Thinking About Threes

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SWBAT use Google Draw to create arithmetical patterns observed when making designs involving products with a factor of 3 and state the corresponding multiplication equation as a division equation .

Big Idea

Within every pattern in math there hides another amazing pattern!

Division Reteach

6 minutes


10 minutes

I begin today by explaining to students that while they are creating designs to represent multiplication equations with factors of three, there will be two tasks to which they need to attend:

  • What is the division problem that is the inverse of the multiplication equation?
  • What patterns can they observe either about the multiplication equations and division equations or about their design?

If needed, review how to use Google Draw in Google Drive.  If students aren't familiar with it, additional time will be needed for this lesson, at least 20 minutes, to show students how to use Google Draw.

If a computer lab is available, this would be a great lesson to practice developing computer skills as well as mathematical understanding.  Here is an official video that explains how to use Google Draw.  I suggest it for teacher use, and then the teacher can demonstrate the basics of Google Draw to the students.  Only the basics are needed for this lesson.


My computer lab set up is 2 students to 1 computer, so I have students sit with partners and watch on their teeny laptop screens as I go through how to get to their Google Drive (in my district they have district sponsored gmail addresses), open a Draw document, and use the tools.

If Google Draw isn't an option, Paint on Microsoft systems might work, though it is less forgiving than Google Draw.  If you have iPads or Macs, I'm sure there are many more drawing programs for you to choose from.  


45 minutes

SW create design that represents the factors and products of the following equations.  They will use Google Draw or they may draw by hand.  Grouping choices:  all the multiplication facts on one page, all the division facts on another; groups by fact families; several fact families together; student choice.

1 x 3 = 3    3 ÷ 1= 3

2 x 3 = 6     6 ÷ 2 = 3

3 x 3 = 9     9 ÷ 3 = 3

4 x 3 = 12     12 ÷ 4 = 3

5 x 3 = 15     15 ÷ 5 = 3

6 x 3 = 18     18 ÷ 6 = 3

7 x 3 = 21    21 ÷ 7= 3

8 x 3 = 24     24 ÷ 8 = 3

9 x 3 = 27     27 ÷ 9 = 3

This student created a representation of products and dividends with some groupings by 3.

Another student created separate documents with multiplication and division grouped together in a very obvious way, demonstrating their understanding.

If a child creates a drawing of products and dividends without groupings by 3 you will want to talk with them to insure that they can verbally represent how their drawing shows the division and multiplication facts.  This particular student created a key that provides evidence of understanding.


5 minutes

Ask students to explain one of their drawings to a partner.  Call on 3 random students to report out on what their partner created.

Why a partner share? In my reflection I share why partner shares are a powerful tool in a teacher's toolbox.