Multiplication and Areas

Albert Michael                 Robert Fulton Elementary School
                               5300 S. Hermitage 
                               Chicago IL 60609
                               (312) 535-9000

Objectives (Grades 3-5):

To learn two-digit multiplication using math facts.

To find areas of rectangles and squares.

To review addition and subtraction facts.

To be able to fill an order of items of equal and different prices and 
   quantities.

Materials Needed:

rulers, stamps (new and/or used, singles and sheets of different denominations 
and sizes), magazine ads stamps (from the Ed McMahon $10,000,000 Sweepstakes), 
stamp order catalogues, play money (dollars and change), transparent grids and 
Lego platforms with different numbers of squares and dots, scissors, order forms

Strategies:

Show the students 3x4, 4x5, 6x4 square grids, or various sizes of Lego platforms
and ask them to count the squares and the dots one at a time.  Next, show them 
large size grids and Lego platforms and have them count the dots individually.
Tell them to count the number of squares or dots in one row across and another 
row down and multiply the two numbers.  Point out that it is much easier and 
faster to count the total by this method.  Demonstrate this on the board.  

Distribute 3x3, 4x3, and 4x4 sheets of stamps.  Ask the students to find the
total area of each sheet and then find how much each sheet costs.  Ask how much
would you pay if each sheet costs 4 times the face value.  Have one student
from each group be the stamp dealer from whom the children can buy stamps.

Pass out sheets of different denominations, sizes, and quantities.  Ask the 
students to find the area of one stamp and then the area of the whole sheet.  
Next, find the total price of each sheet.  

Distribute single, square stamps, preferably used, each attached to a piece of
cardboard paper for easy manipulation and protection from being mutilated.  Find 
the area of each stamp and then determine how many stamps would fit in an area 
of 24x24 sq. cm., 28x28 sq. cm., and 35x35 sq. cm., for example.  You may want 
to reverse all activities to look like this one. 

Here is an example for another activity: 
Suppose you spilled some liquid on one of the sheets that you treasure very much
and you are willing to pay any reasonable price to replace it.  The sheet has
40 stamps of 22 cents each.  The dealer asks for an extra 15 cents per stamp
over the face value.  Find out how much you would pay per stamp, then for the
sheet.  Also calculate the profit the dealer made.

Distribute sheets of different quantities.  Ask students to find the face value 
of each sheet by multiplying the price of one stamp by the number of stamps in 
the sheets.  Look for current prices in the catalogues and decide how much each 
sheet would cost today.  Next, find the area for one stamp and then for the 
whole sheet. 

Notes: All the above activities may be used for the fifth grade for teaching 
division.  First, ask to find the area of the whole sheet and then the area of a 
single stamp. 

The same activities may be used to teach social studies.  Ask questions about
the event or person the commemorative stamp was issued for.

Performance Assessment:

Pass out the sheets of magazine ads stamps.  Choose a denomination and write it 
down on the lower right hand of each stamp.  Find the area for one stamp and 
then for the whole sheet.  A dealer offers you 68% of the face value.  Calculate 
your loss if you decide to sell. 

Pass out copies of order forms and ask them to order as many sheets or single 
stamps as they want and write them in the proper columns in the form.  Find out 
the total of the order.  Add sales tax and shipping and handling charges. 

Write on the board the years in which the rate of first class mail went up in 
one column, and the rate increase in another at random.  Ask students to arrange 
them chronologically.  Next, ask them to make a line or a bar graph to show the 
rate hike.  Then have them calculate the percentage of the increase each time it 
occurred.