Mathematics 7
Student E-Book
Semester 1
2014-2015
Table of Contents
List of Student Resources
Year-Round Problem Solving Process
Week 1 - Problem-Solving Workshop
Integers
a. Topics and Vocabulary
b. Overview – Let’s see what you know before we start
the unit
c. Integers Workshops – Regular Track
d. Integers – Compacting Assignments
e. Integers – Final Review
Fractions, Percentages & Decimals (FPD)
a. Topics and Vocabulary
b. Overview - Let’s see what you know before we start
the unit
c. FPD Workshops – Regular Track
d. FPD – Compacting Assignments
e. FPD – Final Review
Geometry
a. Topics and Vocabulary
b. Geometry Assignments
c. Geometry Compacting Assignment
d. Geometry - Final Review
************************** End of Semester 1 ******************
List of Student Resources
When you cannot find your notes,
When you don’t remember,
When you want to find the meaning of a math word,
When you want some help,
And when you want to learn something new….
Here are some places you might be able to find the answers to
your questions on any topic. Use the search engine of the
following websites:
http://www.mathisfun.com
https://www.khanacademy.org/math
http://www.brainpop.com/math/
Username = asfmbp, Password = asfmbp
http://www.mathplayground.com/index.html
Year-Round Problem-Solving Process
When you’re confronted with a word problem that you need to
solve, follow the following steps and they will help you
understand the problem and figure out how to solve it.
1) Read the problem
2) Underline/highlight/circle the important
information that will help you solve the problem.
3) Know the answer to this question: What is the problem
asking?
4) Pick a strategy that you think will help you come to the
right answer:
i. Make a list
ii. Make a table/chart
iii. Draw a picture or build something
iv. Find a pattern
v. Guess and Check
vi. Work backwards
vii. Act it out!
viii. Make an equation or a number sentence
ix. Use another strategy that makes sense to you…
5) Solve the problem using the strategy you chose above.
6) Check your work and answers by looking over your work
or using another strategy to come to the same answer.
7) Write a sentence answering the question posed in the
problem.
Week 1 - Problem-Solving Workshop
Instructions:
1) Tackle each problem on your own for 5 minutes before seeking
someone else’s help.
2) Do at least one of these problems using a Bamboo tablet and do the
other problems however you want.
3) Use the problem-solving process we discussed in class.
4) Make a folder called “Problem Solving Week 1” in your Math folder in
GoogleDocs.
5) Take pictures of your pencil-paper work (if any) and your Bamboo
notebook pages. Upload these pictures, and your saved Bamboo
notebook page (that has your tablet work on it) your Problem-Solving
folder in GoogleDocs. Upload any videos you made as well (if you made
some).
6) Name every file according to the question your answering.
Problem 1:
Jasmine got a bag of marbles for her birthday. She kept half for
herself and gave the other half to her 3 brothers. The 3 boys
divided the marbles equally among themselves. The youngest
brother gave half of his marbles to his friend Cody. Cody got 10
marbles.
How many were in the bag Jasmine got for her birthday?
Problem 2:
Nestor is drawing and connecting points on his paper. Each
line connects only 2 points and each point is connected to
every other point.
How many lines would he draw to connect 9 points in the same
way?
Problem 3:
A team of 7 explorers came to a river they needed to cross.
They found 2 girls who had a rowboat. The boat was only big
enough to carry the 2 girls or one explorer at a time.
a) How can all of the explorers get across the river using the
girls’ rowboat?
b) How many trips across the river will it take to get all 7
explorers to the other side and both girls back to the starting
side?
Unit 1 – Integers
Topics to be covered in this unit:
1. Using a Number line
2. Positive and Negative Numbers
3. Comparing Numbers
4. Absolute Value
5. Add positive and negative Numbers
6. Subtract Positive and Negative Numbers
7. Multiplication with Negative Numbers and Zero
8. Dividing Negative Numbers
9. Order of Operations
Math Lingo:
Word
Integer
Ascending
Descending
Deposit
Withdraw
Elevation
Absolute value
APEMDAS
Factor
Product
Divisor
Dividend
Quotient
Meaning (in your
own words)
Find/draw a
picture that
describes the
word
Unit 1 – Integers Overview
Let’s see what you know before we start the unit!!!
1.
What is an integer?
2.
Integers on a Number line
0
a) Place the numbers -35, -5, -23, 9, 1, 15 on the number line above.
b) Write the temperatures in order from coldest to warmest:
-21°C, 12°C, 17°C, 8°C, -30°C, 0°C
3.
Integers in a real-life context
Represent the following situations with an integer:
Scenario
A submarine descended 258 m.
Cristina deposited 76 dollars into
her account.
The climbers ascended 750m on
the mountain.
Pablo withdrew 5000 pesos from
his account.
Integer Representation
4.
Absolute Value
a) What does it mean to calculate the absolute value of a number?
b) Calculate the absolute value of -5, 7, -89, 543, and 0.
5.
Word problems involving integers. Express you answer
as an integer with units.
a) Kenny ascended 15m up on Huasteca canyon, then he
descended 6m and ascended another 2m. How high up the
mountain is Kenny?
b) In Montreal, the temperature rose as high as 17°C and went
down as low as -5°C in the spring of 2010. What was the
difference in temperature?
c) Valeria had 56 dollars in her bank account. She withdrew 12
dollars every month for 6 months. What is Valeria’s account
balance?
d) There was a drought in Whoville and people were dying
because there was less and less food to eat. The population
was 1800 by the end of the year 2000 and 600 by the end of
the year 2003. If the same number of people died every year,
calculate the death rate in whoville?
6.
Multiplying and dividing with big integers that have
zeros in them.
a) -2000 ÷ -50 =
b) -600 x 30 =
c) 18000 ÷ -900 =
7.
d) 40 x 70 =
Computation with integers and PEMDAS.
1. (3 + 5) + 9 – (2 + 1) = _______
2. 3 + 4(3 – 8) =
3. 15 + 3 • 25 + 2=
_______
4. –15 – (–55) = _______
5.
_______
6.
8(5) × 15- 20 =
- -20 + 10
=
-5
_______
_______
Integers - Workshop 1 – Regular Track
Rename this file – “Integer-Workshop1-Period
Number-YOUR NAME”.
Activity 1: Watch the following videos to
better understand integers
Go to this website:
http://learnzillion.com/lessonsets/94-understanding-how-positive-and-negative-numbersdescribe-quantities
Watch the 4 videos about positive and negative numbers on this
website.
Activity 2: Represent the following
scenarios with an integer and units.
Scenario
Ms. Khare ascended the Salkantay
mountain located close to Cuzco (Peru)
to a maximum height of 4600m above
sea level.
A small manned submarine, the
bathyscape Trieste, descended
10916m below sea level.
Ms. Hernandez has 554 pesos but she
owes Ms. Khare 253 pesos. How much
money does Ms. Hernandez actually have
to her name?
Mrs. Fernandez has a debt of
50000pesos that she must pay to
Banorte.
Mr. Rogers withdrew 45000pesos from
his bank account on Saturday.
Yukina had 15023pesos deposited into
her bank account.
Integer with units
The temperature in Anchorage, Alaska
was 13 degrees above freezing.
In December, the temperature in
Montreal, Canada was 23 degrees below
freezing.
Activity 3: Integers War (many negatives
and few positives)
Take a deck of cards. Watch this video, play war for 10 rounds and record your
rounds on this table as you play.
Player 1(integer)
Player 2 (integer)
Who won?
Activity 4: Battleship using GeoSketchpad
Watch the video posted on Edu2.0 to get a better idea of how to
set up your Battleship game.
Use Geometer’s Sketchpad to construct your own Battleship game.
1) The domain (x-values) of your board should be from -10 to +10. The range of
your board should be from -10 to +10.
2) You should construct 4 ships as lines on your board. See below:
3) The red dots are the coordinates at which your opponent can shoot your boat
down.
4) Pick a friend with whom you would like to play battleship with. Open up a
whole new GSP5 file with only a square grid on it – this will be your tracking
board. Have your battleship file be open as well next to the file with the
empty square grid.
5) As you play battleship with your friend, record your hits and misses on your
friend’s battleships on the empty square grid. Have green dots represent hits
and orange dots represent misses.
6) Change the color of the dots on your battleships as your opponent hits them.
7) Record the hits and misses you make on your opponents ships, on the table
below. Extend the data table as you play.
