3.NF.A.2.A
*This standard is part of a major cluster
Standard
Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.
Standard Unpacked
The number line diagram is the first time student’s work with a number line for numbers that are between whole numbers (e.g., that 1⁄2 is between 0 and 1). Students need ample experiences folding linear models (e.g., string, sentence strips), manipulating objects on n to help them reason about and justify the location of fractions, such that 1⁄2 lies exactly halfway between 0 and 1.
For 3.NF.A.3.A, students are beginning to explore ONLY the unit fraction, fractions with a numerator of 1. For this standard they are exploring the fractions 1/2, 1/3, 1/4, 1/6, and 1/8 on a number line. For 3rd grade, students should work with fractions with denominators of 2,3,4, 6, and 8.
It is essential to continue the use of the language that was developed in earlier grades when describing a shape that has been partitioned. Avoid the phrase “three out of four” (unless talking about ratios or probability) or “three over four” and instead say “three fourths” (Van de Walle 2012). This practice supports using precise language, Math Practice 6, and does not aid to the development of misconceptions about ratio development in later grades.
We must provide students with adequate time and experiences to develop a deep conceptual understanding of this critical area of mathematics. Fractions are a critical foundation for students, as they are used in measurement across various professions, and they are essential to the study of algebra and more advanced mathematics, This understanding must go well beyond recognizing that 3/5 of an area is shaded (Van de Walle, 2012). Experiences must include ample opportunities to experience modeling using manipulatives, constructive discourse, and rich math tasks to support the learning of fractions, which may extend far beyond textbook driven experiences and looking at pictures of pre-made shaded in fractions.
Example of the Unit Fraction Identified on Number Lines:
Questions/ Activities to check for understanding and increase rigor:
• Provide an empty ("unticked") number line. Ask students to place 0 and 1 on the line. (Students can use a ruler for precision) Have students use a marker such as a coin, paper clip, etc to move the marker to indicate where they think ½ is, 1/3, ¼, 1/6, 1/8. Have students explain their reasoning.
• Show 0-1 number line with ⅓ etc. marked with a dot (unlabeled), what value do you think the dot represents? Explain your reasoning.
• Ask students to draw a number line and place the following values on the line: 0, ¼, ½, 1. Encourage students to use precision with this activity and then explain their reasoning.
• Give students two number lines, one with endpoints of 0 and 1 and the other with endpoints marked 0 and ½ . Ask students to place ¼ on both lines. Explain why ¼ is placed differently on each number line.
• Provide a 12 inch number line 0 and 1 as the endpoints. Have students locate and label ⅙, 1/4, 1/3, and 1/6 on the line. Students should explain their reasoning.