Fraction Fun Run

Ages 7–9 · 8 minutes · Math

Cheer for Troy and track his progress in the Fraction Fun Run!

In this fractions lesson, students will learn and practice:

- Tracking progress using fractions like 1/6, 2/6, and 3/6
- The notion of equivalent fractions like 2/6 = 1/3
- The connection between fractions and division

Part of

Intro to Fractions

Standards alignment

Common Core State Standards

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.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.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.c — Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.

Alabama

MA19.3.13 — Demonstrate that a unit fraction represents one part of an area model or length model of a whole that has been equally partitioned; explain that a numerator greater than one indicates the number of unit pieces represented by the fraction.
MA19.3.15 — Explain equivalence and compare fractions by reasoning about their size using visual fraction models and number lines.
MA19.3.14 — Interpret a fraction as a number on the number line; locate or represent fractions on a number line diagram.
MA19.3.15a — Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers.

Alaska

3.NF.1 — Understand a fraction 1/b (e.g., 1/4) as the quantity formed by 1 part when a whole is partitioned into b (e.g., 4) equal parts; understand a fraction a/b (e.g., 2/4) as the quantity formed by a (e.g., 2) parts of size 1/b. (e.g., 1/4)
3.NF.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.3.a — Understand two fractions as equivalent if they are the same size (modeled) or the same point on a number line.
3.NF.3.c — Express and model whole numbers as fractions, and recognize and construct fractions that are equivalent to whole numbers. For example: 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.

Arizona

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.b — Recognize and generate simple equivalent fractions. Explain why the fractions are equivalent.
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 if they have the same relative size compared to 1 whole.
3.NF.A.3.c — Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.

Arkansas

3.NPV.11 — Use number lines and visual models to recognize and generate equivalent fractions, explaining how they are equivalent in real-world and mathematical situations. • Fractions include: denominators 2, 3, 4, 6, and 8
3.NPV.6 — Identify fractions as parts of a whole and parts of a collection or set. • Fractions include: denominators 2, 3, 4, 6, and 8
3.NPV.9 — Identify and represent a non-unit fraction as a number on the number line, including fractions greater than one. • Fractions include: denominators 2, 3, 4, 6, and 8
3.NPV.8 — Identify and represent a unit fraction as a number on the number line. • Fractions include: denominators 2, 3, 4, 6, and 8

California

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.b — Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 1/2). Explain why the fractions are equivalent, e.g., by using a visual fraction model.
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.c — Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.

Colorado

3.NF.A.1 — Describe 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.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.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.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 — Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

Connecticut

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.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.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.c — Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.
3.NF.A.2 — Understand a fraction as a number on the number line; represent fractions on a number line diagram.

Delaware

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.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.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.c — Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.

Florida

MA.3.FR.1.1 — Represent and interpret unit fractions in the form 1/n as the quantity formed by one part when a whole is partitioned into n equal parts.
MA.3.FR.2.2 — Identify equivalent fractions and explain why they are equivalent.
MA.3.FR.1.2 — Represent and interpret fractions, including fractions greater than one, in the form of <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle mathsize="10px"><mfrac><mi>m</mi><mi>n</mi></mfrac></mstyle></math> as the result of adding the unit fraction <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle mathsize="10px"><mfrac><mn>1</mn><mi>n</mi></mfrac></mstyle></math> to itself m times.
MA.3.FR.1.3 — Read and write fractions, including fractions greater than one, using standard form, numeral-word form and word form.

Georgia

3.NR.4.1 — Describe a unit fraction and explain how multiple copies of a unit fraction form a non-unit fraction. Use parts of a whole, parts of a set, points on a number line, distances on a number line and area models.
3.NR.4.4 — Recognize and generate simple equivalent fractions.
3.NR.4 — Represent fractions with denominators of 2, 3, 4, 6 and 8 in multiple ways within a framework using visual models.
3.NR.4.3 — Represent fractions, including fractions greater than one, in multiple ways.

Hawaii

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.3b — 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 — Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
3.NF.A.3a — Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
3.NF.A.3c — Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.

