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In first grade, students build an understanding of part-whole relationships by composing and decomposing plane or solid figures. Additionally, students partition circles and rectangles into two and four equal shares, and describe those shares using the words halves, fourths, and quarters, as well as using the phrases half of, fourth of, and quarter of.

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In Kindergarten, there is not much of any emphasis on fractions. However, students compose simple shapes to form larger shapes, which seems to be a precursor to part-whole relationships.

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In second grade, students partition a rectangle into rows and columns of same-sized squares and count to find the total number of them. Additionally, students partition circles and rectangles into two, three, or four equal shares and describe those shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, or four fourths. Students must also recognize that equal shares of identical wholes need not have the same shape.

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In third grade, students develop an understanding of fractions, beginning with unit fractions. Students view fractions in general as being built out of unit fractions, and they use fractions along with visual fraction models to represent parts of a whole. Students also understand that the size of a fractional part is relative to the size of the whole. Lastly, students are able to use fractions to represent numbers equal to, less than, and greater than one. They solve problems that involve comparing fractions by using visual fraction models and strategies based on noticing equal numerators or denominators.

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In fourth grade, students develop an understanding of fraction equivalence and operations with fractions. Students can recognize that two different fractions can be equal and they develop methods for generating and recognizing equivalent fractions. Students extend previous understandings about how fractions are built from unit fractions, composing fractions from unit fractions, decomposing fractions into unit fractions, and using the meaning of fractions and the meaning of multiplication to multiply a fraction by a whole number.

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In fifth grade, students apply their understanding of fractions and fraction models to represent the addition and subtraction of fractions with unlike denominators as equivalent calculations with like denominators. They develop fluency in calculating sums and differences of fractions, and make reasonable estimates of them. Students also use the meaning of fractions, of multiplication and division, and the relationship between multiplication and division to understand and explain why the procedures for multiplying and dividing fractions make sense. Students also use the relationship between decimals and fractions to understand and explain why the procedures for multiplying and dividing finite decimals makes sense.

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In sixth grade, students use the meaning of fractions, the meaning of the meanings of multiplication and division, and the relationship between multiplication and division to understand and explain wbny the procedures for dividing fractions make sense. Students then use these operations to solve problems.

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In seventh grade, students develop a unified understanding of recognizing fractions. Students also compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. Lastly, students solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically.

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In eighth grade, students understand that the slope of a line is a constant rate of change, so that if the input or x-coordinate changes by an amount A, the output or y-coordinate changes by the amount (m x A). Slope is depicted as a fraction in which the numerator represents the change in y and the denominator represents the change in x.