Common Core State Standards and  Fractions. Conceptua Fractions is closely correlated to the Common Core State Standards (CCSS) of Mathematical Practice. Like the CCSS, our software focuses on the development of conceptual understanding, visual learning and step-by-step development of skills in problem solving.

Overview of the CCSS

Responding to concerns raised by the National Math Panel and others, the Common Core State Standards (CCSS) are more rigorous in addressing fractions. In fact, fraction skills are now contained in a separate domain, not just part of Number and Operations. The CCSS balance the need for students to develop both conceptual understanding and procedural skills. There is also an emphasis on the use of visual models by teachers to teach fractions and by students to show their understanding.

Download the Conceptua Fractions alignment to the Common Core State Standards >

While grade two does not contain a Numbers and Operations-Fractions domain, students do work on developing an understanding of partitioning and equal shares as a component of geometry. In third grade, a part of the new Numbers and Operations- Fractions domain, students move beyond the concept of equal shares developed previously to learn that fractions are more than parts of a whole, but are in fact numbers. There is an emphasis on the use of a number line to gain this understanding. In fourth grade students are expected to understand fraction equivalency and ordering and to apply that understanding to operations. By the end of fifth grade students are expected to be proficient in addition, subtraction, multiplication and division of fractions.
 

Sample of Standards Addressed by Conceptua Fractions (by grade)

Grade 2: Reason with shapes and their attributes

2.G.3. Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.

partition fraction circle
Grade 3: Develop an understanding of fractions as numbers.


3.NF.2. Understand a fraction as a number on the number line; represent fractions on a number line diagram.

a) 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.

b) Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.

represent fractions on a number line
Grade 4: Extend understanding of fraction equivalence and ordering.


4.NF.1. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

equivalent fractions sentences
 
equivalent fractions models
 
4.NF.3. Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
c) Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

 
add mixed fractions with like denominators


Grade 5: Use equivalent fractions as a strategy to add and subtract fractions.


5.NF.1. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.

subtract mixed fractions with unlike denominators

Related Resources

Common Core State Standards: Key Points in Mathematics

Common Core State Standards of Mathematical Practice
(full text)

Blog Posts:
The Common Core Standards of Mathematical Practice (Robyn Silbey)
Transitioning to the Common Core State Standards (Lauri Susi)