traffic speeds

**Rates 2.5**

GOAL:

Determine and apply

rates to solve a problem.

A rate is a comparison of two

quantities measured in different

types of units.

Wait... Are ratios rates?

40km/hour

Common Rates We Use

$15/hour

working wages

Unit Rate

To make the second term 1, simply divide both terms by the second term.

$10/2 hours

$5/1 hour

32km/2 hours

$300/25 hours

64L/8 seconds

Practice

Problem Solving

Erica has been trying to save for a vacation in Europe. She determines that the flight cost of the trip would be $800. If she is paid $95 for a 10 hour workday, how many hours would she need to work to cover the cost of her flight?

Representing Percentages 2.6

GOAL:

Represent and calculate percents that involve whole numbers, or decimals and whole number percents that are greater than 100%.

Last year Greensborough P.S. had 500 students. If the population this year has increased by 7%, how many students are there now?

To model percent, create a grid of 100 squares and determine how many students are represented by one square. How? Engage your past knowledge of

RATIOS

!

500:100 = 5:1

Scale factor of 100, divide both terms by 100.

Therefore, one box, or one percent, equals 5 students!

5+5+5+5+5+5+5=35

500+35=535

There are therefore 535 students this year.

What percent of this 100 grid is coloured?

What percent of the 100 grid is not coloured?

Out of 200 students, 27% of them are vegetarians.

How many students are represented by each square?

How many students are vegetarians?

Ryan is looking to buy a new phone and has found two sales for the model he wants. Which store is offering the best sale?

Store A:

25% off of $800

Store B:

20% off of $750

Solving Percent

Problems 2.7

Use proportions to solve percent problems.

GOAL:

We can use proportions to solve problems!

Out of 29 students, 4 wanted more homework.

What percent want more homework?

We know that a percent is out of 100 so we can express it as:

?

100

=

4

29

We know that 4 we are looking for 4 out of 29 students.

?

100

=

4

29

Once we set up the problem, find the scale factor.

The scale factor will be determined by the two known numerators OR denominators. Simply divide the right side by the left side.

29 ÷ 100 = 0.29

When finding solving for percentage, or the left

side of the equivalency, divide the other known

number by the scale factor:

4 ÷ 0.29 = 13.79%

Therefore 13.79% of the students want more homework.

13.79

100

=

4

29

?

100

=

12

120

50

100

=

11

?

Always find the scale factor by dividing

the ride side by the left side.

What is different? What is the same?

Scale factor:

Left Side (÷):

Scale factor:

Right Side (×):

Practice

?

100

=

4

10

5

100

=

4

?

16

100

=

?

66

47

100

=

?

100

?

100

=

800

991

77

100

=

32

?

Mr. Quan decided that if 80% of students got over 80% on a Math check in this Friday that he would give extra time for DPA that day.

If 28 students are taking the check in, how many students need to get over 80% for the extra DPA time?

Terrence was promised by his parents that he would get a raise in his weekly allowance if he scored over 90% on his next Science test.

Today, Terrence got his mark back and he scored 43/49. Did he get a high enough score for a raise in his allowance?

Decimals & Percent Problems 2.8

Use percents to solve problems that involve everyday situations.

GOAL:

Expressing a

percent

as a

decimal

can sometimes help you solve problems.

Question:

What is 40% of 200?

First, turn 40% into a decimal:

40% = 40 ÷ 100 = 0.40

Then simply multiply the number by the decimal:

200 x 0.40 = 80

Practice

Convert into decimals and solve.

Show your work!

30% =

23% =

64% =

89% =

30% of 340

23% of $60

64% of 1010

89% of 24 hours

340 x ____ =

$60 x ____ =

1010 x ____ =

24h x ____ =

Problem Solving

Samantha has saved $750 to purchase a new state of the art bicycle. The current price is $850 but also has two discount coupons to choose from (she can only use one). Which coupon provides the best discount?

1) Receive 18% off the purchase price!

2) An instant in store $150 rebate!

To solve, you must first determine the amount saved and then compare values.

1) 18% = 18 ÷ 100 = 0.18

$820 x 0.18 = $147.60

The first coupon saves $147.60.

2) This coupon saves a flat $150.

Therefore, Samantha should choose the second coupon because it saves more money.

Problem Solving

When you purchase items on a credit card, the total value of your purchases on that credit card, or money borrowed, is charged interest.

