Students deepen their understanding of halves, thirds, and fourths to understand fractions as equal partitions of a whole, and are exposed to additional fractional units such as fifths, sixths, eighths, ninths, and tenths.
In Unit 6, students extend and deepen Grade 1 work with understanding halves and fourths/quarters (1.G.3) as well as Grade 2 practice with equal shares of halves, thirds, and fourths (2.G.3) to understanding fractions as equal partitions of a whole. Their knowledge becomes more formal as they work with area models and the number line. Throughout the module, students have multiple experiences working with the Grade 3 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 of wholes into equal parts (e.g., concrete fraction strips and pictorial area models) (3.G.2), allowing this supporting cluster content to enhance the major work of Grade 3 with fractions. They identify and count equal parts as 1 half, 1 fourth, 1 third, 1 sixth, and 1 eighth in unit form before introduction to the unit fraction $$\frac{1}{b}$$ (3.NF.1). Then, 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). Next, students transfer their work to the number line. 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 recognize that whole numbers can be written as fractions, including writing 1 as $$\frac{1}{1}, \frac{2}{2}, \frac{3}{3}$$, etc., as well as writing whole numbers as fractions with a denominator of 1, e.g., 2 as $$ \frac{2}{1}$$, 3 as $$\frac{3}{1}$$, etc. Lastly, 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). Students “use their developing knowledge of fractions and number lines to extend their work from the previous grade by working with measurement data involving fractional measurement values” (MD Progression, p. 10), 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 Grades 4 and 5 (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: 31 instructional days (28 lessons, 2 flex days, 1 assessment day)
For guidance on adjusting the pacing for the 2020-2021 school year due to school closures, see our 3rd Grade Scope and Sequence Recommended Adjustments.
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denominator
equivalent fraction
fraction
fractional unit
numerator
unit form
unit fraction
unit interval
whole
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This assessment accompanies Unit 6 and should be given on the suggested assessment day or after completing the unit.
3.G.A.2
3.NF.A.1
Partition a whole into equal parts, identifying and counting unit fractions using concrete area models.
3.G.A.2
3.NF.A.1
Partition a whole into equal parts, identifying and counting unit fractions using concrete tape diagrams (i.e., fraction strips).
3.G.A.2
3.NF.A.1
Partition a whole into equal parts, identifying and counting unit fractions using pictorial area models and tape diagrams, identifying the unit fraction numerically.
3.NF.A.1
Build and write non-unit fractions less than one whole from unit fractions.
3.NF.A.1
Identify the shaded and unshaded parts of a whole.
3.NF.A.1
Build and write non-unit fractions greater than one whole from unit fractions.
3.NF.A.1
Identify fractions in a whole that is not partitioned into equal parts.
3.NF.A.1
Draw the whole when given the unit fraction.
3.NF.A.1
Identify a shaded fractional part in different ways, depending on the designation of the whole.
3.NF.A.2
Partition a number line from 0 to 1 into fractional units.
3.NF.A.2
Place any fraction on a number line with endpoints 0 and 1.
3.NF.A.2
Place a fraction greater than 1 on a number line with endpoints 0 and another whole number larger than 1.
3.NF.A.2
Place any fraction on a number line with endpoints greater than 0.
3.NF.A.2
3.NF.A.3.D
Place various fractions on a number line where the given interval is not a whole.
3.NF.A.3.A
3.NF.A.3.B
Understand two fractions as equivalent if they are the same point on a number line referring to the same whole. Use this understanding to generate simple equivalent fractions.
3.NF.A.3.A
3.NF.A.3.B
Understand two fractions as equivalent if they are the same sized pieces of the same sized wholes, though not necessarily the same shape. Use this understanding to generate simple equivalent fractions.
3.NF.A.3.C
Express the whole number 1 as fractions.
3.NF.A.3.C
Express whole numbers greater than 1 as fractions.
3.NF.A.3.C
Express whole numbers greater than 1 as fractions whose unit is 1 (e.g., $$3=\frac{3}{1}$$).
3.NF.A.3.A
3.NF.A.3.B
3.NF.A.3.C
Explain equivalence by manipulating units and reasoning about their size.
3.NF.A.3.D
Compare unit fractions (a unique case of fractions with the same numerators) by reasoning about the size of their units. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <.
3.NF.A.3.D
Compare fractions with the same numerators by reasoning about the size of their units. Record the results of comparisons with the symbols >, =, or <.
3.NF.A.3.D
Compare fractions with the same denominators by reasoning about their number of units. Record the results of comparisons with the symbols >, =, or <.
3.NF.A.3
Compare and order fractions using various methods.
3.NF.A
Understand fractions as numbers.
Key: Major Cluster Supporting Cluster Additional Cluster
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