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

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%

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)

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)