Curriculum / Math / 4th Grade / Unit 4: Fraction Equivalence and Ordering / Lesson 10
Math
Unit 4
4th Grade
Lesson 10 of 15
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Recognize and generate equivalent fractions with larger units using factors.
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
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Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding
a. Andre drew a number line and marked a point on it. Label the point with the fraction it represents.
b. To find other fractions that the point represents, Andre made copies of the number line. He grouped fractional units together by drawing circles around them to make larger fractional units. Label the tick mark between the circles Andre drew on each number line.
c. Jamari wrote the same fractions for the points but used a different strategy, as shown. Analyze his reasoning.
$${{3\over6} = {{3\div3}\over{6\div3}} = {1\over2}}$$
How do you think Andre’s and Jamari's strategies are related?
Grade 4 > Lesson 11 > Activity 1, accessed on Feb. 17, 2022, 4:01 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.
Find an equivalent fraction with larger units for each of the following:
a. $${{6\over9}}$$
b. $${{20\over12}}$$
Find an equivalent fraction with the largest unit for each of the following:
a. $${{6\over12}}$$
b. $$\frac{81}{72}$$
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 two fractions that are equivalent to $${{{12}\over18}}$$ and whose numerators are less than 12.
Explain how you know $$\frac{21}{28}$$ is equivalent to $$\frac{21\div 7}{28\div7}$$. Use a model to support your reasoning.
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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 9
Lesson 11
Topic A: Factors and Multiples
Identify multiples and determine if a whole number is a multiple of another number.
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 smaller units using multiples.
Recognize and generate equivalent fractions with larger units using visual models.
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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