Use Cuisenaire rods to explore fractional relationships. This lays the foundation for work with challenging fraction concepts like equivalence.
- One set of Cuisenaire rods per student
OR
Relationship Rods Printout
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Lesson 2 Activity Sheet
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Lesson 2 Activity Sheet Answer Key
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Assessment Downloadable
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Assessment Downloadable Answer Key
Introduce
To begin the lesson, give students one set of Cuisenaire rods (either homemade or commercial) and a few minutes to explore the materials.
Ask them "What do you notice?" Examples of things students might mention include:
- Rods of the same color are the same size.
- I see ten different sizes.
- I notice that some rods can be put together to make other rods.
- Some students will notice that the various colors can be stacked one on top of the other to create a staircase, as in the picture below. This configuration makes comparing the various fractions much easier and is illustrative of the linear model of fractions.
Explore
Distribute the Lesson 2 Fraction Activity Sheet (download from Materials section above). Work together as a class to model the situation where the red is equal to 1. Ask students to grab a red rod and ask:
- “Let’s say this represents 1 (red rod). What do the white rods represent?”
- “How do you know? How did you decide?”
Direct students to model this relationship with the rods. (See diagram)
Ask:
- "What fraction of the red is the white?" [Write the fraction ½.]
Using the lime green as one whole, work together with the students to find how many white rods it takes to equal one lime green rod.
Ask:
- What fraction of the lime green rod does the white rod represent?
- How do you write that number? [⅓.] What does the numerator (1) represent? What does the denominator (3) represent? [The 1 in the numerator represents one of three equal sized pieces. The 3 in the denominator tells us that the whole is divided into 3 equal pieces.]
Using the purple as one whole, ask:
- “How many white rods does it take to equal one purple rod?” [4]
- “What other color rod can be used to make a purple rod?” [2 reds will make a purple.]
Teacher notes - This activity is used to help students recognize the structure of fractions and build equivalence (SMP 7). For example: When the purple rod represents one whole unit, it takes 4 white rods to equal the purple. Therefore, each white rod equals 1/4 of the purple. It takes 2 red rods to equal the purple, so each red is 1/2 of the purple. (Extension: two whites = one red or 2/4 = 1/2.)
At this point determine which students need more guided practice and which are ready to work independently. Circulate as they work and monitor for understanding.
Individual/small group work:
Dark green = 1 whole (See teacher notes below.)
Teacher notes - This activity is used to help students recognize the structure of fractions and build equivalence (SMP 7). For example: When the dark green rod represents one whole unit, it takes 6 white rods to equal the dark green. Therefore, each white rod equals 1/6 of the dark green whole. It takes 3 red rods to equal the dark green, so each red is 1/3 of the dark green whole. (Extension: Two whites = one red or 2/6 = 1/3.)
This is a great opportunity to formatively assess students by observing and listening to students work. Use students' work to facilitate discussion in the class. Have student pair-share their thinking by presenting on one of the questions on the activity sheet.
Synthesize
To summarize/synthesize what they have hopefully noticed about the structure of the fractions (SMP 7), discuss the following questions:
Ask:
"How do the unit fractions we created using the rods help us understand numbers less than one whole? Will these numbers help us solve problems in our everyday lives?" [Students might talk about sharing pizza among 4 friends. Each friend would get ¼ of the pizza.]
"Let's think about the rods in a different way.
- “If the white is ½, what is the whole?” [Red.]
- “If the white is ⅓, what is the whole?” [Lime green.]
- “If the white is ¼, what is the whole?” [Purple.]
- “What does the 1 in the numerator stand for in ¼?” [One of the four white rods that make up the whole purple rod.]
- “What does the 4 in the denominator stand for in this fraction?” [The whole is divided into 4 equal pieces.]
Assessment
Exit Ticket (SMP 3):
Sarah thinks that two white rods are ⅓ of a dark green. Judd thinks that two whites are 2/6 of the dark green. Who do you agree with and why?
Teacher Reflection
- How can you determine which students understand that a fraction can be represented as part of a linear region? What activities are appropriate for students who have not yet developed this understanding?
- How can you determine which students can identify fraction relationships using different “wholes” as a reference? What activities are appropriate for students who have not yet developed this understanding?
- What parts of the lesson went smoothly? What parts should be modified for the future?
Leave your thoughts in the comments below.