Coordinates Shot at
Hit/Miss/Sink
8) Constantly save both GSP5 files that you have on your computer as you play.
At the end of the game, insert the screenshots of your tracking board,
battleship board and the 2 boards of your opponent in this document. Label
each picture with the name of the person and whether it’s the battleship
board or tracking board.
Save and upload this entire word document
onto your Math folder on GoogleDrive when you
have finished all the work on it.
Integers – Workshop 2 – Absolute Value
THIS WORKSHOP MUST BE DONE BY REGULAR-TRACK AND
COMPACTING STUDENTS.
INSERT ALL YOUR WORK AND ANSWERS INTO THIS WORD
DOCUMENT. YOU MAY USE THE BAMBOO TABLET TO SHOW YOUR
WORK AND INSERT SCREEN SHOTS IN THIS DOCUMENT.
SAVE ALL YOUR WORK!!!
THIS WORKSHOP IS DUE AT THE END OF THE PERIOD NEXT CLASS.
YOU DO NOT HAVE HOMEWORK FOR TONIGHT!
Objectives for today:
1) Learn about absolute value
2) Learn about how absolute value is used in the real world.
Activity 1 – BrainPop on Absolute Value
a) Watch the following video and learn about absolute value http://www.brainpop.com/math/numbersandoperations/absolutevalu
e/
username = asfmbp
password = asfmbp
b) At the end of the video choose “Take the Quiz” and answer all the
questions in the “Review Quiz”. Record your answers here:
1)
6)
2)
7)
3)
8)
4)
9)
5)
10)
Activity 2: Guess their age???
Absolute value can also be thought of as the difference between a guess and the
actual value. You will be exploring this definition of absolute value through the
following activity.
It is important that you don’t cheat when you do this activity!!! That is the only way
you’ll be able to understand absolute value a little better.
1) Guess the age of the following people on this table and record
your guess.
Name
Your substitute teacher (Nina)
Ms. Khare
Barack Obama
Enrique Pena Nieto
Mother Teresa (when she passed away)
Chris Martin (Cold Play)
Bono (U2)
Nick Vujicic (man without limbs)
Bill Gates
Eesha Khare
Mark Zuckerberg
Li Na
Hiram Mier (Rayados)
Guess his/her age
2) Research the actual age of the people in the table above.
Name
ACTUAL age
Your substitute teacher (Nina)
Ms. Khare
Barack Obama
Enrique Pena Nieto
Mother Teresa (when she passed away)
Chris Martin (Cold Play)
Bono (U2)
Nick Vujicic (man without limbs)
Bill Gates
Eesha Khare
Mark Zuckerberg
Li Na
Hiram Mier (Rayados)
3) The difference between the guessed age and the actual age is an
absolute value and it is expressed as a number without a sign.
Name
Your substitute teacher (Nina)
Ms. Khare
Barack Obama
Difference between guess
and actual age
Enrique Pena Nieto
Mother Teresa (when she passed away)
Chris Martin (Cold Play)
Bono (U2)
Nick Vujicic (man without limbs)
Bill Gates
Eesha Khare
Mark Zuckerberg
Li Na
Hiram Mier (Rayados)
Activity 3 – Difference in Temperature
Research the highest and lowest temperatures for the following cities in 2012
(google it and choose the link that reads “Historical weather for 2012). The
difference between the highest and lowest temperatures is also expressed as an
absolute value. Fill out the table:
City
Monterrey
(Mexico)
Montreal (Canada)
Anchorage
(Alaska)
Sydney (Australia)
Highest
Temperature (°C)
in 2012
Lowest
Difference
Temperature (°C) between highest
in 2012
and lowest
temperatures (°C)
Integer – Workshop 3 – Regular Track
Addition and Subtraction
Use the number line to answer the following questions. You
can copy and paste this assignment into another word
document and show your work in that document. You can also
show your work on paper or Bamboo Tablet. Upload the
pictures for your work into a folder called “Integers –
Workshop 3” on GoogleDocs when you’re done.
1) 6 + 5 + 1 =
2) 10 + (−12) + (−8) =
3) −40 + (−60) + (−50) =
4) 10 − 15 − 9 =
5) 5 − 17— 3 =
6) −4— 2 − 7 =
7) −40— 20— 10 =
8) 9 − 6 − 8 − 12 =
Use your problem-solving strategies to answer the
following questions:
9) In golf, par means the average number of strokes needed
by an expert golfer to complete the round. People who
score less than this get a score under par. For example,
2 under par is a score of -2.
Jeannie’s scores in 4 games of mini-putt golf were -4, -6, 2
and -3. Cameron’s scores were -2, -3, -1 and -3.
How did Jeannie’s total score for the 4 games compare to
Cameron’s?
10)
The table shows the performance of 2 stocks on the
Stock Exchange over 5 days last week. ExMac started the
week at $23, and MaxLine started at $25. Which
company ended the week with a higher price?
Stock
Mon
ExMac
+5
MaxLine -2
Tues
-1
+1
Wed
+2
-5
Thurs
-3
0
Fri
+4
+7
11)
The Kelvin temperature scale starts with absolute
zero. This is the temperature at which there is no energy
left. It cannot get any colder. To get the kelvin
temperature from Celsius temperature, add 273. Write
each Celsius temperature in kelvin (symbol K).
a. 0°C
b. -40°C
c. -100°C
d. -273°C
Did you know?
The Kelvin Scale was invented by Lord Kelvin – a British
inventor and scientist. Google him to find out more!!!
12) Mount Everest is the tallest mountain in the world, measured
from sea level. Mount Mauna Kea, in Hawaii is the tallest
mountain when measured from its base. It rises from 5854m
below sea level to 4349m above sea level. How tall is Mount
Mauna Kea?
13) Liquid oxygen and hydrogen are used as fuels to make a space
shuttle fly. On the space shuttle, liquid oxygen is stored at 183°C. The oxygen is heated to a temperature of 260°C, and then
it is mixed with hydrogen. Hydrogen is stored at a temperature
of -250°C. The mixture that results burns at a temperature of
3315°C.
a) By how much is the liquid oxygen heated before it is mixed with
hydrogen?
b) How much hotter is the temperature at which the mixture burns
than the temperature at which the hydrogen is stored?
Integers – Workshop 4 – Regular Track
Multiplying and Dividing
(Show your work and answers on Bamboo
or by writing in your notebook. Take
screenshoots/pictures and hand them in
Math folder on Google Drive)
Activity 1: Find out how to multiply and
divide integers
What is the sign of the answer of the following problems?
1. -5(-3) =
2. -10 i0 =
3. 4(-11) =
4. 8 ¸ - 4 =
5. - 6 ¸ - 3 =
6. -18 ¸ 2 =
Activity 2: Multiplication and Division with Integers
Write the integer equation and solve. Indicate whether
your answer is negative or positive.
1) The temperature rise’s an average of 2C every
hour. How many degrees does it rise in 4 hours?
2) In an investment game, Allen lost $50 in each of 4
turns. How much did he lose?
3) A submarine went down at a rate of 25m per
minute for 8 minutes. How far did the submarine
go down in total?
4) A stock decreased in price by 24$ over 4 days.
What was the average daily decrease in price?
5) You owe your parents $35 to be paid in 5 equal
installments. How much is each installment?
6) You owe $100 dollars to your parents. You find a
job cutting lawns and are paid $6 each time. You
use that money to repay your loan.
a) How much do you still owe after cutting 8 lawns?
b) How many more lawns do you need to cut to pay
off the rest of your debt?
Activity 3 – Absolute Value (Bonus!!!)
As you play the game on the following website, record
the questions, your work and the answers.
http://www.math-play.com/Absolute-ValueEquations/Absolute-Value-Equations.html
Integers Workshop 5 – Regular Track
Order of Operations
Use the number line to answer the following questions. You
can copy and paste this assignment into another word
document and show your work in that document. You can also
show your work on paper or Bamboo Tablet. Upload the
pictures for your work into a folder called “Integers –
Workshop 5” on GoogleDocs when you’re done.
Watch this video:
http://www.youtube.com/watch?v=OWyxWg2-LTY
Read these notes:
You’ll be using APEMDAS to solve the following
questions!
A – Absolute Value
P – Parentheses
E – Exponents
M – Multiplication
D – Division
A – Addition
S - Subtraction
Read these instructions:
1) Show all your work for each question that
requires 2 steps or more to complete. Write on
your paper notebook or Bamboo notebook and take
pictures of your work to upload into a folder called
“Integers Workshop 5” on Google Drive.
