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Grade 8 - Math

This Prezi is intended to cover the Ontario, Grade 8 Math curriculum. This project is starting a month and a half into the school year and therefore does not completely cover all materials intended to be taught in Grade 8 at this time.
by

Mark Quan

on 1 December 2016

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Transcript of Grade 8 - Math

Multiple Patterns
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
Full transcript