Curriculum / Math / 3rd Grade / Unit 6: Fractions / Lesson 19
Math
Unit 6
3rd Grade
Lesson 19 of 24
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Compare and order fractions using various methods.
The core standards covered in this lesson
3.NF.A.3 — Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
The foundational standards covered in this lesson
2.MD.A.2 — Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
Choose either fraction cards with pictures or fraction cards without pictures for this lesson (see Note in Anchor Task 1).
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Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding
Play the following game with a partner using a set of cards (Template 1 or Template 2). The goal is to compare the two fractions appearing on each card, determining if they are equivalent and, if not, which is greater. Instructions for the activity are as follows:
Comparing Fractions Game, accessed on March 19, 2019, 11:35 a.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
a. Place the following fractions on the number line.
$$\frac{4}{1},\ \frac{2}{4},\ \frac{1}{4},\ \frac{4}{2},\ \frac{2}{2}$$
b. Compare each of the following pairs of fractions. Record your answer with <, >, or =.
i. $$\frac{2}{4}$$ and $$\frac{2}{2}$$
ii. $$\frac{4}{2}$$ and $$\frac{2}{2}$$
iii. $$\frac{4}{1}$$ and $$4$$
iv. $$\frac{2}{4}$$ and $$\frac{4}{2}$$
c. Order the fractions in Part (a) from least to greatest.
Which is closer to 1 on the number line, $$\frac{4}{5}$$ or $$\frac{5}{4}$$? Explain.
Which is Closer to 1?, accessed on March 19, 2019, 11:36 a.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
Problem Set
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Arrange your fractions in order from least to greatest. Explain your answer.
a. $$\frac{3}{8},\frac{3}{3},\frac{3}{4}$$
b. $$\frac{4}{6},\frac{2}{6},\frac{7}{6}$$
The Extra Practice Problems can be used as additional practice for homework, during an intervention block, etc. Daily Word Problems and Fluency Activities are aligned to the content of the unit but not necessarily to the lesson objective, therefore feel free to use them anytime during your school day.
Extra Practice Problems
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Lesson 18
Lesson 20
Topic A: Understanding Unit Fractions and Building Non-Unit Fractions
Partition a whole into equal parts using area models, identifying fractional units.
3.G.A.2 3.NF.A.1
Partition a whole into equal parts using tape diagrams (i.e., fraction strips), identifying and writing unit fractions in fraction notation.
Partition a whole into equal parts using area models and tape diagrams, identifying and writing non-unit fractions in fraction notation.
3.NF.A.1
Identify fractions of a whole that is not partitioned into equal parts.
Draw the whole when given the unit fraction.
Identify a shaded fractional part in different ways, depending on the designation of the whole.
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Topic B: Fractions on a Number Line
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.
Place any fraction on a number line with endpoints 0 and another whole number greater than 1.
Place any fraction on a number line with endpoints greater than 0.
3.NF.A.2 3.NF.A.3.C
Place various fractions on a number line where the given interval is not a whole.
3.NF.A.2 3.NF.A.3.D
Topic C: Equivalent Fractions
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.
Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.
3.NF.A.3.C
Explain equivalence by manipulating units and reasoning about their size.
3.NF.A.3.A 3.NF.A.3.B 3.NF.A.3.C
Topic D: Comparing Fractions
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 <.
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
Understand fractions as numbers.
3.NF.A
Topic E: Line Plots
Measure lengths to the nearest half inch.
3.MD.B.4
Measure lengths to the nearest quarter inch.
Generate measurement data and represent it in a line plot.
Create line plots (dot plots).
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