Students start to operate on fractions, learning how to add fractions with like denominators and multiply a whole number by any fraction.
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 fractions with like denominators and multiply a whole number by any fraction. 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 5, 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 divisor of the other, which helps prepare students for similar work with decimal fractions in Unit 7. After working with all three numerical cases in the context of fraction addition and subtraction, they work with fraction multiplication, learning strategies 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 7, 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 on 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 (22 lessons, 2 flex days, 1 assessment day)
This assessment accompanies Unit 6 and should be given on the suggested assessment day or after completing the unit.
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fraction greater than one
mixed number
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Intellectual Prep for All Units
Unit-specific Intellectual Prep
4.NF.B.3.B
Decompose fractions as a sum of unit fractions and as a sum of smaller fractions.
4.NF.B.4.A
Decompose non-unit fractions and represent them as a whole number times a unit fraction.
4.NF.B.3.A
4.NF.B.3.B
Add and subtract fractions within 1 with the same units.
4.NF.B.3.D
Solve word problems that involve the addition and subtraction of fractions where the total is less than or equal to one.
4.NF.B.3.B
4.NF.B.4.A
Decompose non-unit fractions less than or equal to 2 as a sum of unit fractions, as a sum of non-unit fractions, and as a whole number times a unit fraction.
4.NF.B.3.A
4.NF.B.3.B
Add and subtract fractions that require regrouping where the total is less than or equal to two.
4.NF.B.3.A
4.NF.B.3.B
Add two fractions where one denominator is a divisor of the other using the denominators 2, 3, 4, 5, 6, 8, 10, and 12.
4.NF.B.3.B
4.NF.B.4.A
Decompose and compose non-unit fractions greater than two as a sum of unit fractions, as a sum of non-unit fractions, and as a whole number times a unit fraction.
4.NF.B.3.B
4.NF.B.3.C
4.NF.B.4.A
Convert fractions greater than 1 to mixed numbers.
4.NF.B.3.B
4.NF.B.3.C
4.NF.B.4.A
Convert mixed numbers to fractions greater than 1.
4.NF.B.3.C
Compare and order fractions greater than 1 using various methods.
4.NF.B.3.C
Add a mixed number and a fraction.
4.NF.B.3.C
Add mixed numbers.
4.NF.B.3.C
Subtract a fraction from a mixed number.
4.NF.B.3.C
Subtract a mixed number from a mixed number.
4.NF.B.3.D
Solve word problems involving addition and subtraction of fractions.
4.NF.B.4.B
Multiply a whole number by a non-unit fraction.
4.NF.B.4.B
Multiply a whole number by a mixed number.
4.NF.B.4.C
Solve word problems involving multiplication of fractions.
4.NF.B.3.D
4.NF.B.4.C
Solve word problems involving addition, subtraction, and multiplication of fractions.
Key: Major Cluster Supporting Cluster Additional Cluster
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