1. Fractions in Second Grade Tomoko Keilholtz Jessica Lunerdelli Amber Player Clair williams https://www.youtube.com/watch?v=6ooKWyPI0i4

2. 2.G.A.2 Partition Rectangles – Summary: – This standard begins the formal foundation of the idea of area development. Since we measure area in square units, it is natural to begin with rectangles and partition them into square regions so that we can easily count the total.

3. Developing the Standard: – Have students finish partitioning a rectangular cake that has already been divided into equal rows. – Have students draw a picture to show how one could cut a cake into square pieces. – Heavy use of pictures will facilitate student understanding of this standard. – The use of graph paper should make the task of partitioning a rectangle easier and allow for students to see the idea without getting bogged down in detailed measurement.

4. Questions to Focus Instruction: – Can students find the total number of squares on a checkerboard and then use the checkerboard as a pattern to divide a different sized square into a grid of squares and count the total number? – Can students use graph paper to represent the same rectangle as being composed of many short rows as well as a few long columns? – Can students use unifix cubes to create rectangular prisms and then determine through skip counting how many unifix cubes were used?

5. Skills: – Prior to: In first grade, students began measuring using iterated units. (See 1.MD.A.2). They should also be familiar with the grade-level work of using rectangular arrays of 5 (see 2.OA.C.4), and with composing and decomposing shapes. At Grade Level: Students are beginning to construct the idea of area. Moving Beyond: Students will partition shapes, including rectangles into equal parts. They will then express each section as a fraction of the whole rectangle. 1.MD.A.22.OA.C.4

6. 2.G.A.3 Partition Circle and Rectangles into Halves, Thirds and Fourths Summary: – Students will recognize the "part-whole" relationship in whole pieces and their fractional parts. Students should describe and partition a whole into two halves, three thirds, etc. within the shapes of circles and rectangles and refer to these pieces with that language. At this grade level, students should not be using the formal symbols of “½”, “1/3”, and “¼”. Using the numbers can create misconceptions that ¼ is larger than ½ since 4 is bigger than 2. – Students will also recognize that equal shares of an identical whole may not be the same shape.

7. Developing the Standard: – Manipulatives such as circle fractions provide a wonderful opportunity to introduce the part- whole relationship that exists with fractions. Begin with the whole, half, thirds, and fourths pieces to create a basic understanding of this concept. Allow students to explore using the fourths to make halves and wholes in order to show the equal relationship among the pieces. – Allow ample opportunity for students to make partitions of circles and rectangles write the words (whole, halves, thirds, and fourths) with each picture and concrete representations. – Introduce real-life examples of the part-whole relationship through such experiences as cutting a pizza, pie or large cookie cake. The bigger the pieces, the fewer pieces are yielded. However, the more times the circle must be divided, the individual pieces become smaller in size. – Students should compare their ways of partitioning shapes, and then ask whose half (or third, etc.) is bigger.

8. Questions to Focus Instruction: – Can my students recognize that a whole circle that already existed before partitioning is still there, as 2 halves, 3 thirds, or 4 fourths? – Do my students understand that by separating a circle into more pieces, it yields smaller pieces of the whole? – Can students use grid paper to divide a shape into equal pieces that are not the same in shape? – Can students compare a fourth, a third, and a half and place them in order of size? – Can students partition circles and rectangles into a given number of equal shares, and use the correct vocabulary to describe their actions?

9. Skills: – Prior to: Students are able to correctly identify pieces that represent wholes, halves and fourths. Students can create picture representations or drawings that depict these concepts as well. Additionally, students can use appropriate vocabulary to describe the relationship between the pieces and the whole. See 1.G.A.3. At Grade Level: Students will identify wholes, halves, thirds, and fourths as fractions of rectangles and circles that represent the relationship between the parts and the whole. Moving Beyond: Students will express a section of a whole shape as 1/2, 1/3, or 1.4. Further, they will identify equivalent fractions and compare fractional pieces with one another.1.G.A.3 https://www.youtube.com/watch?v=DnFrOetuUKg

10. Is this a whole circle? What do we need to complete the circle?

11. Part 2 Activity: Find your whole Which group has the most people? Which group has the fewest people? Which group has the biggest piece? Which group has the smallest piece?

12. Part 3: Drawing a circle from one part to the whole What type of part do I have? 1.Glue your piece to the paper. 2.Draw the rest of the missing pieces of your whole on the paper. 3.Check your partners work.

13. These two students each have 1 third of a rectangle. How many thirds do you see altogether? What do they need to complete whole rectangle?

14. Each student has 1 fourth of a square. What do they need to complete the whole square?

15. References Bhutto Muhammad Ilyas, W. Q., & Rawat, K. J. (2014). Effect of teaching of fractions through constructivist approach on learning outcomes of public sector primary schools teacher. Bulletin of Education and Research, 36(1) Mendiburo, M., Hasselbring, T., & Biswas, G. (2014). Teaching fractions with technology: What type of support do students need as they learn to build and interpret visual models of fractions ordering problems? Journal of Cognitive Education and Psychology, 13(1), 76- 87. Moyer-Packenham, P. p., Bolyard, J. J., & Tucker, S. I. (2014). Second-graders' mathematical practices for solving fraction tasks. Investigations In Mathematics Learning, 7(1), 54-81. North Carolina Department of Public Instruction (2012). http://www.dpi.state.nc.us/docs/acre/standards/common-core tools/unpacking/math/2nd.pdfhttp://www.dpi.state.nc.us/docs/acre/standards/common-core tools/unpacking/math/2nd.pdf Pien, C., & Dongsheng, Z.(2011). Making Connections. Mathematics Teaching, 223, 23-25 Small, Marian. (2014). Uncomplicating Fractions to meet Common Core Standards in math, K-7. New York: Teachers College. Tennessee Department of Education. http://www.readtennessee.org/ Wickstrom, Megan. (2014). Piecing It Together. Teaching Children Mathematics, 21(4), 220–227. http://doi.org/10.5951/teacchilmath.21.4.0220 http://doi.org/10.5951/teacchilmath.21.4.0220