Grade 3 · Mathematics
Quarter 2 · Week 2 · TEKS
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This Grade 3 mathematics lesson focuses on composing and decomposing fractions a/b where the numerator is greater than zero and less than or equal to the denominator, as sums of unit fractions 1/b. Students will also solve problems involving partitioning objects or sets among recipients using pictorial fraction models with denominators 2, 3, 4, 6, and 8, and represent equivalent fractions using various models including number lines. The lesson is grounded in TEKS standards and designed for direct teaching, guided practice, and reflection within the Number and Operations strand.
Students should understand basic fraction concepts, including what numerator and denominator represent, and be familiar with simple fraction notation and partitioning shapes into equal parts.
A fraction a/b represents a part of a whole divided into b equal parts, where a is the number of those parts considered. A unit fraction is a fraction with numerator 1, written as 1/b, representing one part of the whole divided into b equal parts. For example, 1/4 means one part out of four equal parts.
To compose a fraction a/b means to express it as a sum of a unit fractions 1/b added together a times. For example, 3/4 can be composed as 1/4 + 1/4 + 1/4. This shows that the fraction is made up of three parts each equal to one-fourth.
Decomposing a fraction means breaking it down into a sum of unit fractions. For example, if given 5/8, students can decompose it as 1/8 + 1/8 + 1/8 + 1/8 + 1/8. This helps students understand the fraction as multiple equal parts combined.
Pictorial models such as fraction strips, circles, or rectangles divided into equal parts help students visualize fractions. For example, shading 3 parts out of 4 equal parts on a rectangle shows 3/4. These models support composing and decomposing fractions by counting shaded unit parts.
Partitioning problems involve dividing an object or set of objects equally among recipients. For example, if 6 cookies are shared equally among 3 friends, each friend gets 2 cookies, which can be represented as 2/6 or simplified. Using pictorial fraction models helps students see how the whole is divided and shared.
Equivalent fractions are different fractions that represent the same amount. For example, 2/4 and 1/2 are equivalent. Using fraction strips or number lines, students can see that these fractions occupy the same length or area, reinforcing the concept of equivalence.
Students may think fractions with larger denominators are always larger, which is incorrect. They may also confuse numerator and denominator roles. Emphasize that the denominator shows how many equal parts the whole is divided into, and the numerator shows how many parts are considered.
Write the fraction 4/6 as a sum of unit fractions.
Since the denominator is 6, each unit fraction is 1/6. The numerator 4 tells us how many unit fractions to add. So, 4/6 = 1/6 + 1/6 + 1/6 + 1/6.
4/6 = 1/6 + 1/6 + 1/6 + 1/6
If 8 cookies are shared equally among 4 friends, what fraction of the cookies does each friend get? Represent this using a pictorial model.
Dividing 8 cookies among 4 friends means each friend gets 8 ÷ 4 = 2 cookies. The whole is 8 cookies, so each friend gets 2/8 of the cookies. Using a pictorial model, divide a rectangle into 8 equal parts and shade 2 parts for one friend.
Each friend gets 2/8 of the cookies, shown by shading 2 out of 8 parts in the pictorial model.
Show a fraction strip divided into 4 equal parts with 3 parts shaded. Ask students what fraction is shaded and how they can write it as a sum of smaller parts.
Observe the fraction strip and respond that 3 parts out of 4 are shaded, representing 3/4. Suggest that 3/4 can be written as 1/4 + 1/4 + 1/4.
This activity introduces the idea that fractions can be composed of multiple unit fractions added together, helping students visualize and understand the concept.
Provide fraction strips or circles for denominators 2, 3, 4, 6, and 8. Ask students to compose and decompose fractions like 5/8 or 2/3 using the materials.
Use fraction strips or circles to build fractions by combining unit fractions and break down given fractions into sums of unit fractions.
Hands-on use of fraction models helps students concretely understand composing and decomposing fractions as sums of unit fractions.
Demonstrate on the board how to write fractions as sums of unit fractions and solve a partitioning problem involving sharing objects among recipients using pictorial fraction models.
Watch the demonstration and practice writing fractions as sums of unit fractions and solving partitioning problems with pictorial models.
Direct instruction clarifies the process of composing and decomposing fractions and applying this understanding to solve partitioning problems.
Introduce equivalent fractions using fraction strips and number lines. Have students represent fractions like 1/2 and 2/4 and discuss their equivalence.
Use fraction strips and number lines to represent and compare fractions, identifying equivalent fractions.
Exploring equivalent fractions deepens fraction understanding and connects to composing and decomposing fractions.
Ask students to compose and decompose given fractions as sums of unit fractions and solve a partitioning problem using pictorial fraction models. Collect responses or observe explanations.
Write fractions as sums of unit fractions and solve partitioning problems with pictorial models, explaining their reasoning.
Assessment through demonstration and explanation confirms students' understanding of composing, decomposing, and applying fractions.
Use fraction strips or circles to build fractions by combining unit fractions and break down given fractions into sums of unit fractions.
Write the fraction 4/6 as a sum of unit fractions.
4/6 = 1/6 + 1/6 + 1/6 + 1/6.
If 8 cookies are shared equally among 4 friends, what fraction of the cookies does each friend get?
Each friend gets 2/8 of the cookies, shown by shading 2 out of 8 parts in the pictorial model.
Use concrete fraction strips and manipulatives to build fractions physically. Provide step-by-step guided questions to help break down fractions into unit fractions. Use visual aids and repeated examples to reinforce concepts.
Use clear, simple language and visuals to explain fraction terms. Label fraction parts with both words and numbers. Encourage students to explain their thinking using sentence frames.
Challenge students to compose and decompose fractions with larger denominators. Introduce more complex partitioning problems involving multiple recipients. Explore equivalence with improper fractions and mixed numbers.
Ask students to find examples of fractions in their home, such as slices of pizza or pieces of fruit, and describe how these fractions can be composed or decomposed into unit fractions. They can draw pictures or use objects to explain.
In this lesson, students learned to compose and decompose fractions a/b with numerator greater than zero and less than or equal to the denominator as sums of unit fractions 1/b. They practiced solving partitioning problems using pictorial fraction models and explored equivalent fractions using fraction strips and number lines. These skills build a strong foundation for understanding fractions and their relationships in real-world contexts.
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