Curriculum / Math / 4th Grade / Unit 4: Fraction Equivalence and Ordering / Lesson 8
Math
Unit 4
4th Grade
Lesson 8 of 15
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Lesson Notes
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Recognize and generate equivalent fractions with smaller units using multiples.
The core standards covered in this lesson
4.NF.A.1 — Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
The foundational standards covered in this lesson
3.NF.A.3 — Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
4.OA.A.1 — Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.
4.OA.B.4 — Find all factor pairs for a whole number in the range 1—100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1—100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1—100 is prime or composite.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
As a supplement to the Problem Set, students can play a game to practice finding equivalent fractions with smaller units with increasing efficiency, such as “Fraction Scattergories” from Games with Fraction Strips and Fraction Cards on The Max Ray Blog.
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Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding
25-30 minutes
Allen drew an area model to represent $${{7\over8}}$$, as shown to the bottom left. He partitioned it to find an equivalent fraction, then covered the model to the bottom right.
a. What equivalent fraction did Allen come up with? How do you know?
b. Chin says she can represent this relationship with an equation: $$\frac78=\frac{7\times4}{8\times4}=\frac{28}{32}$$. How is this equation related to Allen’s images above?
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Van de Walle, John A. Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades 3-5 (Volume II). Pearson, 2nd edition, 2013.
Find a fraction that is equivalent to each of the following using Chin's method from Anchor Task 1:
a. $$\frac{1}{9}$$
b. $${{4\over7}}$$
c. $${{14\over11}}$$
Determine whether each of the following equations are true. Correct those that are false by changing either the numerator or denominator in the fraction on the right-hand side of the equation.
a. $${{9\over5}={27\over15}}$$
b. $${{3\over4}={15\over16}}$$
Grade 4 Mathematics > Module 5 > Topic B > Lesson 8 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..
15-20 minutes
Problem Set
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
Find two fractions that are equivalent to $${{7\over12}}$$ whose numerators are greater than $$7$$.
Determine if the following fractions are equivalent. Then explain how you know.
$${{5\over3}={15\over9}}$$
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
Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.
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Recognize and generate equivalent fractions with larger units using visual models.
Topic A: Factors and Multiples
Identify multiples and determine if a whole number is a multiple of another number.
Standards
4.OA.B.4
Explore patterns in multiples of various whole numbers.
Find factor pairs for numbers to 100 and recognize that a whole number is a multiple of each of its factors.
Determine whether a given number is prime or composite.
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Topic B: Equivalent Fractions
Recognize and generate equivalent fractions with smaller units using tape diagrams.
4.NF.A.1
Recognize and generate equivalent fractions with smaller units using number lines.
Recognize and generate equivalent fractions with smaller units using area models.
Recognize and generate equivalent fractions with larger units using factors.
Topic C: Comparing and Ordering Fractions
Compare two fractions where one numerator or denominator is a factor of the other by replacing one fraction with an equivalent one.
4.NF.A.2
Compare two fractions by replacing both fractions with equivalent ones.
Compare two fractions using one whole as a benchmark.
Compare two fractions using one half as a benchmark.
Compare and order fractions using various strategies.
4.NF.A
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