📊🤔 Explore B - Lesson 3.5 Commutative Property of Multiplication

Part 1

Recall

Factors: The numbers multiplied to get a product.

Product:  The answer to a multiplication problem.

Commutative Property of Multiplication: Changing the order of factors does not change the product.

Commutative comes from the word commute.  Commute means to move around.  

Look at the following table and compare what is the same and what is different.

Commutative Property of Addition	Commutative Property of Multiplication
$8+6\:\:\:and\:6\:+\:8$	$3\times5\:\:\:and\:\:\:5\times3$
$4+5\:\:\:and\:\:\:\:5+4$	$6\times2\:\:and\:\:2\times6$
$80\:+\:7\:\:\:\:and\:\:\:\:7\:+\:80$	$7\times4\:\:\:and\:\:\:4\times7$

Did you notice that for each  expression, the sum or the product is the same?

Difference:

$3\times5$

means 3 groups of 5

or 3 bags with 5 candies each

$5\times3$

means 5 groups of 3

or 5 bags with 3 candies each

The multiplication meaning changes, where in addition the meaning does not change.

1 apple + 2 apples is the same as 2 apples + 1 apple.

Watch the Video: Interpret products by drawing pictures. Links to an external site.

Part 2

What does this look on a number line?

Watch the Video: Interpret products using a number line. Links to an external site.

$3\times5$

3 jumps of 5.

$5\times3$

5 jumps of 3.

Note:  Both answers are 15, but the way the objects are grouped is different in each situation.