What is the monthly interest charge on the following bill if the interest rate is 19.7%

October 2016

1) Shoes - $90

2) Dinner - $82

3) Smart Phone - $750

4) Gum - $1

**Unit 2 Round Up**

Solve word problems that require you to engage skills throughout Unit 2.

**GOAL:**

According to a 2007 census report, Canada's population was 23 500 000. Over the next 3 years, Canada's population began increasing at an inconsistent rate. From 2007-2008 the population grew 3.5%. For the next 5 years, it was determined that the growth rate grew by 15%.

Determine the growth rate and population for 2008, 2009 and 2010.

Year

Population

Growth Rate

2007

23.5 mil

n/a

2008

3.5%

2009

2010

A factory producing staplers produced approximately 1400 staplers over an 8 hour day.

The management found that if for 50% of the day they provided more lighting, production would increase by 75%.

How many staplers are produced over 3 days when more lighting is provided.

Information That May Help:

1) What is the hourly rate?

2) How many hours a day have

increased production?

3) What is the increased

production rate?

**Unit 2:**

**proportional**

**Strand - Number Sense**

It’s almost Hallowe’en and the Burr family is preparing for another busy year of trick-or-treating. Mr. Burr insists on a proper ratio of one chocolate bar to two lollipops for every trick-or-treater that comes to their door. At the last family meeting, it was decided that they should estimate how much money they would expect to spend on treats and they had the following information:

1) Last year, 95 trick-or-treaters came to their door;

2) it is expected that they will see a maximum 25% increase this year in trick-or-treaters;

3) a bag of 10 chocolates cost $5.00 plus taxes;

4) a bag of 15 lollipops cost $4.00 plus taxes; and

5) the sales tax in Ontario is 13%.

Based on the above information, how much money will be spent to insure that all trick-or-treaters this year will be given the proper ratio of treats?

First, determine the expected number of trick-or-treaters base on a 25% increase of 95.

95 x (25 ÷ 100) + 95 = 118.75

Since you can't have a fraction for a person, I will round up to 119.

Next, we need to determine how many chocolates/lollipops given the ratio in the question and the fact that every person gets 1 chocolate bar.

1 : 2 = 119 : ___ (scale factor: 119)

1 : 2 = 119 : 238

They will need 119 chocolate bars and 238 lollipops.

Finally, we need to determine how many bags we need of each and multiply that by the price. Since the sale tax is the same on all of the bags, we can add the two together and add 13% tax for the final solution.

119 ÷ 10 = 11.9 (therefore 12 bags of chocolate)

238 ÷ 15 = 15.87 (therefore 16 bags of lollipops)

(12 x $5.00) + (16 x $4.00) = $124.00

Plus Tax = $124 x (13 ÷ 100) + $124.00 = $140.12

Therefore, the Burr Familiy will need to spend $140.12 to pay for the expected 119 trick-or-treaters.

**Relations**

**Unit 3:**

**DATA**

**MANAGEMENT**

Organizing and

Presenting Data 3.1

Organize and present data to solve problems and make decisions.

GOAL:

Did you remember...

Can we remember?

In your table groups, brainstorm for one minute.

There are many graphical ways to represent data, or information.

Used to compare different categories.

Similar to a

Bar Graph

.

Easier visual representation that can

grab the viewer's attention.

Bar Graph

Pictograph

Line Graph

Used to observe trends.

Most Common Answer

Less Common

Extra points if you thought of these!

Scatter Plot

Used to determine relations

between two things. What does this

Scatter Plot

find? What is that

Red Line

?

Circle Graph

Compares the parts that

make up the whole.

Stem & Leaf

Stem and Leaf

plots can help you determine frequency.

When there is a lot of data,

it can be difficult to understand it. Graphs are highly effective tools.

Time for us to organize some data. Below are the types of sports played by kids over the weekend. Make a

bar graph

to determine which was the most popular sport.

soccer

baseball

tennis

hockey

rugby

volleyball

hockey

rugby

volleyball

soccer

baseball

rugby

hockey

volleyball

hockey

rugby

hockey

volleyball

1) Label your X and Y axis.

2) Determine the intervals.

3) Transfer your data.

4) Give your graph a title.

5) Enjoy the glory of your

bar graph

.

Compare the data on the left page and now on the right page. What do you find?

Exploring

Sample Size 3.2

Explore how sample size represents a population and how well it does this.