2) After you answer each question, check your
answers by inputting questions into this website:
http://www.wolframalpha.com
Complete these questions and show your work:
1. 18 + (–12) =
______
2. –6 + 18 =
_______
3. 24 – 58 =
______
4. –10 – 73 =
_______
5. 15 + (–5) =
_______
6. –24 – (–42) =
_______
7. (3 + 5) + 9 – (2 + 1) = _______
8. 3 + 4(3 – 8) =
_______
9. 15 + 3 • 25 + 2=
10. –15 – (–55) =
_______
12. 8 + (3 – 2) – (- 5) =
_______
_______
11. –7 + (- 4) + 5 – (- 8) = _______
Complete these questions and show your work:
1. –9(6) =
_______
2. –12(–3) =
6
_______
3. –4(–3) (–2) =
_______
4. –15(–3) =
_______
5. 63 ÷ (–21) =
_______
6. –3(4)(–5) =
_______
7. -4(9) =
______
-2
–9
8. -5(2)(-9) = =
_______
3
Complete these questions and show your work:
1. –28=
2. |10 – 5| – |4 – 7| =
______
3. |3 – 10| + |4 • 2| = _______
4. - –50=
_______
5. 4 × 5-10 =
_______
6. 8(5) × 15- 20 =
_______
7. -5× 4 =
_______
8.
-2
_______
- -20 + 10
=
-5
______
Use a calculator to complete these questions. Show your
work.
1)
(|7 ∙ −5| + 254 − 5 − 1)
3
2)
-58· 4
- 7 ( 31) =
-2
3) -54 + 5·-7 - (8+ 89·3) =
Integers – Compacting 1
Time Zones
You can copy and paste this assignment into another word
document and show your work in that document. You can also
show your work on paper or Bamboo Tablet. Upload the
pictures for your work into a folder called “Integers –
Compacting 1” on GoogleDocs when you’re done.
Time zones are an area in which integers are widely
used.
Some background watching and reading:
1)
http://www.brainpop.com/socialstudies/geograph
y/timezones/
username – asfmbp
password – asfmbp
2) To electronically find out the time in any city
around the world:
http://www.worldtimeserver.com
3) To access a time zone map:
http://www.satellitecitymaps.com/timezones/
Warm up!!
The table below gives time zone references for 4 cities:
City
Time
Zone
Charlottetown, CAN
-4
Monterrey, MX
-7
Beijing, China
+8
Tel Aviv, Isreal
+2
Greenwich, England
0
If Greenwich is 0, Tel Aviv is 2 hours ahead of
Greenwich and Monterrey is 7 hours behind Greenwich.
a) Make a number line and label all the time zones on it.
b) If it is 6pm in Tel Aviv, what time is it in Beijing?
c) If it is 3am in Monterrey, what time is it in Tel Aviv?
d) If it is 11:30pm in Beijing, what time is it in
Charlottetown?
e) If it is 10:45am in Monterrey, what time is it in Beijing?
YOUR PROJECT:
Imagine you’re an engineer working for Microsoft at the office in
Monterrey. You would like to schedule 5 conference calls with people at
the Microsoft offices in Bangalore, India and Seattle, USA to finalize
details for a project you’ve been working on for a month. Each
conference call should take up to 1 hour maximum with 2 calls possible
on only one day (you choose which day). Today is August 28th, 2013
and you can start making calls from 7am today. Your project deadline is
at 5pm on September 1, 2013 (Bangalore time). All calls must be
completed before that time.
People at the Bangalore office get to work by 7am everyday and they
leave work at 7pm every evening. People at the Seattle office work from
home but they generally login to work by 8am every morning and
logout at 6pm every evening. You wake up at 6am every morning and
would like to go to bed by 10:30pm every night.
Make a call schedule that you could forward to your partners in
Bangalore and Seattle such that you can coordinate conference calls
with them (at the same time) within their working hours. Show and
organize all your work in such a way that you can prove it is possible to
make such a schedule.
Integers – Compacting 2
Addition, Subtraction, Multiplication and
Division
You can copy and paste this assignment into another word
document and show your work in that document. You can also
show your work on paper or Bamboo Tablet. Upload the
pictures for your work into a folder called “Integers –
Compacting 1” on GoogleDocs when you’re done.
1) Bryce’s bank statement for July shows his deposits and
withdrawals. When he pulled the statement out of the
envelop, he tore off part of it.
a. Calculate Bryce’s balance at the end of this month.
b. In August, Bryce had a total of 4 transactions. His
final balance was $62. What could the 4
transactions have been? Give another 4 transaction
possibilities for this question.
Bryce Brown
125 Main St.
Bank Balance for July 2004
Opening Balance: $124
Date
Transaction
July 2
Withdrawal
July 5
Withdrawal
July 8
Deposit
July 21
Withdrawal
July 23
Withdrawal
July 24
Deposit
July 29
Deposit
July 31
Withdrawal
Amount
$28
$48
$32
$89
$33
$20
$15
$49
Balance
Did you know?
A bank may allow you to have a negative balance in your
account. A negative balance is called an overdraft. The
bank may charge a fee for this service.
2) The diagram below shows elevations compared to sea
level, of the surface and deepest points of the 4 Great
Lakes in Canada.
a. How deep is each lake?
b. How far below the bottom of Lake Erie is the bottom
of Lake Superior?
c. The CN Tower in Toronto is 553m tall. If it were
standing on the bottom of Lake Ontario, would it by
submerged or would it be visible above the surface.
By how much?
d. The Skylon Tower in Niagara Falls is 160m tall. How
many Skylon Towers could be stacked in Lake
Superior and still be submerged?
3) Is this statement true or false? Test it and explain why or
why not.
“When you subtract two numbers, the difference is always
smaller than the first number.”
4) In a tropical ocean location, the temperature decreases
by about 3°C for every 25 m in depth. The temperature
at the surface is 25°C.
a. What is the water temperature 125 m below the
surface?
b. The clearnose skate (Google it if you don’t know
what this animal is) can live in water with
temperatures from 6°C to 27°C. How far below the
surface can the skate live?
5) On the stock market, the price of one share of High Flier
Airlines dropped by an average of 15 cents per day over
30 days.
a. What was the total price change during the first 5
days?
b. What was the total price change over the entire 30day period?
c. You buy shares on the 10th day. How much money
will you lose, per share, if you sell them on the 20th
day?
6)
a. List all the possible combinations of 3 different
integers that have a product of -12.
b. Find all the possible combinations of 3 different
integers whose product is 30.
7) Eleanor is tracking a whale. It descends at a steady rate
of 120m in 20 minutes.
a. What is the whale’s rate of descent (how much does
the whale descend per minute)?
b. How far does the whale descend in 10 minutes?
c. The whale needs to come to the surface to breathe
after 45 minutes under water. How deep can it dive
if it descends and ascends at the same rate?
8) Plot the points A(2, -1), B(-3, -4), and C(-5, 2) on the
coordinate grid on Geometer’s Sketchpad. Join them to
form a triangle.
a. Multiply the x- and y-coordinates of A, B and C by 2
and graph the results in Sketchpad. Describe the
resulting triangle.
b. Multiply the x- and y-coordinates of A, B and C by -2
and graph the results. Describe the resulting
triangle.
c. What do you think would happen if you multiplied
the x-coordinates by 2 and the y-coordinates by -2.
Integers – Compacting 3
Order of Operations
A – Absolute Value
P – Parentheses
E – Exponents
M – Multiplication
D – Division
A – Addition
S - Subtraction
Show your work in your notebook or Bamboo and handin screenshots/pictures of your work on Google Drive.
Use http://www.wolframalpha.com to check your work
and answers.
Evaluate each expression. Show your work.
1. –28=
_______
2. |10 – 5| – |4 – 7| =
_______
3. |3 – 10| + |4 • 2| = _______
4. - –50=
_______
5. 4 × 5-10 =
_______
6. 8(5) × 15- 20 =
_______
7. -5× 4 =
_______
8.
- -20 + 10
=
-5
_______
-2
Evaluate each expression. Show your work.
1. 18 + (–12) =
______
2. –6 + 18 =
_______
3. 24 – 58 =
______
4. –10 – 73 =
_______
5. 15 + (–5) =
_______
6. –24 – (–42) =
_______
7. (3 + 5) + 9 – (2 + 1) = _______
8. 3 + 4(3 – 8) =
_______
9. 15 + 3 • 25 + 2=
10. –15 – (–55) =
_______
12. 8 + (3 – 2) – (- 5) =
_______
_______
11. –7 + (- 4) + 5 – (- 8) = _______
Evaluate each expression. Show your work.
