Students are exposed to general methods and strategies to recognize and generate equivalent fractions, and learn to compare fractions with different numerators and different denominators.
In this 13-day unit, students develop general methods and strategies to recognize and generate equivalent fractions as well as to compare and order fractions.
Students began their study of fractions in Grades 1 and 2, where students learned to partition rectangles and circles into halves, thirds, and fourths. In Grade 3, students developed an understanding of fractions as numbers rather than simply equal parts of shapes. Students work with number lines, which help to “reinforce the analogy between fractions and whole numbers” (Progressions for the Common Core State Standards in Math, p. 4). Students also begin their work with recognizing and generating equivalent fractions in simple cases, using a visual fraction model to support that reasoning. This also involves the special case of whole numbers and various fractions, e.g., $${1={2\over2}={3\over3}={4\over4}...}$$. Lastly, students begin to compare fractions in cases where the two fractions have a common numerator or common denominator.
Thus, students begin this unit where they left off in Grade 3, extending their understanding of and strategies to recognize and generate equivalent fractions. Students use area models, tape diagrams, and number lines to understand and justify why two fractions $${{{a\over b}}}$$ and $${{{(n\times a)}\over{(n\times b)}}}$$ are equivalent, and they use those representations as well as multiplication and division to recognize and generate equivalent fractions. Next, they compare fractions with different numerators and different denominators. They may do this by finding common numerators or common denominators. They may also compare fractions using benchmarks, such as “see[ing] that $${{7\over 8} < {{13\over12}}}$$ because $${{7\over8}}$$ is less than $$1$$ (and is therefore to the left of $$1$$) but $${13\over12}$$ is greater than $$1$$ (and is therefore to the right of $$1$$)” (Progressions for the Common Core State Standards in Math, pp. 6–7).
Students engage with the practice standards in a variety of ways in this unit. For example, students construct viable arguments and critique the reasoning of others (MP.3) when they explain why a fraction $${{{a\over b}}}$$ is equivalent to a fraction $${{{(n\times a)}\over{(n\times b)}}}$$. Students use appropriate tools strategically (MP.5) when they choose from various models to solve problems. Lastly, students look for and make use of structure (MP.7) when considering how the number and sizes of parts of two equivalent fractions may differ even though the two fractions themselves are the same size.
Students will only work with fractions of the form $${{{a\over b}}}$$, including fractions greater than $$1$$. Students will develop an understanding of mixed numbers in Unit 6, where they will use fraction addition to see the equivalence of fractions greater than $$1$$ and mixed numbers. Beyond that special case, students will encounter all cases of addition and subtraction of fractions with like denominators, as well as multiplication of a whole number by a fraction. Then, in Unit 7, students will work with decimal fractions, understanding decimal notation for fractions and comparing decimal fractions, including adding decimal fractions with respective denominators $$10$$ and $$100$$. Students continue their work with fraction and decimal computation in Grades 5 and 6. Thus, the 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” forms the basis for much of their upcoming work in Grade 4, as well as Grades 5 and 6.
Pacing: 13 instructional days (11 lessons, 1 flex day, 1 assessment day)
This assessment accompanies Unit 5 and should be given on the suggested assessment day or after completing the unit.
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benchmark fraction
common denominator
common numerator
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4.NF.A.1
Recognize and generate equivalent fractions with smaller units using tape diagrams.
4.NF.A.1
Recognize and generate equivalent fractions with smaller units using number lines.
4.NF.A.1
Recognize and generate equivalent fractions with smaller units using area models.
4.NF.A.1
Recognize and generate equivalent fractions with smaller units using multiplication.
4.NF.A.1
Recognize and generate equivalent fractions with larger units using visual models.
4.NF.A.1
Recognize and generate equivalent fractions with larger units using division.
4.NF.A.2
Compare two fractions with related numerators or related denominators by finding common units or number of units.
4.NF.A.2
Compare two fractions with unrelated numerators and denominators by finding common units or number of units.
4.NF.A.2
Compare two fractions using one half as a benchmark.
4.NF.A.2
Compare two fractions using one whole as a benchmark.
4.NF.A
Compare and order fractions using various strategies.
Key: Major Cluster Supporting Cluster Additional Cluster
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