Transcript CCSS 101: Standards for Math Practices

Addition and Subtraction of
Fractions Part 2
Class 4
October 23, 2012
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
.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013
Homework Discussion
Read your partner’s homework reflections. Use a
post-it note to comment on either:
1)Reflection: Connect one of the grade 4 or grade 5
standards for operating on fractions to the content in
this chapter.
2)Using quotes from the chapter and examples of
student work share ideas that are important as you
implement a standards-based classroom.
Repeat 2 more times.
2011
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013
Further Exploration:
Addition of Fractions
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013
Learning Intentions
We are learning to
 Use concrete models to explore and generalize about addition of
fractions.
 Read and interpret the cluster of CCSS standards related to
addition/subtraction of fractions.
We will know we are successful when we can
 Justify our thinking when adding and subtracting fractions using
concrete models and estimation strategies.
 Clearly explain and provide examples for specific CCSS standards.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013
Exploring Addition (Subtraction) of Fractions
1
2
3
4
1
1
4
1
1
2
• Choose a target number from this set that is less than 1 or more than 1.
• Make a model of that number using your fraction strips to serve as a
reference.
• Using your fraction strips find combinations to represent your target
number.
• Start with combinations of 2 fractions, then 3, then 4, etc.
• Record your combinations. Also record any conjectures your group makes
as you work on the task.
• If you feel that you have explored all combinations for your first target
number, pick a second one and do subtraction.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013
Example of target # less than 1
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013
Addition Fraction Combinations: Debrief
•What patterns emerged as you made your
combinations?
•What ideas about addition of fractions surface
as you engaged in these explorations?
•How did the fraction strip model support your thinking?
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013
Connections to Standards
4.NF.3a, 4.NF.3b and 5.NF.1
1. Read these standards, highlighting important words and
phrases.
4.NF.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
a. Understand addition and subtraction of fractions as joining and separating parts referring to the
same whole.
b. Decompose a fraction into a sum of fractions with the same denominator in more than one way,
recording each decomposition by an equation. Justify decompositions, e.g., by using a visual
fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 +
1/8.
5.NF.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing
given fractions with equivalent fractions in such a way as to produce an equivalent sum or
difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In
general, a/b + c/d = (ad + bc)/bd.)
2. In your group, discuss highlighted key ideas in this
standard and questions you may have about these
standards.
3. Work as a group to cite three specific examples of how
the previous activity made sense of these standards.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013
NF Progression Document
1. Study the sections, diagrams, and margin notes on
“Adding and Subtracting Fractions.”
• Read Grade 4, page 6.
• Read Grade 5, page 10.
2. Highlight important words and phrases, and
note surprising ideas or questions raised.
3. In particular, note how the standard’s progression
grows from grade 4 to grade 5
4. In your group, discuss highlighted key ideas and
your questions about them.
Common Core Leadership in Mathematics Project, University
4.9of Wisconsin-Milwaukee, 2012 - 2013
Don’t Forget Mixed
Numbers
The distance from Hank’s house to school is
3
2 1/5 miles. His car broke 5down 3/5 of a mile
from school. How far is Hank from his house?
• Estimate the answer- do not compute.
• Use a model to find the answer.
• Use at least two different strategies to find
the answer. How does the model match this
work?
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013
Connections to 4.NF.3c, 4.NF.3d
4.NF.3c Add and subtract mixed numbers with like
denominators, e.g., by replacing each mixed number with an
equivalent fraction, and/or by using properties of operations
and the relationship between addition and subtraction.
4.NF.3d Solve word problems involving addition and
subtraction of fractions referring to the same whole and
having like denominators, e.g., by using visual fraction models
and equations to represent the problem.
1. Read and highlight important phrases and ideas in these
standards.
2. In your group, discuss highlighted key ideas in this standard and
questions you may have about the standards.
3. Write an example on your slate for each standard.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013
What Did We See in our Tasks Today?
What connections can you make between your
work as participants and the mathematical
practices? Be specific.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013
2. Reason abstractly and quantitatively.
3. Construct viable arguments and
critique the reasoning of others.
6. Attend to precision.
1. Make sense of problems and
persevere in solving them.
Standards for Mathema cal Prac ce
4. Model with mathematics.
5. Use appropriate tools strategically.
7. Look for and make use of structure.
8. Look for and express regularity
in repeated reasoning.
Reasoning
and
Explaining
Modeling
and
Using Tools
Seeing
Structure and
Generalizing
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013
Learning Intentions
We are learning to
 Use concrete models to explore and generalize about addition of
fractions.
 Read and interpret the cluster of CCSS standards related to
addition/subtraction of fractions.
We will know we are successful when we can
 Justify our thinking when adding and subtracting fractions using
concrete models and estimation strategies.
 Clearly explain and provide examples for specific CCSS standards.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013