Fraction Picking

Ages 7–9 · 8 minutes · Math

Grab a snack and practice with fractions greater than 1!

In this fractions lesson, students will learn and practice:

- Working with fractions greater than 1
- Using mixed fraction notation
- Adding basic fractions

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.
4.NF.B.3 — Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
4.NF.B.3.a — Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
4.NF.B.3.d — Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

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.
MA19.4.14 — Compare two fractions with different numerators and different denominators using concrete models, benchmarks (0, 1/2, 1), common denominators, and/or common numerators, recording the comparisons with symbols >, =, or <, and justifying the conclusions.
MA19.4.15b — Add and subtract fractions and mixed numbers with like denominators using fraction equivalence, properties of operations, and the relationship between addition and subtraction.
MA19.4.16a — Model and explain how a non-unit fraction can be represented by a whole number times the unit fraction.

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)
4.NF.3 — Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
4.NF.3.a — Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
4.NF.3.d — Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators (e.g., by using visual fraction models and equations to represent the problem).
3.NF.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).

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.
4.NF.B.3 * — Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
3.NF.A.3.d — Compare two fractions with the same numerator or the same denominator by reasoning about their size. Understand that comparisons are valid only when the two fractions refer to the same whole. Record results of comparisons with the symbols >, =, or < , and justify conclusions.
4.NF.B.3.a — Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

Arkansas

3.NPV.10 — Decompose and compose a non-unit fraction 𝑎/𝑏 as the quantity formed by the sum of unit fractions. • 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
4.NPV.7 — Decompose fractions, including fractions greater than one and mixed numbers, into unit fractions, using concrete models, drawings, and/or the number line. • Fractions include denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
3.NPV.5 — Compare two fractions with the same numerator or denominator by reasoning about their size based on the same whole; use symbols (<, =, >) and justify the conclusion using visual fraction models, concrete objects, or words.
4.CAR.5 — Add and subtract fractions, including mixed numbers, with like denominators, using visual fraction models and equations. • Fractions include: denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100

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.
4.NF.B.3 — Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
4.NF.B.3.a — Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
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.

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.
4.NF.B.3 — Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
4.NF.B.3.a — Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
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.

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.
4.NF.B.3 — Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
4.NF.B.3.a — Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
4.NF.B.3.d — Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

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.
4.NF.B.3 — Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
4.NF.B.3.a — Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
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.

Florida

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.
MA.3.FR.2.1 — Plot, order and compare fractional numbers with the same numerator or the same denominator.

Georgia

3.NR.4.3 — Represent fractions, including fractions greater than one, in multiple ways.
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.4.1 — 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.
4.NR.4.6 — Add and subtract fractions and mixed numbers with like denominators using a variety of tools.

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.
4.NF.B.3 — Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
4.NF.B.3a — Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
3.NF.A.3d — 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.

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.d — Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize the comparisons are valid only when the two fractions refer to the same whole. Record the results of the comparisons with the symbols >, = , and <, and justify the conclusion using visual representations and/or verbal reasoning.
4.NF.B.3 — Understand a fraction a/b with a > 1 as a sum of fractions 1/b
4.NF.B.3.a — Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

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.
4.NF.B.3 — Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
4.NF.B.3.a — Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
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.

Indiana

4.NS.2 — Model mixed numbers and improper fractions using visual fraction models such as number lines and area models. Use a visual fraction model to show the equivalency between whole numbers and whole numbers as fractions.
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)
4.CA.6 — Add and subtract fractions with common denominators using visual fraction models. Decompose non-unit fractions to represent them as iterations of unit fractions. (E)
4.NS.4 — Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark, such as 0, 1/2, and 1). Explain why comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols > , = , or < , and justify the conclusions (e.g., by using a visual fraction model). (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 .
4.NF.B.3 — Understand a fraction a/b with a > 1 as a sum of fractions 1/b. For example, 3/4 = 1/4 + 1/4 + 1/4$.
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 conclusion. For example, by using a visual fraction model.
4.NF.B.3.a — Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

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.
4.NF.3 — Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
4.NF.3.a — Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
4.NF.3.d — Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g. by using visual fraction models and equations to represent the problem.
3.NF.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 relational symbols > , < , = , or ≠ , and justify the conclusions, (e.g. by using a visual fraction model.)

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.4.NF.3 — Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
KY.4.NF.3.a — Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
KY.4.NF.4.a — Understand a fraction a/b as a multiple of 1/b.

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.
4.NF.B.3 — Understand a fraction a/b with a > 1 as a sum of fractions 1/b. (Denominators are limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100.)
4.NF.B.3.a — Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
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.