1. –9(6) =
_______
2. –12(–3) =
_______
3. –4(–3) (–2) =
_______
4. –15(–3) =
_______
5. 63 ÷ (–21) =
_______
6. –3(4)(–5) =
_______
7. -4(9) =
_______
8. -5(2)(-9) = =
_______
-2
6
–9
3
Integers Final Review
This is a PowerPoint file that you’ll be able to access from
Edu2.0. Complete the review in your notebook and show all
your work. Check your answers with the answers below:
On Monday morning it was -5°C in Montreal and by evening the temperature had
risen to +9°C. What was the change in temperature throughout the day?
9 – (-5) = 14°C
1) How much deeper is the Dead Sea compared to Death Valley?
The Dead Sea 310m deeper than Death Valley.
2) Kingston shows the highest change in temperature.
3) Alejandro did not make a profit. He still owes his aunt $50:
(-200) +150 = - $50
4)
2 |- 7 – 8| = + 30
2 (- 7 - 8) = - 30
5)
1 – (10 – 15) = +6
- (10 – 15) = +5
6)
– 8 – (– 15) + 12 = +19
7)
8 + 3 • 2 + 42 = +30
8)
|9 – 15| + |3 • (– 8)| = +30
9)
|12 – 30| – |23 + 5| = +5
10)
2 • 3 (– 4) + |– 3| • (– 8) = - 48
11)
5 – (-15) – 2 |5-12| - (7 - 10) = +9
12)
- |6 + (-8)|  |-2 + 11| = -18
13)
4 (-9) = +9
-4
14)
– 8 (– 3) (– 2) = -12
4
15)
– 2 (– 8) • |–2| = -4
(- 8)
16)
- |8 – 18| - (12 – 6) = +4
-4
17)
9 – 19
= -10
|6 – 1 – (-5)|
+10
= -1
18) - 789 + 135 – 560 – 25 = - 1239m
19) 36 ÷ 3 = 12 people/year
Unit 2 – Fractions, Percentages and Decimals (FPD)
Topics to be covered in this unit:
1. What are fractions, percentages and decimals and what
is the relationship between them?
2. Equivalent Fractions/ Simplifying Fractions
3. Decimals – Place value tens, ones, tenths, hundredths,
thousandths.
4. Converting Fractions (simple, mixed, improper) to
percentages to decimals and vice versa.
5. Adding and Subtracting Positive and negative Fractions
6. Multiplication of Fractions
7. Division of Fractions
Math Lingo:
Word
Improper fractions
Mixed-number fractions
Simplified/reduced
fractions
Numerator
Denominator
Equivalent fractions
Reciprocal
Percentage
Decimal
Fraction
Tip
Tax
Discount
Meaning (in your own
words). Give an
example.
Find/draw a picture that
describes the word and
tell us how it’s used in
the real world.
Unit 2 – FPD Overview
Let’s see what you know before we start the unit!!!
Equivalent Fractions
Fill in the missing number.
1.
26
=
65
5
2.
49
=
3
7
Converting Fractions, Decimals and Percentages.
Fill in the missing information. Convert the numbers to fractions, decimals or
percents.
Fraction
Percent
Decimal
Improper or
Mixed Fraction
Proper Fraction
3.
2.06
4.
1.5
5.
4
3
5
6.
64%
Word Problems involving fractions and percents
Show all your work and clearly state your answer.
5
7. Mario walked of his journey. If the journey was 16 km long, how far did he
8
walk?
8.
3
of students are boys and the remainder girls. If there are 40 students in the
10
school, how many are girls?
9. In Serena's high school, 27% of the students walk to school. What fraction of the
students walk to school?
10. In Janie's class, 7 out of 25 students have blue eyes. What percent of Janie’s class
has blue eyes?
11. There are 50 people. 80% of all people voted Obama for President. How many
people voted for Obama?
Ordering positive and negative fractions, percents and decimals
Order the following from least to greatest. Use the number line if needed.
12.
4
5
0.91
13.
8
7
-1
2
3
7
8
84%
3
2
-1
1
6
Operations with Fractions
14. Kim ate
1
of a pie in the morning
5
15. Sandra had 6
feet of rope.
14
and then
of the same pie at night. How
20
tie balloons.
She cut
much of the pie did she eat altogether?
Then she cut 2
13
feet to
6
feet to give
to Peter. How
much did she have
left?
æ 5ö 9
16. ç -2 ÷ – =
è 8ø 5
18.
3
·7=
4
æ 3 ö æ 11ö
20. ç -3 ÷ ç ÷ =
è 4ø è 6 ø
æ 3ö æ 1 ö
17. ç -1 ÷ - ç -1 ÷ =
è 8ø è 6 ø
19.
3
¸6 =
5
æ 3ö æ 5ö
21. ç - ÷ ¸ ç -1 ÷ =
è 4 ø è 3ø
7
8
FPD – Workshop 1 – Regular Track
Introduction to Fractions
You can copy and paste this assignment into another word
document and show your work in that document. You can also
show your work on paper or Bamboo Tablet. Upload the
pictures for your work into a folder called “FPD-Workshop1”
on GoogleDocs when you’re done.
Activity 1: Equivalent fractions and Reducing fractions
Listen to the following videos if you need to understand what
equivalent fractions and reduced fractions are. If you think
you already know, you may skip these videos.
Videos:
Equivalent fractions http://www.khanacademy.org/math/arithmetic/fra
ctions/Equivalent_fractions/v/equivalent-fractions
Equivalent fractions example
http://www.khanacademy.org/math/arithmetic/fra
ctions/Equivalent_fractions/v/equivalent-fractionsexample
Fractions in lowest terms
http://www.khanacademy.org/math/arithmetic/fra
ctions/Equivalent_fractions/v/fractions-in-lowestterms
Complete these questions:
Find equivalent fractions. Copy each row of fractions into
your Bamboo notebook or paper notebook and show your
work and answers.
Simplify the following fractions. Copy each row of
fractions into your Bamboo notebook or paper notebook
and show your work and answers.
Activity 2: Proper Fractions and Improper fractions
Watch this video to learn about improper fractions and
mixed number fractions.
http://www.brainpop.com/math/numbersandoperations
/mixednumbers/
Convert the following improper fractions to mixed number
fractions. Copy each row of fractions into your Bamboo
notebook or paper notebook and show your work and
answers.
Convert the following mixed number fractions to improper
fractions. Copy each row of fractions into your Bamboo
notebook or paper notebook and show your work and
answers.
FPD – Workshop 2 – Regular Track
Comparing and Ordering Fractions
You can copy and paste this assignment into another word
document and show your work in that document. You can also
show your work on paper or Bamboo Tablet. Upload the
pictures for your work into a folder called “FPD – Workshop2”
on GoogleDocs when you’re done.
***If you don’t know how to compare and order fractions,
watch this video:
http://www.mathplayground.com/howto_comparefractio
ns.html
Activity 1: Fraction Wars – Ordering positive fractions
1)
This is a game that involves 2 players.
2)
Each player flips over 2 cards and tries to make the
biggest fraction.
3)
J = 10, Q = 11, K = 13, A = 1.
4)
The 2 players compare their fractions and choose who
wins the round. SHOW YOUR WORK IN YOUR
BAMBOO NOTEBOOK OR IN YOUR PAPER NOTEBOOK
for each round.
5)
Whoever wins the round, gets all 4 cards used in the
round.
6)
Players should record their rounds on the table below.
7)
Round
Play 8 rounds.
Player 1
biggest
fraction
Player 2
biggest
fraction
Who has
the bigger
fraction?
Who won
the round?
Activity 2: Ordering Positive and Negative Fractions
Show your work for each question in your Bamboo
notebook or your paper notebook. You can use a number
line if you want.
***Remember: THE NEGATIVE FRACTION THAT IS CLOSER
TO ZERO IS THE BIGGER NEGATIVE FRACTION***
1)
2)
3)
4)
5)
Activity 3 – Word problems with comparing fractions
Show your work for each question in your Bamboo
notebook or your paper notebook.
6
13
1) If Andros ate of a pizza. Sandra ate of another pizza.
7
15
Who ate more pizza and how do you know?
