In this unit, students begin their work with operating with fractions by understanding them as a sum of unit fractions or a product of a whole number and a unit fraction. Students will then add and subtract fractions with like denominators and multiply a whole number by a fraction, including mixed numbers. Students will apply this knowledge to word problems and line plots.
In Grade 3, students developed their understanding of the meaning of fractions, especially using the number line to make sense of fractions as numbers themselves. They also did some rudimentary work with equivalent fractions and comparison of fractions. In Grade 4 Unit 4, they deepened this understanding of equivalence and comparison, learning the fundamental property that “multiplying the numerator and denominator of a fraction by the same non-zero whole number results in a fraction that represents the same number as the original fraction” (NF Progression, p. 6).
Thus, in this unit, armed with a deep understanding of fractions and their value, students start to operate on them for the first time. The unit is structured so that students build their understanding of fraction operations gradually, first working with the simplest case where the total is a fraction less than 1, then the case where the total is a fraction between 1 and 2 (to understand regrouping when operating in simple cases), and finally the case where the total is a fraction greater than 2. With each of these numerical cases, they first develop an understanding of non-unit fractions as sums and multiples of unit fractions. Next, they learn to add and subtract fractions. And finally, they apply these understandings to complex cases, such as word problems or fraction addition involving fractions where one denominator is a multiple of the other, which helps prepare students for similar work with decimal fractions in Unit 6. After working with all three numerical cases in the context of fraction addition and subtraction, they work with fraction multiplication, learning methods for multiplying a whole number by a fraction and a mixed number and using those skills in the context of word problems. Finally, students apply this unit’s work to the context of line plots. Students will solve problems by using information presented in line plots, requiring them to use their recently acquired skills of fraction addition, subtraction, and even multiplication, creating a contextual way for this supporting cluster content to support the major work of the grade. The unit provides lots of opportunity for students to reason abstractly and quantitatively (MP.2) and construct viable arguments and critique the reasoning of others (MP.3).
Students’ understanding of fractions is developed further in Unit 6, in which students explore decimal numbers via their relationship to decimal fractions, expressing a given quantity in both fraction and decimal forms (4.NF.5—7). Then, in Grade 5, students extend their understanding and ability with operations with fractions (5.NF.1—7), working with all cases of fraction addition, subtraction, and multiplication and the simple cases of division of a unit fraction by a whole number or vice versa. Students then develop a comprehensive understanding of and ability to compute fraction division problems in all cases in Grade 6 (6.NS.1). Beyond these next few units and years, it is easy to find the application of this learning in nearly any mathematical subject in middle school and high school, from ratios and proportions in the middle grades to functional understanding in algebra.
Pacing: 25 instructional days (21 lessons, 2 flex days, 1 assessment day)