3.1 Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:

  • B. Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution.
  • C. Select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems.
  • D. Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
  • E. Create and use representations to organize, record, and communicate mathematical ideas.
  • F. Analyze mathematical relationships to connect and communicate mathematical ideas.
  • G. Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

3.3 Number and operations. The student applies mathematical process standards to represent and explain fractional units. The student is expected to:

  • A. Represent fractions greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 using concrete objects and pictorial models, including strip diagrams and number lines; Supporting Standard.
  • C. Explain that the unit fraction 1/b represents the quantity formed by one part of a whole that has been partitioned into b equal parts where b is a non-zero whole number; Supporting Standard.
  • D. Compose and decompose a fraction a/b with a numerator greater than zero and less than or equal to b as a sum of parts 1/b; Supporting Standard.   
  • E. Solve problems involving partitioning an object or a set of objects among two or more recipients using pictorial representations of fractions with denominators of 2, 3, 4, 6, and 8; Supporting Standard.
  • F. Represent equivalent fractions with denominators of 2, 3, 4, 6, and 8 using a variety of objects and pictorial models, including number lines; Readiness Standard.
  • G. Explain that two fractions are equivalent if and only if they are both represented by the same point on the number line or represent the same portion of a same size whole for an area model; Supporting Standard.
  • H. Compare two fractions having the same numerator or denominator in problems by reasoning about their sizes and justifying the conclusion using symbols, words, objects, and pictorial models; Readiness Standard.

Common Core

Number & Operations ­ Fractions:
Develop understanding of fractions as numbers.

  • 3.NF.A.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
  • 3.NF.A.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
    • 3.NF.A.3.A Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
    • 3.NF.A.3.B Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model.
    • 3.NF.A.3.C Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.
    • 3.NF.A.3.D Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.