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Objective
I can represent multiplication and division on a
number line and with counters.
I can use multiplication and division to solve real
life problems.
Multiplying with Positive Numbers
How many
groups
2 4=
How many in
each group
Represent on Number Line
How many
groups
2 4=
How many in
each group
First Group Second
of 4
Group of 4
\
Multiplying with Unlike Signs
How many
groups
2 (-4)=
How many in
each group
Represent on Number Line
How many
groups
2 (- 4)=
How many in
each group
Second
Group of 4
\
First Group
of 4
Multiplying with Negative Numbers
- 2 (-4)=
What is the
opposite of a
positive?
If the first number
is negative, we
must switch the
sign of both
numbers.
Represent on Number Line
How many
groups
-2 -4=
If the first number is
negative, switch the
sign for both numbers!
How many in
each group
First Group Second
of 4
Group of 4
\
Tony’s Job
• Tony is working at a coal mine. The elevator in
the mine shaft descends 250 feet per minute.
How many feet would he descend in 2
minutes? If we were to label the amount on a
number line, would this be negative or
positive?
Homeroom Instruction
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Come in quickly & quietly
Go to your desk.
Take out your AR book and read
Raise your hand to ask to sharpen your pencil.
Put your backpack underneath your desk.
No talking.
Bellwork Day Three
• Caleb ate c carrots and p pickles each day for
a full week. He used the expression to 7(c+p)
represent the number of vegetables he ate
that week. Which equation correctly shows
the Distributive Property?
• A. 7(c + p) = 7(cp)
• B. 7(c + p) = 7c + p
• C. 7(c + p) = 7c + 7p
• D. 7(c + p) = 7 + (c + p)
Word of the Week
• Associative Property: states that the change in
grouping of three or more addends or factors does
not change their sum or product.
Addition: (2 + 3) + 5 = 2 + (3 + 5)
Multiplication:(4 x 5) x 10 = 4 x (5 x 10)
• Associative property holds good for both addition and
multiplication, but not for subtraction and division.
Review-Think, Pair, Share
Objective
• I can multiply and divide
rational numbers
Multiply Fractions & Mixed
Numbers
-
Rules to Remember
Positive x Positive= Positive
Positive x Negative= Negative
Negative x Negative = Positive
Fractions-Multiply across
Mixed Numbers- Convert to
improper fractions and multiply
across. Simplify
Dividing Fractions & Mixed
Numbers
You Try!
Dividing Fractions & Mixed
Numbers
Homeroom Instruction
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Come in quickly & quietly
Go to your desk.
Take out your AR book and read
Raise your hand to ask to sharpen your pencil.
Put your backpack underneath your desk.
No talking.
Bellwork Day Four
• The square root of 105 is between which two
• numbers?
• F. 4 and 5
• G. 9 and 10
• H. 10 and 11
• J. 20 and 21
Answer:
Show your Work:
Why?
Word of the Week
• Associative Property: states that the change in
grouping of three or more addends or factors does
not change their sum or product.
Addition: (2 + 3) + 5 = 2 + (3 + 5)
Multiplication:(4 x 5) x 10 = 4 x (5 x 10)
• Associative property holds good for both addition and
multiplication, but not for subtraction and division.
Guess that Word
Objective
• I can identify math properties.
• I can use properties to solve problems.
Why Learn about Properties
36 2/3
Properties
• Commutative Property: Reversing the order of
addition or multiplication will produce the
same product or sum
-Addition: a + b= b+ a
-Multiplication: 5 x6 = 6x 5
• Associative Property: changing a grouping
rearranged parenthesis, but kept everything
else in the same order will produce the same
product or sum
-Addition: (2 + 3) + 5 = 2 + (3 + 5)
-Multiplication: :(4 x 5) x 10 = 4 x (5 x 10)
Properties
• Distributive Property: product of a
number and a sum is equal to the sum of the
individual products of addends and the
number
-Multiplication over Addition: 3(4+5)=27
-Multiplication over Subtraction: 3(4-5)=-3
Identity Property: states that the sum of zero
and any number or variable is the number or
variable itself/ product of 1 and the number is
itself
Activity/Matching Cards
• Order the cards
• Match the correct property with
the equations
• Place card back in ziplock bag
Grading Quiz
• A students has just turned in an assignment
and you are going to check their quiz.
• You will mark the incorrect answer with a
check and give them feedback about why their
answer or reasoning is not correct.
• Post their grade at the top of the sheet
Homeroom Instruction
•
•
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Come in quickly & quietly
Go to your desk.
Take out your AR book and read
Raise your hand to ask to sharpen your pencil.
Put your backpack underneath your desk.
No talking.
Bellwork Day Five
• Which equation is
true for all the xand y-values in
the table?
X
Y
1
-1
A. y = 3x + 2
B. y = 3x − 2
C. y = 2x + 3
D. y = 2x − 3
Answer:
Show your Work:
Why?
2
1
3
3
4
5
Word of the Week
• Associative Property: states that the change in
grouping of three or more addends or factors does
not change their sum or product.
Addition: (2 + 3) + 5 = 2 + (3 + 5)
Multiplication:(4 x 5) x 10 = 4 x (5 x 10)
• Associative property holds good for both addition and
multiplication, but not for subtraction and division.
Objectives
• I can identify variables.
• I can understand the order of
operations.
• I can solve equations and word
problems with substitution.
Variables & Substitution
• Variable:A symbol for a number we don't
know
-Example- x y a b
• Constant: a non-varying value
• Substitution: place in for another
Example: Evaluate 2 (a + b) if a=2 b=4
Examples #1
2
2b -3a
Evaluate
a= 5 b=3
Example #2
½ (x- 1 ¾) for x=2
Example #3: Word Problems
• A florist uses a formula to determine
the cost for making a bouquet : c=
4.50 + 1.25h, where c is the cost of
making the bouquet and h is the
height, in inches, for each bouquet.
What is the cost of making a 20-inch
bouquet?
Homeroom Instruction
•
•
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•
•
Come in quickly & quietly
Go to your desk.
Take out your AR book and read
Raise your hand to ask to sharpen your pencil.
Put your backpack underneath your desk.
No talking.
Bellwork Day One
• Johnna’s reading rate is 150 words per minute. She
is reading a 364-page book that has about 275
words on each page. At this rate, which is closest to
the amount of time Johnna should take to read the
book?
• F. 10 hrs
• G. 11 hrs
• H. 12 hrs
• J. 13 hrs
• Answer:
• Show Work:
• Why?
Bellwork Day Two
John bought 25 ½ yards of rope. He is going
to cut the ribbon into smaller pieces that are
each ¾ yard long. What is the maximum
number of ¾ yard-long pieces of ribbon that
can be cut from the original length of the
ribbon?
• Answer:
• Show Work:
• Why?
Word of the Week
• Ratio: A ratio shows the relative sizes of two
or more values.
• Example: if there is 1 boy and 3 girls you could
write the ratio as:
1:3 (for every one boy there are 3 girls)
¼ are boys and 3/4 are girls
0.25 are boys (by dividing 1 by 4)
25% are boys (0.25 as a percentage)
Objective
• I can solve word problems
using division and
multiplication
Key Word for Multiplication & Division
• Multiplication
of
times,
multiplied by
product of
increased/decreased
by a factor of
doubled, tripled,
quadrupled, etc.
• Division
-per, a
-out of
-ratio of, quotient of
-percent (divide by 100)
How to Solve it
• Understand the Problem
-Underline the question
- Circle Key word
- Restate the question
• Devise a plan
• Carry out the Plan
• Check Your Work
Faith’s Rope
Faith bought 8 2/3 yards of ribbon. She is going
to cut the ribbon into smaller pieces that are
each 1/3 yard long. What is the maximum
number of 1/3 yard-long pieces of ribbon
that can be cut from the original length of the
ribbon?
Bill’s Construction Company
• A construction company is
building concrete pillars at the
entrance of an auditorium. Each
pillar require 5 ½ cubic yards of
concrete. How many cubic yards
will require to construct 6 pillars?
Word Problem Instructions
• Pick 3 word problems from the “Rational
Number Choice Board” worksheet
• Write the entire word problem on the “word
problem” section. Personalize the problems.
• Show your work and solve the problem in the
“Show your Work” section. Circle your answer
• Write a detailed explanation of how you
solved the problem in the “Explain Your
Answer” section
• Draw a picture and create a title. Please color
and decorate.
Homeroom Instruction
•
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Come in quickly & quietly
Go to your desk.
Take out your AR book and read
Raise your hand to ask to sharpen your pencil.
Put your backpack underneath your desk.
No talking.
Bellwork Day Two
John bought 25 ½ yards of rope. He is going
to cut the ribbon into smaller pieces that are
each ¾ yard long. What is the maximum
number of ¾ yard-long pieces of ribbon that
can be cut from the original length of the
ribbon?
• Answer:
• Show Work:
• Why?
Word of the Week
• Ratio: A ratio shows the relative sizes of two
or more values.
