Thursday, June 23, 2016

Summer Math Project

My Summer Road Trip Book
It’s time to plan your summer vacation! Use the next few pages to decide your
destination, vehicle, and hotel. You will have a budget of $900. Be sure to spend wisely so
that you will have money left over in case of emergencies!

Choosing a Destination      
Distance from Chicago
790.8 miles to New York City
926.1 miles to New Orleans
759.19 miles to Philadelphia
799.99 miles to Richmond
1,156.07 miles to Orlando
989.33 miles to Boston
297.21 miles to St. Louis
697.03 miles to Washington D.C.

1. Which city is the furthest distance from Chicago?
2. Which city is the closest to Chicago?
3. How much farther from Chicago is Richmond than St. Louis?
4. How much farther from Chicago is New Orleans
than NYC?
5. How much farther from Chicago is Orlando than
Boston?
6. ABOUT how far is Washington D.C. from
Chicago?
7. ABOUT how far is Philadelphia from Chicago?
8. ABOUT how much farther from Chicago is
Richmond than Philadelphia?

Order the cities by distance (Nearest to Farthest) from Chicago

Round each city’s distance from Chicago to the nearest mile.

New York City
New Orleans
Orlando
Boston
Philadelphia
Richmond
St. Louis
Washington D.C

Thinking about Gas
If the national Average for gas per gallon in the United States is cur-
rently $3.49, how much will you be spending on gas for your trip?
Choosing your Vehicle  Car Mileage Weigh your Options
Do the Math to find out how much you would spend on gas to your two top destination choices.

Toyota Prius 48miles per gallon
Jeep Wrangler 21 miles per gallon
Honda CRV 31 miles per gallon

How do calculate the cost?
Divide the total distance in miles by your car’s miles
per gallon to find out how many gallons of gas you will
need for your trip. Then, multiply that number by the
average cost of a gallon of gas. Don’t forget to
multiply by two for a round trip.

How many hours are you willing to drive per day? How much ground will you cover?
Safe Speed—60 MPH
# of Hours
Miles Driven
1
60
2
120
3
180
4

5
300
6

7

8

9


How many hours/miles are you willing to drive per day? WHY?
For some destinations, you will need to break your trip into two days.
Calculate how many days of driving each destination will take.
New York City
New Orleans
Orlando
Boston
Philadelphia
Richmond
St. Louis
Washington D.C
HOTEL COSTS
Hotel
Cost per Day
Special Features
La Quinta Inn
$49.92
Low Ratings             Breakfast
Outside Pool Only    AC/Cable
Days Inn
$59.62
Okay Ratings           No Breakfast
Outside Pool            AC/Cable/WiFi
Comfort Suites
$96.72
Okay Ratings           Breakfast
Inside Pool              AC/Cable/WiFi
Hampton Inn
$93.48
Great Ratings           Breakfast
Outside Pool            AC/Cable/WiFi
Courtyard by Marriot
$84.52
Good Ratings           Breakfast
Inside/Outside          Pool AC/Cable
1. How much more money does the Courtyard cost than La Quinta Inn?
2. How much more money does Comfort Suites cost than Hampton Inn?
3. How much more money does Days Inn cost than La Quinta Inn?
How many days will you need to stay in a hotel?
Days on the road ____________ (Based on mileage– If you need to stop to stay at a hotel
because the distance is farther than what you are willing to drive in one day Remember, you
will need to do this twice for a round trip!)
Days at destination _______________
What is the cost of your hotel stay?
Round the daily rate of your selected hotel to the nearest dollar amount. Then,
multiply that amount by the number of nights you will be staying in a hotel.
Total Cost of my Hotel Stays:_______________________

Use the chart below to help you decide where you would like to visit! :)
City
Things to Do
Washington D.C
National Zoo-Free
National Children’s Museum $10
Six Flags America $39
New Orleans
Ghost Tours $25
Swamp & Bayou Tours $49
Cool Zoo Water Park $11
Richmond
Museum of Fine Arts$13
History Tours $27
Go Carts $32
Boston
McDonald’s Museum- $10
Whale Watching- $36
Mayflower Tour- $14
Philadelphia
Insectarium $9
Musical/Theatre $16
Sesame Place $63
St. Louis
Gateway Arch-$18
Six Flags- $40
“M”yseum- $10
NYC
Coney Island $24
Big Apple Circus $32
Botanical Garden $10
Orlando
Universal Studios $99
Lego Land $55
Magic Kingdom $102
Further Research
Use an online search engine to help you find more information about the cities you are considering,
City
City
Research Notes





Research Notes
Weighing Your Decision
Take your two top choices and weigh the costs and benefits of each
Choice #1: _____________________________
Costs
Benefits  
*

