About two weeks ago, I was fortunate to spend the day talking and learning with and from a group of fourth grade teachers. We spent the day working on our understanding of the content contained in the CCSS Domain of Numbers and Operations–Fractions. Our conversation focused on the shifts we are going to need to make as we implement the common core standards for mathematical content and mathematical practice. We talked about pedagogy, pedagogical content, reasoning, communication, and a whole lot more. We definitely will be doing some stretching in our professional practice.
During the day, we spent some time using fraction circles. Fraction circles are a tool that can be used to foster conversation and to promote opportunities for students to reason. They can be a vehicle to support the precise use of language. In addition, the fraction circles can also be used to explore both grade 3 and grade 4 standards. The more we worked with the fraction circles and explored the content of the domain of Numbers and Operations–Fractions, we determined that they can be utilized to create opportunities for students to build their foundational knowledge. We wanted to ensure that their experiences include working with fractions as numbers (3.NF.1 and 2), unit fractions, the idea of partitioning, and number lines. In addition, we want students to work with equivalence and comparison (3.NF.3). These essential understandings are the foundation for the fourth grade standards, particularly, 4.NF.3 and 4.NF.4.
So, we worked on how the fraction circles could help us accomplish some of the goals we had outlined. We created several sets of number strings to offer our students so that they could explore ideas and concepts that are essential and enduring.
JUST A HINT: Included with the number strings are photos of the set of fraction circles we used. We learned that different manufacturers use different colors for fractional pieces. So, if you use some of the number strings, which we hope you do, check to see if the fraction circles you have match what we have.
Number String #1
1. If the black circle = 1, build 2/3. What color pieces did you use? How many 1/3 sized pieces are there?
2. If the black circle = 1, build 5/6. What color pieces did you use? How many 1/6 sized pieces make up 5/6? How could you represent 5/6 using addition? Using multiplication?
3. If the black circle = 1, build 7/12. What color pieces did you use? How many 1/12 sized pieces make up 7/12? How could you represent 7/12 using addition? Using multiplication?
4. If the black circle = 1, what value do three brown pieces have? How many 1/8 sized pieces make up 3/8? What is the value of one brown piece? Each brown piece? How can you represent 3/8 using addition?
Number String #2
1, Take out 4 red pieces. If the black circle = 1, how many red pieces does it take to make the whole? What is the value of one red piece? What is the value of each red piece? What is the value of the 4 red pieces?
2. Take out 1 green piece. If the black circle = 1, how many green pieces does it take to make the whole? What is the value of one green piece?
3. If the black circle = 1, how many 1/6 pieces are needed to make 1/2? What color is a 1/6 sized piece? What color is a 1/2 sized piece? How many 1/6 sized pieces does it take to make 2 black circles? How many 1/6 sized pieces does it take to make 3/2?
4. If the black circle = 1, how many 1/6 sized pieces does it take to make 1/3?
5. If the black circle = 1, how many 1/12 sized pieces does it take to make 1/2?
Number String #3
1. Build 2/2 with the fraction circles, if one black circle = 1.
2. Build 3/2 with the fraction circles, if one black circle = 1.
3. Build 7/2 with the fraction circles, if one black circles = 1.
4. Build 8/4 with the fraction circles, if one black circles = 1.
5. Build 10/4 with the fraction circles, if one black circles = 1.
6. Take out a number line. Plot each of the numbers from questions 1-5 on the number line.
We know that these are just an initial set of number strings that we will use to provide students with opportunities to explore and investigate ideas about fractions. But, we’re feeling pretty good about setting up some new learning situations for our students and the professional conversations we had as we designed them. We look forward to talking about the impact on student learning at our next conversation.