GOAL:

Do we need to survey everyone to get a

reasonable

answer to a question?

While surveying

everyone

, known as a

census

, is ideal, it is not always possible or efficient.

A

sample

is a part of the population that can be used to make predictions about the whole population.

But when is it best to use it? How big should a sample be to represent the population?

Testing a Sample

You have a choice between three flavours of ice cream:

1) Chocolate

2) Strawberry

3) Vanilla

Write your choice

SECRETLY

on a small piece of paper and hand it to Mr. Ng. You must choose one of these three... no arguing... you know who you are...

We also need a volunteer to help fill out the chart to the right. There should be tallies in each row equal to the sample size.

Thinking

:

When does the sample start to proportionally represent the entire class? When does the sample turn into a census?

Time to experiment!

This is a difficult topic.

Most of your

THINKING

questions will start from your understanding of a sample versus a census.

We will continue this discussion next class.

Practice with textbook questions and wait for homework to be announced at the end of class.

Real Life Data

3.3 (Modified)

Understand how real life data is graphically represented in the media.

GOAL:

There's so much

information

out there...

The hardest thing to do is to turn that information into something we can easily understand.

Let's look at some real life

data

.

Canadian

Federal

Election, 2015

These are the local results in Markham-Stouffville.

This chart is quite graphic and helpful. But would it be helpful with voting information missing?

What's the best type of chart/graph to display this information?

Let's take a closer look!

School Populations 2010-2016

Create a chart that shows all three school's populations from 2010-2016.

Create a bar graph that compares the

three schools over four years.

Based on the charts, what is the trend

for all three schools?

Make a prediction. What do you think the populations be in 2017?

Are these numbers samples or censuses?

Histograms 3.4

Use histograms to describe appropriate data.

GOAL:

What's different?

Bar Graphs

look like

Histograms

but they are

very different.

Histograms graph the frequency of data ranges.

Histograms have no gaps in between... why?

Histograms measure variance, or differences, in one characteristic.

For example:

Times to run 100m.

Test score results.

Money spent per customer in a store.

Mr. Quan wanted to analyze the frequency of results when it came to test scores. If the majority of students scored 75%-85%, he created a balanced test.

Here are the results:

1. 75%

2. 81%

3. 95%

4. 64%

5. 55%

6. 60%

7. 90%

8. 84%

9. 73%

10. 74%

11. 57%

12. 77%

13. 68%

14. 63%

15. 71%

16. 62%

17. 59%

18. 91%

19. 81%

20. 79%

Mean, Median & Mode 3.5

Determine the mean, medium and mode of sets of data.

GOAL:

Mean

Knowing the mean, median, and mode of data sets can help compare groups of data and make it more accurate.

The mean is the average, or the sum of the set divided by the number of numbers in the set.

7, 8, 10, 13, 13, 20

(7+8+10+13+13+20) ÷ 6 =

mean

71 ÷ 6 =

mean

11.84

=

mean

Median

The median is the middle value in a set of ORDERED data. When there is an odd number of numbers, the median is the mean of the two middle numbers.

First

, order this data: 12, 17, 9, 11, 15

First

, order this data: 12, 17, 9, 13, 11, 15

Mode

The mode is the number that occurs most often in a set of data; there can be more than one mode, or there might might be no mode.

16, 18, 12, 12, 14, 19

12, 19, 20, 32, 40, 41

12, 13, 15, 6, 25, 30, 15

Practice

Mean:

Median:

Mode:

**Unit 4:**

**Patterns & Relationships**

Fibonacci Sequence 4.1

Identify and discuss relationships within a number pattern.

GOAL:

BIAS ALERT

The Fibonacci Sequence is

one of Mr. Quan's favourite

mathematical concepts.

In mathematics, the Fibonacci numbers are the

terms

in the following integer sequence, called the Fibonacci sequence, and characterized by the fact that every number after the first two is the sum of the two preceding ones.

Term

: A term is one number in a sequence.

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610...

1

1

2

3

Creating Pattern

Rules 4.2 (2 Lessons)

Identify and discuss relationships within a number pattern.

GOAL:

Single Pattern

Fig 0. Fig 1. Fig 2. Fig 3. Fig 4.

