Investigating Fractions,
Decimals, and Percents
POSTER OVERVIEW
“The heart of the math workshop consists of ongoing investigations
developed within contexts and situations
that enable children to mathematize their lives”
Catherine Twomey Fosnot
Building learning around rich, instructionally-sound contexts was an overarching goal during the development of the Contexts
for Learning Mathematics series. Throughout the series context is used to set the stage for learning. It establishes a terrain that
will intrigue children and ignite their imaginations. The contexts are situations children can imagine—either realistic or fictional—that enable them to reflect on what they are doing and apply mathematical thinking to their own world.
Contexts for investigations are typically developed with stories and pictures. These are carefully crafted to involve students in
meaningful investigations of the big ideas, strategies, and models that shape mathematical thinking.
3 The images and texts are engaging and include age-appropriate children using mathematics to solve real-world problems.
3 The numbers referenced represent landmark numbers or number relationships that are significant and telling.
3 The models and metaphors within a context make relationships and strategies more tangible and explicit.
The contexts for the five units in Investigating Fractions, Decimals, and Percents (Grades 4–6) are established through 16 vibrant
posters (15” x 24”) that meld humor, intrigue, and good math sense.
Field Trips and Fund-Raisers: Introducing Fractions
Contexts for Learning Mathematics; Investigating Fractions, Decimals, and Percents; Field Trips and Fund-Raisers; 3 of 5
© 2007 Catherine Twomey Fosnot from Contexts for Learning Mathematics (Portsmouth, NH: Heinemann)
Contexts for Learning Mathematics;
Investigating Fractions, Decimals,
and Percents; Field Trips and
© 2007 Catherine Twomey Fosnot from Contexts
Contexts for Learning Mathematics;
Fund-Raisers; 2 of 5
and Percents; Field Trips and (Portsmouth, NH: Heinemann)
Investigating Fractions, Decimals,
for Learning Mathematics
Twomey Fosnot from Contexts
© 2007 Catherine
Contexts for
Learning Mathema
tics; Investigat
ing Fractions,
Decimals and
© 2007 Catherine Twomey
Contexts for Learning Mathematics; Investigating Fractions, Decimals, and Percents; Field Trips and Fund-Raisers; 1 of 5
Percents; Field
Fund-Raisers; 4 of 5
for Learning Mathematics
(Portsmouth, NH: Heinemann)
The fair-sharing of submarine sandwiches on a
school field trip provides the context for exploring
big ideas related to fractions in Field Trips and
Fund-Raisers. In attempting to settle arguments
about the fair distribution of sandwiches, students
explore the connection between division and fractions as well as ways to compare fractional amounts.
As the unit progresses, students use the double
number line as a model and explore equivalent
fractions.
Trips and Fund-Rais
ers; 5 of 5
Fosnot from
Contexts for
Learning Mathematics
(Portsmouth,
NH: Heinemann)
© 2007 Catherine Twomey Fosnot from Contexts for Learning Mathematics (Portsmouth, NH: Heinemann)
for additional information 800-225-5800 or contextsforlearning.com
The California Frog-Jumping Contest: Algebra
The California Frog-Jumping Contest uses the
context of the famous short story by Mark Twain—
The Celebrated Jumping Frog of Calaveras County—
to develop equivalence and its use in solving algebraic
problems. This context leads to using the number line
as a tool for solving problems with an unknown: the
length of a frog jump. As the unit progresses, students
investigate equivalent lengths of different-sized jumps
and work with these equivalences flexibly to solve
problems.
