## 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
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 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 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

#### 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.

## 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.

• 3-D Math Games
• Matholpolis- Improve your mental power

## 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?

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?

#### 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.