Step 1: Find the

rate of change

(new blocks each time): _____

Step 2: Find the

initial value

, or Figure 0: _____

Step 3: Form the equation.

y =

(rate of change

)x +

initial value

y =

3

x +

3

Fig 0. Fig 1. Fig 2. Fig 3. Fig 4.

Step 1: Find the

rate of change

(new blocks each time): _____

Step 2: Find the

initial value

, or Figure 0: _____

Step 3: Form the equation.

y =

(rate of change

)x +

initial value

x

y

Fig 0. Fig 1. Fig 2. Fig 3. Fig 4.

Rate of Change

:

Initial Value

:

Equation:

__________

__________

__________

Remember

y=(

RoC

)x +

IV

CHALLENGE YOURSELF HERE

Fig 0. Fig 1. Fig 2. Fig 3. Fig 4.

Rate of Change

:

Initial Value

:

Equation:

__________

__________

__________

Remember

y=(

RoC

)x +

IV

HINT: Break up the pattern into parts and combine equations.

Go Beyond!

General Term of a Sequence 4.3

Write an algebraic expression for the general term of a sequence.

GOAL:

CHALLENGE YOURSELF HERE

Discover the pattern and determine The Rule with a

geometric sequence

.

Consider the following:

Go Beyond!

Sandy earns $5 a day just from doing chores around the house. After the first day she finds that she has $55.

Make a term chart and determine an algebraic expression.

Term

Number (x)

0

1

2

3

4

5

6

Term

Value (y)

___

$55

$60

$65

$70

___

___

What is the Rate of Change (

RoC

)?

How much money did she start with? (

IV

)

y=(

RoC

)x +

IV

y=

How much money will she have after 10 days?

John is building a fence that is 10m long. His first meter of fencing requires 6 pieces of wood. After that, each meter only requires an additional 5 pieces. How much wood does he need to buy?

Make a term chart and determine an algebraic expression.

Term

Number (x)

0

1

2

3

4

Term

Value (y)

6

What is the Rate of Change (

RoC

)?

How much money did she start with? (

IV

)

y=(

RoC

)x +

IV

y=

How much wood would he need if he was building 20m?

n

1

2

3

4

5

Value

10

30

90

270

810

Hint: y = xr

"r" stands for Common Ratio, that is, what is it multiplied by each time?

What should x always be?

What would the 10th term be?

n

(n - 1)

Term

Number (x)

0

1

2

3

4

Term

Value (y)

What is the Rate of Change (

RoC

)?

y=(

RoC

)x +

IV

y=

How many circles would be present by the 100th term?

Term 1

Term 2

Term 3

Relating Number Sequences to Graphs 4.5

Relate a sequence to its scatter plot.

GOAL:

CHALLENGE YOURSELF HERE

The graphs you will plot in grade 8 are linear, that is, they make a line graph which rises or falls in a straight lne.

Can you create a non-linear line graph?

Go Beyond!

What would a graph look like with the expression:

1

2

3

4

1

2

3

4

x

y

y = x + 1

Term (x)

0

1

2

3

4

Value (y)

What would a graph look like with the expression:

1

2

3

4

1

2

3

4

x

y

y = 2x + 1

Term (x)

0

1

2

3

4

Value (y)

y

x

**Unit 5:**

**Measurement of Circles**

Do You Remember? 5.0

Review the skills required for this unit.

GOAL:

Before we get

into the business

of understanding circles. we need to review some measurement skills.

Area or Perimeter?

Can you remember which is which?

The amount of fencing to surround an animal pen.

The amount of tiles to cover the kitchen floor.

The size of a door decoration to beat Mrs. Maybury.

The total distance around the track.

m or cm

km or mm

cm or m

Which is bigger?

3mm or 0.04cm

1m or 1700mm

160cm or 1.5m

Calculating Area & Perimeter

7cm

3cm

1 cm

1 cm

0.5 cm

0.5 cm

2 cm

0.5 cm

2.5 cm

3 cm

1 cm

1 cm

2 cm

2.2 cm

Exploring Circles 5.1

Use information about circles to draw them and draw polygons within them.

GOAL:

Parts of a Circle

Circles are incredibly useful...

While it may be obvious why wheels are circles, why are sewer covers circular?

Circles are one of the most complex shapes.

A triangle has 3 points... a square has 4... how many does a circle have?

Arc

Part of the circumference between the ends of an arc.

Chord

A line that joins any two point on the circumference of a circle.

Creates 2 arcs.

