Name: _____________________________________________ Period ___ Date _________________
Lesson 7-7: Exploring Equivalent Expression & Applying Properties of Operations
ESSENTIAL QUESTION: How can we use Properties of Math Operations to write equivalent
math expressions?
WARM UP:
State whether the following number sentences are true or false.
a)
4+6 = 5+5
_______
b)
4+5 = 6+5
______
Instructions:
Open Agile Mind Lesson 7-7 “Applying Properties of Math Operations”
Follow the steps on this activity sheet. Read each page carefully. Complete the online
lesson and be sure to show your work on the activity sheet and check your answers as you
go.
1) Go to Page 9: Consider another fruit equation:
a) The expressions on either side of the equal sign are equivalent.
How do you know they are equivalent?
b) What numbers could the plum represent that would make the sentence true?
c) Would the two expressions still be equal if the operation was changed?
2) Go to Page 10: Think about some
other fruit equation puzzles.
For each puzzle, decide whether the
expressions are equivalent.
In other words, is the equation true or
false?
When you are finished click the Check
buttons to check your thinking.
3) Go to Page 11: Read the descriptions of the Commutative Properties of Addition and
Multiplication.
a) What does the word commute mean? ______________________________________
4) Go to Page 12: Read the descriptions of the Associative Properties of Addition and
Multiplication.
a) What does the word “associate” mean? _____________________________________
b) Will the Associative & Commutative Properties work for subtraction and division? _____
Explain your reasoning: __________________________________________________
_____________________________________________________________________
5) NOTES: Write the algebraic rule for the first four properties.
Property
Commutative Property of
Addition
Commutative Property of
Multiplication
Associative Property of
Addition
Associative Property of
Multiplication
Distributive Property of
Multiplication over Addition
Algebraic Rule
Example
6) Identify which Property is being used:
a)
14 + 10 = 10 + 14
Associative or Commutative
b)
(7 + 5) + 11 = 7 + (5 + 11)
Associative or Commutative
c)
45 • (5 • 3) = (45 • 5) • 3
Associative or Commutative
d)
45 • (5 + 3) = (5 + 3) • 45
Associative or Commutative
7) Go to Page 13: What do you remember about the Distributive Property?
View and discuss the animation with your partner.
8) Go to Page 14: Can you represent the Distributive Property of Multiplication over
Addition with symbols? Insert each variable into the correct box below and check your
thinking by completing Page 14.
Now go back to the NOTES on the previous page
and write the Distributive Property algebraically.
Use the Distributive Property to write the following expressions in an equivalent form.
9) 3 • (5 + 25)
10)
24 + 36
11)
4 ( 100 + 11)
12) Use the Distributive Property to write the following expression in an equivalent form.
a) ( 6 • 8 ) + ( 6 • 10)
= _________________________________________
COMPLETE THE PRACTICE PROBLEMS at the end of the Agile Mind Lesson:
GA #9: Identifying the Properties:
GA #10:
Use the Distributive Property to write each of the following expressions in an
equivalent form.
MP #10
Match up the equivalent expressions to complete the table.