Expressions & Equations

Grade 6

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Warm up

1)18n – 3 = 6

2)5 = 15b + 2

3)27.8 + 7.5v = 32.75

4)2.5 (w+ 2) = 14

5)30k -12 = 28 + 10k

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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

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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

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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

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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

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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

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Shaina is three years older than her sisterShaina is three years older than her sister

The number is twice as much The number is twice as much

The weight is 5 less than half of it The weight is 5 less than half of it

Examples

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Addition Subtraction

Words used to express Addition/Subtraction

PlusSumMore than Increased by Total

MinusDifferenceLess thanLessDecreased by

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Words used to express Multiplication/Division

Multiplication Division

TimesProductMultipliedOf TwiceThrice

DividedQuotient

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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

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PHRASE TO EXPRESSION

Phrase Expression

The sum of six and a number

6 + x

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Sentence Equation

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

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Sentence Inequality

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

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USING A VERBAL MODELUSING A VERBAL MODEL

Phrase Expression

=

Sentence Equation

Sentence Inequality

The sum of six and a number is twelve.

6 + x = 12

In this sentence, “is” says thatone 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

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TRANSLATING VERBAL PHRASES

Seven divided by a number

The sum of six and a number 6 + x

Eight more than a number

A number plus five

A number increased by seven

A number decreased by nine

Ten times a number

y + 8

10 • n or

n

n + 5

x + 7

n – 9

(10n)

7x

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Break Time

Try These!

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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!

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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

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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.

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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?

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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?

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Addition Subtraction

Words used to express Addition/Subtraction

PlusSumMore than Increased by Total

MinusDifferenceLess thanLessDecreased by

Lets review what we have learned in this lesson

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Words used to express Multiplication/Division

Multiplication Division

TimesProductMultipliedOf TwiceThrice

DividedQuotient

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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

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TRANSLATING VERBAL PHRASES

Eleven divided by a number

The sum of five and a number 5 + x

Twelve more than a number

A number minus nine

A number increased by four

A number decreased by nine

Six times a number

m + 12

6 • n or

n

n -9

x + 4

n – 9

(6n)

11x

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You had a Great lesson today

Be sure to practice what you have learned