Objective
Explain equivalence by manipulating units and reasoning about their size.
Common Core Standards
Core Standards
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.
Number and Operations—Fractions
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.
Number and Operations—Fractions
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.
3.NF.A.3.C— Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.Example: express 3 in the form 3 = 3/1; recognize that 6/1 = 6.Example: locate 4/4 and 1 at the same point of a number line diagram.
Number and Operations—Fractions
3.NF.A.3.C— Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.Example: express 3 in the form 3 = 3/1; recognize that 6/1 = 6.Example: locate 4/4 and 1 at the same point of a number line diagram.
Foundational Standards
The foundational standards covered in this lesson
2.MD.A.2
Measurement and Data
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.
Criteria for Success
The essential concepts students need to demonstrate or understand to achieve the lesson objective
- Understand that since equivalent fractions represent the same-sized part of the same-sized whole, the whole that is partitioned into more pieces must have more relevant pieces that constitute its equivalent fraction (MP.7, MP.8). Begin to see this relationship as a multiplicative one (although this explicit understanding is not required until Grade 4).
- Generate simple equivalent fractions in all cases, including those with whole numbers.
- Explain the equivalence of fractions in all cases, including those with whole numbers, using an area model, number line, or other method (MP.3, MP.5).
Tips for Teachers
Suggestions for teachers to help them teach this lesson
This lesson previews the work of Grade 4 of developing an algorithm for finding equivalent fractions, but it also recaps every case of equivalent fractions students have seen thus far in the unit. Therefore, this lesson is optional though highly encouraged since it serves to summarize their work thus far as well as connect to future work on the topic.
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Anchor Tasks
Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding
Problem 1
a.
Partition the following area model into thirds. Then write a fraction to represent the whole.
Partition the following area model into sixths. Then write a fraction to represent the whole.
Partition the following area model into ninths. Then write a fraction to represent the whole.
b.What do you notice about the number of parts and the size of each part in each model in Part (a)? What do you wonder?
Guiding Questions
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Problem 2
a.
- Partition the following number line into wholes. Label each tick mark with a fraction.
- Partition the following number line into halves. Label each tick mark with a fraction.
- Partition the following number line into fourths. Label each tick mark with a fraction.
- Partition the following number line into eighths. Label each tick mark with a fraction.
b.What do you notice about the number of parts and the size of each part in each model in Part (a)? What do you wonder?
Guiding Questions
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Problem Set
Problem Set
Answer Keys
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Discussion of Problem Set
- How did you use the patterns we noticed in the Anchor Tasks to solve #1 without needing to draw a model for every fraction?
- What happened to the size of the equal parts in #2a? What happened to the number of equal parts in #2a? How are those related?
- How did you share the chocolate bars equally? What fraction of a chocolate bar did each friend get? What fraction of all the chocolate bars collectively did each friend get? How do these questions demonstrate the importance of specifying the whole?
- Describe the approach you took to solving #5. Is there more than one correct answer?
Target Task
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Two fractions have different numerators and denominators. Is it possible for the two fractions to be located at the same point on the number line? Why or why not?
Student Response
An example response to the Target Task at the level of detail expected of the students.
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Additional Practice
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
Extra Practice Problems
Answer Keys
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Word Problems and Fluency Activities
Word Problems and Fluency Activities
Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.
Lesson 14
Lesson 16