2
1
2) Eduardo ate of a cake and Sandra ate of another cake. In
3
2
the end Sandra ate more cake than Eduardo. How is this
possible? Give an example that makes this possible.
FPD – Workshop 3 – Regular Track
Converting from Fractions to Percentages
to Decimals
You can copy and paste this assignment into another word
document and show your work in that document. You can also
show your work on paper or Bamboo Tablet. Upload the
pictures for your work into a folder called “FPD-Workshop3”
on GoogleDocs when you’re done.
Activity 1: Converting from Fraction to Percentage to
Decimal
Play this game. Show your work in your Bamboo notebook
or paper notebook.
http://www.math-play.com/Fractions-Decimals-PercentsJeopardy/fractions-decimals-percents-jeopardy.html
Activity 2 – Word Problems
Show your work on the bamboo notebook or in your paper
notebook.
1)
There are 16 hats.
5
of the hats are blue.
8
How many hats are blue?
2)
There are 24 players on a basketball team.
2
of the players are mathematicians.
3
How many players are mathematicians?
3)
There are 60 slices of pizza.
5
of the slices are pepperoni.
12
How many slices are pepperoni?
4)
There are 15 flowers in a vase.
3
of the flowers are roses.
5
How many flowers are roses?
5)
2
6)
5
7)
12
of the tulips are dying. What percent of the tulips are
dying?
5
of the footballs are muddy. What percent of the
footballs are muddy?
6
of the cows gave milk today. What percent of the
cows gave milk today?
36
Activity 3: Constructing a Circle Graph using Percentages
Read the information on the following website FIRST:
http://www.mathsisfun.com/data/pie-charts.html
1) Pick one of the following topics to conduct a survey:
a) What type of film do you prefer watching? (romance, horror,
documentary, adventure)
b) What genre of book do you prefer reading? (romance, horror,
science fiction, non-fiction, adventure, humor)
c) What type of music do you like listening to? (pop, rock, indie,
house, classical)
d) Pick your own survey question to do a survey and check it with
the teacher. Choose 4 categories for answers.
2) Fill out the following:
Survey Question:
___________________________________________________________________________________
4 Possible Answers to survey question:
_a________________________________________________
b_____________________________________________
_c________________________________________________
d____________________________________________
3) Survey 20 students in the classroom and tally their responses in
the table below:
Answer
a
Tally
b
c
d
3) After collecting data in the table above, fill out this table:
Answer
a
b
c
Fraction out of
20 students
with that
answer
Percent of
students with
that answer
Degrees out of
360 on a circle
graph
d
4) Make the circle graph below using a protractor. Label the
sections of the circle graph and the percent in each section.
FPD – Workshop 4 – Regular Track
Problem Solving
You can copy and paste this assignment into another word
document and show your work in that document. You can also
show your work on paper or Bamboo Tablet. Upload the
pictures for your work into a folder called “FPD-Workshop4”
on GoogleDocs when you’re done.
Activity 1: Fractions and Percent Word problems
Do these word problems in your Bamboo notebook or
paper notebook or on this document. Show all your
work!!!
Do the following problems:
1) Ricardo has 30 cars.
1
6
of his cars are green. How many cars are
green?
2) There are 24 students in Ms. Khare`s class.
3
8
are absent on the
last day of school How many students are absent?
3) Elisa has 60 silly bands.
2
3
of her silly bands are purple. How
many silly bands are purple?
4) Sofia has 36 minutes to finish all her homework. She uses
3
12
of
her time to complete her math homework. How many minutes
does she spend on her math homework?
5) Pedro has 100 days of vacation. He spends
7
10
of this time in
Disney World. How many days does Pedro spend in Disney
world?
Convert the following fractions into percents:
1)
21
30
=
2
2) of Ms. Khare´s class could go to the homework challenge. What
3
percent of her class could go to homework challenge?
3) There were 25 words on the spelling test and Sandra got 20
words correct. What percent of the words did Sandra spell
correctly?
4)
7
21
=
5) There are 40 candies in total and 25 candies are red. What
percent of the candies are red?
Do the following problems:
1) There are 32 balloons in total. 75% are red. How many balloons
are red?
2) There are 25 flags. 40% are blue. How many flags are blue?
3) There are 80 students in grade 5. Yesterday, 75% of the students
were missing. How many students were missing?
4) There are 15 books. 66.66 % of the books have yellow pages in
them. How many books have yellow pages in them?
5) There are 20 shirts. 37.5% of the shirts are size “small”. How
many shirts are size “small”?
Activity 2: Who wants to be a millionaire?
Copy the question and show your work and answer in your
Bamboo notebook or paper notebook or on this document.
http://www.math-play.com/Changing-Fractions-andDecimals-to-Percents/changing-fractions-and-decimals-topercents-millionaire.html
Activity 3 - Are you up for a challenge?
Do these word problems in your Bamboo notebook or
paper notebook or on this document. Show all your
work!!!
1) In a school, 25 % of the teachers teach basic math. If there are 50
basic math teachers, how many teachers are there in the school?
2) Maya bought a sweater at a discount of 25%. She saved $18.
What was the sale price of the sweater?
3) Nick has 20% more video games than Brian. Together, they have
55 video games. How many video games does Brian have?
4) Jack and Jill drove in separate cars to their favorite hill, leaving
from the same place at the same time. Jill drove 20% faster than
Jack and arrived half an hour earlier. How many hours did Jack
drive?
FPD – Workshop 5 – Regular Track
Adding and Subtracting Fractions
You can copy and paste this assignment into another word
document and show your work in that document. You can also
show your work on paper or Bamboo Tablet. Upload the
pictures for your work into a folder called “FPD-Workshop5”
on GoogleDocs when you’re done.
Activity 1: Practicing Adding and Subtracting Fractions
Solve the following problems. Show your work in your
Bamboo notebook or in your paper notebook. Take a
picture of your work and insert it below.
1)
1
3
+
1
12
=
Estimate first by putting an X on the number line showing
about where you think the answer would be on this line.
Now compute the answer:
2)
3
5
4
8
1 + =
Estimate first by putting an X on the number line showing
about where you think the answer would be on this line.
Now compute the answer:
3)
5
6
1
− =
2
Estimate first by putting an X on the number line showing
about where you think the answer would be on this line.
Now compute the answer:
4)
1
11
12
1
− =
3
Estimate first by putting an X on the number line showing
about where you think the answer would be on this line.
Now compute the answer:
Activity 2 – Practice problems
Solve the following problems. Show your work in your
Bamboo notebook or in your paper notebook. Take a
picture of your work and insert it below.
2
1
3
2
2 −1 =
13
1
+3 =
4
3
1
5
2 −1 =
2
6
4
1
2 −3 =
5
2
Activity 3 – Word problems
Solve the following word problems. Show your work on
the bamboo tablet or in your paper notebook.
2
1) Natalia has of a cup of brown sugar left in the sugar
3
1
bowl. Her recipe for chocolate chip cookies requires
2
cup of brown sugar. How much brown sugar will she
have left after making her chocolate chip cookies?
2) You have taken up jogging. On the first day you ran 2
1
2
5
miles. On the next day you ran 1 miles. How far did you
3
run in two days?
1
5
3) Ms. Khare ran 3 miles so far in the race. The race is 5
4
8
miles long. How much farther does she have to run?
4) You’re riding your bike in a 3-day bike-a-thon. The total
1
6
distance is 26 miles. On the first day you rode 8 miles.
2
8
1
On the second day you rode 9 miles. How far did you
2
1
ride on the third day to cover all 26 miles?
2
FPD – Workshop 6 – Regular Track
Multiplying and Dividing Fractions
You can copy and paste this assignment into another word
document and show your work in that document. You can also
show your work on paper or Bamboo Tablet. Upload the
pictures for your work into a folder called “FPD-Workshop6”
on GoogleDocs when you’re done.
Activity 1 – Multiplying Fractions
Show all your work!!!
Read this website
http://www.mathsisfun.com/fractions_multiplication.htm
l to understand how to multiply fractions. Then play the
game on the following website with a partner and practice
multiplying fractions:
http://www.math-play.com/Multiplying-FractionsMillionaire/Multiplying-Fractions-Millionaire.html
Each person must answer 5 questions correctly and show
your work for these 5 questions in his/her Bamboo
notebook or paper notebook.
Activity 2 - Dividing Fractions
Show all your work!!!
