Transcript PowerPoint file - University of Wisconsin–Milwaukee

What are Fractions?
Part 1
Common Core Leadership in Mathematics
(CCLM^2)
This material was developed for use by participants in the
Common Core Leadership in Mathematics (CCLM^2)
Tuesday, July 10, 2012
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
Learning Intentions and Success Criteria
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.
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
Fractions in Grade 1 (Geometry Domain)
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.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012
Fractions in Grade 2 (Geometry Domain)
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.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012
Fractions in Grade 3 (Geometry Domain)
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.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012
Debrief of Language
Attending to precision ...
What specific language was used to describe
the ideas students need to understand about
fractions?
What language was left out?
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 Models
How 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?
Area Model
How are equal
parts defined?
The whole is
determined by the
Equal area
area of a defined
region
What does the
fraction indicate?
The part covered
of whole unit area
The count of
objects in the
Set Model
subset of the
defined set of
objects.
The location of a
point in relation to
Unit of distance or
the distance from
Number Line
length
Equal distance
zero with regard
(continuous)
to the defined
unit.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012
The whole is
determined by
Equal number of
definition (of what objects
is in the set)
Standard 3.NF.1. Unit Fractions
Read the first part of the standard.
In pairs, practice using the language of this
standard to describe your 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.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012
Learning Intentions and Success
Criteria
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.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012