Idaho

3.NF.A.1 — Understand a fraction 1/b as the quantity formed by one part when a whole (a single unit) is partitioned into 𝑏 equal parts; understand a/b as the quantity formed by a parts of size 1/b
3.NF.A.3.b — Recognize and generate simple equivalent fractions, and explain why the fractions are equivalent, such as by using a visual fraction model.
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.c — Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.

Illinois

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.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 — 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.c — Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.

Indiana

3.NS.2 — Model unit fractions as the quantity formed by 1 part when a whole is partitioned into equal parts; model non-unit fractions as the quantity formed by iterations of unit fractions. [In grade 3, limit denominators of fractions to 2, 3, 4, 6, 8.] (E)
3.NS.4 — Use fraction models to represent two simple equivalent fractions with attention to how the number and size of the parts differ even though the quantities are the same. Use this principle to generate simple equivalent fractions (e.g., 1/2 = 2/4, 4/6 = 2/3).
3.NS.3 — Model a non-unit fraction on a number line by marking equal lengths from 0, identifying each part as a unit fraction and locating the non-unit fraction as the endpoint on the number line. (E)

Iowa

3.NF.A.1 — Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into 𝑏𝑏 equal parts; understand a fraction a/b as the quantity formed by a part of size 1/b .
3.NF.A.3.b — Recognize and generate simple equivalent fractions. For example, 1/2 = 2/4 , 4/6 = 2/3 . Explain why the fractions are equivalent. For example, by using a visual fraction model.
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.c — Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers. For example, 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.

Kansas

3.NF.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.3.a — Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
3.NF.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.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.

Kentucky

KY.3.NF.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.
KY.3.NF.3.a — Understand two fractions as equivalent (equal) if they are the same size, or same point on a number line.
KY.3.NF.3.b — Recognize and generate simple equivalent fractions. Explain why the fractions are equivalent through writing or drawing.
KY.3.NF.3.c — Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers.

Louisiana

3.NF.A.1 — Understand a fraction 1/b, with denominators 2, 3, 4, 6, and 8, 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.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 — Explain equivalence of fractions with denominators 2, 3, 4, 6, and 8 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.c — Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.

Maine

3.NF.A.1 — Understand a unit 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.3b — 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 — Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
3.NF.A.3a — Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
3.NF.A.3c — 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.

Maryland

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.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.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.c — Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.

Massachusetts

3.NF.A.1 — Understand a fraction 1/b as the quantity formed by 1 part when a whole (a single unit) 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.b — Recognize and generate simple equivalent fractions, e.g., ½ = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model.
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.c — Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. For example, 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.

Michigan

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.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 — 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.c — Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.

Minnesota

3.1.3.1 — Read and write fractions with words and symbols. Recognize that fractions can be used to represent parts of a whole, parts of a set, points on a number line, or distances on a number line. For example: Parts of a shape (3/4 of a pie), parts of a set (3 out of 4 people), and measurements (3/4 of an inch).
4.1.2.1 — Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions.

Mississippi

3.NF.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.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.3.a — Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. Recognize that comparisons are valid only when the two fractions refer to the same whole.
3.NF.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.

Missouri

3.NF.A.1 — Understand a unit fraction as the quantity formed by one part when a whole is partitioned into equal parts.
3.NF.A.2 — Understand that when a whole is partitioned equally, a fraction can be used to represent a portion of the whole.
3.NF.A.5 — Recognize and generate equivalent fractions using visual models, and justify why the fractions are equivalent.
3.NF.A.4 — Demonstrate that two fractions are equivalent if they are the same size or the same point on a number line.
3.NF.A.3 — Represent fractions on a number line.

Montana

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.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.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.c — Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.

Nebraska

3.N.2 — Fractions: Students will develop understanding of fractions as numbers.
3.N.2.b — Find parts of a whole using visual fraction models.
3.N.2.d — Show and identify equivalent fractions using visual representations including pictures, manipulatives, and number lines.
3.N.2.e — Justify whole numbers as fractions and identify fractions that are equivalent to whole numbers.
3.N.2.c — Represent and understand a fraction as a number on a number line.

Nevada

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.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.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.c — Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.

New Hampshire

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.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.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.c — Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.

New Jersey

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.3a — Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
3.NF.A.3b — 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 — Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
3.NF.A.3c — 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.

New Mexico

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.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.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.c — Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.

