During Unit 3, your children will extend their understanding of fraction equivalence and ordering. They will use visual fraction models to explore how the number and size of the parts differ between two fractions even though they are equivalent. Your children will recognize and generate equivalent fractions. They will compare two fractions with different numerators and different denominators by creating common denominators or numerators, or by comparing them to a benchmark fraction such as ½ or 1 whole. Your children will use the symbols >, =, and < to record their comparison and use visual fraction models to justify their conclusions. They will extend their understanding of addition as putting together when they see the way fractions are built from unit fractions. Your children will decompose and compose fractions with the same denominator, and add and subtract fractions with the same denominator. They will convert an improper fraction to a mixed number by decomposing the fraction into a sum of a whole number and a number less than 1.
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Students need to:
- Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
- Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
- Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.
- 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 differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
- 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 ½. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or < and justify the conclusions, e.g. by using a visual fraction model.