multiplication part 2

Common Core Leadership in Mathematics ProjectUniversity of Wisconsin-Milwaukee, Summer Institute 2012

MultiplicationPart 2

Common Core Leadership in Mathematics (CCLM)Monday July 9, 2012

Homework Debrief

Share with your shoulder partner a few ideas that strike you as critical to developing a sound understanding of multiplication and division.


Learning Intentions

We are learning to…

• Understand how the CCSSM views the development of multiplicative thinking.

• Apply strategies that promoting fluency with single-digit multiplication.

We will be successful when we can …

• Help students apply properties of operations as strategies to multiply.


Dot Images

• How many dots so you see?

• How do you see It?

• Draw what you see in your notebook.


Image 2

Grounding Thinking in CCSSM

3.OA.5: Apply properties of operations as strategies to multiply and divide.

– Commutative

– Associative

– Distributive

With your shoulder partner, use an

example, remind each other how these

“rules of numbers work.”

With your shoulder partner, use an

example, remind each other how these

“rules of numbers work.”


Reflect back on 3.OA.5.

Think about how the images were described.

Where do the properties show up in the reasoning?


As a group, pick one card

Individually:• Quickly glance at the dot image and determine

the number of dots.

• On your white board, jot down how you saw the image using words.

• Write an equation that matches your image and your description.

• Identify the property or properties you used.

Turn and share.


Image 4

Image 5

Image 6

Revisit Standard 3.OA.5 and 3.OA.7

Take turns with a Shoulder Partner to summarize:

• Reflecting on our “dot image” work, what are the main messages of these standards?

• How do dot images promote multiplicative thinking?



What facts do you struggle with?

• List 3-4 multiplication facts that you have a hard time remembering.

• Think about how you find your answer or how you remember it

• Share


Finding Easier Facts Inside Hard Ones

• What is your go-to strategy for helping students learn their multiplication facts?

• What is your back-up strategy when the first one fails?

• What is your back-up to the back-up?


“What is a 3 by 4?”

• What is an Array?– An array is any arrangement of things in rows

and columns, such as a rectangle of square tiles or blocks

• Is there a difference?– Rows How many groups?

– Columns How many per group?


3x4 and 4x3

• Build a 3 x 4 array with your tiles.


Breaking Apart a 3x4 Array

• What are the ways a 3 x 4 array can be broken apart? – Split rows or columns, not individual tiles

• (3x3) + (3x1)

• (3x2) + (3x2)

• (2x4) + (1x4)

RevisitingLearning Intentions & Success Criteria

• We are learning to…– Understand how the CCSSM views the

development of multiplicative thinking.– Apply strategies that promoting fluency with

single-digit multiplication.

• We will be successful when…– We can help students apply properties of

operations as strategies to multiply.


multiplication part 2

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