Multiplication Using Manipulatives 

Grade Level: 3-6 (extensions possible in upper grades)
Objectives:

• The student will be about to "Build" multiplication problems using a paper or plastic combo kit.
• The student will be able to draw solutions to multiplication problems.
• The student will be able to record and write about solutions to multiplication problems.
• The student will be able to use concrete methods to build, draw, record and write about multiplication problems involving one, two and three digit numbers.

Strands:

• Number and Number Sense
• Estimation and Computation
  

MULTIPLICATION MODEL:

Beginning steps to teaching multiplication using manipulatives.

• Students must have a knowledge of how to build rectangles: 2 x 6 = 12 or 3 x 4 = 12 or 1 x 12 = 12 or 6 x 2 = 12 or 4 x 3 = 12 or 12 x 1 = 12
  
• Students need to have the knowledge of how to "prove" two numbers are equals by using the "train" method.
  
• Start off by having the students make a given number between 11 and 19. Ask for all the possible ways to make that number using only 2 pieces. For example: 16. You could have 10 + 6, 11 + 5, 12 + 4, 13 + 3, 14 + 2, 15 + 1, 8 + 8 and so on. Try to make sure someone comes up with the 8 + 8.
  
• Now ask the students if using their combinations anyone can use their two pieces to make a rectangle....only the 2-8's can be used. Talk about the dimensions of this rectangle. Either 2 x 8 or 8 x 2.
  
• Now give them a number like 15 and ask them if anyone can make a rectangle using two pieces. They will find out that they can't make one. Ask about three pieces? They should come up with 3-5's will make 15. Then ask about 4 pieces, then 5 pieces they will come up with 5-3's also make 5.
  
• Talk about a multiplication problem and what it actually means: 6 x 7. This means you take 6 and build it 7 times to make your rectangle.
  
• After doing this for a couple of problems you are ready to start modeling a problem using the "L-Bar". First write the problem 8 x 4 on the board and ask the students what the problem actually means. Place the 8 horizontally and the 4 vertically. Now walk through the problem with the students and have them build the 8 once, then twice then three times then four times. Ask them what their answer is.
  
• Continue to build several one digit problems until everyone is comfortable with this model. You are now ready to go to a problem like 12 x 6. Ask them to tell you what this problem means. You will first build it like before but after several problems the students will be able to place 10 - 6's and 10 - 2's on the L Bar and then give you the answer. You are now ready to start recording and writing.
  
• Refer to the visual guide below as to how, using the combo kit, 23 x 12 was set up.

	10 + 10 + 3 = 23

The relation of this concrete model to a paper model would be the following:

    
 

    
 

    
23 x 12 = 200
                +30
                +40
                +  6
                276

Another way to look at the paper and pencil model from the concrete model, that relates to 
the standard paper algorithm is:

     

    
 


    
 


    
40 + 6 = 46

    


    

200 + 30 = 230

46
+230  
276