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

Friday, March 21, 2014

Tri-Fold Booklet


Scoring Rubric:
Math explanation-  Uses accurate math terminology, steps of what was done to solve the problem, explains why each step was done, completely explains how I found my answer.
Strategy- Includes pictures, lists, charts, or symbols to shows solution for the problem.  Shows how the parts of solving the problem relate to each other, shows more than one approach to solving the problem.
Accuracy-  Clear math thinking and accurate calculations, math concepts are well developed, labels are used accurately.

Foldable steps: 
1. Fold an 8 1/2 by 11 piece of paper in half the long way
2. Hold the long way and fold it in thirds by making two folds 3 3/4 inches from the sides
3. Cut down the two folds to fold in the center of the paper.
4. Fold the three flaps down
5. Fold the two side flaps on to the center panel.




Tuesday, February 4, 2014

Valentine's Day Project

What is your favorite type of candy for Valentine's Day?
Candy comes in many different packages, and often has a variety of kinds.   For example, a typical box of chocolates has fruit, cream, and nut fillings.  The different types of chocolate can be quantified using these categories.

Type    Quantity    Fraction
Fruit     6                6/22

Cream   4              4/22

Nuts   12               12/22

Total      22            22/22


Each of type can be described as a part of the whole box.  In the chart above the amount of candies that have either fruit or cream filling would be 10/22 or 5/11 of the chocolates.

If a candy company decided that it wanted to increase the amount of fruit and creams so it was 8/11 to satisfy its customers what would be the number of nuts filled candies in the box?




Thursday, January 30, 2014

Poster Problems

A rectangular field is 30 feet long and 20 feet wide.
There are 4 evenly sized sections to the field, what is the area of each section?
What are other possible ways the field could be divided into evenly sized sections?

A Super Bowl drawing has prime numbers as winners. What is the probability of a getting a prime number if the numbers included are 2-29?  Would the probability be greater or less if it was numbers 2-10?



Wednesday, December 11, 2013

World's Fair Math Explanation Example

Surface Area and Volume of a Building

The Harold Washington Library is in the shape of a rectangular prism for the main building.  I want to find the surface area and volume of the building.  The surface area of is the total area of all the faces.  Surface area is measured in square units (cm²) because like area it is the amount of material that covers a flat surface and can be put into square units of measure.  The other measurement that I want to show is the volume which is the space inside the figure.  Volume is measured in cubic units (cm³) because it is measuring the units inside of a 3 dimensional figure. 

The HWL is approximately 50 feet long, 25 feet wide and 30 feet tall.

Surface area = Sum of all 6 of the rectangular faces 

SA= 2 (lxw) + 2 (lxh) +2 (wxh)
SA= 2 (50x25) + 2 (50x30) + 2(25x30)
SA = 2 (1,250) + 2 (1500) + 2 (750)
SA = 2,500 + 3000 + 1500
SA = 5,500 + 1500
Surface Area = 7,000 square feet  

I found the surface area of the rectangular prism by measuring the area of the 6 faces of the prism.  I knew there were 6 faces from the net drawing of a rectangular prism.  First I knew the building was 50 ft. length, 25 ft. width, and 30 ft. height and put them into the equation.  SA= 2 (lxw) + 2(lxh) + 2(wxh). I multiplied inside parentheses first.  For example, 50x25=1,250. Then I knew that the 2 on the outside meant to multiply since there was a number next to a parentheses.   So I multiplied 2 times 1,250 to get 2,500 using mental math. I multiplied by two because I knew the top and the bottom of the prism were the same size. The front and back sides were each 750 square feet, or 25 times 30, and the top and bottom were each 1,250 which was found by multiplying 50 by 25.  Then I doubled the front to find the total area of the front and back sides since they were both 25 by 30. 1500 times 2 equaled 3,000.  The combined surface area was found by adding all these areas together 2,500 + 3,000 + 1,500 was 7,000 square feet.  I checked my answer using a calculator and found the surface area of the rectangular prism would be 7,000 square feet.

