![]() They use concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction, relating the strategy to a written method and explain the reasoning used (MP.1). Then, the unit shifts its focus toward decimals, relying on their work in 4th grade of adding and subtracting decimal fractions (e.g., $$\frac$$) and their deep understanding that one can only add like units, including tenths and hundredths as those units, to add and subtract decimals (5.NBT.7). Then, students use this general method in more advanced contexts, including adding and subtracting more than two fractions, assessing the reasonableness of their answers using estimation and number sense (MP.1), and solving one-, two-, and multi-step word problems (5.NF.2), (MP.4). Throughout this progression, students also progress from using more concrete and visual strategies to find a common denominator, such as constructing area models or number lines, toward more abstract ones like multiplying the two denominators together and using that product as the common denominator (5.NF.1). They start with computing without regrouping, then progress to regrouping with small mixed numbers between 1 and 2, and then to regrouping with mixed numbers. Then, students move toward adding and subtracting fractions with unlike denominators. While students are expected to already have these skills, they help to remind students that one can only add and subtract quantities with like units, as well as remind students how to regroup units (i.e., wholes). Unit 4 starts with a refresher on work from 4th grade, starting with generating equivalent fractions and adding and subtracting fractions with like terms. Students also add and subtract fractions with like denominators (4.NF.3) and multiply a fraction by a whole number (4.NF.4), work which they will rely on in this and the next unit. Then, in 4th grade, students extend their understanding of fraction equivalence and comparison. Students also start to compare fractions in special cases, including identifying equivalent fractions (3.NF.3). In 3rd grade, they build on this geometric idea of a fraction to develop an understanding of fractions as numbers themselves, using number lines as a representation to make that connection (3.NF.2). In 1st grade and 2nd grade, students start to explore the idea of a fraction of a shape, visually representing halves, thirds, and fourths (1.G.3, 2.G.3). ![]() ![]() Students begin learning about fractions very early. In Unit 4, 5th grade students extend their computational work to include fractions and decimals, adding and subtracting numbers in those forms in this unit before moving to multiplication and division in subsequent units. ![]()
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