Students understand fractions as numbers on the number line and explore fraction equivalence and comparison in simple cases, then apply this fractional understanding to measure fractional lengths and represent them on a number line plot.
Math
Unit 6
3rd Grade
In Unit 6, 3rd grade students extend and deepen 1st-grade work with understanding halves and fourths/quarters (1.G.3) as well as 2nd grade practice with equal shares of halves, thirds, and fourths (2.G.3) to understanding fractions as numbers. Their knowledge becomes more formal as they work with area models and the number line. Throughout the unit, students have multiple experiences working with the 3rd grade specified fractional units of halves, thirds, fourths, sixths, and eighths. To build flexible thinking about fractions, students are exposed to additional fractional units such as fifths, ninths, and tenths.
Students begin the unit by partitioning different models (like area models and fraction strips) of wholes into equal parts (3.G.2), allowing this supporting cluster content to enhance the major work of 3rd grade with fractions. They identify equal parts as halves, fourths, thirds, sixths, and eighths, then are introduced to fraction form and write unit fractions in the form $$\frac{1}{b}$$ (3.NF.1). Next, they make copies of unit fractions to build non-unit fractions, understanding unit fractions as the basic building blocks that compose other fractions (3.NF.1). Then, their focus shifts to fractions on the number line, a particularly important representation that helps students see fractions as numbers. They begin by using the interval from 0 to 1 as the whole and then extend to mark fractions beyond a whole. Noticing that some fractions with different units are placed at the exact same point on the number line, they come to understand equivalent fractions (3.NF.3a). Students express whole numbers as fractions and recognize fractions that are equivalent to whole numbers. Next, students use their understanding of the number of units and the size of each unit to compare fractions in simple cases, such as when dealing with common numerators or common denominators by reasoning about their size (3.NF.3d). Lastly, students measure lengths with fractional units and use data generated by measuring multiple objects to create line plots (3.MD.4). Lastly, students “use their developing knowledge of fractions and number lines to... [work] with measurement data involving fractional measurement values” (MD Progression, p. 10), and use that measurement data to create line plots (3.MD.4), thus using this supporting cluster work to enhance the major work of fractions.
This unit affords ample opportunity for students to engage with the Standards for Mathematical Practice. Students will develop an extensive toolbox of ways to model fractions, including area models, tape diagrams, and number lines (MP.5), choosing one model over another to represent a problem based on its inherent advantages and disadvantages. Students construct viable arguments and critique the reasoning of others as they explain why fractions are equivalent and justify their conclusions of a comparison with a visual fraction model (MP.3). They attend to precision as they come to more deeply understand what is meant by equal parts, and being sure to specify the whole when discussing equivalence and comparison (MP.6). Lastly, in the context of line plots, “measuring and recording data require attention to precision (MP.6)” (MD Progression, p. 3).
Unfortunately, “the topic of fractions is where students often give up trying to understand mathematics and instead resort to rules” (Van de Walle, p. 203). Thus, this unit places a strong emphasis on developing conceptual understanding of fractions, using the number line to represent fractions and to aid in students' understanding of fractions as numbers. With this strong foundation, students will operate on fractions in 4th grade and 5th grade (4.NF.3—4, 5.NF.1—7) and apply this understanding in a variety of contexts, such as proportional reasoning in middle school and interpreting functions in high school, among many others.
Pacing: 27 instructional days (24 lessons, 2 flex days, 1 assessment day)
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The following assessments accompany Unit 6.
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 11.
Use the resources below to assess student understanding of the unit content and action plan for future units.
Before you teach this unit, unpack the standards, big ideas, and connections to prior and future content through our guided intellectual preparation process. Each Unit Launch includes a series of short videos, targeted readings, and opportunities for action planning to ensure you're prepared to support every student.
area model |
Example: The following shape represents 1 whole. $$\frac{1}{6}$$ of it is shaded. |
fraction strip/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 $$\frac{1}{6}$$. |
line plot |
denominator
equivalent fractions
fraction
numerator
unit fraction
To see all the vocabulary for Unit 6, view our 3rd Grade Vocabulary Glossary.
Topic A: Understanding Unit Fractions and Building Non-Unit Fractions
Topic B: Fractions on a Number Line
Topic C: Equivalent Fractions
Topic D: Comparing Fractions
Topic E: Line Plots
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 5
Shapes and Their Perimeter
Unit 7
Measurement
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