Curriculum / Math / 3rd Grade / Unit 6: Fractions / Lesson 12
Math
Unit 6
3rd Grade
Lesson 12 of 24
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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.
The core standards covered in this lesson
3.NF.A.3.A — Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
3.NF.A.3.B — Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding
Ebony and Shaun both have the same length string. Ebony cuts her string into three equal-length pieces to make necklaces, and Shaun cuts his string into six equal-length pieces to make bracelets. Ebony uses two of her pieces of string and Shaun uses four of his pieces of string. Who used more string, Ebony or Shaun? Draw a picture to support your reasoning.
a. Place the following fractions on the number line below.
b. Is $$\frac{2}{4}=\frac{1}{2}$$? How do you know?
c. Find a different fraction that is equivalent to $$\frac{2}{4}$$.
Scott drew this picture:
Then he said
This shows that $$ \frac{\mathbf{1}}{\mathbf{4}}$$ is equal to $$\frac{\mathbf{4}}{\mathbf{8}}$$.​​​​​​​
a. What was his mistake?
b. Rewrite Scott’s statement by replacing either fraction so that it is a true statement. Then draw a number line to support your answer.
Comparing Fractions with a Different Whole, accessed on March 28, 2018, 1:21 p.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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A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Find a fraction that is equivalent to $$\frac{2}{4}$$. Show or explain how you know they are equivalent using a number line.
An example response to the Target Task at the level of detail expected of the students.
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Lesson 11
Lesson 13
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
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 <.
Compare and order fractions using various methods.
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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