

(1) By using an area model in which part of a region is shaded, students can see how fractions are related to a unit whole, compare fractional parts of a whole, and find equivalent fractions.
Standards 2000 p. 150
(2) During grades 35, students should build their understanding of fractions as parts of a whole and as division. They will need to see and explore a variety of models for fractions . . . .
Standards 2000 p. 150
(3) Students in these grades [35] should use models and other strategies to represent and study decimal numbers. For example, they should count by tenths verbally or use a calculator . .
Standards 2000 p. 150
(4) Negative integers should be introduced at this level [35] through the use of familiar models such as temperature or owing money. The number line is also an appropriate and helpful model . .
Standards 2000 p. 151
(5) With models or calculators, students can explore dividing by numbers between 0 and 1, such as 1/2, . . Explorations such as these can help dispel common, but incorrect, generalizations such as "division always makes things smaller."
Standards 2000 p. 152
(6) Further meaning for multiplication should develop as students build and describe area models, showing how a product is related to its factors.
Standards 2000 p. 152
(7) A significant amount of instructional time should be devoted to rational numbers in grades 35. The focus should be on developing students’ conceptual understanding of fractions and decimals . . . rather than on developing computational fluency
Standards 2000 p. 152
(8) Research suggests that by solving problems that require calculation, students develop methods for computing and also learn more about operations and properties (McClain, Cobb, and Bowers 1998; Schifter 1999).
Standards 2000 p. 153
(9) As students move from third to fifth grade, they should consolidate and practice a small number of computational algorithms for addition, subtraction, multiplication, and division that they understand well and can use routinely.
Standards 2000 p. 155
(10) The conventional algorithms for multiplication and division should be investigated in grades 35 as one efficient way to calculate.
Standards 2000 p. 155
(11) Estimation serves as an important companion to computation. It provides a tool for judging the reasonableness of calculator, mental, and paperandpencil computations.
Standards 2000 p. 155
(12) Students in grades 35 will need to be encouraged to routinely reflect on the size of an anticipated solution. If 3/8 of a cup of sugar is needed for a recipe and the recipe is doubled, will more or less than one cup of sugar be needed?
Standards 2000 p. 156
(13) The teacher plays an important roll in helping students develop and select an appropriate computational tool (calculator, paperand pencil algorithm, or mental strategy).
Standards 2000 p. 156
(14) In grades 35, students should be able to reason about numbers by, for instance, explaining that 1/2 + 3/8 must be less than 1 because each addend is less than or equal to 1/2.
Standards 2000 p. 33
(15) Students who have a solid conceptual foundation in fractions should be less prone to committing computational errors than students who do not have such a foundation.
Standards 2000 p. 218
(16) In the middle grades, in part as a basis for their work with proportionality, students need solidify their understanding of fractions as numbers.
Standards 2000 p. 33
(17) The study of rational numbers in the middle grades should build on students’ prior knowledge of wholenumber concepts and skills and their encounters with fractions, decimals, and percents in lower grades and in everyday life.
Standards 2000 p. 215
(18) In the middle grades students should encounter problems involving ratios (e.g., 3 adult chaperons for every 8 students) and rates (e.g., scoring a soccer goal on 3 of every 8 penalty kicks)
Standards 2000 p. 216

