enVision Math Grade 5- Adapted Notes
Name- _____________
Topic 3 Lesson 1- Multiplication Properties
Objective: Identify and apply the commutative, associative, identity, and zero properties of
multiplication.
Recall: Commutative Property of Multiplication- the order of factors can be _______________, but
the product stays the ______________________ .
Example _______________= ______________________
Recall: Associative Property of Multiplication- change the grouping of the factors with _________,
but the product stays the ____________________.
Example (2 x 5) x 3= ______________________________
Vocabulary:
Define: Identity Property of Multiplication- when you multiply any number by ______, the product
is __________ ______________________.
Example _____________________
Define: Zero Property of Multiplication- When you multiply any number by _______, the product
is _______.
Example _____________________
Essential Understanding:
The properties of multiplication can be used to simplify computation and verify mental math and
paper & pencil algorithms.
enVision Math Grade 5- Adapted Notes
Name- _____________
Topic 3 Lesson 2- Using Mental Math to Multiply
Objective: Mentally compute products of whole numbers using place-value patterns and properties
of multiplication.
Vocabulary:
Define: Factors- numbers that are ________________ _______________ Example- _____________
Define: Product- the ____________ to a ______________ problem. Example- __________________
Define: Multiple- a product of a given whole number and ____________ ____________ __________
Example- Multiples of 6- _____, ____, _____, _____, _____, ______, ______, _____, _____...
Examples:
1. How can you use mental math to multiply by multiples of 10, 100, or 1000?
Step 1
Step 2
Step 3
Find the product of the
Count the total number of
Place the total number
non-zero digits
zeros in both factors
of zeros after the
Notice the pattern
product of the non-
5 x7= _____; 50x7= _______
zero digits
500x7=______; 5x70=_______
5x700= ______; 50x700=_______
2. How can multiplication properties help you use mental math?
 Use properties of multiplication and mental math to find 25x17x4
Think
_____ & _____ are compatible #’s
and is easy to multiply.
_____x ______=______ and ______x______=______
So, ____________________= __________
Write
Commutative property
____________________=_________________
Associative property
____________________= _________________
enVision Math Grade 5- Adapted Notes
Name- _____________
Topic 3 Lesson 3- Estimating Products
Objective: Use rounding or compatible numbers to estimate products of whole numbers
Vocabulary:
Define: underestimate- when both numbers used to estimate were ________ than the actual
numbers.
Define: overestimate- when both numbers used to estimate were __________ than the actual
numbers.
Examples:
1. View the question at the top of page 68
$525 rounds to __________
31 rounds to ________
Find _________x __________= _________________
2. How can you use compatible numbers to estimate products?
24 _________
X39 __________
* Think: It is easy to find _______x______,
since ______x______ are compatible #’s.
_____x______ =_________
So, ________x ________= ___________
enVision Math Grade 5- Adapted Notes
Name- _____________
Topic 3 Lesson 4- Exponents
Objective: Use exponential notation
Vocabulary:
Define: base- the number to be _______________. Example- _______________
Define: exponent- the number that tells how many times the base is used as a __________
Example- __________
Define: power- another name for an _________________
Example- ________ can be read as _________ _____ ______ __________ ___________
Exceptions- _________ can be read as _______________ _______________ AND
__________ can be read as ________________ ____________________
Can be written in three different ways:
1. Exponential Notation: ______________
2. Expanded Form: ___________________
3. Standard Form: ____________________
Examples
1. Write 4 x 4 x 4 in exponential notation- _______________________________
2. Write 10^4 in expanded form- _______________________________________
3. Write 2^5 in standard form- _________________________________________
_________________________________________
enVision Math Grade 5- Adapted Notes
Name- _____________
Topic 3 Lesson 5- Distributive Property
Objective: Use the Distributive Property to simplify expressions and solve equations.
Vocabulary:
Define: Distributive Property- multiplying a sum (or a difference) by a number is the same as
multiplying each sum (or difference) by the number and adding (or subtracting) the __________.
Examples:
1. 6x27= _______+ ________
2. Look at the question at the top of page 72: What expressions can you write to represent the
number of square units inside the rectangle?
Step 1 Think of ______ rows of ______ in each. ______x______
Step 2 Think of ______ as (_____+_____)
Step 3 Think of the rectangle in two separate parts as seen below:
6
6
10
8
Step 4 The total is the sum of the two parts. (_____ x_____) + (_____x_____)
Homework Help:
Using the Distributive Property to state that multiplication distributes over addition
a x (b+c)= (a x b) + (a x c)
Using the Distributive Property to state the multiplication distributes over subtraction
a x (b-c) = (a x b) – (a x c)
#19 you will need to draw the rest of the chart to fill it in
enVision Math Grade 5- Adapted Notes
Name- _____________
Topic 3 Lesson 6- Multiplying by 1- Digit Numbers
Objective: Use partial products or traditional algorithms to multiply multi-digit numbers by a onedigit number
Option 1
Option 2
36
36
x 7
x 7
Examples:
1. A theater has five sections with 347 seats in each section. What is the total number of seats
in the theater?
Option 1
Option 2
enVision Math Grade 5- Adapted Notes
Name- _____________
Topic 3 Lesson 7- Multiplying 2-Digit by 2- Digit Numbers
Objective: Multiply two-digit numbers by two digit numbers
Vocabulary:
Define: partial products- products found by breaking one of two factors into ________, ______,
_______________, and so on and then multiplying each of these by another factor.
Examples:
1. Look at the example at the top of page 78
Step 1
Step 2
Multiply the ones,
Multiply the tens,
regroup if necessary
regroup if necessary
38
x12
__________
+____________
_________________
2.
68
X57
_____________________
+____________________
_________________________
Step 3
Add partial products
enVision Math Grade 5- Adapted Notes
Name- _____________
Topic 3 Lesson 8- Multiplying Greater Numbers
Objective: Multiply two-digit numbers by factors with more than two digits.
Recall: Remember to use the same methods learned in the previous two lessons to help solve
problems in this lesson
Examples:
1. Look at the example at the top of page 80
Step 1
Step 2
Multiply the ones,
Multiply the tens,
regroup if necessary
regroup if necessary
Step 3
Add partial products
389
389
389
x 12
x 12
x 12
_____
_____
_____
+_______
+ ______
________
2.
789
x
73
*Tip: when multiplying be sure to keep the numbers
in the correct columns to make sure the numbers
____________ _________.
Homework Help:
#38 think estimation
enVision Math Grade 5- Adapted Notes
Name- _____________
Topic 3 Lesson 9- Problem Solving- Draw a picture and write an equation
Objective: Use diagrams and write equations to solve problems.
Steps:
1.
2.
3.
4.
After reading the problem, ask yourself “_________ ______ _____ ________?”
“What am I asked to ______________?”
Plan
Solve
Examples:
1. Look at the top of page 82 for the example
What do I know?
*_______________________
What am I asked to find?
________________________
*_______________________
Draw (Plan)
2006
1990
Write an equation (Solve)
_______________= p
_______________= p
2. Each artist at a large art show is assigned to a team of five judges. There are nine teams of
judges at the show. If each team reviews the work of 27 artists, how many artists attend the
show?
What do I know?
What am I asked to find?
*_______________________
_________________________
*_______________________
_________________________
Write an equation (Solve)
_______________________= a
Draw (Plan)
_______________________= a