New York

NY-3.NF.1 — Understand a unit fraction, 1/b, is 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.
NY-3.NF.3.a — Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
NY-3.NF.3.b — Recognize and generate equivalent fractions. Explain why the fractions are equivalent.
NY-3.NF.3.c — Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.
NY-3.NF.2.b — Represent a fraction a/b on a number line 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.

North Carolina

NC.3.NF.3 — Represent equivalent fractions with area and length models by: • Composing and decomposing fractions into equivalent fractions using related fractions: halves, fourths and eighths; thirds and sixths. • Explaining that a fraction with the same numerator and denominator equals one whole. • Expressing whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.
NC.3.NF.1 — Interpret unit fractions with denominators of 2, 3, 4, 6, and 8 as quantities formed when a whole is partitioned into equal parts; • Explain that a unit fraction is one of those parts. • Represent and identify unit fractions using area and length models.
NC.3.NF.2 — Interpret fractions with denominators of 2, 3, 4, 6, and 8 using area and length models. • Using an area model, explain that the numerator of a fraction represents the number of equal parts of the unit fraction. • Using a number line, explain that the numerator of a fraction represents the number of lengths of the unit fraction from 0.

North Dakota

3.NO.NF.3 — Represent equivalent fractions using visual representations and number lines.
3.NO.NF.2 — Represent and understand a fraction as a number on a number line.
3.NO.NF.4 — Recognize whole numbers as fractions and express fractions that are equivalent to whole numbers.
3.NO.NF.1 — Partition two-dimensional figures into equal areas and express the area of each part as a unit fraction of the whole. Describe using the language of sixths, eighths, a sixth of, and an eighth of.

Ohio

3.NF.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.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.3 — Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
3.NF.3.a — Understand two fractions as equivalent (equal) if they are the same size or the same point on a number line.
3.NF.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.

Oklahoma

3.N.3.2 — Model fractions using length, set, and area for halves, thirds, fourths, sixths, and eighths.
3.N.3 — Use and justify fractional representations in real-world and mathematical problems.
3.N.3.1 — Read and write fractions with words and symbols using appropriate terminology (i.e., numerator and denominator).

Oregon

3.NF.A.3 — Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
3.NF.A.1 — Understand the concept of a unit fraction and explain how multiple copies of a unit fraction form a non-unit fraction.
3.NF.A.2 — Understand a fraction as a number on the number line; Represent fractions on a number line diagram.

Pennsylvania

CC.2.1.3.C.1 — Explore and develop an understanding of fractions as numbers.

Rhode Island

3.NF.A.1 — Understand a fraction 1/b as the quantity formed by 1 part when a whole (a single unit) 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.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.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.c — Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. For example, 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.2.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.

South Carolina

4.NSF.1 — Explain why a fraction (i.e., denominators 2, 3, 4, 5, 6, 8, 10, 12, 25, 100), <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>a</mn><mi>b</mi></mfrac></math>, is equivalent to a fraction, <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>n</mi><mo>×</mo><mi>a</mi></mrow><mrow><mi>n</mi><mo>×</mo><mi>b</mi></mrow></mfrac></math>, 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.
3.G.2 — Partition two-dimensional shapes into 2, 3, 4, 6, or 8 parts with equal areas and express the area of each part using the same unit fraction. Recognize that equal parts of identical wholes need not have the same shape.

South Dakota

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 (example: 1 part out of 4 equal parts is the same as 1/4); understand a fraction a/b as the quantity formed by a parts of size 1/b. (example:3/4 is the same as 3 one-fourths (1/4, 1/4, 1/4).
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 — 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.c — Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.

Tennessee

3.NF.A.1 — Understand a unit fraction, 1/b, as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a non-unit fraction, n/b, as the quantity formed by n parts of size 1/b. For example, 3/4 represents a quantity formed by 3 parts of size 1/4.
3.NF.A.3.b — Recognize and generate simple equivalent fractions (e.g., 1/2 = 2/4, 4/6 = 2/3) and explain why the fractions are equivalent using a visual fraction model.
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.c — Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers. For example, express 3 in the form 3 = 3/1; recognize that 6/1= 6; locate 4/4 and 1 at the same point on a number line diagram.