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.
4.NF.B.3 — Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
4.NF.B.3a — Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
4.NF.B.3d — Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

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.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.
4.NF.B.3.a — Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

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.
4.NF.B.3 — Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
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.
4.NF.B.3.a — Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. (The whole can be a set of objects.)

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.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.
4.NF.B.3 — Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
4.NF.B.3.a — Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

Minnesota

4.1.2.2 — Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. For example: Locate 5/3 and 1 3/4 on a number line and give a comparison statement about these two fractions, such as " 5/3 is less than 1 3/4."
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).
4.1.2.3 — Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators.
5.1.2.4 — Recognize and generate equivalent decimals, fractions, mixed numbers and improper fractions in various contexts. For example: When comparing 1.5 and 19/12 , note that 1.5 = 1 1/2 = 1 6/12 = 18/12, so 1.5 < 19/12.

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.
4.NF.3 — Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
4.NF.3.a — Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
3.NF.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.

Missouri

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.2.a — Describe the numerator as representing the number of pieces being considered.
3.NF.A.2.b — Describe the denominator as the number of pieces that make the whole.
4.NF.B.4 — Understand addition and subtraction of fractions as joining/composing and separating/decomposing parts referring to the same whole.
4.NF.B.6 — Solve problems involving adding and subtracting fractions and mixed numbers with like denominators.
3.NF.A.6 — Compare two fractions with the same numerator or denominator using the symbols > , = or < , and justify the solution.

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.
4.NF.B.3 — Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
4.NF.B.3.a — Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
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.

Nebraska

4.N.2.a — Explain and demonstrate how a mixed number is equivalent to a fraction greater than one and how a fraction greater than one is equivalent to a mixed number using visual fraction models and reasoning strategies.
3.N.2.f — Compare and order fractions having the same numerators or denominators by reasoning about their size.
4.N.3.b — Explain the meaning of addition and subtraction of fractions with like denominators using visual fraction models, properties of operations, and reasoning strategies.
4.N.2.c — Compare and order fractions having unlike numerators or denominators using number lines, benchmarks, reasoning strategies, and/or equivalence.

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.
4.NF.B.3 — Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
4.NF.B.3.a — Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
4.NF.B.3.b — Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model.

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.
4.NF.B.3 — Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
4.NF.B.3.a — Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
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.

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.
4.NF.B.3 — Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
4.NF.B.3a — Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
3.NF.A.3d — 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.
4.NF.B.3d — Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

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.
4.NF.B.3 — Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
4.NF.B.3.a — Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
4.NF.B.3.d — Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

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-4.NF.3 — Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
NY-4.NF.3.a — Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
NY-3.NF.3.d — Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons rely on the two fractions referring to the same whole. Record the results of comparisons with the symbols >, =, or < , and justify the conclusions.

North Carolina

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.
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.4 — Compare two fractions with the same numerator or the same denominator by reasoning about their size, using area and length models, and using the > , < , and = symbols. Recognize that comparisons are valid only when the two fractions refer to the same whole with denominators: halves, fourths and eighths; thirds and sixths.
NC.4.NF.3 — Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. • Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. • Decompose a fraction into a sum of unit fractions and a sum of fractions with the same denominator in more than one way using area models, length models, and equations. • Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. • Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem.

North Dakota

4.NO.NF.2 — Explain and demonstrate how a mixed number is equivalent to a fraction greater than one and how a fraction greater than one is equal to a mixed number using visual fraction models and reasoning strategies (proper and improper fractions limited to denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100).
4.NO.NF.6 — Solve authentic word problems by adding and subtracting fractions and mixed numbers with like denominators (proper and improper fractions limited to denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100).
4.NO.NF.5 — Compare and order fractions having, unlike numerators or denominators. Record comparisons using the symbols >, < and =. Justify using a visual fraction model (proper and improper fractions limited to denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100).

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.
4.NF.3 — Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
4.NF.3.a — Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
3.NF.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.
4.NF.3.d — Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

Oklahoma

3.N.3.1 — Read and write fractions with words and symbols using appropriate terminology (i.e., numerator and denominator).
4.N.3.3 — Use models to order and compare whole numbers and fractions less than and greater than one, using comparative language and symbols.
3.N.3.3 — Apply understanding of unit fractions and use this understanding to compose and decompose fractions related to the same whole.
4.N.3.5 — Use models to add and subtract fractions with like denominators.
3.N.3.2 — Model fractions using length, set, and area for halves, thirds, fourths, sixths, and eighths.

Oregon

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.
4.NF.B.3 — Understand a fraction (a/b) as the sum (a) of fractions of the same denominator (1/b). Solve problems in authentic contexts involving addition and subtraction of fractions referring to the same whole and having like denominators.
3.NF.A.3 — Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

Pennsylvania

CC.2.1.3.C.1 — Explore and develop an understanding of fractions as numbers.
CC.2.1.4.C.2 — Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
CC.2.1.4.C.1 — Extend the understanding of fractions to show equivalence and ordering.

