with Variables on Both Sides

Objective Solve one-step equations in one variable by using addition or subtraction.

Objective Solve one-step equations in one variable by using addition or subtraction.

Equations …. are mathematical sentences stating that two expressions are equivalent.

Purpose 2-1 Students will be able to solve one-step equations in one variable by using addition or subtraction.

Solving Equations.

Do Now Solve. n + 9 = z = 55 n = x = z = -16

Solving Equations by 2-1 Adding or Subtracting Warm Up

The Substitution Method

Warm- Up: Solve by Substitution

Presentation transcript:

Why do some problems have one solution and other problems have more than one?

Bag the Beans by Becky McCraw and Suzanne Padgett

Objectives Develop thinking skills Explore numerical relationships Solve equations

Directions Make groups of 4 students. Sort the beans into piles. Discuss the rule used to sort the beans.

Questions for Sorting Beans How many piles of beans did you make? How would you describe each of the piles you have made? What was your rule? Can you sort the beans using a different rule?

Steps to Solving Problems Understand the problem Plan a solution Carry out the plan Examine the solution

Understand the Problem This bag contains one fewer Lima bean than Red beans. There are four more Black beans than Lima beans. There are 11 beans in all. Known Total = 11 beans Red > Lima Black > Lima Unknown How many of each bean are in the bag?

Plan a Solution Use a table. Type of BeanLimaRedBlackTotal Formula

Carry Out the Plan Type of BeanLimaRedBlackTotal Formula XX + 1X Complete the table with known information. 2.Use a variable, X, in a formula corresponding to the known information. 3.Set: Lima bean = X, Red bean = X+1, Black bean = X +4

Carry Out the Plan (cont.) 4.Find the value of X by setting the addends (formulas) equal to 11. (X) + (X + 1) + (X + 4) = 11 5.Combine like terms, X, and digits. (X + X + X) + (1 + 4) = 11 6.Add variables and digits. 3X + 5 = 11 7.Isolate the variable. 3X = 11 – 5 3X = 6 8.Divide both sides by the coefficient of X in order to isolate the variable. 3X ÷ 3 = 6 ÷ 3 X = 2

Examine the Solution Type of Bean LimaRedBlackTotal FormulaXX + 1X Solution = = = 11 1.Substituted the variable, X, with the solution, 2. 2.Solve each formula with X = 2. 3.Check the total by adding the three solutions. 4.Does your answer check?

You Try! This bag contains at least eight beans. There are three times as many Red beans as Black beans. There is one more Lima bean than Red beans. What is your solution? Can there be a different solution?

Assessment Check for correct answers on student’s worksheet. Enrichment Have students create his or her own Bag the Beans problem for classmates to solve. Remedial Have students complete an additional on-line, interactive site, in order to practice sorting skills.

Benchmarks 2C The Nature of Mathematics: Mathematical Inquiry (3-5) #1 12B Computation and Estimation #1 Retrieved from: