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

2 4=How many groups

How many in each group

Represent on Number Line

2 4=How many groups

How many in each group

\

First Group of 4

Second Group of 4

Multiplying with Unlike Signs

2 (-4)=How many groups

How many in each group

Represent on Number Line

2 (- 4)=How many groups

How many in each group

\

First Group of 4

Second 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

-2 -4=How many groups

How many in each group

\

First Group of 4

Second Group of 4

If the first number is negative, switch the

sign for both numbers!

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

• 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

• 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 21Answer: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)=-3Identity 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

-Additive Identity: 4+0=4-Multiplicative Identity 4x1=4

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

• 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 x- and y-values in the table?

A. y = 3x + 2B. y = 3x − 2C. y = 2x + 3D. y = 2x − 3Answer:Show your Work:Why?

X Y

1 -1

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

Evaluate 2b2-3aa= 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

• 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 girls0.25 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 • Division -per, a

-out of-ratio of, quotient of-percent (divide by 100)

oftimes, multiplied byproduct ofincreased/decreased by a factor ofdoubled, tripled, quadrupled, etc.

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

• 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 girls0.25 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 girls0.25 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 girls0.25 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, non-terminating, 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