# Discovering Equivalent Fractions

Author: Dana Hill
Lesson Plan:

Objectives
Students will:
• Demonstrate understanding that a fraction can be represented as part of a linear region
• Describe part of a linear region using fractions
• Compare fractions to determine if one fraction is greater than, less than, or equal to another fraction
• Identify sets of equivalent fractions
Standards
• Standard 1:    Analysis, Inquiry, and Design Students will use mathematical analysis, scientific inquiry, and engineering design, as appropriate, to pose questions, seek answers, and develop solutions.
• Standard 2:   Information Systems Students will access, generate, process, and transfer information using appropriate technologies.
• Standard 7:   Interdisciplinary Problem SolvingStudents will apply the knowledge and thinking skills of mathematics, science, and technology to address real-life problems and make informed decisions.
Anticipatory Set
To grab students’ attention, a large picture of an unwrapped Hershey’s chocolate bar will be displayed on the SMART Board. Underneath will be these questions:
Would you rather…
Have ½ of the Hershey’s bar, or 6/12 of the Hershey’s bar?
Have ¼ of the Hershey’s bar, or 3/12 of the Hershey’s bar?
Why? Discuss your thoughts with a partner.
This “hook” will likely engage student interest because it involves food, and because of the accompanying (mouth-watering) visual.

Teaching: Input
1. Students will each receive a model of a Hershey’s bar, which has been divided into 12 equal parts. They will use the model to determine the answers to the questions asked during the Anticipatory Set. Students will come to the conclusion that ½ = 6/12 and ¼ = 3/12.
2. The term equivalent fractions be introduced and displayed. Equivalent fractions are those fractions that describe the same fractional part.
3. We can use models (strips) to identify equivalent fractions. (The class will have previously made fraction strips to use during this lesson; they will have these strips: one whole, ½, ¼, 1/8, 1/3, and 1/6.)
4. Identify the task: Students will work in partnerships. Using their set of fraction strips, they will identify at least six pairs of equivalent fractions. They will list and sketch each pair on an accompanying student sheet.
Teaching: Modeling
1. On the SMART Board, display a set of fraction strips that matches the sets that students have created.
2. Manipulate the fraction strips to demonstrate that ½ is equivalent to 2/4: Place two fourths directly on top of ½ to show that the two fractions occupy the same amount of space, and thus are equivalent.
3. Display the student sheet that students will be using to record their work. List and sketch the equivalent fraction pair that has been “discovered.”
Teaching: Checking for Understanding
1. Ask students to work in small groups to find another pair of equivalent fractions.
2. Once they find a pair, they should record it on their student sheets, using the format shared during the “Modeling” portion of the lesson.
3. As students discuss and record their ideas, circulate to check for understanding and/or misconceptions.
4. Identify a partnership to share its work. They will manipulate the SMART Board strips to show equivalence, and they will their pair to the whole-class student sheet that the teacher began.
Guided Practice
Students will work in teacher-selected partnerships to complete the task outlined in the “Input” phase of the lesson. As they work, the teacher will circulate to ensure understanding and to promote critical thinking.
Closure
Following completion of the task, the class will join together to review their understanding of equivalent fractions.
1. The class will work together to create a definition of equivalent fractions that can be posted in the room.
2. Partnerships will share (and prove) the pairs of equivalent fractions that they found. As they demonstrate on the SMART Board, the teacher will record their findings on a chart that will be displayed for future use. She will attach the corresponding fraction strip models, and write equivalent fraction number sentences.
Independent Practice
Students will be introduced to the website that provides further practice with this concept: http://illuminations.nctm.org/ActivityDetail.aspx?id=80. For homework, they will be provided with a recording sheet identical to that used during today’s lesson. They will be responsible for spending 10-15 minutes on the website and for recording and sketching the equivalent fraction pairs that they find during this investigation. The following day, they will share their findings with their math partner, and they will be invited to add their equivalent fraction pairs to the whole-class chart.
Materials
SMART Board display: Unwrapped Hershey’s chocolate bar with “hook” questions
Fraction strips created the previous day
SMART Board display: Fraction strips to match those created by students (one whole, ½, ¼, 1/8, 1/3 and 1/6)
Student sheet: The Hunt for Equivalent Fractions (classwork and homework)
Whole-class chart: The Hunt for Equivalent Fractions
Duration

45-60 minutes