*

*
*

*

*
Choice #2: _____________________________
Costs
Benefits  
*

*

*
*

*

*
My Destination Choice
Use the space below to tell about your decision making process.
The city I choose to visit is ____________________________ because ________________
The Logistics
Miles (Round Trip– Multiply the distance by 2!) ___________________
Vehicle: _________________ Mile per Gallon: ________________
Total Cost of gas (Round Trip): ______________________________
Number of Nights I will stay in a hotel: _______________________
Total cost of hotel stays: ______________________________
Selected Activities (Entertainment Budget):
_______________________________________________________
Total Cost of Selected Activities: ___________________________
Total Food Cost: ________________________
$$TOTAL TRIP COST$$
__________________
How much money have you left for emergencies or unforeseen
circumstances?_________________

The Plan
Use the space below to jot down your plan for each day. Will you be driving? If so, how far? Will you
be spending a night in the hotel? Which one? Will you be going sight seeing? Where?
Day 1


Day 2


Day 3


Day 4


Day 5



Day 6


Day 7


My Trip Scrapbook
Use the space to draw pictures of the memories made on your trip. Use the
space beside the photos to describe your memory.



Tuesday, June 23, 2015

Summer Math Project Board

The project ideas listed below are some ways to do math over the summer. Give yourself a challenge and work to earn at least 50 points.
Math Project Board
Make a math vocabulary dictionary.  
20 points
 Write a compare and contrast essay about area and perimeter.
20 points  
 Make a math poster explaining about your topic.
30 points
Watch a Khan Academy video and complete the practice questions.  (Create an account)
10 points
Make a math puzzle and include a solution to the puzzle
10 points
Long division practice sheet

10 points
Create an informational booklet about your math topic.
30 points
Solve an investigation problem
30 points
Create a math song/skit to learn a math skill.
20 points

Examples of "Investigation Problems"
  • What are the different ways can you find the area of each polygons? Write a number sentence or an algebraic expression that would represent each of your methods.      
  •  What different shapes can you make with 5 cubes?  Compare the surface area of each of these different shapes, what do you notice?  Compare the volume of the 3-D shapes what do you notice?

Examples of "Math Puzzles"
  • Operations Puzzle- Which operations (+, -, X, /) must be performed to get the solution?  
    •  For example
      (4 * 1) * (6 * 2) = 1 
      (The correct answer is (4 + 1) - (6 - 2) = 1 or in simplest form 5 - 4 = 1) 
    •  More examples   (6 * 4) * 12 = 12;  (4 * 2) * (4 * 3) = 24;  (6 * 5) * (9 * 2) = 19
  • Equations Card Game- Write an equation showing (First Expression)=(Second Expression)
    • For example:  6 cards numbered 6, 4, 8, 7, 2, 10                                                             (Possible answers 8+2=6+4, 10-4= 8-2, and using Exponents 10^2 - 8^2 =  6^2)
    • Game directions and more math puzzles are at:  Home Page for Math Games and Puzzles  
Math Topic Ideas for Project Board (above)
Area, Volume, Surface Area Least Common Multiple/ Greatest Common Factor
Ratios 3-D Shapes
Equations                       Experimental Probability
Number  Patterns Scientific Notation
Inequalities Fractions

Slope of a line Parabolas and Quadratic Equations

Thursday, April 2, 2015

Percent of Body Height

Complete the chart below by measuring your body parts and total height.

Body Part                   height (in)                  total height                % of body
head                           ________                  _________                ________
torso                           ________                  _________                ________
leg                               ________                  _________                ________
neck                           ________                  _________                ________
foot                             ________                  _________                ________


Example
Body Part     Body Part Height (in.)  Total Body Height(in)  Work Steps   % of body
head                           10 inches                   72                        10/72=.14       14%
torso                          25 inches                   72                        25/72= .35       35%
legs                            30 inches                  72                         30/72= .42       42%
neck                           4 inches                     72                         4/72=  .05        5%
foot                             3 inches                    72                          3/72=  .04       4%
                                                                                                            1.0       100%

Friday, March 27, 2015

Writing Addition and Subtraction Expressions

Writing Addition and Subtraction Expressions

Expressions can be modeled using a bar diagram like the one below.  This example shows the number of biographies (x) currently in our classroom library and the increase of 13 new biographies from the school book fair.  This expression x + 13 represents the total number of biographies the library has now.


 This expression can also be written as 13 + x to represent this situation.   One way to test the equivalency of the expressions is to substitute values for x and see if the sum of both equations are still the same.   If x = 2,   x+ 13 = 13+ x,   2 + 13 = 13 + 2,   If x= -1   -1 + 13 = 13 + -1
As a result of the commutative property of addition these expressions are also proven equivalent.