Read this website
http://www.mathsisfun.com/fractions_division.html to
understand how to divide fractions. Then play soccer
alone on the following website and practice dividing
fractions:
http://www.math-play.com/soccer-math-dividing-fractionsgame/soccer-math-dividing-fractions-game.html
Answer 5 questions correctly and show your work for
these 5 questions in your Bamboo notebook or paper
notebook.
Activity 3 – Fraction addition, subtraction, multiplication
and division word problems
Use the problem solving process to solve these problems.
Act it out if you need to. It will help you better understand
the problems. Show your work in your Bamboo or paper
notebook.
1) Elena and her friends ordered a 24-slice pizza:
a. She and her friends ate 2/3 of the pizza. How many
slices did they eat?
b. Her brother Marcus eats ½ of what is left. What
fraction of the pizza does Marcus eat?
2) There were 9 cupcakes. Simon ate 3 and 1/3 cupcakes
and Jasmine gave 2 and 7/8 cupcakes away. How many
cupcakes were leftover?
3) Adina had 3/5 of a pizza. She gave Richard ¾ of her
portion of pizza to Richard. What fraction of the pizza did
Richard get? Did he get more or less than 1 entire pizza?
4) Jonah found 2/3 of a bag of cookies in the cupboard. He
and his friends each ate 1/6 of the bag of cookies for
snack. How many people ate cookies?
5) For a camping trip, Albert bought 6 bags of trail mix that
he wants to split into portions that are 3/7 of a whole.
How many portions can he make?
6) Every year the school participates in a read-a-thon.
About 4/7 of the class collected money for the event.
Close to 3/8 of these students raised over $50 each?
a. What fraction of the class raised over 50$?
b. What fraction of the class raised less than 50$?
c. If there are 28 students in the class, how many
students raised over $50?
7) Natalie has one large bowl of popcorn. She invites 3
friends over to watch a movie. Her brother takes 1/5 of
the popcorn for himself. Natalie must share the rest of
the popcorn equally with her 3 friends. How much of the
bowl of popcorn does each person get?
8) A car starts with a full tank of gas. After a drive around
the city, 1/7 of the gas has been used. With the rest of the
gas in the car, the car can travel from San Pedro to Saltillo
3 times. What fraction of a tank of gas does each
complete trip use?
FPD – Workshop 7 – Regular Track
Tip, Tax and Discount
Show your work for every question. You can copy and paste
this assignment into another word document and show your
work in that document. You can also show your work on paper
or Bamboo Tablet. Upload the pictures for your work into a
folder called “FPD-Workshop7” on GoogleDocs when you’re
done.
Activity 1: Calculating Taxes
Watch the following videos to learn about what taxes are, why they are
important and how to calculate them:
Brainpop:
Username – asfmbp
Password – asfmbp
http://www.brainpop.com/math/ratioproportionandpercent/taxes/
http://www.scholastic.com/browse/article.jsp?id=3746968
Play this game and show your work:
http://www.math-play.com/Sales-Tax/Sales-Tax.html
Activity 2: Calculating Tip and Discount
Watch this video on how to calculate tip:
http://www.mathplayground.com/howto_percentwp.html
What is discount?
How do you think people calculate discount and sales price after
discount?
Play this game, copy the questions and show your work:
http://www.mathplayground.com/mathatthemall2.html
FPD – Compacting 1
Fractions, Percentages and Decimals
Show your work for every question. You can copy and paste
this assignment into another word document and show your
work in that document. You can also show your work on paper
or Bamboo Tablet. Upload the pictures for your work into a
folder called “FPD-Compacting1” on GoogleDocs when you’re
done.
Activity 1: Flags and Fractions
Activity 2: Building Shapes and Using Fractions
1) Watch the video “Building Shapes and using Fractions” on
Edu2.0 and learn what you need to do with the wooden blocks.
2) SHOW YOUR WORK FOR ALL QUESTIONS IN AN ORGANIZED
WAY!!!
Answer the following:
a) Trace out a hexagon that is
1
2
red
1
3
blue and
1
6
green.
What percent of the hexagon is red?
What percent is blue?
What percent is green?
Write all these percentages as decimals rounded to the nearest
hundredth place.
Add up all the percentages. What do you get?
Add up all three decimals. What do you get?
b) Trace out a triangle that is
2
9
green,
1
3
red and
4
9
blue.
What percent of the triangle is green and red?
Write these percentages as decimals rounded to the nearest
hundredth place.
c) Trace out a parallelogram that is
3
8
red,
1
2
blue and
1
8
green.
What percent of the triangle is red?
What percent is blue?
What percent is green?
Write all these percentages as decimals rounded to the nearest
hundredth place.
Activity 3: If the World was a Village of 100 People!!!
YOU MAY USE A CALCULATOR TO COMPLETE THIS
ACTIVITY…
The current world population is 7 billion, 182 million people
(7,182, 000, 000) and that’s a big number.
Of these people:
3,591,000,000 are male
3,591,000,000 are female
574,560,000 are from Latin America
143,640,000 are Mexican
1,351,000,000 are Chinese
1,237,000,000 are Indian (From India)
2,370,060,000 are Christian
502,740,000 speak Spanish
646,380,000 speak English
1,237,000,000 are between the ages of 10 and 19
5,961,060,000 can read and write
502,740,000 have a college degree
1,580,040,000 own or share a computer
It becomes much easier to learn about the people of the world
using smaller more manageable numbers. So, why don’t we
imagine the world as a village of 100 people.
Fill out the following table using the statistics above to find
out more about our world today:
If the world
was a village
of 100
people, how
many…
What
percent is
that?
… would be
from Latin
America?
8%
… would be
from Mexico?
… would
speak
Spanish?
… would
speak
English?
… would be
between ages
What
decimal is
that?
If a class of
25 students
was the
world, how
many…
0.02
7%
2.25 people
10 and 19?
18
… would
NOT be able
to read or
write?
… would
have a
college
degree?
… would own
or share a
computer?
… would
have clean
safe water to
drink?
13
7%
0.22
FPD – Compacting 2
Ordering Positive and Negative Fractions
and Decimals
You can copy and paste this assignment into another word
document and show your work in that document. You can also
show your work on paper or Bamboo Tablet. Upload the
pictures for your work into a folder called “FPD-Compacting2”
on GoogleDocs when you’re done.
Find the correct path from start to finish through the maze. Proceed from one
circle to the next only if the second number is greater than the first number. Use
strategies that get you to finish this activity effectively and efficiently.
FPD – Compacting 3
Fractions, Percentages and Food and
Exercise
Show your work for every question. You can copy and paste
this assignment into another word document and show your
work in that document. You can also show your work on paper
or Bamboo Tablet. Upload the pictures for your work into a
folder called “FPD-Compacting3” on GoogleDocs when you’re
done.
** YOU CAN USE A CALCULATOR FOR THIS PROJECT BUT YOU MUST
STILL SHOW ALL YOUR WORK IN YOUR BAMBOO NOTEBOOK OR
PAPER NOTEBOOK OR IN THIS DOCUMENT**
You all are at a stage in your life when your bodies are growing and
going through many changes. The eating and exercise habits you
develop at this age will influence how you look and feel when you’re
older.
Food and drinks are made of 3 main components – fat,
carbohydrates and protein. You get some calories of energy from
each component and each component is used in your body in different
ways. Calories are the amount of energy that a food or drink will
produce when it is digested by the body.
To maintain a healthy weight, you need to balance the amount of
calories you consume through food and drink with the amount of
calories you burn (or use up) through physical activity.
In this activity, you will choose items you will like to have for lunch. You
will calculate the amount of calories contained in this food and how
much exercise you need to do in order to burn those calories and
maintain a healthy weight.
Part 1: Eat!!!
1. In the table below, record the 5 items you chose. Fill in the rest of the table and
write the total number of calories for each column.
Food
Total Calories
Calories from
Fat
Calories from
Carbohydrate
Calories from
protein
Total
What percent of the total number of calories in your lunch comes from fat? _____
From carbohydrate? _______
From protein? _________
3. Nutritionists recommend that, at most, 30% of the total number of calories
comes from fat, about 12% of the calories from protein, and at least 58% of the
calories from carbohydrates.
Does the lunch you chose meet these recommendations? _________
4. Plan another lunch. This time, try to limit the percent of calories from fat to
30% or less, from protein to between 10% and 15%, and from carbohydrate to
between 55% and 60%.
