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Download a Sequence of Instruction Graphic Sequence of Instruction

Although it is not necessary to use every unit in the suggested order, they are designed with specific topics and grade levels in mind. For a graphic that provides a visual representation of the sequence and relationships of the components in Investigating Fractions, Decimals, and Percents click on the attached pdf.

Grades 4–5

Field Trips and Fund-Raisers: Introducing Fractions
by Catherine Twomey Fosnot
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 explore magnitude of fractional amounts and develop a ratio table of equivalent ratios for the cafeteria workers to use to ensure that everyone will always get three-fourths of a sub. In the second week, the double open number line is introduced as students design a 60k bike course with various landmark fractions in equivalent forms. The unit was designed to be used at the end of grade 4 or the beginning of grade 5.

The California Frog-Jumping Contest: Algebra
by Bill Jacob and Catherine Twomey Fosnot
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 involves the use of the open number line as a tool for solving problems with unknowns—the lengths of the jumps of various frogs in the competition. The representation encourages students to develop a variety of strategies and to understand algebraic expressions as objects that can be operated on. Students also design benches for the competition with two different lengths of lumber and use a combination chart to explore equivalent expressions and possible exchanges further. As the unit progresses, students are challenged with simultaneous equations within the context of various jumping contests in the Olympics, and the idea of variation is emphasized. The unit was developed to be used in grade 4 or 5.

Grades 5–6

The Mystery of the Meter: Decimals
by Bill Jacob, John Michael Siegfried, and Catherine Twomey Fosnot
In The Mystery of the Meter, five meter dials on the side of a house initiate a series of investigations focusing 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 examine how decimals increase and are ordered. Place value understandings are the focus, and computation with decimals is related to whole-number computation. The unit was designed to introduce students to decimals and is appropriate for grade 5 or 6.

Best Buys, Ratios, and Rates: Addition and Subtraction of Fractions
by Bill Jacob and Catherine Twomey Fosnot
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 birdseed sold by weight. Students also explore ratios as they label the proportions of ingredients on a variety of different size containers of gourmet pet food. As the unit progresses, students use the double open number line for addition and subtraction of fractions in order to investigate the readings on a farm truck's gas tank over the course of various trips. Various minilessons also are employed to support computation fluency. This unit was developed to be used in grade 5 or 6.

Exploring Parks and Playgrounds: Multiplication and Division of Fractions
by Lynn D. Tarlow and Catherine Twomey Fosnot
In Exploring Parks and Playgrounds, road race results and training data create a context for constructing some 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 portion of a park that will have a playground (with a portion of that area blacktopped). In this unit, double open number lines, the open array, and the ratio table are used as helpful models to support fluent computation with rational numbers. The unit was designed for grade 6.

Minilessons for Operations with Fractions, Decimals, and Percents
by Lynn D. Tarlow and Catherine Twomey Fosnot
Minilessons for Operations with Fractions, Decimals, and Percents is a resource of approximately 75 minilessons that you can choose from throughout the year. The relationships between the problems in the minilesson will support students as they progress through the string. Several models are employed that can be helpful for computation. Money and the clock enable students to work with landmark fractions easily. The double open number line allows for generalizable strategies such as the use of common denominators for addition and subtraction. The open array and the ratio table are used with multiplication and division throughout to represent student strategies.


Grades K–3
 
Grades 3–5
 
Grades 4–6