Transcript Addition and Subtraction of Fractions Part 2

Addition and Subtraction of Fractions
Part 2
Class 8
June 29, 2011
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
Learning Intentions
We are learning to
 Develop “operation sense” related to adding and subtracting fractions.
 Understand how estimation should be an integral part of fraction
computation development.
 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, Summer Institute 2011
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, Summer Institute 2011
Example of target # less than 1
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
Addition Fraction Combinations:
Debrief
• What did you understand about fractions
• that allowed you to make combinations?
• 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, Summer Institute 2011
Connections to Standards 4.NF.3 ,
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.
3. Work as a group to cite three specific examples of how
the previous activity made sense of this standard.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
Don’t Forget Mixed
Numbers
The distance from Hank’s house to school is 2 1
5
3
miles. His car broke down 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, Summer Institute 2011
Connections to 4.NF.3c, 4.NF.3d
1. Read these standards, highlighting
important words and phrases.
2. In your group, discuss highlighted key ideas
in this standard and questions you may
have.
3. Write an example on your slate for each
standard.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
Looking at the Clusters of Content
Standards
• Domain: Number and Operations: Fractions
1. Each person chooses one standard card from the
envelope.
2. Prepare a summary of what this standard means
and what students should know and be able to
do.
3. Present your summary to the other teachers at
your table, answering questions as necessary.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
What did we see in our tasks today?
• What did you as students do to bring
the standards alive?
• What did the facilitator as a teacher do to
bring the standards alive?
• What else might you as teachers in your
classroom do to bring the standards alive?
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
Success Criteria
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 an example
for specific CCSS standards
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011