Food
Total Calories
Calories from
Fat
Calories from
Carbohydrate
Calories from
protein
Total
What percent of the total number of calories in your lunch comes from fat? _____
From carbohydrate? _______
From protein? _________
Part 2: Eat More and Exercise!!!
Research says that, children between the ages of 9 and 13
need to consume an average of 2000 calories a day in order
to carry out their regular functions. If you want to lose weight
in a healthy way, you need to use more energy than you
consume.
1) What percent of your daily 2000 calories come from
your total lunch in Part A?
2) A) How many calories are left for breakfast and dinner?
B) What food would you have for breakfast and dinner so
that you meet your 2000-calories-per- day limit (you
can go over 2000 calories if necessary but not too
much over)?
C) What percent are your breakfast and dinner calories
of your 2000-calories-limit?
3)
A) Go to http://www.caloriescount.com/getMoving.aspx
B) Pick an activity. Choose the amount of time that you’ll
do the activity for. Type in your weight in pounds (use google
search to convert your weight from kilograms to pounds if you
need to).
C) Click on “Compute Calories” and find out how many
calories you will burn by engaging in the physical activity that
you choose.
D) What percent is the calories that you burn by doing
this exercise, of the 2000 calories that you consume
per day?
E) If people eat too much on a certain day, they might
want to burn off those extra calories on the same day. How
long would you have to do the activity that you chose in A to
burn 100 calories?
FPD – Compacting 4
Fractions, Percentages and Art
Be Artistic with Fractions!!!
Create a sample mural on the white paper that you are given. Cut and
paste the color paper on top of the white paper such that the mural you
create is:
1)
2)
3)
4)
5)
1/8 orange
2/5 green
1/16 yellow
5/16 blue
The rest is red.
Make sure that ½ of the red section has thin white vertical stripes.
Make sure that 1/4 of the green section has white polka dots.
Make sure that 1/8 of the blue section has thin diagonal lines.
Make sure that ½ of the blue-section-with-thin-diagonal-lines has your
name written in it.
Complete the following questions:
1) What is the area of the blue portion of the mural?
2) What is the area of the orange portion of the mural?
3) What fraction of the entire mural is green with white polka dots?
4) What fraction of the entire mural as your name written in it?
FPD – Compacting 5
Fractions, Percentages, Decimals and
Genes & Probability
Show your work for every question. You can copy and paste
this assignment into another word document and show your
work in that document. You can also show your work on paper
or Bamboo Tablet. Upload the pictures for your work into a
folder called “FPD-Compacting5” on GoogleDocs when you’re
done.
It’s all in your genes!!!
Mirror, mirror on the wall... why do I look like my parents at all?
You've been selected to join a team of genetic researchers to find an
answer to this very question. On this adventure, you'll learn how to
use a Punnett square. Then you'll gather information about the genetic
traits of your classmates. You'll also make genetic predictions based on
an analysis of your findings. So grab your lab coat and your probability
and statistics tool kits. This is one adventure you don't want to miss.
The reason you look the way you do is because you have inherited
genetic material (DNA) in your cells from your mom and dad that
make you look the way you do. Half the DNA in your cells is from
your mom and the other half is from your dad.
If the blue circle below is a cell in your body, the red lines are
DNA from your mom and the yellow lines are DNA
from your dad.
GENE 3
GENE 2
GENE 1
The DNA from your mom and dad are divided into pieces called
GENES. Each gene codes for a certain trait. Some genes are
DOMINANT, in that they take over and other genes are recessive, in
that they remain hidden. More people express traits from dominant
genes and fewer people express traits from recessive genes.
Watch these movies:
http://www.youtube.com/watch?v=d4izVAkhMPQ
http://www.youtube.com/watch?v=prkHKjfUmMs
Task 1: Class survey
Collect data from 20 students.
Trait
Non-blue eyes
Blue eyes
Unattached Ear
Lobes
Attached Ear
Lobes
Widow’s Peak
Straight
Hairline
Dimple
No Dimples
Dark Hair
Light Hair
How many
students?
Task 2: Assign symbols for each type of gene.
Fill out the table:
Which trait is
dominant and
which is
recesive?
Trait
Assign a symbol
for each type of
gene (“CAPITAL”
letter for dominant
gene and “lower”
case letter for
recessive gene)
Non-blue eyes
Blue eyes
Unattached Ear Lobes
Attached Ear Lobes
Widow’s Peak
Straight Hairline
Dimple
No Dimples
Dark Hair
Light Hair
What will your children look like? Answer the questions below
to find out.
1) Look at your mom and dad and grandparents. Make an
educated guess as to what genes they possess for each trait.
What genes do you think you have inherited from your mom
and which genes have you inherited from your dad for each of
the 5 traits above? Fill out the table below.
Traits
Eyes
Grandma
(2 possible
genes)
Grandpa
(2 possible
genes)
Mom
(2 possible
genes)
Dad
(2 possible
genes)
Me
(2 possible
genes)
Ear lobes
Hairline
Dimples
Hair
2) If you got married to someone with blue eyes, what is the
probability that your kids will have blue eyes? Express your
answer as a fraction. Draw a Punett square and show your
work.
3) If you got married to someone with dimples, what is the
probability that your kids will have dimples? Express you
answer as a percent. Draw a Punett square and show your
work.
4) If you got married to someone with a widow’s peak and had 8
kids, how many of those kids would have a straight-hairline?
Draw a Punett square and show any other work that you need
to get to the answer.
5) If you got married to someone with unattached ear lobes and
had 3 children, how many of those children would have
unattached ear lobes? Draw a Punett square and show any
other work that you need to get to the answer.
6) TALK TO MS. KHARE BEFORE YOU DO THIS QUESTION!!!
If you got married to someone with widow’s peak and light hair,
what fraction of your kids will have a straight hairline and dark
hair? Express your answer as a percentage and a decimal.
FPD – Final Review
Your review including solutions will be given to you in the
form of PowerPoint presentations on Edu2.0.
Unit 3 – Geometry
Topics to be covered in this unit:
1. Properties of quadrilaterals (squares, rectangles,
parallelograms, trapezoids) Area and perimeter.
Relationship between area and perimeter.
2. Properties of triangles (scalene, right, equilateral,
isosceles) and talk about acute, obtuse and right angles.
Area and perimeter. (Pythagorean theorem if time
permits).
3. Properties of Circles - radius, diameter, circumference,
area
4. Volume - What is it? Cube, rectangular/triangular
prisms, cylinder, cone, pyramid
5. Square root and Cube Roots – Area of squares &
Volume of cubes
Math Lingo:
Word
Perimeter
Area
Dimensions
base
height
Length
Width
Parallelogram
Trapezoid
Meaning (in your
Find/draw a picture
own words). Give an that describes the
example.
word and tell us how
it’s used in the real
world.
Pentagon
Hexagon
Parallel lines
Perpendicular lines
Right angle
Acute angle
Obtuse angle
Equilateral triangle
Isosceles triangle
Scalene triangle
Complementary
angles
Supplementary angles
Regular polygon
Irregular polygon
Volume
Cube
Rectangular prism
Triangular prism
Cylinder
Cone
Square pyramid
Quadrilateral
Radius
Diameter
Circumference
Pi (π)
Square root
Cubic root
Geometry – Assignment 1 – Regular Track
Area and Perimeter of Rectangles
This assignment will be given to you on paper. You’ll have
to complete it in class and hand it in.
Building Rectangular Gardens
Investigate the relationship between Area and Perimeter of rectangles
1) Draw as many different rectangles as you can that have the area
of the number given to you by the teacher. Make these drawings
on graph paper.
2) When you are sure that you have all possible rectangles, go see
the teacher and explain to her how you know.
3) Fill out the table below.
Rectangle
1
2
3
4
5
6
7
8
Length
Width
Perimeter (Show
your work)
Answer these follow-up questions:
1) What is the area of each of your rectangles?
2) Is the perimeter the same for all your rectangles?
3) What is the relationship between the length and width of your
rectangles and the area of each of them?
4) Write these rectangles in order of decreasing perimeter. Look at
the dimensions of each rectangle. What do you notice about the
way their dimensions are changing as the perimeter decreases?
5) What do you notice about the way the rectangle looks as the
perimeter decreases?
6) If you wanted to build a rectangular garden with an area of 36m2,
what would be the dimensions of this garden such that it would
require the least amount of fencing? Show your work on graph
paper.
Show your work and calculate the area below.