Write my own algebraic expression...
1. Start with an input such as "12" (miles from home to downtown)  
2. Add in a variable such as "d" (distance traveled) 
3. Put it together into a situation like I want to get downtown but have already traveled d miles.  How far do I still have to go?
4. Define your variable(s)  D= distance traveled.  
5. Finally, Write the expression   12 - d
Now test out your algebraic expression....  If d= 6.5 how far is the distance from downtown?
12- d   Substitute in 6.5 for d,   12-6.5=  5  
If d= 6.5, I have to go only 5 more miles.

Sample Practice Questions about writing expressions.  Write an algebraic expression to represent each of the following situations.
  • The height (h) increased by 6 inches.  
  • 43 more than (t);  t= time
  • Carrie sold 50 bags of popcorn today.  Carrie sold (p) fewer bags than Terry.    
  • Seven less than a number (n)




Tuesday, March 10, 2015

Graphing on a Coordinate Plane

Graphing Stories

Does a graph always begin at the origin?  

What is the steepest part of the graph where it shows the greatest increase?

We have been learning from graphing videos and answering some of these questions.

Here is some graphing vocabulary to help springboard our discussions.
y-intercept-  the point on a graph where the line crosses the y-axis.
slope- a measure of the steepness of a line.  (Change in 2 y values divided by Change in the 2 matching x values)





Monday, September 1, 2014

About Me...By the Numbers



First day "about me by the numbers" activity

About me...By the Numbers is a project that uses numbers to show a picture about You.
So, Which numbers have special meaning for you?
The picture above shows an example project from Pinterest.
Directions: 1.  Write your name in the center of the paper.  2.  Brainstorm facts about you that involve numbers.  For example my dad had 16 siblings, my birthday is 6/27, and I my baby daughter weighed 6 pounds 11 ounces when she was born.  3. Write 5 or more numbers about yourself in the area outside your name.  4. Decorate and add a short description about the meaning of the numbers.

Numbers important to me....
 Fractions:  Birth date, favorite holiday, # of ____ in family / total family members.
Large Numbers: distance from my house to a relative's house, number of days until Christmas Break, height in centimeters
Decimals: cost of favorite candy  $0.25, distance of a 5 kilometer race= 3.1 miles, weight of a baby 7.2 pounds


Monday, July 14, 2014

Keeping a Writer's Notebook

"As a writer, words are your paint. Use all the colors.” ~Rhys Alexander. 

 Being a writer is very much like being an artist.  I wanted to share my seed story starters, summer math problems, and resonating writing ideas.  I look forward to crafting new stories, solving math problems, and sharing things I've learned.    

Summer moments make for great seeds for a Notebook of ideas.

  • "After a hot evening on the field, a team that is down by one run comes up to bat"
  • "A girl sings to the movie as her favorite song begins to play"
  • "The alarm sounds at 5:30am, as my feet hit the floor I prepare for the big day"

Here are some great examples of writing notebook ideas from an inspiring writer/teacher on Jordan's blog page: Writing Notebook Ideas 

Math problems are very rewarding after figuring out the solutions and then telling how you found the answer.

  • Summer programs include instrumental music, art, and dance.  Out of 40 students, 15% chose art. How many students are signed up for art? how many signed up for music or dance?
  • A bedroom is 8 feet tall, 12 feet wide, and 9 feet long.  How many square feet of paint are needed to paint the 4 walls and ceiling?
Ready for more?  Try 16 fun math problems from a website called, Analyze Math: Math Word Problems

Summer Writing Ideas to Begin With...
  1. Types of writing to try:  Compare and Contrast two of your favorite comics, books, or magazines.
  2. Write a story about one of the characters from a book you are reading. 
  3. A story about a loved one and how they have made a difference in your life. 
  4. Which type of (phone) do you prefer; (iPhone or Android)?
  5. Research and then explain about a (country) that you have always wanted to know more about. 
Always love to hear YOUR comments:) 


Tuesday, June 17, 2014

Summer Math Fun

Where can you find math in your life?  What ways do you like to do math?   Summer math activities are fun and will definitely sharpen your mind.  Which of the ideas below work best for you?   You probably have already tried many of these, so feel free to leave comments about math activities you enjoy.

Playing Card or Dice Games  

Multiplication- Each player draws two cards and multiplies the numbers.  The player with the higher product wins.  Challenge: Use 2 digit numbers or decimals by drawing four cards instead of two.


Fractions- Each player draws four cards and arrange in any order.  Add the fractions, the player with the greater sum wins.  Challenge: Use mixed numbers by drawing six cards instead of four.


