Patterns with 3, 6, or 9 (as factor, divisor, or quotient)

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SWBAT to discover and describe addition patterns and choose/create a model to represent their understanding of a pattern's rate of change.

Big Idea

Looking for patterns with 3, 6, and 9 is an interesting and engaging way to build in more practice with and understanding of these essential facts!


8 minutes

I explain to students that they will have choices about which fact groups they wish to explore, and that the common expectation is that they will describe, in complete written and oral sentences, the patterns they unearth.

I review some sentence stems and we read through them, using the 2 facts as examples.

Teacher/Class: “A pattern in the multiplication facts that have 2 as a factor is that…”

Student:  A pattern in the multiplication facts that have 2 as a factor is that all the products are even numbers.

Teacher/Class: “A pattern in the facts that have 2 as a divisor is that…

Student:  “A pattern in facts that have 2 as a divisor is that the quotient can be an even or odd number.”

Teacher/Class:  “A pattern in the _____________ facts that helps me (understand/ remember them) is…”

Student:  “A pattern in 2 facts that helps me remember them is that the products are counting by twos forward and the quotients are counting by twos backwards.”

Active Engagement

40 minutes

Students choose a set of multiplication and/or division facts with which to work.  I have students write out the facts themselves, especially if they are working with the basic multiplication facts or basic division facts.  If a student chooses to extend a pattern beyond the facts required for 3rd grade, I encourage them to work it through on their own but they may check their work with a calculator.  An alternative is to provide printed fact pages, but getting some experience with a calculator is a good thing.

Students look for patterns of any kind and then color code them or, if they wish, copy the facts that follow the pattern onto a separate piece of paper.  They choose what works for them.  After they have identified several patterns, the next step is to reason through the pattern and explain it, try to explain why the pattern exists or explain how the pattern can help them master these basic facts so they are fluent.

Exit Ticket

5 minutes

I have been conferring with students throughout this activity. As their exit ticket I ask them to be prepared to explain one of the patterns they discovered today.  For homework they will need to explain a pattern to an adult or older sibling.  When a student is willing to take a risk and explain one of the patterns, I listen carefully to hear the underlying message and I work to help them clarify language.  Explanations of this sort are rigorous and take practice, and I balance being supportive of students' developing abilities with math explanations with gentle (I hope!) redirections.