Expressions & Equations Grade 6 Confidential1

2 Warm up 1)18n – 3 = 6 2)5 = 15b + 2 3) v = )2.5 (w+ 2) = 14 5)30k -12 = k

Confidential3 1.Combine like terms 2. Isolate the variable you wish to solve for 3.Substitute your answer into the original equation and check that it works Steps for Solving Two step Equations Lets recap what we have learnt in the last lesson

Confidential4 Step 1: Combine Like Terms Combine together the terms containing the variable Like terms are terms that contain the same variable or group of variables raised to the same exponent, regardless of their numerical coefficient. Step 1

Confidential5 When the variable does not have a coefficient of one, we will need to isolate the variable itself When the variable we wish to isolate is either multiplied or divided by a numerical coefficient or other variables that are not equal to one, we need to use either multiplication or division to isolate the variable Step 2 Step 2: Isolate the variable itself

Confidential6 Substitute Your Answer into the Original Equation Substitution is a process of replacing variables with numbers or expressions By substituting, we switch or exchange values, often replacing a variable with a numerical value We often substitute to minimize the number of variables in an expression, or to actually evaluate the expression or equation Step 3

Confidential7 Lets get Started Words or phrases often suggest addition, subtraction, multiplication and division In this lesson we will see how to translate verbal phrases in to algebraic expressions

Confidential8 Shaina is three years older than her sister The number is twice as much The weight is 5 less than half of it Examples

Confidential9 AdditionSubtraction Words used to express Addition/Subtraction Plus Sum More than Increased by Total Minus Difference Less than Less Decreased by

Confidential10 Words used to express Multiplication/Division MultiplicationDivision Times Product Multiplied Of Twice Thrice Divided Quotient

Confidential11 USING A VERBAL MODEL In Mathematics there is a difference between a phrase and a sentence. Phrases translate into expressions; sentences translate into equations or inequalities Expressions Phrases Equations or Inequalities Sentences

Confidential12 PHRASE TO EXPRESSION PhraseExpression The sum of six and a number 6 + x

Confidential13 SentenceEquation The sum of six and a number is twelve. 6 + x = 12 In this sentence, “is” says that one quantity is equal to one another. SENTENCE TO EQUATION

Confidential14 SentenceInequality The sum of six and a number is less than twelve. 6 + x < 12 In this sentence, the words “is less than” indicate an inequality. SENTENCE TO INEQUALITY

Confidential15 USING A VERBAL MODEL PhraseExpression = SentenceEquation SentenceInequality The sum of six and a number is twelve. 6 + x = 12 In this sentence, “is” says that one quantity is equal to one another In this sentence, the words “is less than” indicate an inequality The sum of six and a number is less than twelve. 6 + x < 12 is less than twelve. 6 + x < 12 The sum of six and a number 6 + x

Confidential16 TRANSLATING VERBAL PHRASES Seven divided by a number The sum of six and a number 6 + x Eight more than a numberA number plus five A number increased by seven A number decreased by nineTen times a number y n or n n + 5 x + 7 n – 9 (10n) 7 x

Confidential17 Break Time

Try These! Confidential19 1)Three runs less than the pirates scored 2)Twice as many tomatoes as last year 3)Five more than a number is 25 4)Six fewer hours than her sister 5)Half the population of Texas

Try These! Confidential20 6) Seven times the cost is $63 7) He weighs 180 pounds, which is 22 pounds less than double her weight 8) 4 times as many bees 9) Five more hits than the Martins 10) Three more than 8 times as many trees is 75 trees

Confidential21 1)You and three friends are having a dim sum lunch at a Chinese restaurant that charges $2 per plate. You order lots of plates. The waiter gives you a bill for $25.20, which includes tax of $1.20. Use mental math to solve the equation for how many plates your group ordered.

Confidential22 2) JET PILOT A jet pilot is flying from Los Angeles, CA to Chicago, at a speed of 500 miles per hour. When the plane is 600 miles from Chicago, an air traffic controller tells the pilot that it will be 2 hours before the plane can get clearance to land. The pilot knows the speed of the jet must be greater then 322 miles per hour or the jet could stall. At what speed would the jet have to fly to arrive in Chicago in 2 hours?

Confidential23 3) Shopping networks on television are a popular way to shop. In addition to the cost of the items, you usually pay a shipping fee. Ramya wanted to order several pairs of running shorts that cost $12 each. The total shipping fee is $7. How many shorts can she order with $55?

Confidential24 Addition Subtraction Words used to express Addition/Subtraction Plus Sum More than Increased by Total Minus Difference Less than Less Decreased by Lets review what we have learned in this lesson

Confidential25 Words used to express Multiplication/Division MultiplicationDivision Times Product Multiplied Of Twice Thrice Divided Quotient

Confidential26 USING A VERBAL MODEL In Mathematics there is a difference between a phrase and a sentence. Phrases translate into expressions; sentences translate into equations or inequalities Expressions Phrases Equations or Inequalities Sentences

Confidential27 TRANSLATING VERBAL PHRASES Eleven divided by a number The sum of five and a number 5 + x Twelve more than a numberA number minus nine A number increased by four A number decreased by nineSix times a number m n or n n -9 x + 4 n – 9 (6n) 11 x

Confidential28 You had a Great lesson today Be sure to practice what you have learned