Radius

Diameter

r

d

The

Area

of a circle is still referred to as

Area

.

The outside edge of a circle is known as the

circumference

.

This unit will focus on two major topics:

Area

Circumference

Just for Fun

Circumference & Diameter 5.2 & 5.3

Investigate the relation between circumference and diameter and calculate circumference.

GOAL:

Diameter and Circumference

How is the diameter of a circle related to its circumference?

d = 5cm

C = 15.7cm

Divide the circumference

by the diameter.

d = 15cm

C = 47.1cm

Divide the circumference

by the diameter.

Time to discover an amazing, irrational number with no end.

So just how long is pi?

http://www.geom.uiuc.edu/~huberty/math5337/groupe/digits.html

Time to Calculating Circumference!

If you know the radius, or diameter, of a circle you can determine the circumference.

C = 2 r

or

C = d

4 cm

12 cm

10 cm

Radius & Area

5.4 & 5.5

Estimate areas of circles and then develop a formula to determine area.

GOAL:

Can we estimate area?

How is the radius

of a circle related

to its area?

d = 6cm

A = 28.26 cm

Can we find a relationship between these numbers?

r = 9cm

How do these numbers relate to pi?

Time to Calculate Area!

If you know the radius, or diameter, of a circle you can determine the area.

4 cm

12 cm

10 cm

2

A = 254.34 cm

2

How are the internal measurements of the circle related to the area?

Turn to 5.4 in your Workbook.

You will have 5 minutes to work on question 1.

Pi! Back at it again!

When you divide the area by the square of the radius you get pi!

What does that mean?

A = r

2

Area is equal to pi times r squared.

A

r

=

2

A = r

2

**Unit 6:**

**Integer Operations**

Do You Remember? 6.0

Review the skills required for this unit.

GOAL:

What's an integer?

How can a number

be negative?

How do you represent

negative numbers?!

Number Line

The Early Years

Comparing Integers

2 ___ 3

4 ___ 3

10 ___ 4

Relating Integer Subtraction to Addition 6.2

Subtract integers by measuring the distance between them.

GOAL:

Two Simple Rules

How do we

add

or

subtract

negative

numbers?

Are there easy

rules

for us to remember?

Mt. Everest is 8839m above sea level.

What is the

difference

?

Multiplication of Integers 6.4

Develop and appy strategies to multiply integers.

GOAL:

The Rules of Multiplying

Negative Integers

What does it mean to multiply negative integers?

Are there rules?

Rule 1

: (+) x (-) = (-)

Every month Mr. Quan collects $5 from each student to pay for classroom supplies. There are 10 months of school.

What is the total deduction for Sakeen?

Multiplication Using a Variety of Tools 6.3

Explore models of, and patterns for, integer multiplication.

GOAL:

How can we visually model problems involving negative integers?

0 1 2 3 4 5 6 7 8 9 10

In the early years, the number line was easy.

It went in one direction with ever increasing integers.

Then... in the 7th century... EVERYTHING CHANGED

0 1 2 3 4 5 6 7 8 9 10

-9 -8 -7 -6 -5 -4 -3 -2 -1

Positive Numbers (+)

Negative Numbers (-)

Number Line

New and Improved

> < =

-2 ___ -3

-7 ___ -3

-8 ___ -2

The Marianas Trench is

11000m below sea level.

8839 - (- 11000)= difference

8839 + 11000 = 19839

What's the

rule

?

Subtracting a negative

is the same as

adding a positive

.

Adding a negative

is the same as

subtracting a positive

.

10 - (-7) = 10 + 7

10 + (- 7) = 10 - 7

Old School

Two negatives make a positive.

Old School

A negative and a positive make a negative.

Hot air makes the balloon go up (positive).

Weight in the basket makes it go down (negative).

If you add more hot air, you are adding a positive number.

If you take away hot air, you are subtracting a positive number.

If you add weight you are adding a negative number.

If you take away weight, you are subtracting a negative number.

10 + (- 5) =

What's the

rule

?

Convert, Predict and Solve

7 + (-7) =

10 - (-5) =

-20 + 5 =

-7 + (-8) =

-10 - (-5) =

320 + (-120) =

Multiplying a positive and negative integer results in a negative number.

(+) x (-) = (-)

Rule 1

Multiplying two negative integers results in a positive number.

