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. 

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As always, I welcome your thoughts and suggestions!