Fraction Meanings

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**1. **Fraction Meanings EDN 322

**2. ** Students should be given the opportunity to develop concepts as well as number sense with fractions and decimals.
NCTM (2000) The Principles and Standards for School Mathematics emphasize that students should be given the opportunity to develop concepts as well as number sense with fractions and decimals.
If we look at past mathematics assessments of the National Assessment of Educational Progress, we see that concepts and models underlying fractions are not well developed by grade 4. The Principles and Standards for School Mathematics emphasize that students should be given the opportunity to develop concepts as well as number sense with fractions and decimals.
If we look at past mathematics assessments of the National Assessment of Educational Progress, we see that concepts and models underlying fractions are not well developed by grade 4.

**3. **North Carolina Standard Course of Study Kindergarten 1.02 Share equally (divide) between two people; explain.
First Grade
1.04 Create, model, and solve problems that use addition, subtraction, and fair shares (between two or three).

**4. **North Carolina Standard Course of Study Second Grade
1.02 Use area or region models and set models of fractions to explore part-whole relationships in contexts.
1.03 Create, model, and solve problems that involve addition, subtraction, equal grouping, and division into halves, thirds, and fourths (record in fraction form).
Third Grade
1.05 Use area or region models and set models of fractions to explore part-whole relationships.

**5. **North Carolina Standard Course of Study Fourth Grade
1.03 Solve problems using models, diagrams, and reasoning about fractions and relationships among fractions involving halves, fourths, eighths, thirds, sixths, twelfths, fifths, tenths, hundredths, and mixed numbers.
Fifth Grade
1.02 Develop fluency in adding and subtracting non-negative rational numbers (halves, fourths, eighths; thirds, sixths, twelfths; fifths, tenths, hundredths, thousandths; mixed numbers).

**6. **Cookies to Share Does this teacher accomplish NCTM’s goal of developing concepts as well as number sense with fractions?
Are the NCTM process standards covered in this lesson?
Other observations? (use of materials, etc.)

**7. **Three Meanings of Fractions 1. Part-Whole
2. Quotient
3. Ratio Part-whole – indicates that a whole has been partitioned in so many parts. For example 2/3, a whole has been partitioned into three parts and we’re referring to two of the the three parts.
Underlying the idea of part-whole is the meaning of part and of whole. The whole is whatever is specified as the unit. Children must learn to partition the whole into equal parts, and then to describe those parts with fractional names. One good example, is to ask students if they want 1/3 or ½ of a candy bar. Students will quickly tell you ½. If the teacher has partitioned a small candy bar into halves and a large candy bar into thirds, which is the greater quantity? Knowing the whole or the unit is very important to understanding the fraction.
The fraction can be thought of as a quotient. 2 divided by 3
Ratio – We can talk about ratio of males to females in our class. We have 29 students and four of you are male. The ratio of males to females is 4 to 25. You can see this is very different conceptually, and we’ll come back to this representation on Thursday.
In the region model, the region is the whole (the unit) and the parts are congruent (same size and same shape). The region may be any shape, circle, rectangle, square, or triangle. A variety of shapes should be used when presenting the region model so children don’t always think of the fraction as “part of a pie.”
Length is modeled by any unit of length being partitioned into fractional parts with each part being equal in length. Can use a numberline to model fractions using length.
The set model uses a set of objects as a whole. This can cause confusion at first because students are not used to thinking of the unit as a set. In this room, 5/29 are male. Five things out of a set of twenty-nine are being represented.
The area model is like the region model but more sophisticated. In the area model, the parts must be equal in area but not necessarily congruent. This model is more appropriate for third grade on up.
Making fractions meaningful – Explaining all the meanings and models in order, as we’ve done is not a very effective way to teach fractions. If you are beginning to teach fractions at the conceptual level, begin with the part-whole/ the region model , then move on to other representations such as length, set and area.
Part-whole – indicates that a whole has been partitioned in so many parts. For example 2/3, a whole has been partitioned into three parts and we’re referring to two of the the three parts.
Underlying the idea of part-whole is the meaning of part and of whole. The whole is whatever is specified as the unit. Children must learn to partition the whole into equal parts, and then to describe those parts with fractional names. One good example, is to ask students if they want 1/3 or ½ of a candy bar. Students will quickly tell you ½. If the teacher has partitioned a small candy bar into halves and a large candy bar into thirds, which is the greater quantity? Knowing the whole or the unit is very important to understanding the fraction.
The fraction can be thought of as a quotient. 2 divided by 3
Ratio – We can talk about ratio of males to females in our class. We have 29 students and four of you are male. The ratio of males to females is 4 to 25. You can see this is very different conceptually, and we’ll come back to this representation on Thursday.
In the region model, the region is the whole (the unit) and the parts are congruent (same size and same shape). The region may be any shape, circle, rectangle, square, or triangle. A variety of shapes should be used when presenting the region model so children don’t always think of the fraction as “part of a pie.”
Length is modeled by any unit of length being partitioned into fractional parts with each part being equal in length. Can use a numberline to model fractions using length.
The set model uses a set of objects as a whole. This can cause confusion at first because students are not used to thinking of the unit as a set. In this room, 5/29 are male. Five things out of a set of twenty-nine are being represented.
The area model is like the region model but more sophisticated. In the area model, the parts must be equal in area but not necessarily congruent. This model is more appropriate for third grade on up.
Making fractions meaningful – Explaining all the meanings and models in order, as we’ve done is not a very effective way to teach fractions. If you are beginning to teach fractions at the conceptual level, begin with the part-whole/ the region model , then move on to other representations such as length, set and area.

**13. **What fraction of the musical instruments have strings?

**14. **What fraction of the fish have stripes?