(-) x (-) = (+)

Rule 2

10 x (-5) = -$50

Rule 2

: (-) x (-) = (+)

This school year, Mr. Quan removes half of the $5 monthly deduction over the ten months.

How much money is not collected?

-10 x (-2.5) = $25

The Rules of Multiplying

Negative Integers

Multiplying a positive and negative integer results in a negative number.

(+) x (-) = (-)

Rule 1

Multiplying two negative integers results in a positive number.

(-) x (-) = (+)

Rule 2

Let negative numbers be represented by red counters. Let positive numbers be represented by black counters.

2 x (-3) =

+ = -6

2 x 3 =

+ = 6

3 x (-3) =

5 x (-3) =

The hot air balloon can sustain lift if the carrying capacity is no more than 200kg.

Three boxes will be added. They each weigh 50kg.

-200kg -150kg -100kg -50kg 0kg

Division of Integers 6.5 & 6.6

Develop and apply strategies to divide integers (positive and negative).

GOAL:

The Rules of Dividing

Negative Integers

What does it mean to divide negative integers?

Are there rules?

Division Using Counters

In this awesome example, let's do the following with negative counters (

red

):

(-9) ÷ 3 =

Dividing a positive and negative integer results in a negative number.

(+) ÷ (-) = (-)

Rule 1

Dividing two negative integers results in a positive number.

(-) ÷ (-) = (+)

Rule 2

Division Using a Number Line

Can we represent (-6) ÷ 2 = ?

0 1 2 3 4 5 6 7 8 9 10

-9 -8 -7 -6 -5 -4 -3 -2 -1

Predict the

Outcome

(-7) ÷ 2 =

2 ÷ 8 =

(-11) ÷ (-4) =

(6 - 10) ÷ 2 =

(-10) ÷ (-3) =

2

Solve It

(-20) ÷ 2 =

(-2) ÷ 4 =

(10 - 10) ÷ (-4) =

(7 - 11) ÷ (-2) =

(-2) ÷ (10) =

5

Check In:

Let's See What You Remember!

Can Mr. Quan trick you and make you feel like you need to study more?

GOAL:

Four Simple Rules

There are a total of 4 rules

to remember with negative integers. Can you remember them all?

It's time to be MATHLETES

Two rules apply to addition and subtraction.

These two rules

convert

an expression.

Rule 1

Rule 2

Two rules apply to multiplication and division.

These two rules are

predictive

.

Rule 1

Rule 2

https://www.jeopardy.rocks/negativenumeracy

Order of Operations 6.7

Apply the rules of BEDMAS with integers.

GOAL:

BEDMAS

How do we handle multiple operations?

Does it change when we have negative integers?

Why hello there old friend!

BEDMAS

BEDMAS indicates that operations should be done in a specific order:

Brackets

Exponents/Roots

Division/Multiplication

Addition/Subtraction

There are

IMPORTANT NOTES

:

Family operations? Go left to right.

Division by fraction goes last.

Have fun and practice often!

THE MOST IMPORTANT SLIDE

Jerry

[6 + (-5) x (-10)] + (-6) ÷ 2 =

Focus on the

Brackets

first.

[6 + (-5) x (-10)]

+ (-6) ÷ 2 =

[6 +

(-5) x (-10)

]

+ (-6) ÷ 2 =

Multiplication

first!

[6 +

50

]

+ (-6) ÷ 2 =

56

+ (-6) ÷ 2 =

Get that

division

!

56 +

(-6) ÷ 2

=

56 +

(-3)

=

Subtraction

last.

56 + (-3)

= 53

BEDMAS

PRACTICE

BEDMAS, the best thing since...

[21 x (-2) ] x [8 ÷ (-8) + 5]

[10 + (-10) x (-1) x (-1)

2

2

3

Level 3

VERSUS

*Level 4+

THINKING

Make these equations true.

6 × ___ + 4 ÷ (-2)

5 - (-5)

2

2

= - 0.02

6 × (-1) + [4 ÷ (-2)]

[5 - (-5)]

2

2

= - 0.02

Answer

HINT

:

What are the likely numerator and denominator values which will result in -0.02?

What must be true?

(-2) × 5 + (-6) = 2

Answer

(-2) × [(5) + (-6)] = 2

HINT

:

Determine what must be done to insure a positive integer.

...nothing changes

It's all in the tiny details.

Consider this...