• Example: if there is 1 boy and 3 girls you could
write the ratio as:
1:3 (for every one boy there are 3 girls)
¼ are boys and 3/4 are girls
0.25 are boys (by dividing 1 by 4)
25% are boys (0.25 as a percentage)
Word Problem Instructions
• Pick 3 word problems from the “Rational
Number Choice Board” worksheet
• Write the entire word problem on the “word
problem” section. Personalize the problems.
• Show your work and solve the problem in the
“Show your Work” section. Circle your answer
• Write a detailed explanation of how you
solved the problem in the “Explain Your
Answer” section
• Draw a picture and create a title. Please color
and decorate.
Homeroom Instruction
•
•
•
•
•
•
Come in quickly & quietly
Go to your desk.
Take out your AR book and read
Raise your hand to ask to sharpen your pencil.
Put your backpack underneath your desk.
No talking.
Bellwork Day Three
• Tonya feeds 21 ¾ ounces of dog
food to three dogs. If each dog
eats an equal amount, how many
ounces of dog food does each
dog eat?
• Answer:
• Show Work:
• Why?
Word of the Week
• Ratio: A ratio shows the relative sizes of two
or more values.
• Example: if there is 1 boy and 3 girls you could
write the ratio as:
1:3 (for every one boy there are 3 girls)
¼ are boys and 3/4 are girls
0.25 are boys (by dividing 1 by 4)
25% are boys (0.25 as a percentage)
Homeroom Instruction
•
•
•
•
•
•
Come in quickly & quietly
Go to your desk.
Take out your AR book and read
Raise your hand to ask to sharpen your pencil.
Put your backpack underneath your desk.
No talking.
Homeroom Instruction
•
•
•
•
•
•
Come in quickly & quietly
Go to your desk.
Take out your AR book and read
Raise your hand to ask to sharpen your pencil.
Put your backpack underneath your desk.
No talking.
Bellwork Day Four
• Cathy is cutting 5 ½ foot strips of ribbon from
a 60-foot roll. How many full strips can she cut
from the roll? Once she cuts the maximum
number of full strips from the roll, how many
feet of ribbon will be left over?
• Answer:
• Show Work:
• Why?
Word of the Week
• Ratio: A ratio shows the relative sizes of two
or more values.
• Example: if there is 1 boy and 3 girls you could
write the ratio as:
1:3 (for every one boy there are 3 girls)
¼ are boys and 3/4 are girls
0.25 are boys (by dividing 1 by 4)
25% are boys (0.25 as a percentage)
Review
• Convert 5/8 to a decimal
• Convert 1 ¼ to a decimal
• Convert 1/3 to a decimal
Objective
• I can convert rational numbers to fractions
and decimals
• I can categorize numbers.
Number Conversion
1
2
2
3
Division is used
to convert
fractions to
decimals
Convert the fractions to
decimals. What are the
difference between the
two numbers?
Vocabulary
• Terminating decimal:
has a finite number of
digits (the decimal will
end or terminate)
Examples: ½ = .5,
4.56746352, 7/8=
0.875
• Non-terminating
decimal:
a decimal in which a
digit, or a group of
digits, repeats without
end.
Example: 1/3, pi, the
square root of 2
Vocabulary
• Repeating Decimal:
a decimal in which a digit, or
a group of digits, repeats
without end.
• Examples: (Draw a line over
repeating numbers)
• 2/3=.6
• 6/7= .857142
Bar Notation (Vinculum)
• Non-repeating Decimal:
a decimal that neither
terminates nor repeats.
Example: ¼ =.25
the square root of 7
pi=3.141592654…..
Guided Practice:
• Use two minutes to quietly convert the answers to
decimals and identify if they are terminating, nonterminating, repeating or non-repeating.
Terminating-Stand
Repeating-Clap
Non-terminating: Sit in seat
Non-repeating- stomp twice
2/3=
pi=
9/11=
5/32=
Homeroom Instruction
•
•
•
•
•
•
Come in quickly & quietly
Go to your desk.
Take out your AR book and read
Raise your hand to ask to sharpen your pencil.
Put your backpack underneath your desk.
No talking.
Bellwork Day Three
• Answer:
• Show Work:
• Why?
Bellwork Day One
• Answer:
• Show Work:
• Why?
Word of the Week
• Rate: a ratio that compares two quantities
that are measured in different units
• Example: 2 Snickers Candy Bars for $1.00= .50
$1.00/2 or 2:1
60 miles in two hours= 30 mph
60/2 or 60:2 or 30:1