Algebra Standard 25.0

 

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:

Standard 25.1

Students use properties of numbers to construct simple, valid arguments (direct and indirect) for, or formulate counterexamples to, claimed assertions.

1= Which property was used incorrectly, making the result below invalid?

Original: 3(x + 2) + 4

Step 1: 3x + 6 + 4

Step 2: 3x + (0 + 4)

Step 3: 3x + 10

Step 4: 3(x + 7)

 

Standard 25.2

Students judge the validity of an argument according to whether the properties of the real number system and the order of operations have been applied cor­rectly at each step.

2= What step in the order of operations must have been done out of order to make the result invalid?

Standard 25.3

Given a specific algebraic statement involving linear, quadratic, or absolute value expressions or equations or inequalities, students determine whether the state­ment is true sometimes, always, or never.

 

RQ***

3==John’s solution to an equation is shown below.

Given: x2 +5 x+6 =0

Step 1: (x+2)(x+3)=0

Step 2: x+2=0 or x+3=0

Step 3: x=-2 or x=-3

Which property of real numbers did John use for Step 2?

multiplication property of equality

zero product property of multiplication

commutative property of multiplication

distributive property of multiplication over addition

 

 

 

4==Stan’s solution to an equation is shown below.

 

Given: n + 8(n + 20) = 110

 

Step 1:

n+8 +20 =110

Step 2:

9n+20 =110

Step 3:

9n=110

Step 4:

9n=90

Step 5:

9n  =   90

=

 

9          9

Step 6:

n=10

 

5== Which statement about Stan’s solution is true?

 

Stan’s solution is correct.

Stan made a mistake in Step 1.

Stan made a mistake in Step 3.

Stan made a mistake in Step 5.

 

6== When is this statement true?

 

The opposite of a number is less than the original number.

 

This statement is never true.

This statement is always true.

This statement is true for positive numbers.

This statement is true for negative numbers.

*

7= Determine if the inequality below is true sometimes, always, or never, when domain of x is all real numbers.

 

x + 5 > x + 5

 

8= When is    true for all real numbers?