60 ÷ (-5) × (-2)

60 ÷ [(-5) × (-2)]

**Unit 9:**

**Fraction OPerations**

Adding & Subtracting Fractions (9.1 & 9.2)

Add and subtract fractions using at least one model.

GOAL:

Before we start with adding and subtracting fractions, do you know what it means to add and subtract fractions?

Modeling addition and subtraction.

Relating Integer Subtraction to Addition 6.2

Subtract integers by measuring the distance between them.

GOAL:

Two Simple Rules

How do we

add

or

subtract

negative

numbers?

Are there easy

rules

for us to remember?

Mt. Everest is 8839m above sea level.

What is the

difference

?

The Marianas Trench is

11000m below sea level.

8839 - (- 11000)= difference

8839 + 11000 = 19839

What's the

rule

?

Subtracting a negative

is the same as

adding a positive

.

Adding a negative

is the same as

subtracting a positive

.

10 - (-7) = 10 + 7

10 + (- 7) = 10 - 7

Old School

Two negatives make a positive.

Old School

A negative and a positive make a negative.

Hot air makes the balloon go up (positive).

Weight in the basket makes it go down (negative).

If you add more hot air, you are adding a positive number.

If you take away hot air, you are subtracting a positive number.

If you add weight you are adding a negative number.

If you take away weight, you are subtracting a negative number.

10 + (- 5) =

What's the

rule

?

Convert, Predict and Solve

7 + (-7) =

10 - (-5) =

-20 + 5 =

-7 + (-8) =

-10 - (-5) =

320 + (-120) =

Division of Integers 6.5 & 6.6

Develop and apply strategies to divide integers (positive and negative).

GOAL:

The Rules of Dividing

Negative Integers

What does it mean to divide negative integers?

Are there rules?

Division Using Counters

In this awesome example, let's do the following with negative counters (

red

):

(-9) ÷ 3 =

Dividing a positive and negative integer results in a negative number.

(+) ÷ (-) = (-)

Rule 1

Dividing two negative integers results in a positive number.

(-) ÷ (-) = (+)

Rule 2

Division Using a Number Line

Can we represent (-6) ÷ 2 = ?

0 1 2 3 4 5 6 7 8 9 10

-9 -8 -7 -6 -5 -4 -3 -2 -1

Predict the

Outcome

(-7) ÷ 2 =

2 ÷ 8 =

(-11) ÷ (-4) =

(6 - 10) ÷ 2 =

(-10) ÷ (-3) =

2

Solve It

(-20) ÷ 2 =

(-2) ÷ 4 =

(10 - 10) ÷ (-4) =

(7 - 11) ÷ (-2) =

(-2) ÷ (10) =

5

Check In:

Let's See What You Remember!

Can Mr. Quan trick you and make you feel like you need to study more?

GOAL:

Four Simple Rules

There are a total of 4 rules

to remember with negative integers. Can you remember them all?

It's time to be MATHLETES

Two rules apply to addition and subtraction.

These two rules

convert

an expression.

Rule 1

Rule 2

Two rules apply to multiplication and division.

These two rules are

predictive

.

Rule 1

Rule 2

https://www.jeopardy.rocks/negativenumeracy

Do you remember?

Case 1: A Fractured

Heart

Can you make an expression, in the form of a fraction, if I have the top right piece of the heart in my hand?

Case 2:

Valentine's Day

Quagmire

Mr. Quan, having eaten a few chocolates, 4 out of 10, and losing 11 of his 12 roses, is curious if he can turn his Valentine's Day problem into an addition fraction problem instead . Can he? Why or why not?

The

Fraction Strip Model

can be used for both addition and subtraction.

Marlie has 2/3 cup of flour. She uses 1/6 cup for a recipe. How much flour does she have left?

Number Lines

, while always useful, are not the easiest to construct.

In a bag of M&Ms, 3/4 were blue and 1/7 were brown. Since Mr. Quan only eats blue and brown M&Ms, what fraction of the bag did he give to his students?

Counters

can help you find the common denominator.

Models

are an

awesome

way to check your work.

But,

models

are not always the fastest method to add or subtract fractions.

Do you remember

equivalent fractions

?

We'll need to activate that prior knowledge!

4

10

100

=

3

4

1

5

+ =

Practice!

5 2

6 3

11 5

12 8

5 1

10 4

3 2 2

4 3 5

+ =

+ =

+

- =

- =