The Progression of Multiplicationfres.hcpss.org/sites/default/files/Q1 Math Workshop 2018...Change...
Transcript of The Progression of Multiplicationfres.hcpss.org/sites/default/files/Q1 Math Workshop 2018...Change...
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The Progression of Multiplication
@HCPSSElemMath
Michele GlennMathematics Support Teacher
Elementary Mathematics
September 12, 2018
Connie HaymonFourth Grade Teacher
Forest Ridge Elementary
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Session Outcomes
Participants will be able to:● Understand the progression of multiplication standards.
● Learn ways to support your child at home.
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Change Your Math Mindset
● I’m not good at math.
● I’m not a math person.
● That’s the new math. I learned it the
old way.
● That way is too complicated.
● Math is just a bunch of numbers.
● I know a trick for that problem.
● I can learn something new. Can you show
me how you learned it?
● Now I know more strategies.
● I can show you how I understand this.
● I use math to help me solve problems
every day.
From To
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Progression
Third Grade:
• Concept of Multiplication
• Arrays
• Area Model
• X ➗
Fourth Grade:
• 2-digit X 1-digit
• 3-digit X 1-digit
• 4-digit X 1-digit
• 2-digit X 2-digit
(3rd and 4th quarter)
• Problem Solving: Multiplicative comparison
Fifth Grade:
• 3-digit X 1-digit
• 4-digit X 1-digit
• 3-digit X 2-digit (2nd and 3rd quarter)
• 4-digit X 2-digit (2nd and 3rd quarter)
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The Progression of Multiplication
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The Concept of Multiplication
● Students are encouraged to think about multiplication in many
ways. This begins with in-context or real-life situations.
● Multiplication can be conceptualized as:○ Repeated addition
○ Equal groups
○ Rows and columns in an array
○ Area
● Strong focus on vocabulary
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Multiplication Vocabulary
3 x 2 = 6 factor factor product
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Multiplication Vocabulary
3 x 2 = 6 factor factor product
Equal Groups3 groups of 2
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Multiplication Vocabulary
Array
3 rows, 2 in each row
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Multiplication Vocabulary
Array
3 rows, 2 in each row
Area Model
3
2
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Building Conceptual Understanding
Students should be able to:
• Recognize that multiplication is the process of counting equal groups• Interpret the language of multiplication as it appears in story
problems.• Interpret multiplication situations• Solve multiplication problems• See patterns in multiplication situations• See the connection between multiplication and division
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Counting Equal Groups
• How Many Cups?
• Build an Array
• Build an Area Model
• Circles and Stars
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Progression
Third Grade:
• Concept of Multiplication
• Arrays
• Area Model
• X ➗
Fourth Grade:
• 2-digit X 1-digit
• 3-digit X 1-digit
• 4-digit X 1-digit
• 2-digit X 2-digit
(3rd and 4th quarter)
• Problem Solving: Multiplicative comparison
Fifth Grade:
• 3-digit X 1-digit
• 4-digit X 1-digit
• 3-digit X 2-digit (2nd and 3rd quarter)
• 4-digit X 2-digit (2nd and 3rd quarter)
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Additional Multiplication Vocabulary
Factors- All whole numbers have at least two whole numbers you can multiply to get your number
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Additional Multiplication Vocabulary
Factors- All whole numbers have at least two whole numbers you can multiply to get your number
What are all the factor pairs for 12?
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Additional Multiplication Vocabulary
Factors- All whole numbers have at least two whole numbers you can multiply to get your number
What about 29??
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Additional Multiplication Vocabulary
Why is this important?
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Additional Multiplication Vocabulary
Why is this important?● Basic fact recall● Division● Fractions● Prime and Composite
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Additional Multiplication Vocabulary
Multiples- when you skip count you say multiples of a number
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Additional Multiplication Vocabulary
Multiples- When you skip count you say multiples of a number
-A multiple is a number that can be divided by another number a certain number of times without a remainder.
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Additional Multiplication Vocabulary
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Additional Multiplication Vocabulary
Why is this important?
● Division● Fractions● Algebra standards
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Multiplicative vs. Additive Comparison
Multiplicative
Phil ran 2 miles. Sally ran 3
times the distance that Phil
ran. How many miles did
Sally run?
Additive
Phil ran 2 miles. Sally ran 3
more miles than Phil. How
many miles did Sally run?
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Multiplicative Comparison: Bar Models
Phil ran 2 miles. Sally ran 3 times the distance that Phil ran.
How many miles did Sally run?
2 miles
2 miles2 miles2 milesSally
Phil
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Multiplicative Comparison
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Modeling with Base Ten Blocks
Use base ten blocks to model 3 X 23
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Partial Products and Area Model
549 x 8
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Partial Products and Area Model
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Area Model
The area model connects to multiplication arrays
that your child learned in previous years. A model
is created using the values of each digit in the
factors. All parts are then multiplied by this/these
factor(s) (distributive property).
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Partial Products and Area Model
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Area Model with Place Value Discs
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Area Model with Place Value Discs
26 x 6
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Area Model
400 + 70 + 8
55 x 4 hundreds =
20 hundreds5 x 7 tens =
35 tens5 x 8
ones =40 ones
478 x 5
30 + 6
10
+
30 x 10 =300
6 x 10 = 60
4 30 x 4 = 120 6 x 4 =24
36 x 14
2,000 + 350 + 40 = 2,390
300 + 120 + 60 + 24 = 504
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Area Model--You try!
Please use your place value discs to model the
following problem(s):
3rd Grade Parents - 3 x 10
4th Grade Parents - 3 x 45
5th Grade Parents - 3 x 145
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Partial Products
Using partial products, students break apart the factors into
“parts” using the place value of each digit and then
multiplying to find a “partial” product. These products are
added together to arrive at the final product.
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Partial Products
63 x 7
7 x 3 = 217 x 60 = + 420
441
25 x 61
1 x 5 = 51 x 20 = 2060 x 5 = + 300
60 x 20 = 1,2001,525
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Partial Products--You try!
3,048 x 9
324 x 16
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1,50020
Standard Algorithm
25 x 61
1 x 5 = 51 x 20 = 2060 x 5 = + 300
60 x 20 = 1,2001,525
25 x 61
500
+3
+
1,525
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Standard Algorithm
26 x 4
Standard Algorithm
26
x 4
24
+ 80
104
Alternative Strategy
26 x 4
(25 + 1) x 4
(25 x 4) + (1 x 4)
100 + 4
104
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Final Thought: Number Talks
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Thank you!
• Next Workshop on Thursday, November 15th• Feedback at https://tinyurl.com/yaru8fhw• Canvas Resources