Texas

3.3A — 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;
3.3F — represent equivalent fractions with denominators of 2, 3, 4, 6, and 8 using a variety of objects and pictorial models, including number lines;
3.3C — 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;
3.3G — 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; and

Utah

3.NF.1.a — Understand a fraction 1/b as the quantity formed by one part when a whole is partitioned into b equal parts.
3.NF.1.b — Understand a fraction a/b as the quantity formed by a parts of size 1/b. For example: 1/4 + 1/4 + 1/4 = 3/4.
3.NF.3.b — Recognize and generate simple equivalent fractions, such as 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent by using a visual fraction model, for example.
3.NF.3.a — Understand two fractions as equivalent if they are the same size, or the same point on a number line.
3.NF.3.c — Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. For example, 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.

Vermont

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.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.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.c — Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.
3.NF.A.2.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.

Virginia

3.NS.3a — Represent, name, and write a given fraction (proper or improper) or mixed number with denominators of 2, 3, 4, 5, 6, 8, and 10 using:
3.NS.3h — Represent equivalent fractions with denominators of 2, 3, 4, 5, 6, 8, or 10, using region/area models and length models.
3.NS.3 — The student will use mathematical reasoning and justification to represent and compare fractions (proper and improper) and mixed numbers with denominators of 2, 3, 4, 5, 6, 8, and 10), including those in context. Students will demonstrate the following Knowledge and Skills:
2.NS.3a — Model and describe fractions as representing equal-size parts of a whole.

Washington

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.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.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.c — Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.
3.NF.A.2.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.

Washington, D.C.

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.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 — 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.c — Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.

West Virginia

M.3.15 — 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/bas the quantity formed by a parts of size 1/b. Instructional Note: Fractions in this standard are limited to denominators of 2, 3, 4, 6, and 8.
M.3.17 — Explain equivalence of fractions in special cases and compare fractions by reasoning about their size. a. Understand two fractions as equivalent ( equal) if they are the same size or the same point on a number line. 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). c. Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers (e.g., 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). 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). Instructional Note: Fractions in this standard am limited to de~nominators of 2, 3, 4, 6, and 8.
M.3.16 — Understand a fraction as a number on the number line and 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 O locates the number 1/b on the number line (e.g., given that b parts is 4 parts, then 1/b represents¼; students partition the number line into fourths and locate 1/4 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/band that its endpoint locates the number a/b on the number line (e.g., given that a/b represents 3/4 or 6/4, students partition the number line into fourths and represent these fractions accurately on the same number line; students extend the number line to include the number of wholes required for the given fractions). Instructional Note: Fractions in this standard are limited to denominators of 2, 3, 4, 6, and 8.

Wisconsin

M.3.NF.A.1 — Understand a unit fraction as the quantity formed when a whole is partitioned into equal parts and explain that a unit fraction is one of those parts (e.g., 1/4). Understand fractions are composed of unit fractions.
M.3.NF.A.3 — Explain equivalence of fractions and compare fractions by reasoning about their size. a. Understand two fractions as equivalent (equal) if they are the same size or name the same point on a number line. b. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3) and explain why the fractions are equivalent by using a visual fraction model (e.g., tape diagram or number line). c. Express whole numbers as fractions (3 = 3/1), and recognize fractions that are equivalent to whole numbers (4/4 = 1). 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. Justify the conclusions by using a visual fraction model (e.g., tape diagram or number line) and describe the result of the comparison using words and symbols ( >, =, and < ).
M.3.NF.A.2 — Understand and represent a fraction as a number on the number line. a. Understand the whole on a number line is defined as the interval from 0 to 1 and the unit fraction is defined by partitioning the interval into equal parts (i.e., equal-sized lengths). b. Represent fractions on a number line by iterating lengths of the unit fraction from 0. Recognize that the resulting interval represents the size of the fraction and that its endpoint locates the fraction as a number on the number line.

Wyoming

3.NF.F.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.F.3.B — Recognize and generate simple equivalent fractions. Explain why the fractions are equivalent. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.
3.NF.F.3 — Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
3.NF.F.3.A — Understand two fractions as equivalent if they are the same size, or the same point on a number line.
3.NF.F.3.C — Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.