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.
Math
Unit 4
4th Grade
In this unit, students gain familiarity with factors and multiples, then use that understanding to 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 worked with number lines, which help to “reinforce the analogy between fractions and whole numbers” (Progressions for the Common Core State Standards in Math, p. 8). Students also began their work with recognizing and generating equivalent fractions in simple cases, using a visual fraction model to support that reasoning. This also involved the special case of whole numbers and various fractions, e.g., $${1={2\over2}={3\over3}={4\over4}...}$$. Lastly, students began to compare fractions in cases where the two fractions have a common numerator or common denominator. Another key understanding from 3rd grade that students will rely on in this unit is their fluency with single-digit multiplication and division, aiding their understanding of factors and multiples and their relationship to fraction equivalence.
Students begin the unit by investigating factors and multiples within 100, as well as prime and composite numbers (4.OA.4). Then, in Topic B, 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. Lastly, they compare fractions with different numerators and different denominators in Topic C. 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, p. 11). Throughout the discussion of fraction equivalence and ordering in Topics B and C, students’ work with factors and multiples, a supporting cluster content standard, engages them in the major work of fraction equivalence and ordering, e.g., by identifying a common factor of the numerator and denominator to generate an equivalent fraction in larger units.
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. They also encounter all cases of addition and subtraction of fractions with like denominators, as well as multiplication of a whole number by a fraction in that unit. Then, in Unit 6, students will work with decimal fractions, developing an understanding of decimal notation for fractions, comparing decimal fractions, and adding decimal fractions with respective denominators $$10$$ and $$100$$. Students continue their work with fraction and decimal computation in Grades 5 and 6, including adding and subtracting fractions with unlike denominators by replacing the given fractions with equivalent ones. 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" provides an important foundation for much of their upcoming work in Grade 4, as well as Grades 5 and 6 (Progressions for the Common Core State Standards in Math, p. 10).
Pacing: 17 instructional days (15 lessons, 1 flex day, 1 assessment day)
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The following assessments accompany Unit 4.
Have students complete the Pre-Unit Assessment and Pre-Unit Student Self-Assessment before starting the unit. Use the Pre-Unit Assessment Analysis Guide to identify gaps in foundational understanding and map out a plan for learning acceleration throughout the unit.
Have students complete the Mid-Unit Assessment after lesson 10.
Use the resources below to assess student mastery of the unit content and action plan for future units.
Use student data to drive your planning with an expanded suite of unit assessments to help gauge students’ facility with foundational skills and concepts, as well as their progress with unit content.
Unit Launch
Prepare to teach this unit by immersing yourself in the standards, big ideas, and connections to prior and future content. Unit Launches include a series of short videos, targeted readings, and opportunities for action planning.
Area model |
Example: The following shape represents 1 whole. $$\frac{1}{6}$$ of it is shaded. |
Tape diagram |
Example: The following shape represents 1 whole. $$\frac{1}{6}$$ of it is shaded. |
Number line |
Example: The point on the number line below is located at $$\frac{1}{6}$$. |
benchmark fraction
common denominator
common numerator
composite number
factor pair
multiple
prime number
To see all the vocabulary for Unit 4, view our 4th Grade Vocabulary Glossary.
Word Problems and Fluency Activities
Access daily word problem practice and our content-aligned fluency activities created to help students strengthen their application and fluency skills.
Topic A: Factors and Multiples
Topic B: Equivalent Fractions
Topic C: Comparing and Ordering Fractions
Key
Major Cluster
Supporting Cluster
Additional Cluster
CCSS.MATH.PRACTICE.MP1 — Make sense of problems and persevere in solving them.
CCSS.MATH.PRACTICE.MP2 — Reason abstractly and quantitatively.
CCSS.MATH.PRACTICE.MP3 — Construct viable arguments and critique the reasoning of others.
CCSS.MATH.PRACTICE.MP4 — Model with mathematics.
CCSS.MATH.PRACTICE.MP5 — Use appropriate tools strategically.
CCSS.MATH.PRACTICE.MP6 — Attend to precision.
CCSS.MATH.PRACTICE.MP7 — Look for and make use of structure.
CCSS.MATH.PRACTICE.MP8 — Look for and express regularity in repeated reasoning.
Unit 3
Multi-Digit Division
Unit 5
Fraction Operations