This lesson serves as an introduction to equivalent fractions. It addresses standards for both 3rd and 4th grade but can be used with a variety of age groups to support students’ foundational understanding of fractional equivalence. Here, students will use manipulatives, such as fraction strips, to visually compare fractions and determine equivalence. In addition, students will use pattern finding, structure, and repeated reasoning to begin developing strategies for comparing fractions, determining equivalence, and generating equivalent fractions.
CCSS.Math.Practice.MP4 | Model with mathematics. |
CCSS.Math.Practice.MP5 | Use appropriate tools strategically. |
CCSS.Math.Practice.MP7 | Look for and make use of structure. |
CCSS.Math.Practice.MP8 | Look for an express regularity in repeated reasoning. |
CCSS.Math.Content.3.NF.A.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. | CCSS.Math.Content.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. |
CCSS.Math.Content.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. | |
CCSS.Math.Content.3.NF.A.3.C- Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram. | |
CCSS.Math.Content.3.NF.A.3.D- a Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. |
CCSS.Math.Content.4.NF.A.1- Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) |
CCSS.Math.Content.4.NF.A.2- Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. |
Students will be able to define equivalence.
Students will be able to use visuals, manipulatives, and their understanding of numbers to compare fractions and determine equivalence.
Students will be able to use visuals, manipulatives, and their understanding of numbers to generate equivalent fractions.
Students will be able to support their conjectures about fractional equivalence in writing.
• The Building Blocks of Math series, specifically Fractions
• Scratch paper
• Pencils
• Discovering Equivalent Fractions Worksheet (1 per student)
• Fraction Manipulatives (1 per student)
Optional: Printable Fraction Strips
• Fraction Worksheets (1 set per student, depending on learning needs and abilities):
Lowest cognitive demand: The Swamp’s Strongest Lifters and River Bottom Surprises
Average cognitive demand: Over the Net and Swamp Flip-Flop
Highest cognitive demand: Lost! and Winter Olympic Trivia
• Optional: Equivalent Fractions Chart
• Answer key
Approximately 45-65 minutes.
Before engaging in this lesson, students should have prior knowledge of comparing whole numbers using >, <, and = so they are prepared to use those same symbols to compare fractions.
Students should also be familiar with the vocabulary terms fraction, numerator, and denominator. They should know that in a fraction that shows equal parts of a whole, the numerator shows how many equal parts there are and the denominator shows the total number of parts within one whole. For students still struggling with these concepts, please see the Fractions book, specifically pages 4 - 11.
Numerator – the number above the line in a fraction, which shows how many parts are taken.
Denominator – the number below the line in a fraction, which states the size of the parts in their relation to the whole.
Fraction – one or more of the equal parts of a whole number: 2/3, 3/4, and 7/8 are fractions.
Equalivalent – the same in value; equal.
Opportunities for differentiation have been built into this lesson plan. For example, the differentiation strategy of choice is used in the Application Activity section of this lesson plan as students are allowed a choice of working independently or with a peer.
You may choose to differentiate further in the Independent Application and Demonstration of Learning section of this lesson plan by assigning any of three leveled sets of independent practice to students with different learning needs:
For students who need more time and practice with the foundational ideas of equivalence, consider pulling a small group and using the Equivalent Fractions Chart to complete The Swamp’s Strongest Lifters and River Bottom Surprises.
For students who are working within their own Zone of Proximal Development (ZPD), considering having them complete Over the Net and Swamp Flip-Flop.
For students who need extension or enrichment, consider having them complete Lost! and Winter Olympic Trivia.
Time Guidelines:
Approximately 5-10 minutes
Teacher Actions
Begin with an open-ended question: Jonah ate 4/6 of his personal pizza. Molly ate 2/3 of her personal pizza. Who ate more pizza? How do you know?
Provide 3-4 minutes for students to engage in productive struggle with this problem. Encourage students to model the story situation with a picture to help them visualize.
Bring students back to the whole group setting and ask them what they noticed about their answers. Students should notice that both Jonah and Molly ate the same amount of pizza. Ask what this tells us about the fractions 4/6 and 2/3. Use this as an opportunity to introduce the word equivalent; Jonah and Molly ate the same amount, or an equivalent amount, of pizza. Equivalent fractions are those that represent the same amount out of a whole.
Time Guidelines:
Approximately 10-15 minutes
Teacher Actions
Elaborate on the idea of equivalence by explaining that even though two fractions may represent the same amount out of a whole, they can have completely different numerators and denominators.
One way to determine whether two fractions are equivalent is to compare them visually. Today we will use fraction manipulatives, such as fraction strips, to help us visually compare.
Model how to “line up” your fraction strips to compare two values. Use the following examples, or create your own:
Next, transition to generating equivalent fractions. Model how to find another fraction equivalent to 1/2 with your manipulatives. For example, consider 1/2 and the fraction strip broken into sixths, your new denominator. Line up the two strips and count the number of pieces needed to equal 1/2. That number becomes the new numerator of your equivalent fraction. We can show 1/2 = 3/6. Continue modeling how to generate equivalent fractions with the following:
Provide time for students to ask questions about equivalence and finding equivalent fractions before transitioning to the next phase of the lesson.
Time Guidelines:
Approximately 15-20 minutes
Teacher Actions
Pass out copies of the Discovering Equivalent Fractions worksheet and review the instructions with students. Depending on your students’ level of independence, consider modeling the first few problems here before sending students to work either independently or in pairs.
Return to the whole group setting and review what students learned about equivalent fractions. Use the following prompts to facilitate a discussion focused on equivalent fractions, strategies for comparing, and any patterns students identified:
Next, explain that students will use their creativity to write a follow-up headline. The goal here is to show how results vary based on changes in supply and demand. Stores Place Restrictions on Number of Toilet Paper Products Individuals Can Purchase.
Time Guidelines:
Approximately 10-15 minutes
Teacher Actions
Pass out the Headlines Activity sheet and place students into pairs or groups (or individually) as you see fit. Review the directions with students and allow them to work collaboratively to analyze, predict, provide reasoning, and write a follow-up headline.
If needed, pull a group of students for extra support or for further extension.
Time Guidelines:
Approximately 5-10 minutes
Teacher Actions
Bring students back to the whole group setting. Explain that they spent time today working with manipulatives to determine equivalence and compare fraction sizes. Students also used the mathematical skills of looking for and making use of structure as well as expressing regularity in repeated reasoning to identify patterns within equivalent fractions. Some students even started coming up with their own strategies for finding equivalent fractions or comparing fractions without manipulatives!
Revisit the objectives by reviewing the idea that two fractions are equivalent if they represent the same amount, even if their numerators and denominators are different.
Consider allowing students to keep their manipulatives and/or their Equivalent Fractions Chart for use throughout the remainder of related lessons.
What went well?
What changes might be beneficial?
Reteaching Needs
Extension Needs