Assembling Fractions

Ages 7–10 · 8 minutes · Math

Combine fractions and know-how to build something incredible!

In this fractions lesson, students will learn and practice:

- Adding fractions with common denominators
- Visualizing fraction addition

Part of

Intro to Fractions

Standards alignment

Common Core State Standards

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 — Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
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

MA19.4.15 — Model and justify decompositions of fractions and explain addition and subtraction of fractions as joining or separating parts referring to the same whole.
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.
MA19.4.15c — Solve word problems involving addition and subtraction of fractions and mixed numbers having like denominators, using drawings, visual fraction models, and equations to represent the problem.

Alaska

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

Arizona

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.

Arkansas

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
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
4.CAR.9 — Solve real-world problems involving the addition and subtraction of fractions; include mixed numbers with like denominators, using visual fraction models or equations. • Fractions include: denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100

California

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.

Colorado

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 — Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
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.

Connecticut

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

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.

Florida

MA.4.FR.2.2 — Add and subtract fractions with like denominators, including mixed numbers and fractions greater than one, with procedural reliability.
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.4.AR.1.2 — Solve real-world problems involving addition and subtraction of fractions with like denominators, including mixed numbers and fractions greater than one.
MA.3.FR.1.3 — Read and write fractions, including fractions greater than one, using standard form, numeral-word form and word form.

Georgia

4.NR.4.6 — Add and subtract fractions and mixed numbers with like denominators using a variety of tools.
4.NR.4 — Solve real-life problems involving addition, subtraction, equivalence, and comparison of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100 using part-whole strategies and visual models.
4.NR.4.4 — Represent whole numbers and fractions as the sum of unit fractions.

Hawaii

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

Idaho

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, including mixed numbers, with the same denominator. Justify the conclusions using a visual fraction model and/or verbal reasoning.
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

Illinois

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.

Indiana

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.CA.8 — Solve real-world problems involving addition and subtraction of fractions referring to the same whole and having common denominators (e.g., by using visual fraction models and equations to represent the problem). (E)

Iowa

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$.
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, by using visual fraction models and or equations to represent the problem.

Kansas

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

Kentucky

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.3.d — Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators.

Louisiana

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

Maine

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

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.

Massachusetts

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.

Michigan

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 — Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
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.

Minnesota

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.

Mississippi

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.

Missouri

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.

Montana

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 within cultural contexts, including those of Montana American Indians, 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.

Nebraska

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.3.c — 4.N.3.d 4.N.3.e Add and subtract fractions and mixed numbers with like denominators. Solve authentic problems involving addition and subtraction of fractions and mixed numbers with like denominators. Multiply a fraction by a whole number using visual fraction models and properties of operations.
4.N.3 — Operations with Fractions: Students will understand and demonstrate fractional computation.
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.

Nevada

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 — Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
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 Hampshire

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 Jersey

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.

New Mexico

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-4.NF.3.a — Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
NY-4.NF.3 — Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
NY-4.NF.3.d — Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators.

North Carolina

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.
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

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.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).

Ohio

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.

Oklahoma

4.N.3.5 — Use models to add and subtract fractions with like denominators.
3.N.3.3 — Apply understanding of unit fractions and use this understanding to compose and decompose fractions related to the same whole.
3.N.3.1 — Read and write fractions with words and symbols using appropriate terminology (i.e., numerator and denominator).

Oregon

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.1 — Understand the concept of a unit fraction and explain how multiple copies of a unit fraction form a non-unit fraction.

Pennsylvania

CC.2.1.4.C.2 — Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

Rhode Island

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

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

4.NF.B.3.a — Add and subtract of fractions e.g., joining and separating parts referring to the same whole.
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.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.

Tennessee

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 — 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.d — Solve contextual problems involving addition and subtraction of fractions referring to the same whole and having like denominators.

Texas

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;
4.3A — represent a fraction a/b as a sum of fractions 1/b, where a and b are whole numbers and b>0, including when a>b;
3.3D — 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;

Utah

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.
4.NF.3.a — Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
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.d — Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, for example, by using visual fraction models and equations to represent the problem.

Vermont

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.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.
4.CE.3 — The student will estimate, represent, solve, and justify solutions to single-step problems, including those in context, using addition and subtraction of fractions (proper, improper, and mixed numbers with like denominators of 2, 3, 4, 5, 6, 8, 10, and 12), with and without models; and solve single-step contextual problems involving multiplication of a whole number (12 or less) and a unit fraction, with models. Students will demonstrate the following Knowledge and Skills:
4.CE.3a — Estimate and determine the sum or difference of two fractions (proper or improper) and/or mixed numbers, having like denominators limited to 2, 3, 4, 5, 6, 8, 10, and 12 (e.g., 3/8 + 3/8 , 21/5 + 4/5 , 7/4 - 5/4 ) and simplify the resulting fraction. Addition and subtraction with fractions may include regrouping.*
3.NS.3b — Identify a fraction represented by a model as the sum of unit fractions.
4.CE.3b — Estimate, represent, solve, and justify solutions to single-step contextual problems using addition and subtraction with fractions (proper or improper) and/or mixed numbers, having like denominators limited to 2, 3, 4, 5, 6, 8, 10, and 12, and simplify the resulting fraction. Addition and subtraction with fractions may include regrouping.

Washington

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 — Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
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.

Washington, D.C.

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.

West Virginia

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.3.15 — 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.

Wisconsin

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.
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.

Wyoming

4.NF.G.3 — Understand a fraction a/b with a > 1 as a sum of unit fractions (1/b).
4.NF.G.3.A — Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
4.NF.G — Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers (limited to denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100).
4.NF.G.3.D — Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators.