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SIXTH GRADE: Understand ratio concepts and use ratio reasoning to solve problems

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SIXTH GRADE: Understand ratio concepts and use ratio reasoning to solve problems

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Use ratio and rate (a:b) to solve real world problems including price, speed, quantity, and measurement.

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FIFTH GRADE: Use equivalent fractions as a strategy to add and subtract fractions

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FIFTH GRADE: Use equivalent fractions as a strategy to add and subtract fractions

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Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients.

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FIFTH GRADE: Use equivalent fractions as a strategy to add and subtract fractions

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FIFTH GRADE: Use equivalent fractions as a strategy to add and subtract fractions

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Add and subtract fractions with unlike denominators by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem.

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FOURTH GRADE: Understand decimal notation for fractions, and compare decimal fractions

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FOURTH GRADE: Understand decimal notation for fractions, and compare decimal fractions

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Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. Use decimal notation for fractions with denominators 10 or 100. Compare two decimals by hundredths.

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FOURTH GRADE: Build fractions from unit fractions

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FOURTH GRADE: Build fractions from unit fractions

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Interpret multiplication as scaling by comparing fractions without multiplication. Explain why multiplying a fraction by greater than one and less than one produce greater or smaller numbers.

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FOURTH GRADE: Build fractions from unit fractions

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FOURTH GRADE: Build fractions from unit fractions

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Begin to understand the multiplication of a fraction by multiplying a fraction by a whole number. n × (a/b) = (n × a)/b. Incorporate word problems into learning multiplication and division of fractions.

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THIRD GRADE: Develop Understanding of Fractions as Numbers

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THIRD GRADE: Develop Understanding of Fractions as Numbers

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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.

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THIRD GRADE: Develop Understanding of Fractions as Number

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THIRD GRADE: Develop Understanding of Fractions as Number

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Understand fractions as a number on the number line as a distance between zero and one as a whole.

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THIRD GRADE: Develop Understanding of Fractions as Numbers

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THIRD GRADE: Develop Understanding of Fractions as Numbers

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Understand and compare fractions or whole numbers with or without a number line or fraction model. Compare the results with >,<, or = symbols.

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FOURTH GRADE: Extend understanding of fraction equivalence and ordering

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FOURTH GRADE: Extend understanding of fraction equivalence and ordering

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Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts are different even though they are the same size.

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FOURTH GRADE: Extend understanding of fraction equivalence and ordering

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FOURTH GRADE: Extend understanding of fraction equivalence and ordering

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Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Compare the results with >,<, or = symbols.

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FOURTH GRADE: Build fractions from unit fractions

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FOURTH GRADE: Build fractions from unit fractions

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Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Challenge students by working in word problems including adding and subtracting fractions.