Fractions
Unit description: Students will extend their knowledge of fractions from third grade by looking at fractions with denominators of 10 and 12. They will also extend their understanding of fractions equal to 1 whole to multiply and divide fractions by 1 whole to create equivalent fractions. Students will begin to interpret and solve word problems that require combining or separating fractions within the same whole and with the same denominator. Students will also interpret word problems that involve equal groups of a fraction. Students will understand fractions larger than one and how to convert them into mixed numbers.
Essential Outcomes of the Unit
- NY-4.NF.1 Explain why a fraction abis equivalent to a fraction a x nb x nby 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.
- Note: Grade 4 expectations are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
- NY-4.NF.2 Compare two fractions with different numerators and different denominators. Recognize that comparisons are valid only when the two fractions refer to the same whole. e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 12. Record the results of comparisons with symbols >, =, or <, and justify the conclusions. e.g., using a visual fraction model.
- Note: Grade 4 expectations are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
- NY-4.NF.3 Understand a fraction abwith a > 1 as a sum of fractions 1b Note: 1brefers to the unit fraction for ab
- NY-4.NF.3a Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
- NY-4.NF.3b 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 such as, but not limited to:
- 3/8 = 1/8 + 1/8 + ⅛
- 3/8 = 1/8 + 2/8
- 218= 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.
- NY-4.NF.3d Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators.
- NY-4.NF.4 Apply and extend previous understandings of multiplication to multiply a whole number by a fraction.
- NY-4.NF.4a Understand a fraction abas a multiple of 1b e.g., Use a visual fraction model to represent 54 as the product 5 × 14, recording the conclusion with the equation 54= 5 × 14.
- NY-4.NF.4b Understand a multiple of abas a multiple of 1b, and use this understanding to multiply a whole number by a fraction. e.g., Use a visual fraction model to express 3 x 25as 6 x 15, recognizing this product as 65, in general, n × ab= (n x a)b.
- NY-4.NF.4c . Solve word problems involving multiplication of a whole number by a fraction.
Essential Questions and Big Ideas
How can I find equivalent fractions and compare fractions?
- Equivalent fractions can be found by drawing models or by multiplying or dividing by a whole.
- Fractions can be compared by drawing models or by giving the fractions the same denominator and comparing their number of pieces.
How can I use addition to represent non-unit fractions?
- Non-unit fractions can be written as the sum of unit fractions.
How can I use addition and subtraction to relate fractions?
- Fractions with the same denominator or referring to the same whole can be added or subtracted by focusing on the number of parts.
How can I show equal groups relationships with fractions?
- Fractions can exist in equal groups.
- If you have a whole number of equal groups of a fraction, you can multiply the whole number by the numerator to figure out how many total parts you will have. The denominator would remain the same.
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