Transcript CCSS 101: Standards for Math Practices

Revisiting MP2
What actions did you take in the last 2 weeks to
be more conscious of MP2 Reason Abstractly
and Quantitatively?
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012
School Year
Division of Fractions: Balancing
Conceptual and Procedural
Knowledge
This material was developed for use by 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.
November 27, 2012
Common Core Leadership in Mathematics2 (CCLM)
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 20112-13 School Year
Trouble with Fractions?
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee,
2012-2013 School Year
Learning Intentions and Success
Criteria
We are learning to …
• apply and extend understandings of division
to fractions that includes a focus on unit fractions
in the context of real-world problems.
We will be successful when we can…
• explain and provide examples of standard
5.NF.7 using visual models, contexts, and
concept-based language to divide unit fractions
by whole numbers and whole numbers divided
by unit fractions.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012-2013
School Year
Extending Meaning of
Division to Fractions
Building on What We Know
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.
Make up two problems for 56 ÷ 8, one where
the group size is unknown and one where the
number of groups is unknown.
Interpretations of Division
Group Size Unknown
Number of Groups Unknown
I know the total number of objects.
I know the number of groups/shares.
How many objects are in each
group/share?
I know the total number of objects.
I know the number of objects in each
group/share. How many equal
groups/shares can be made?
Example: I have 8 stickers. I am going to
divide them equally between my friend
and myself. How many stickers will we
each get?
Example: I have 8 stickers. I am going
to stick 2 on each card. How many
cards can I make?
8÷2=4
*Partitive division, sharing model, dealing
out.
8÷2=4
* Quotative division, measurement
division, grouping, subtractive model.
Looking at Division
Problems
Launch: Popcorn Party #1
Serving Size:
1/2 cup of popcorn
How many servings can be made from:
 1 cup of popcorn
 2 cups of popcorn
 3 1/2 cups of popcorn
Have we done problems like this in the whole
number world?
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee,
2012-2013 School Year
Explore: Popcorn Party #2
Serving Size:
1/3 cup of popcorn
How many servings can be made from:
 1 cup of popcorn
 2 cups of popcorn
 3 2/3 cups of popcorn
• Individually solve each problem using reasoning and models
• As a group, take turns and share your reasoning
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012-2013
School Year
Explore #2: Juice Party
Serving Size:
1/2 gallon of juice
How can I divide that among:
 2 friends
 5 friends
• Individually solve each problem using reasoning and
models
• As a group, take turns and share your reasoning
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee,
2012-2013 School Year
Looking at the Standards
Standard 5NF 7c
Apply and extend previous understandings of
division to divide unit fractions by whole
numbers and whole numbers by unit fractions.1
c. Solve real world problems involving division of unit
fractions by non-zero whole numbers and division of
whole numbers by unit fractions, e.g., by using visual
fraction models and equations to represent the
problem. For example, how much chocolate will each
person get if 3 people share 1/2 lb of chocolate equally?
How many 1/3-cup servings are in 2 cups of raisins?
Standard 5NF 7a and 5NF 7b
Apply and extend previous understandings of division to divide
unit fractions by whole numbers and whole numbers by unit
fractions.1
a. Interpret division of a unit fraction by a non-zero whole
number, and compute such quotients. For example, create a
story context for (1/3) ÷ 4, and use a visual fraction model to
show the quotient. Use the relationship between multiplication
and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4
= 1/3.
b. Interpret division of a whole number by a unit fraction, and
compute such quotients. For example, create a story context for
4 ÷ (1/5), and use a visual fraction model to show the quotient.
Use the relationship between multiplication and division to
explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.
MP2 Again
“Quantitative reasoning entails habits of
creating a coherent representation of the
problem at hand; considering the units involved;
attending to the meaning of quantities.”
What does it mean to “attend to the meaning of
the quantities”?
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012
School Year
Learning Intentions and Success
Criteria
We are learning to …
• apply and extend understandings of division
to fractions that includes a focus on unit fractions
in the context of real-world problems.
We will be successful when we can…
• explain and provide examples of standard
5.NF.7 using visual models, contexts, and
concept-based language to divide unit fractions
by whole numbers and whole numbers divided
by unit fractions.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee,
2012-2013 School Year