Discovering the Properties of Multiplication

 Properties of Multiplication Flap Book
One of the most interesting discoveries we had when teaching “Bansho Style” (see previous posts), is that the students discovered the Commutative Property of Multiplication on their own.  Of course, they didn’t know it by that name, but they could see that when we made arrays of 3 x 4 and 4 x 3, that the product was the same. I, of course, seized the moment and tried to get them to make the connection to the Commutative Property of Addition by asking:  where have we seen numbers switch places but the result is the same?

It took some thinking, but they finally made the connection.  I had them look at the arrays they had built and find a similar array that used the same factors.  The students could plainly see the that the Commutative Property of Multiplication was very similar to the one for addition, except we were dealing with multiples and different vocabulary.

 Properties of Multiplication PowerPoint
After they had learned that property and had made the connection to the same Property of Addition, I posed the question:  does multiplication have a Zero or Identity Property?  Most of them already knew that multiplying by 1 gives the same factor/product and that multiplying by zero gave a product of zero.  What they could not do is explain why.  Time to bring out the tiles again and have them show me arrays for multiplying by 1 and multiplying by zero.  With the tiles in front of them, they turned to partners and explained what they discovered.  We discussed as a class our findings and saw that the Zero Property of Addition and Multiplication were not the same.  Next, I used my Properties of Multiplication PowerPoint to formally go over each of the properties while the students took notes.

Soon after their discoveries and discussions of these properties it was time to solidify the definitions and examples.  The students then put together the Properties of Multiplication Flap Book which is part of the Properties of Multiplication 5 Pack of Reinforcement Activities.  With the book the students had to match the definition to the property, and glue them down on the inside cover.  Then on the other inside part, match examples.  I wanted to make sure the students knew those definitions and could give examples so as soon as a student was done with the book, it was time to turn into Multiplication Man!

 Multiplication Man to the rescue!
Multiplication Man uses his multiplication powers to teach the Properties of Multiplication in a fun way.  Students cut out a large X and fill in each part of the X with the definition of each of the 4 Properties of Multiplication with examples.  They can write the definitions in their own words or use the Flap Book definitions.  Once completed, the large X is taped to the student’s chest and then he/she turns into Multiplication Man!  The student then teams up with another student.  Facing each other, student 1 either reads the definition or gives example of one of the Properties of Multiplication (by reading the X on the facing student’s chest) and then student 2 has to state the Property of Multiplication it is.  If correct, the students cross arms against the chest for the Multiplication Man salute.  If incorrect, Multiplication Man comes to the rescue and quickly tutors the student on the spot saving the day!  Students had a lot of fun with this activity.
 Students practicing with Multiplication Man

We all know in the end that all these activities and books that we make have to transfer to paper and pencil tasks and assessments.  So after all this, I do give the students some practice with worksheets or workbook problems on the Properties of Multiplication.  If you would like to see more resources for teaching these properties, click on this LINK and see what’s available.