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1-3 Properties of Numbers
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
1-3 Properties of Numbers
Warm Up
Simplify.
1.
2.
3.
4.
10 · 7 + 7 · 10
140
15 · 9 + 61
196
(41 + 13) + (13 + 41) 108
4(32) – 16(8)
0
1-3 Properties of Numbers
Problem of the Day
Ms. Smith wants to buy each of her 113
students a colored marker. If the markers
come in packs of 8, what is the least
number of packs she could buy?
15
1-3 Properties of Numbers
Sunshine State Standards
Prep for MA.8.A.6.3 Simplify real number
expressions using the laws of exponents.
Also Prep for MA.8.A.6.4, Review of
MA.6.A.3.5
1-3 Properties of Numbers
1-3 Properties of Numbers
Vocabulary
conjecture
counterexample
1-3 Properties of Numbers
Reading Math
Equivalent expressions have the same value, no
matter which numbers are substituted for the
variables.
1-3 Properties of Numbers
Additional Example 1A: Identifying Equivalent
Expressions
Use properties to determine whether the
expressions are equivalent.
7 · x · 6 and 13x
7·x·6=7·6·x
Use the Commutative Property.
= (7 · 6) · x Use the Associative Property.
= 42x
Follow the order of operations.
The expressions 7 · x · 6 and 13x are not equivalent.
1-3 Properties of Numbers
Additional Example 1B: Identifying Equivalent
Expressions
Use properties to determine whether the
expressions are equivalent.
5(y – 11) and 5y – 55
5(y – 11) = 5(y) – 5(11)
= 5y – 55
Use the Distributive
Property.
Follow the order of
operations.
The expressions 5(y – 11) and 5y – 55 are
equivalent.
1-3 Properties of Numbers
Check It Out: Additional Example 1A
Use properties to determine whether the
expressions are equivalent.
2(z + 33) and 2z + 66
2(z + 33) = 2(z) + 2(33)
= 2z + 66
Use the Distributive
Property.
Follow the order of
operations.
The expressions 2(z + 33) and 2z + 66 are
equivalent.
1-3 Properties of Numbers
Check It Out: Additional Example 1B
Use properties to determine whether the
expressions are equivalent.
4 · x · 3 and 7x
4·x·3=4·3·x
Use the Commutative Property.
= (4 · 3) · x Use the Associative Property.
= 12x
Follow the order of operations.
The expressions 4 · x · 3 and 7x are not equivalent.
1-3 Properties of Numbers
Additional Example 2A: Application
During the last three weeks, Jay worked 26
hours, 17 hours, and 24 hours. Use properties
and mental math to answer the question.
How many hours did Jay work in all?
26 + 17 + 24
26 + 24 + 17
(26 + 24) + 17
Add to find the total.
Use the Commutative and
Associative Properties to
group numbers that are easy
to add mentally.
50 + 17 = 67
Jay worked 67 hours in all.
1-3 Properties of Numbers
Additional Example 2B: Application
Jay earns $7.00 per hour. How much money
did he earn for the last three weeks?
7(67)
Multiply to find the total.
7(70 – 3)
Rewrite 67 as 70 – 3 so you can
use the Distributive Property to
multiply mentally.
7(70) – 7(3)
Multiply from left to right.
490 – 21 = 469 Subtract.
Jay made $469 for the last three weeks.
1-3 Properties of Numbers
Check It Out: Additional Example 2A
During the last three weeks, Dosh studied 13
hours, 22 hours, and 17 hours. Use properties
and mental math to answer the question.
How many hours did Dosh study in all?
13 + 22 + 17
13 + 17 + 22
(13 + 17) + 22
Add to find the total.
Use the Commutative and
Associative Properties to
group umbers that are easy
to add mentally.
30 + 22 = 52
Dosh studied 52 hours in all.
1-3 Properties of Numbers
Check It Out: Additional Example 2B
Dosh tutors students and earns $9.00 per hour.
How much money does he earn if he tutors
students for 21 hours a week?
9(21)
Multiply to find the total.
9(20 + 1)
Rewrite 21 as 20 + 1 so you can
use the Distributive Property to
multiply mentally.
9(20) + 9(1)
Multiply from left to right.
180 + 9 = 189
Add.
Dosh makes $189 if he tutors for 21 hours a week.
1-3 Properties of Numbers
A conjecture is a statement that is believed to
be true. A conjecture is based on reasoning and
may be true or false. A counterexample is an
example that disproves a conjecture, or shows
that it is false. One counterexample is enough to
disprove a conjecture.
1-3 Properties of Numbers
Additional Example 3: Using Counterexamples
Find a counterexample to disprove the
conjecture, “The product of two whole numbers
is always greater than either number.”
2·1
2·1=2
Multiply.
The product 2 is not greater than either of
the whole numbers being multiplied.
1-3 Properties of Numbers
Check It Out: Additional Example 3
Find a counterexample to disprove the
conjecture, “The product of two whole numbers
is never equal to either number.”
9·1
9·1=9
Multiply.
The product 9 is equal to one of the whole
numbers being multiplied.
1-3 Properties of Numbers
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
1-3 Properties of Numbers
Lesson Quiz
Use properties to determine whether the expressions
are equivalent.
not equivalent
equivalent
1. 3x – 12 and 3(x – 9)
2. 11 + y + 0 and y + 11
3. Alan and Su Ling collected canned goods for 4 days to
donate to a food bank. The number of cans collected each day
was: 35, 4, 21, and 19. Use properties and mental math to
answer each question.
a. How many cans did they collect in all? 79
b. If each can contains 2 servings, how many servings of food
did Alan and Su Ling collect? 158
4. Find a counterexample to disprove the conjecture, “The
quotient of2two
numbers
is always
 1whole
= 2; the
quotient
2 is notless
lessthan
thaneither
eithernumber.”
of the
whole numbers.
1-3 Properties of Numbers
Lesson Quiz for Student Response Systems
1. Which of the following expresssions are
equivalent?
A. 2x – 4 = 2(x – 4)
B. 2x – 4 = 2x – 2 + 2
C. 2x – 4 = 2x – 2 – 2
D. 2x – 4 = 2(x + 4)
1-3 Properties of Numbers
Lesson Quiz for Student Response Systems
2. Which of the following expresssions are
equivalent?
A. 3x + 4 = 2 + 2 + 3x
B. 3x + 4 = 2 + 2 + 3 + x
C. 3x + 4 = 3(x + 4)
D. 3x + 4 = 3(x + 2)
1-3 Properties of Numbers
Lesson Quiz for Student Response Systems
3. Find a counterexample to disprove the
conjecture, “Any number that is divisible
by 2 is also divisible by 4.”
A. 20  2 = 10 and 20  4 = 5
B. 18  2 = 9 and 18  4 = 4.5
C. 20  2 = 20 and 20  4 = 80
D. 18  2 = 36 and 18  4 = 72