DO NOWUse the following to answer parts a –d.

7x + 4 – 2x + 8 = 32

a. Put a circle around all the variables.

b. Put a triangle around all the constants.

c. Put a box around all the terms.

d. Underline all of the coefficients.

ObjectiveThe student will be able to:

• Translate verbal phrases into algebraic expressions and

• demonstrate 100% understanding of properties by correctly matching them to complete the square.

Standard 1.0 Students identify and use the arithmetic properties of subsets of integers and rational, irrational, and real numbers, including closure properties for the four basic arithmetic operations where applicable.

Standard 1.1 Students use properties of numbers to demonstrate whether assertions are true or false.

Standard 25.0 Students use properties of the number system to judge the validity of results, to justify each step of a procedure, and to prove or disprove statements.

VocabularyAlgebraic expression- an expression consisting of one or more numbers & variables along with one or more arithmetic operations.Ex: 4x + 3Variable- symbols used to represent unknown numbers.Equation- a mathematical sentence that contains an equals sign, =. It may contain numbers, variables, or algebraic expressionsEx: 2x + 13 = 15

Activity # 1In your notes create this graphic

organizer.

Addition

(+)

Subtraction

(-)

Multiplication

(x)

Division

(÷)

Equals

(=)

 

 

 

 

 

Activity # 1On your own put the words below under the operation you believe they are describing. You have 3 minutes.

More than Plus Increased by Sum of Less than Subtracted byDifference of Decreased by Times Product of Twice Divided byHalf of Quotient of Total

Here are some more words to add to your graphic organizer….

Addition Subtraction Multiplication Division Equals

added to subtracted from multiplied by divided by total

sum of difference of product of quotient of equal

plus minus times divided intois, results

in

more than less thandouble, triple,

quadrupleratio of yields

increased

bydecreased by of per

is the

same as

Example 1a)Seven more than a numberx + 7b) Eight less than a numberx – 8 c) Half of a number½ x or x ÷2d) Twice a number2x

Example 2a)One half of a number increased by 7.½ x + 7b) The difference of a number squared

and 5.x² - 5 c) 8 less than twice a number2x - 8

• Identify the operations

• What happens to the variable first?

Misconceptions

Example Describe error:

Why is this error made

What’s the correct answer?

Seventeen less than a number17 – n  

Error: order is switched. This says “a number less than 17.”

   

 Why? They took the order that the words were written in and copied that for the algebraic expression. They ignored the fact that we need 17 less than the unknown amount, meaning we start with an unknown amount and then take 17 away from it.

 n – 17

Misconceptions

Example Describe the error:

Why is this error made

What’s the correct answer?

The quotient of 5 and a numbern/5 

Error: the order is incorrect. If we’re finding the quotient of two numbers, the order they’re stated in tells us the order in which to divide: first number divided by second number.

Why: it’s confusing to remember when order in the expression is the same as the order in the verbal phrase.

5/n

Misconceptions

Example Describe the error: Why is this error made

What’s the correct answer?

10 less than half of a number10 – ½ n

Error: the expression was written in the wrong order. This says “10 subtracted by half of a number,” or “half of a number less than 10.” We had half of a number, and we need 10 less than that quantity.

Why: they just wrote down the expression as he read it: first 10, then subtract, then half of a number. We should read the entire expression and determine what’s happening before writing anything down.

½ n – 10

CFU 1: Write an algebraic expression to represent each verbal phrase.

Verbal Phrase Algebraic Expression

a) A number increased by 5  

b) Seventeen less than a number 

c) A number times 10 

d) The quotient of 9 and a number 

e) Eleven more than a number 

f) A number squared 

g) 5 times a number 

VocabularyCommutative Property of Addition - the order in which two numbers are added does not change their sum.

Ex: 5 + 7 = 7 + 5Commutative Property of Multiplication – the order in which two numbers are multiplied does not change their product.

Ex: 3 ∙10 = 10 ∙3

Vocabulary

Associative Property of Addition – the way in which three numbers are grouped when they are added does not change their sum

Ex: (24 + 8) + 2 = 24 + (8 +2)Associative Property of Multiplication – the way in which three numbers are grouped when they are multiplied does not change their product.

Ex: (9 ∙ 4) ∙ 25 = 9 ∙ (4 ∙ 25)  

VocabularyDistributive Property – for any numbers a, b, & c:2(5x + 3) = (2 ∙5x) + (2 ∙ 3) = 10x + 6Additive Identity- for any number a the sum of a and 0 is a. a +0 = a & 0 + a = a5 + 0 = 5 & 0 + 5 = 5 Multiplicative Identity- for any number a the product of a and 1 is a. a · 1 = a & 1 · a = a12 · 1 = 12 & 1 · 12 = 12 

Ex 1:Identify the property shown:

(5 + 3) + 7 = 5 + (3 +7)  

Ex 2:Identify the property shown:

(4 ∙ 3) ∙ 9 = 4 ∙(3 ∙9)

Ex 3: Identify the property shown:

2 + 9 = 9 + 2

Ex 4:Identify the property shown:

5 ∙ 4x = 4x ∙ 5