ng Fractions, Decimals,
ics; Investigati(Portsmouth, NH: Heinemann)
Mathemat
Learning from
Learning Mathematics
Contexts for
Contexts forTwomey
Fosnot
and Percents;
The California
Contest; 3
Frog-Jumping
of 3
© 2007 Catherine
Contexts for Learning
© 2007 Catherine Twomey
Mathematics;
Investigating
Fractions, Decimals,
Fosnot from
Contexts for
Learning Mathematics
(Portsmouth,
and Percents;
NH: Heinemann)
The California
Frog-Jumping
Contest; 2
of 3
Contexts for Learning Mathematics; Investigating Fractions, Decimals, and Percents; The California Frog-Jumping Contest; 1 of 3
© 2007 Catherine Twomey Fosnot from Contexts for Learning Mathematics (Portsmouth, NH: Heinemann)
The Mystery of the Meter: Decimals
In The Mystery of the Meter, five meter dials on the side of a house initiate a
series of investigations that focus on decimals. Periodic reading and data
collection eventually reveal that these are electric meters. Because students
can see how the numbers expressed as decimals increase with time, the
meter is a powerful tool for students to use to determine equivalents and to
examine how decimals increase and are ordered.
Contexts for Learning Mathematics, Investigating Fractions, Decimals, and Percents, The Mystery of the Meter, 1 of 1
© 2007 Catherine Twomey Fosnot from Contexts for Learning Mathematics (Portsmouth, NH: Heinemann)
Best Buys, Ratios, and Rates: Addition and Subtraction of Fractions
Best Buys, Ratios, and Rates uses the context of
comparison shopping to explore equivalence of
fractions, proportional reasoning, and rates. Ratio
tables are used to help students determine the cost
of different amounts of bird seed sold by weight.
The double number line is used for computation as
students investigate the readings on a truck’s gas
tank over the course of various trips.
Contexts for Learning
© 2007 Catherine Twomey Fosnot
and Percents;
Fractions, Decimals,
NH: Heinemann)
Mathematics; Investigating
(Portsmouth,
Contexts for Learning
for Learning Mathematics
Fosnot from Contexts
© 2007 Catherine
Best Buys, Ratios,
Mathematics; Investigating
Contexts for Learning
© 2007 Catherine Twomey Fosnot
and Percents;
Fractions, Decimals,
NH: Heinemann)
Mathematics; Investigating
(Portsmouth,
Contexts for Learning
for Learning Mathematics
Fosnot from Contexts
© 2007 Catherine
Fractions, Decimals, and
from Contexts for
Learning Mathematics
(Portsmouth, NH:
Heinemann)
Percents; Best Buys,
and Rates; 1 of 4
Ratios, and Rates; 2 of
4
Twomey
Best Buys, Ratios,
and Rates; 4 of 4
Mathematics; Investigating
Fractions, Decimals, and
from Contexts for
Learning Mathematics
(Portsmouth, NH:
Heinemann)
Percents; Best Buys,
Ratios, and Rates; 3 of
4
Twomey
Contexts for Learning Mathematics Series
Investigating Fractions, Decimals, and Percents (grades 4–6)
Exploring Parks and Playgrounds: Multiplication and Division of Fractions
Contexts for Learning
Road race results and training data create a context in
Exploring Parks and Playgrounds for investigating big ideas
and strategies related to multiplication and division with
fractions as well as the relationship between these operations. As the unit progresses, students multiply fractions
by other fractions and equivalent forms of fractions—
percentages and decimals—in the context of designing a
playground. In this unit, double number line and array
models are used as helpful tools.
3 of 3
Parks and Playgrounds;
NH: Heinemann)
(Portsmouth,
and Percents; Exploring
Fractions, Decimals, Twomey Fosnot from Contexts for Learning Mathematics
Mathematics; Investigating
© 2007 Catherine
Contexts for Learning
Mathematics; Investigating
Fractions,
Decimals, and Percents;
© 2007 Catherine Twomey
Exploring Parks and
Fosnot from Contexts
for Learning Mathematics
Playgrounds; 1 of
(Portsmouth,
3
NH: Heinemann)
Contexts for Learning Mathematics; Investigating Fractions, Decimals, and Percents; Exploring Parks and Playgrounds; 2 of 3
© 2007 Catherine Twomey Fosnot from Contexts for Learning Mathematics (Portsmouth, NH: Heinemann)
Contexts for Learning Mathematics Series
Investigating Fractions, Decimals, and Percents (grades 4–6)