Volume of a rectangular prism= Length x Width x Height

Volume = 50 x 25 x 30 =  37,500 cubic feet


The volume of the figure was found by using an equation.  I knew that the base of the figure was 50 by 25 feet.   So, I multiplied 50 times 25 to get 1,250 square feet.  The height of the rectangular prism was 30 feet, so I multiplied the base times the height to find out how much volume spans up the height of the prism.  I found that 1,250 times 30 was 37,500 cubic feet.  The volume of the rectangular prism is 37,500 cubic feet.  

Tuesday, November 19, 2013

Reading Projects

Create a culminating project about the novel that you have read.  In your project write about the themes and main topics that were addressed.  Include the vocabulary terms that you learned, character analysis, and conflict/resolutions.
Format: PowerPoint Presentation, Poster Board, or Book Blog.
Grouping Preference: Group vs. Individual Projects
Due Date: December 10th

  • Group Projects or Individual Projects:  Group projects should include multiple aspects of the book, the projects should describe more chapters, or aspects of the book (tone of the book, questions/answers, polls, and other features that you learned from your book)  
  • Individual projects should be focused on a central theme or topic of the book.  The individual project can include some information about a favorite chapter or specific aspect of the book.  (tone, questions/answers, polls and other features)

Friday, November 15, 2013

Triangle Properties

Angles

What is the sum of the interior angles of any triangle?
If angles 1 and 2 are 40 degrees and 60 degrees what is the missing interior angle? What is the measure of the exterior angle?

















Sides

What is the relationship between the sides of any triangle?   If side a is 8 centimeters, what is the length of sides b and c?  When we add two sides of the triangle how does the sum compare to the remaining side?

Tuesday, October 22, 2013

Tax Problems










Janice went to Jewel Food Store and bought a box of Orange Popsicle for $3.30.  The tax rate for groceries was 4%. How much would 4 boxes of Orange Popsicles cost? (Include tax)

Step 1:  $3.30 X 4 boxes = $13.20

Step 2: $13.20 X 1.04 (4% tax) = 13.728      (1.04  = 1 + .04   (1 to get the cost, and .04 for 4/100 tax)

The total with tax would be $13.73 (Rounded to the nearest cent)

Assignment: Write your own tax problem.  Include the cost of the product.  Find out how much the item would cost after a 4% tax is included.                       

Thursday, October 10, 2013

Riddles and Limericks

What riddles do you know?   Halloween riddles from kidspot.com.au

A. What's a ghost's favorite dessert?  

B. What movie do ghosts love to watch?

C. What did the boy ghost say to the girl ghost?

D. What kind of roads do ghosts haunt?

E. What did the polite ghost say to her son?

F. Who was the most famous French skeleton?

And a Limerick...  From briandehumor.com
          Mosquitoes
Mosquitoes are what a bat eats,
For him they are edible treats,
He's known to devour,
A thousand an hour, 
We're happy when he overeats. 






A limerick is... a 5 line poem.  It has rhyme pattern on Lines 1, 2, + 5, Lines 3+4.  The limerick has 36 syllables- 8 each on lines 1,2, + 5, and 6 each on 3+4.  The last line usually has a punch line, or play on words.  
Write a limerick  
1. Start by brainstorming a funny/silly idea. (make a question, + answer it)
2. Write lines 1 and 2 end with a rhyming word.  (Need help with rhymes try- rhymezone.com
3. Add lines 3 and 4 (just 6 syllables each)
4. Finish with your punchline. (answer to question)

        

     Freedom (No Turning Back)                

                         by, Mr. Hull  

     Fresh air rushes into my lungs,
     New life appears like a bell rung.
     My old burdens escape,
     Tears spill free from my face.
     Hope grows for a new life begun.  




Riddle Answers  A. I-scream  B. High S-ghoul Musical  C. You look boo-tiful tonight
D. Dead Ends  E. Don't spook until your spooken to   F. Napoleon Bone-A Part 

Monday, September 30, 2013

Book Club Discussions

Book Club Discussion Starters

Who are the main characters in the story, what challenges do they face?

Describe the setting or background of the story.  (Time period, cultures, family structure)

What is the tone of the story so far?  (Does it feel tense, exciting, sad?  Support with examples)