Geometry – Assignment 2 – Regular Track
Area and Perimeter of Parallelograms and
Trapezoids
Show your work for every question. You can copy and paste
this assignment into another word document and show your
work in that document. You can also show your work on paper
or Bamboo Tablet. Upload the pictures for your work into a
folder called “Geometry-Assignment2” on GoogleDocs when
you’re done.
Challenge 1: Parallelogram
1) Use the Geoboard and make a parallelogram that has no
right angles. If you don’t know what a parallelogram
is – look it up on the website for “Math is Fun”.
2) Ask the teacher for measuring tape.
3) Calculate the perimeter of the parallelogram in
centimeters. Show all your work.
4) Come up with a strategy to calculate the area of the
parallelogram you made in square centimeters. Draw a
picture or write your strategy down in a few sentences
and then actually calculate the area of the parallelogram.
Show all your work.
Challenge 2: Trapezoid
1)
Ask the teacher for measuring tape.
2)
Calculate the perimeter of a trapezoidal desk in this
classroom in centimeters. If you don’t know what a
trapezoid is – look it up on the website for “Math is
Fun”. Show all your work.
3)
Come up with a strategy to calculate the area of the
trapezoidal desk in square centimeters. Draw a picture
or write your strategy down in a few sentences and
then actually calculate the area of the trapezoid. Show
all your work.
Challenge 3 – Wood-Art
Build one of the above vehicles using the wooden blocks
on plain paper. If you want to build something else you
must get it approved by the teacher.
1) Calculate the perimeter of the entire vehicle in
centimeters. Show all your work.
2) Calculate the area of the entire vehicle in square
centimeters. Show all your work.
Geometry – Assignment 3 – Regular Track
Introduction to types of Triangles
This assignment will be completed in a Geometer’s Sketchpad
document that you will access from Edu2.0. This is how the
document will look:
Geometry – Assignment 4 – Regular Track
Angles and Area and Perimeter of
Triangles and other Polygons
Copy and paste this assignment into another word document
and work on that document directly.
Objective: In this assignment you will investigate how to use triangles to find
the sum of all angles in any polygon. You will also learn how to use Sketchpad
to calculate area and perimeter of triangles and other polygons.
1) Open up Geometer’s Sketchpad.
2) Select the polygon tool:
3) Make a triangle on your sketch page.
4) Measure all the angles of your triangle.
Your sketch should look something like this now:
These are the angle
measurements.
5) Select all the angle measurements and click on the “Number” menu and click
on “Calculate”. This calculator should appear on your screen.
6) Select the angle measurements one at a time and sum them up using the
calculator.
7) Your sketch should look something like this now:
8) Connect the points of your triangle with lines to outline the perimeter of your
triangle. Your sketch should look something like this.
9) Add a point somewhere on your sketch beside your triangle.
10)Connect the new point to 2 different points (points that are next to each
other) on your triangle. Your sketch should look something like this now.
Question 1:
If the inside of the four points on your sketch made the area of a shape, it
would have 4 sides. What kind of a shape have you made?
Question 2:
Predict what you think is the sum of all angles of this 4-sided shape. Support
your prediction with reasoning.
11) Calculate the angle the new point makes inside your 4-sided shape.
Question 3:
Calculate the actual sum of all angles in your 4-sided shape using the
calculator in Geo Sketchpad. Was your prediction correct? If your prediction
was not correct, where do you think you went wrong? Why is the correct
answer actually correct?
12)Now make a fifth point beside your 4-sided shape and connect it to 2 points
on your 4-sided shape. Your sketch should look something like this now:
Question 4:
If the inside of the five points on your sketch made the area of a shape, it
would have 5 sides. What kind of a shape have you made?
Question 5:
Predict what you think is the sum of all angles of this 5-sided shape. Support
your prediction with reasoning.
Question 6:
Calculate the actual sum of all angles in your 5-sided shape using the
calculator in Geometer’s Sketchpad. Was your prediction correct? If your
prediction was not correct, where do you think you went wrong? Why is the
correct answer actually correct?
Question 7:
Do you think all 5-sided shapes have the same sum of all angles? Why or why
not? How would you test this prediction using Geometer’s Sketchpad?
Question 8:
What is a 6-sided shape called?
Question 9:
What do you predict is the sum of all angles in a 6-sided shape? Why?
13) Make a NEW 6-sided polygon using the polygon tool.
Question 10:
Calculate the actual sum of all angles in the 6-sided shape by measuring the
angles and using the calculator in GeoSketchpad. Was your prediction
correct? If your prediction was not correct, where do you think you went
wrong? Why is the correct answer actually correct?
Area and Perimeter:
14)Make a new 8-sided shape using the polygon tool in GeoSketchpad.
Question 11:
What is an 8-sided shape called?
15) Calculate the perimeter by selecting the inside of your shape and clicking on
the “Measure” menu. Then click on “Perimeter”.
16) Calculate the area of the 8-sided shape. Select the inside of your shape and
click on the “Measure” menu. Then click on “Area”.
17) Save your sketch as “Angles-Triangles-Polygons” and upload your sketch
and this document with your answers to GoogleDocs.
Geometry – Assignment 5 – Regular Track
Area and Perimeter of complex polgons
and compound shapes
Find the area and perimeter of the following shapes:
5 cm
5 cm
5 cm
13 m
13 m
4 cm
24 m
11 cm
***All the sides on the hexagon are the same.
25 cm
8m
17 cm
17m
30 m
30 m
5m
25 cm
25 cm
7 cm
24 cm
20cm
15cm
15cm
20cm
Geometry – Assignment 6 – Regular Track
Area and Volume – Exponents, Square roots & Cubic roots
Activity 1: Squares and Cubes
Use exponents in your calculations.
1) What is the area of a square with length 9cm?
2) What is the volume of a cube with edge length 6cm?
3) This figure is made up of 6 squares. The perimeter of this figure is
60cm. What is its area?
4) The total length of all edges on a cube is 48cm. What is the
volume of the cube?
Activity 2: Square Roots
Read this website to learn about square roots:
http://www.mathsisfun.com/square-root.html
Watch this video to learn more about square roots:
http://www.brainpop.com/math/numbersandoperations/squ
areroots/preview.weml
Complete the following problems:
1) Rosy wants a large picture window put in the living room
of her new house. The window is to be square with an
area of 49 square feet. How long should each side of the
window be?
2) If the area of a square is 1 square meter, how many
centimeters long is each side?
3) A miniature portrait of George Washington is square and
has an area of 169 square centimeters. How long is each
side of the portrait?
4) Len is baking a square cake for his friend’s wedding.
When served to the guests, the cake will be cut into
square pieces 1 inch on a side. The cake should be large
enough so that each of the 121 guests gets one piece.
How long should each side of the cake be?
5) Cara has 196 marbles that she is using to make a square
formation. How many marbles should be in each row?
6) Tate is planning to put a square garden with an area of
289 square feet in his back yard. What will be the length
of each side of the garden?
7) Al has 324 square paving stones that he plans to use to
construct a square patio. How many paving stones wide
will the patio be?
8) If the area of a square is 529 square inches, what is the
length of a side of the square?
9) A square pie has to be shared by 10 people in total. Each
person should get a rectangular piece of pie. If the total
area of the pie is 900cm2, what are the dimensions of
each rectangular piece?
10)
(Calculator allowed) The playing surface on a
chessboard has an area of 576cm2. If the square
chessboard is made up of 64 smaller squares, what is the
side length of each small square on the board?
11)
Each face of a cube has the area of 36cm2. What is
the volume of the cube?
Activity 3: Cubic roots
Read this website to understand what cubic roots are:
http://www.mathsisfun.com/numbers/cube-root.html
1) The volume of a cube is 125cm3. What is the length of
one side?
2) What is the area of one face of the cube if the volume is
729m3?
3) Minecraft project – TBA. Involves building walls for
houses that can only contain a certain volume.
Geometry – Compacting
The Pythagorean Theorum
Show your work for every question. You can copy and paste
this assignment into another word document and show your
work in that document. You can also show your work on paper
or Bamboo Tablet. Upload the pictures for your work into a
folder called “Exponents-Compacting” on GoogleDocs when
you’re done.
Read this complete website to get some background information:
http://www.mathsisfun.com/pythagoras.html
Do the “Questions” and the “Activities” at the end of the website. Show
your work on a piece of paper or in your Bamboo notebook.
Geometry – Final Review
Your review including solutions will be given to you in the
form of .pdf document posted on Edu2.0.
************************ End of Semester 1 ********************