Unit Summary
The scope and sequence for 4th Grade Math was adjusted in August 2021. The factors and multiples (4.OA.4) topic has been moved out of Unit 2 and into the beginning of this unit. We also moved Shapes and Angles to the end of the 4th grade sequence, so while this was previously Unit 5, it is now Unit 4. Learn more about these updates.
In this 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.
Students begin the unit by investigating factors and multiples within 100, as well as prime and composite numbers (4.OA.4). While this may seem unrelated to fraction equivalence and ordering, this supporting cluster content supports the major work of the rest of the unit by helping students recognize and generate equivalent fractions. Then, students use their knowledge of factors and multiples as well as the fraction foundation built in Grade 3 to extend their understanding of and strategies to recognize and generate equivalent fractions. They 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 5, 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 6, 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: 17 instructional days (15 lessons, 1 flex day, 1 assessment day)
For guidance on adjusting the pacing for the 2021-2022 school year, see our 4th Grade Scope and Sequence Recommended Adjustments.