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What are Fractions? Part 1. Common Core Leadership in Mathematics (CCLM^2) Tuesday, July 10, 2012. - PowerPoint PPT Presentation
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Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012
What are Fractions?Part 1
Common Core Leadership in Mathematics (CCLM^2)Tuesday, July 10, 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, Summer Institute 2012
CCSSM
and Fractions
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012
“Difficulty with learning fractions is pervasive and is an obstacle to further progress in mathematics and other domains dependent on mathematics, including algebra. It has also been linked to difficulties in adulthood, such as failure to understand medical regimens.”
(“Foundations for Success”
The National Mathematics Panel Final Report, 2008-page 28)
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012
Getting Started
with Fractions
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012
We are learning to …
• recognize fractions as numbers using models.
• emphasize partitioning in learning about fractions.
• understand and use unit fraction reasoning.
We will be successful when we can …
•explain the mathematical content and language in
1.G.3, 2.G.3, 3.G.2 and provide examples of the
mathematics and language.
Learning Intentions and Success Criteria
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012
Standards 1.G.3, 2.G.3, and 3.G.2
Individually – Read the standards.– Highlight key words and key phrases.– Use your worksheet to draw a representation
for each standard.
Pairs– Compare highlighted ideas.– Using your worksheet discuss how ideas of
partitioning are developing across grades 1 – 3.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012
1.G.3. Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.
Fractions in Grade 1 (Geometry Domain)
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012
2.G.3. Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.
Fractions in Grade 2 (Geometry Domain)
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012
3.G.2. Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.
Fractions in Grade 3 (Geometry Domain)
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012
Attending to precision ...
What specific language was used to describe the ideas students need to understand about fractions?
What language was left out?
Debrief of Language
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012
Examining Partitioning
....“early experiences with physically partitioning objects or sets of objects may be as important to a child’s development of fraction concepts as counting is to their development of whole number concepts” (Behr and Post, 1992)
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012
Partitioning as a Foundation for Fractions
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012
Equal Shares
Four children are sharing 7 candy bars. How much candy will each child get if they share the candy bars equally?
In groups of four:
•Use paper strips to solve the problem.
•Use the language of 1.G.3, 2.G.3, and 3.G.2, to describe the shares.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012
Stages of Partitioning
Read pgs. 71 – 75 from Focus on Fractions (through stages of partitioning).
Highlight key phrases from the reading.
* Star the important ideas.
? Question mark the confusing thoughts.
Table group discussion: Summarize and clarify thoughts on partitioning.
Work through problem number 1 on pages 77 & 78.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012
Fraction Models: Area, Set, and Number Line
Features of Fraction ModelsHow the whole is defined
How “equal parts” are defined and
What the fraction indicates
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012
Slate Work
Take a slate and divide it in thirds.
On each 1/3 draw a model: an area model, a set model, and a number line.
Discuss the features of each model.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012
Features of Models
What is the whole?
How are equal parts defined?
What does the fraction indicate?
Area Model
The whole is determined by the area of a defined region
Equal areaThe part covered of whole unit area
Set Model
The whole is determined by definition (of what is in the set)
Equal number of objects
The count of objects in the subset of the defined set of objects.
Number LineUnit of distance or length (continuous)
Equal distance
The location of a point in relation to the distance from zero with regard to the defined unit.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012
Standard 3.NF.1. Unit Fractions
3.NF.1. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
Read the first part of the standard.
In pairs, practice using the language of this standard to describe your unit fractions.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012
We are learning to …
• recognize fractions as numbers using models.
• emphasize partitioning in learning about fractions.
• understand and use unit fraction reasoning.
We will be successful when we can …
•explain the mathematical content and language in
1.G.3, 2.G.3, 3.G.2 and provide examples of the
mathematics and language.
Learning Intentions and Success Criteria