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.
4.NF.B.3 — Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
4.NF.B.3.a — Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. (The whole can be a set of objects).
4.NF.B.3.d — Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using drawings or visual fraction models and equations to represent the problem.

South Carolina

3.NSF.3 — Develop an understanding of mixed numbers (i.e., denominators 2, 3, 4, 6, 8, 10) as iterations of unit fractions on a number line.
4.NSF.3 — Develop an understanding of addition and subtraction of fractions (i.e., denominators 2, 3, 4, 5, 6, 8, 10, 12, 25, 100) based on unit fractions.

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).
4.NF.B.3 — Understand a fraction a/b with a > 1 as a sum of fractions 1/b. For example, 4/5 = 1/5 + 1/5 + 1/5 + 1/5.
4.NF.B.3.a — Add and subtract of fractions e.g., joining and separating parts referring to the same whole.
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.

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.
4.NF.B.3 — Understand a fraction a/b with a > 1 as a sum of fractions 1/b. For example, 4/5 = 1/5 +1/5 + 1/5 + 1/5.
4.NF.B.3.a — Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
4.NF.B.3.d — Solve contextual problems involving addition and subtraction of fractions referring to the same whole and having like denominators.
4.NF.A.2 — Compare two fractions with different numerators and different denominators by creating common denominators or common numerators or by comparing to a benchmark such as 0 or 1/2 or 1. Recognize that comparisons are valid only when the two fractions refer to the same whole. Use the symbols > , = , or < to show the relationship and justify the conclusions.

Texas

2.3C — use concrete models to count fractional parts beyond one whole using words and recognize how many parts it takes to equal one whole; and
3.3H — 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.
4.3E — represent and solve addition and subtraction of fractions with equal denominators using objects and pictorial models that build to the number line and properties of operations;

Utah

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.
4.NF.3 — Understand a fraction a/b with a >1 as a sum of fractions 1/b. In other words, any fraction is a sum of unit fractions.
3.NF.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, for example, by using a visual fraction model.
4.NF.3.a — Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

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.
4.NF.B.3 — Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
4.NF.B.3.a — Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
4.NF.B.3.d — Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

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.3c — Use a model of a fraction greater than one to count the fractional parts to name and write it as an improper fraction and as a mixed number (e.g., 1/4, 2/4, 3/4, 4/4, 5/4 = 1 1/4 ).
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:
3.NS.3d — Compose and decompose fractions (proper and improper) with denominators of 2, 3, 4, 5, 6, 8, and 10 in multiple ways (e.g., 7/4 = 4/4 + 3/4 or 4/6 = 3/6 + 1/6 = 2/6 + 2/6 ) with models.

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.
4.NF.B.3 — Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
4.NF.B.3.a — Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
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.

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.
4.NF.B.3 — Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
4.NF.B.3.a — Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

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.4.14 — Understand the fraction a/b, with a> 1, as the sum of a of the fractions 1/b. a. Add and subtract fractions with like denominators. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions by using a visual fraction model (e.g., 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8). c. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction greater than one and/or by using properties of operations and the relationship between addition and subtraction. Identify the two whole numbers a mixed number is between. d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem.
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.

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.4.NF.B.3 — Understand composing and decomposing fractions. a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. b. Decompose a fraction into a sum of unit fractions and/or multiples of that unit fraction in more than one way, recording each decomposition by an equation. Justify decompositions with explanations, visual fraction models, or equations. For example: 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. c. Add and subtract fractions, including mixed numbers, with like denominators (e.g., 3/8 + 2/8) and related denominators (e.g., 1/2 +1/4, 1/3 + 1/6) by using visual fraction models (e.g., tape diagrams and number lines), properties of operations, and the relationship between addition and subtraction. d. Solve word problems involving addition and subtraction of fractions with like and related denominators, including mixed numbers, by using visual fraction models and equations to represent the problem. Students are not required to rename fractions in lowest terms nor use least common denominators.

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.
4.NF.G.3 — Understand a fraction a/b with a > 1 as a sum of unit fractions (1/b).
3.NF.F — Develop understanding of fractions as numbers. (Limited to denominators 2, 3, 4, 6, and 8) * use horizontal fractions.
4.NF.G.3.A — Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
3.NF.F.3.D — Compare two fractions with the same numerator or the same denominator, by reasoning about their size, Recognize that valid comparisons rely on the two fractions referring to the same whole. Record the results of comparisons with the symbols > , = , or < , and justify the conclusions.