Download The Meaning of Multiplication

Welcome Back!!
Strong Start Math Project
Session 6
January 12, 2017
Next class sessions:
• January 26
• February 23
• March 2
• March 23
• March 30 (snow date)
Tonight’s Agenda
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Fluency Discoveries in Envisions 2.0
The Meaning of Multiplication
The Game of Circles and Stars
Strong Start Portfolio Project
Homework
Fluency Debrief
• Where is fluency addressed in your materials?
• How is it treated? (tools, representations,
strategies built on number sense, fluency
checks, etc.)
• How will the Envisions 2.0 curriculum help
address basic fact fluency?
• What connections to “Assessing Basic Fact
Fluency” did you make?
Fluency Debrief
• Reflecting on how Envisions 2.0 treats fluency
for addition and subtraction basic facts:
• What pleases you about what you discovered?
• What concerns you about what you
discovered?
• Based on what we have learned in Strong Start,
how might you address the concerns?
The Meaning of Multiplication
Learning Intentions &
Success Criteria
We are learning to…
– Understand how the CCSSM views the development
of multiplicative thinking.
– Apply strategies that promote fluency with singledigit multiplication and division.
We will be successful when…
– We can help students apply properties of
operations as strategies to multiply.
What is Multiplication?
Respond in writing…
What is multiplication?
• Record your thinking in your notebook.
• Check with a neighbor to see how your thinking
is similar.
What is multiplication?
What does multiplication mean?
Share thinking from your OA mini-assessment
6x8
answer
explanation
picture
story problem
Meaning of the Equation
factor x
6
“number
of groups”
x
factor
=
product
8
=
48
“size of
each group”
“total”
Multiplication Student Work
Peek and Pass to review the three pieces of
student work.
1.Listen for the “cues” to pass to the right.
2.Take notes if you wish in your notebook or on a
post-it.
3.No talking…yet.
Debriefing Student Work
1. What do you notice?
2. As you reflect on the “star diagram,” comment
on the following:
• Through which representations are the
children demonstrating what they know about
multiplication?
• Where do you see evidence of “connections”
or “disconnection” between and among the
representations?
Student
Work A
Student
Work B
Student
Work C
Grounding thinking in CCSSM
3.OA.5: Apply properties of operations as
strategies to multiply and divide.
3.OA.7: Fluently multiply and divide within
100, using strategies such as the relationship
between multiplication and division (e.g.,
knowing that 8 × 5 = 40, one knows 40 ÷ 5 =
8) or properties of operations. By the end of
Grade 3, know from memory all products of
two one-digit numbers.
Think With A Partner
What are the
properties of
operations we use
when we multiply and
divide?
Properties of Operations
• Associative Property (2 × 3) × 4 = 2 × (3 × 4)
• Commutative Property 4 × 2 = 2 × 4
• Multiplicative Identity 5 × 1 = 5
• Distributive Property 4 × 7 = (4 × 2) + (4 × 5)
2 5
Dot Images
• How many dots do you see?
• How do you see them?
• Draw what you see.
Reflect back on 3.OA.5. & 3.OA.7
Think about how the images were
described.
Where do the properties show up
in the reasoning?
Group:
•Each person takes a card.
Individually:
•Quickly glance at the dot image and determine the
number of dots.
•Jot down using “words” describing how you saw the
dots.
•Write an equation that matches your image and your
description.
•Identify the property or properties you used.
•Pass your card to the right.
•Repeat.
Sharing
• Each person shares how they saw the dot
pattern. Share both your “language” and
equation.
• Make an connection between equations that
are different for the same card. How can they
both be correct?
Big Idea behind Dot Images
• Reinforces thinking in Groups
– Unitizing
– Subitizing
• Promotes multiplicative thinking
– Skip Counting
– Repeated Addition
– Relationship between rows and columns
– Number of Sets and Size of sets
Definition of Multiplication
• Revise your definition of multiplication.
• Where did your definition start?
• How did you adjust it? Why?
A GAME OF CIRCLES AND STARS
Activity from Marilyn Burns:
Circles and Stars
1. Roll the die
2. Draw the circles according to the number
rolled
3. Roll the die again
4. Represent the number of stars in each circle.
5. Find the total number of stars and write a
multiplication sentence and a total.
Activity from Marilyn Burns:
Circles and Stars
2 groups of 3
2 sets of 3
3, 6
2x3=6
3 groups of 5
3 sets of 5
5, 10, 15
3 x 5 = 15
• Revisit Standard 3.OA.5 and 3.OA.7
Take turns with a Shoulder Partner
to summarize:
• Reflecting on our “dot image” and
Circles and Stars work, what are the
main messages of these standards?
Learning Intentions &
Success Criteria
We are learning to…
– Understand how the CCSSM views the development
of multiplicative thinking.
– Apply strategies that promoting fluency with singledigit multiplication and division.
We will be successful when…
– We can help students apply properties of
operations as strategies to multiply.
Strong Start Portfolio
• Two selections should “give life” to your Strong
Start Goals
• Two are your choice.
Examples:
Fluency—Basic Fact Strategies
Number Sense
Number Talk
This and That
Homework:
Read and Respond
Number Talk
Strong Start Teaching Portfolio
Next class:
January 26, 2017
Central Services – 206-208
4:30 p.m. – 7:30 p.m.