Art Projects

Draw a scene that has hidden geometric shapes.  Use both basic shapes and more complex shapes in the drawing. Challenge:  Create a fractal design

Computer Games

Play math games that others created or try your hand at coding and make your own game.  Some games allow you to compete against others, whereas others let you try to simply master the game itself. 

Thursday, May 1, 2014

Ratio Projects

Darlene and Jackie decide to share the profits from the latest business venture 5:3.  If Jackie receives $210.00 how much money can Darlene expect?

At the spring festival there are 22 attractions that are split between food and entertainment.  Out of these attractions 6 are food stations.  What percent of the attractions have food?  


Lucy spent 54 Euros on a new pair of gym shoes including tax.  If tax was 10 percent, what was the cost of Lucy's shoes before tax?  

Answers:  
1. $350 dollars for Darlene.  210*5=1050  
1050/3 = 350
2.  27% were food stations  6/22= .272
.273*100 = 27.3%  
3. 49 Euros before tax.   54=1.10x    54/1.10= 49.09

Tuesday, March 25, 2014

Graphing Equations and Inequalities. Which do you prefer?

What types of graphs do you like to create? One of my favorite parts of Math is graphing and finding patterns in problems.  Graphs and Charts are found in many parts of our every day life.  

Pie graphs and bar graphs that are used to compare things like people's opinions for example.  Line Graphs and scatter plots are a type of graph that shows the relationship between two quantities or show can show changes over time.  The pattern on a line graph shows an increase (line goes upward) or a decrease (line goes downward).  

How do I graph an equation?

1. Equations such as y = 2x + 3 can be graphed by making a table of values for both x and y variables.

X
Y
-1
1
0
3
1
5
2
7

Steps to make a table of ordered pairs

a. Choose values for x that include both positive and negative numbers.
b. Substitute the value for x into the equation.
c. Use order of operations to solve the equation and find a value for y.
     Example   x = -1   y = 2x  + 3
                                  y = 2(-1) + 3   Substitute -1 for x
                                  y = -2 + 3       Then multiply 1 * -2
                                  y = 1               Add -2 + 3
2.  Use a coordinate grid to plot the ordered pairs in the table.
Example:  Ordered pairs:  (-1,1), (0,3), (1,5), and (2, 7)

The solid green line shows the pattern of the equation.  It is increasing or going upwards.
Y- Intercept-  The point where the line crosses the                   y-axis.  The green line crosses at (0,3)
Slope-  The slope of the line is how steep the line rises in the graph.  Find the slope in the equation:
Y=2x + 3.  The number that is multiplied by x is the slope. The slope of the green line is 2.





How do I graph an Inequality?

Inequalities have an inequality symbol like <, >, ,≥, or  instead of an equal (=) sign.
1. Inequalities like y ≤  2x +3 are graphed by making a table of values, the same as we did when there was an equal sign.
2.  The points are plotted on a coordinate plane in the same way that the equation y = 2x +3 was done.
3.  Here's the difference, the line that you draw to show the pattern of the points will be solid since the it is   (less than or equal to), and you will color in underneath the line to show all the possible solutions to the inequality y ≤  2x +3.

The purple shaded area shows all the possible solutions of  y ≤  2x +3
The solid blue line shows that the inequality sign is ≤ less than or equal to.  The line is solid since the solution set also includes all the ordered pairs in the equation y = 2x + 3
The slope and y-intercept are the same as the y = 2x + 3 graph.




When the inequality is greater than, the purple shading will be above the line like the image below.

The equation for the image below would be y > 2/3x - 2.  The blue line is dotted because the
    (greater than) symbol does not have a line underneath it.  It is only greater than and not equal to.

The dotted blue line shows that the inequality does not include the solution set y = 2/3x - 2.
The slope is 2/3 because the equation the graph shows that the line is going upwards; the rise is 2 and the run is 3.
Slope is rise ÷ run
The y-intercept is -2 because the blue line crosses the y-axis at -2.








How do I use a graphing calculator to Graph equations or inequalities?  Which of the graphing calculators do you like best?

1.  Go to a free graphing calculator website like Desmos, Meta-Calculator, or NCES Create A Graph.

2.  Write the equation or inequality into the website.  Then, click the "Graph" option.

3.   Many websites allow you to print the graph, or even save it as a picture.

To sum it up, graphing equations and inequalities on computers can be an efficient way to create your graph.  The graphs can then be used to compare data and help you think about the information in new ways.  


Here some equations to graph.  What do you notice about the graphs?  Do the pairs of equations have any common solutions? 
First pair of equations
y= 5x 
y=2x + 3

Second pair of equations
y=3x + 4
y=3x - 2

Inequalities
y > 2x + 3

y > x^2