Transcript PowerPoint file - University of Wisconsin–Milwaukee

Division
Common Core Leadership in Mathematics (CCLM)
Monday July 9, 2012
This material was developed for use by the project staff and participants
in the Common Core Leadership in Mathematics (CCLM^2) project
through the University of Wisconsin-Milwaukee. Use by school district
personnel to support learning of its teachers and staff is permitted
provided appropriate acknowledgement of its source. Use by others is
prohibited except by prior written permission.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012
Learning Intentions
We are learning to…
• Understand two types of division situations.
• Learn division strategies that develop fluency in
basic division facts.
We will be successful when we can …
• Articulate the meaning of third grade standards
that focus on division.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012
Are These Contexts
the Same?
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012
Two Contexts for Division
• Context 1: Connor has 24 Skittles. He puts
them into bags containing 6 Skittles each. How
many bags did Connor use?
• Context 2: Connor has 24 Skittles. He shares
them equally among 6 cousins. How many
Skittles will each cousin get?
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012
Two Interpretations for Division
Context 1 – unknown number of shares
Connor has 24 Skittles. He puts them into bags containing 6
Skittles each. How many bags did Connor use?
Known: Size of the share (number of Skittles in each bag)
Unknown: Number of shares (bags)
Context 2 – unknown number of objects in each share
Connor has 24 Skittles. He shares them equally among 6 cousins.
How many Skittles will each cousin get?
Known: Number of shares (cousins)
Unknown: Size of the share (Skittles)
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012
What Have We Done? 3.OA.2
• Interpret whole-number quotients of whole
numbers, e.g., interpret 56 ÷ 8 as the number of
objects in each share when 56 objects are
partitioned equally into 8 shares, or as a number of
shares when 56 objects are partitioned into equal
shares of 8 objects each. For example, describe a
context in which a number of shares or a number of
groups can be expressed as 56 ÷ 8.
Turn to your shoulder partner and explain this
standard in relationship to what we just
explored.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012
How do the Standards
Support Division?
Division is finding an unknown factor in
problems involving equal sized groups, arrays,
and area models.
For equal size group situations, division can
require finding the unknown number of groups
or the unknown group size.
p. 21 CCSSM 3rd grade critical area #1
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012
Identifying Division Situations
• Read a problem on a card.
• Use the division mat to act out each problem.
Follow the action of the story.
• Is the problem asking you to find the unknown
number of equal shares or the unknown
number of objects in each share?
• Draw a sketch. Write an equation. Label each
accordingly.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012
What Have We Done? 3.OA.2
• Interpret whole-number quotients of whole
numbers, e.g., interpret 56 ÷ 8 as the number of
objects in each share when 56 objects are
partitioned equally into 8 shares, or as a number of
shares when 56 objects are partitioned into equal
shares of 8 objects each. For example, describe a
context in which a number of shares or a number of
groups can be expressed as 56 ÷ 8.
Turn to your shoulder partner and explain this
standard in relationship to what we just
explored.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012
Division
Strategies
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012
Division Strategies
How do you teach the relationship
between Multiplication and Division?
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012
Standards
•
•
•
•
•
3OA2 two types of division
3OA4 relationship between three numbers
3OA5 properties
3OA6 division as unknown factor problem
3OA7 fluency and basic facts
Decide on connections between the standards.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012
3.0A.4
• Determine the unknown whole number in a
multiplication or division equation relating
three whole numbers. For example, determine
the unknown number that makes the equation
true in each of the equations 8 × ? = 48, 5 =
☐ ÷ 3, 6 × 6 = ?.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012
Standard 3.OA.5
• Apply properties of operations as strategies to multiply and
divide. Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is
also known. (Commutative property.) 3 × 5 × 2 can be found
by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 ×
10 = 30. (Associative property.) Knowing that 8 × 5 = 40 and
8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8
× 2) = 40 + 16 = 56. (Distributive property.)
• What is the relationship between these two standards?
Compare and contrast them.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012
Standard 3.0A.6
• Understand division as an unknown-factor
problem. For example, find 32 ÷ 8 by finding
the number that makes 32 when multiplied by
8.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012
Standard 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.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012
Learning Intentions
We are learning to…
• Understand two types of division situations.
• Learn division strategies that develop fluency in
basic division facts.
We will be successful when we can …
• Articulate the meaning of third grade standards
that focus on division
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012