Download Document

NAME: ________________________________________
DATE: ________________
PSSA QUESTION OF THE
DAY PACKET
(COMMON CORE EDITION)
ASSESSMENT ANCHORS (ELIGIBLE CONTENT):
M06.B-E.1.1.5 – Apply the properties of operations to generate
equivalent expressions. (e.g. Apply the distributive property to
the expressions 3(2 + x) to produce the equivalent expression 6 +
3x. Apply the distributive property to the expression 24x + 18y to
produce the equivalent expression 6(4x + 3y).)
NAME: ________________________________________
DATE: ________________
Equivalent expressions are two or more expressions that are equal to any value
of the variable in the expressions. You can use the properties of operations to
write equivalent expressions.
HOW TO GENERATE EQUIVALENT EXPRESSIONS
Ex. Use the Distributive Property to write an equivalent expression.
1. 3(m + 7)
= (3 x m) + (3 x 7)
= 3m + 21
2. 5(9 + 6r)
= (5 x 9) + (5 x 6r)
= 45 + 30r
3. 8(4n – 2n)
= (8 x 4n) – (8 x 2n)
= 32n – 16n
_____________________________________________________________________________________________
WHAT ARE THE BASIC NUMBER PROPERTIES?
1. Associative Property: In any addition or multiplication expression, you
will end up with the sum or product no matter how you group the digits.
Ex. 4 + 8 + 2 = (4 + 8) + 2 = 4 + (8 + 2) = 14
Ex. 8 x 3 x 2 = (8 x 3) x 2 = 8 x (3 x 2) = 48
2. Commutative Property: For any addition or multiplication expression, it
does not matter how you order the digits because you will end up with the
same sum or product.
Ex. 10 + 3 + 5 = 3 + 10 + 5 = 5 + 10 + 3 = 5 + 3 + 10 = 18
Ex. 6 x 4 x 2 = 2 x 6 x 4 = 4 x 2 x 6 = 6 x 2 x 4 = 36
3. Distributive Property: This property is used to break up an expression
into the sum or difference of two products. The operations of addition,
subtraction, and multiplication can be applied to this property.
Ex. 16 = (4 x 5) – (4 x 1) = 4(5 – 1)
Ex. 22 = (2 x 12) – (2 x 1) = 2(12 – 1)
4. Identity Property of 1: Any number multiplied or divided by 1 will equal
itself. (Example: 4 x 1 = 4; 5 ÷ 1 = 5)
NAME: ________________________________________
DATE: ________________
1. Chen bought a basketball for $23, three baseball caps, a pair of
running shoes for $37. To find the total cost in dollars, he wrote the
following:
23 + d + 37 = 23 + 37 + 3d
What property does the equation show?
(a) Associative Property of Addition
(b) Commutative Property of Addition
(c) Distributive Property
(d) Identity Property of 1
Directions:
 Read the question carefully and highlight any key details that will
help you solve the problem.
 Show your work in the space below.
Work Space
NAME: ________________________________________
DATE: ________________
 Use the table below to analyze each of the multiple choice
responses. For each multiple choice response, you are to
determine whether it is incorrect or incorrect and provide an
explanation for your thinking.
RESPONSE
CORRECT OR
INCORRECT?
WHY IS IT CORRECT OR
INCORRECT? (Explain)
This response is correct/incorrect
because……..
a
b
c
d
NAME: ________________________________________
DATE: ________________
2. Tickets for the amusement park cost $36 each. Which expression
can be used to find the cost, in dollars, of k tickets for the
amusement park?
(a) (k + 30) x (k + 6)
(b) (k + 30) + (k + 6)
(c) (k x 30) x (k x 6)
(d) (k x 30) + (k x 6)
Directions:
 Read the question carefully and highlight any key details that will
help you solve the problem.
 Show your work in the space below.
Work Space
NAME: ________________________________________
DATE: ________________
 Use the table below to analyze each of the multiple choice
responses. For each multiple choice response, you are to
determine whether it is correct or incorrect and provide an
explanation for your thinking.
RESPONSE
a
b
c
d
CORRECT OR
INCORRECT?
WHY IS IT CORRECT OR
INCORRECT? (Explain)
NAME: ________________________________________
DATE: ________________
3. A restaurant owner bought b large bags of flour for $45 each and b
large bags of sugar for $25 each. The expression b x 45 + b x 25
gives the total cost, in dollars, of the flour and sugar. Which is
another way to write this expression?
(a) b + (45 + 25)
(b) b x (45 + 25)
(c) b + (45 x b) + 25
(d) b x (45 + b) x 25
Directions:
 Read the question carefully and highlight any key details that will
help you solve the problem.
 Show your work in the space below.
Work Space
NAME: ________________________________________
DATE: ________________
 Use the table below to analyze each of the multiple choice
responses. For each multiple choice response, you are to
determine whether it is correct or incorrect and provide an
explanation for your thinking.
RESPONSE
a
b
c
d
CORRECT OR
INCORRECT?
WHY IS IT CORRECT OR
INCORRECT? (Explain)
NAME: ________________________________________
DATE: ________________
4. Ramon bought 6 packs of football cards, p packs of hockey cards,
and 4p packs of baseball cards. Ramon wrote this number
sentence to find the total number of cards he bought.
(6 + p) + 4p = 6 + (p + 4p)
Which property did Ramon use?
(a) Associative Property of Addition
(b) Commutative Property of Addition
(c) Distributive Property
(d) Identity Property of 1
Directions:
 Read the question carefully and highlight any key details that will
help you solve the problem.
 Show your work in the space below.
Work Space
NAME: ________________________________________
DATE: ________________
 Use the table below to analyze each of the multiple choice
responses. For each multiple choice response, you are to
determine whether it is correct or incorrect and provide an
explanation for your thinking.
RESPONSE
a
b
c
d
CORRECT OR
INCORRECT?
WHY IS IT CORRECT OR
INCORRECT? (Explain)
NAME: ________________________________________
DATE: ________________
Math Constructed Response – Generating Equivalent Expressions
Directions: Be sure to show all your work and fit all of it inside the boxes.
Remember to refer to the Math Constructed Response Rubric to review what
you need to do to get a “4”.
Casey has n nickels. Megan has 4 times as many nickels as Casey has.
A. Write an algebraic expression for the total number of nickels Casey
and Megan have. Then simplify the expression by combining like terms.
Show your work.
B. Use words to explain how you solved the problem. (NOTE: You must
explain each and every step of your work process)