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Tuesday, August 4, 2020 | History

2 edition of Six interpretations of division with fractions found in the catalog.

Six interpretations of division with fractions

Sherri Cianca

# Six interpretations of division with fractions

## by Sherri Cianca

Published .
Written in English

Subjects:
• Division.,
• Fractions.,
• Elementary school teachers -- Training of.,
• Mathematics teachers -- Training of.

The methodology was qualitative. As the teacher/researcher, I assumed a dual role in the classroom: an unobtrusive observer of small group work and a facilitator of whole group discussions. Throughout the project, I used audio- and video recordings to capture the participants" starts, stops, and ultimate success as they untangled various concepts. Other data include the participants" pre-task and post-task journal entries, survey and interviews, observation notes and field notes.The purpose of this investigation was to construct a conceptual tool to assist teachers in the understanding and teaching of division with fractions. To that end, this research investigated the concepts underpinning a robust comprehension of this domain. Also investigated were the processes one group of students used to determine those concepts. The participants were seven prospective elementary teachers enrolled in my math methods course, and me, the teacher/researcher. The study records, in our voices, the concepts and processes the participants constructed as they gained conceptual knowledge of division with fractions.This study provides an in-depth analysis of six interpretations for division with fractions: three interpretations found in the literature, a third briefly mentioned in the literature, two interpretations from my prior research in the field, and one additional interpretation that emerged from the study. I created a conceptual taxonomy to highlight common meanings across interpretations and to distinguish intrinsic differences among interpretations. In addition to the taxonomy, terms found in the literature are articulated, expanded, and applied to the learning process. Some terms not found in the literature, or found to be vague, were constructed to help the participants better communicate implicit understandings. Rich vignettes, diagrams, and authentic word problems report participants" interactions, capturing in detail how their knowledge developed. As a result, these findings may serve as a tool for teachers: a tool to discern the misconceptions of struggling students, to use when planning instruction, and a tool to further both their own learning and the learning of their students.

Edition Notes

The Physical Object ID Numbers Statement by Sherri Cianca. Pagination 239 leaves. Number of Pages 239 Open Library OL20762828M ISBN 10 9780494157671

Example of division of fractions. Let’s take a look at how to solve the following division using mathematical compression: Since division is the inverse operation to multiplication, we have to find a fraction that, when multiplied by 7 / 5 gives us a result of 2 / . Student Book pages 52 - 57 Apply and extend previous understandings of multiplication and division to divide fractions by fractions. TNS.A.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the.

Gary Davis and Catherine Pearn have written a wonderful pdf e-book: Division Of Fractions: A guide for elementary and middle school teachers; Mr. Koh from Whitecorp (whose comment originally launched this post) shared this link in the comments below, but I want to make sure every reader has the chance to see it. Worksheets > Math > Grade 6 > Fractions: multiply/divide > Mixed numbers by fractions. Math worksheets: Dividing mixed numbers by fractions (whole number quotients) Below are six versions of our grade 6 math worksheet on dividing mixed numbers by fractions. All answers are whole numbers. These worksheets are pdf files.. Similar.

Grade Level: 6 Learning Competency: Rational Numbers – Division of Fractions DIVISION OF FRACTIONS: WHOLE NUMBERS BY FRACTIONS This episode discusses the division of whole numbers by fractions. This book lays a foundation for the conceptual understanding fractions and decimals. It shows how the same kinds of intuitive knowledge and sense making that provides the basis for children’s learning of whole number arithmetic can be extended to fractions and decimals.

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### Six interpretations of division with fractions by Sherri Cianca Download PDF EPUB FB2

The Book of Fractions The graphical representation of a fraction 6 F Draw a diagram to show each fraction (use the images on the bottom of this page): 1. A fraction represents a part of a whole. Example 1. The whole is divided into four equal parts. Three part are taken (considered).

A corresponding graphical representation (diagram) is File Size: KB. devoid of context, you cannot determine which interpretation of the fraction is intended.

The various interpretations are needed, however, in order to make sense of fraction problems and situations. Fractions as parts of wholes or part of sets.

One meaning of fraction is as a part of a Size: KB. Division with Unit Fractions will help students practice this key fifth grade skill. See in a Guided Lesson. Grade. 5th grade.

Subject. Math Fractions Multiplying and Dividing Fractions Division with Unit Fractions View aligned standards. 6. Multiplication and Division of Fractions. Recall the following fraction facts: Multiplying fractions. When multiplying by a fraction, multiply numerators and multiply denominators: 2/3xx 5/7=(2xx5)/(3xx7)=10/21 If you can, simplify first.

In this example. This understanding will help the students work through word problems and it gives me a good idea who understands the meaning of division with fractions. Previous Lesson. Next Lesson.

Related Lessons. Whole Numbers Divided by Fractions Using Models. 6th Grade Math» Division with Fractions. Carla : Michelle Schade. Fractions are a part of many second through fifth grade classrooms. These 20 free fraction games, fraction worksheets, activities and resources will help simplify your lesson planning.

There are a range on ideas you can adapt for dividing fractions, equivalent fractions and even simplifying fractions. Manipulative Fractions - Here's a great lesson using manipulatives to. 1 day ago  We can extend this meaning of a fraction as a division to fractions whose numerators and denominators are not whole numbers.

2- Simplifying Algebraic. lesson, with one Study Guide and Intervention and Practice worksheet for every lesson in Glencoe Math Connects, Course 3.

6 Example 4 Find 8 ÷ 2 1 —. (answer key) 6. The numerator (8) is less than the denominator (9), so this fraction is a proper fraction. The numerator (20) is less than the denominator (23), so this fraction is a proper fraction.

The numerator (75) is greater than the denominator (51), so this fraction is an improper fraction. Rewrite each of the following fractions as a whole number. Measurement Interpretation and How it Relates to Division of Fractions: Savannah has 1/2 yard of fabric to make placemats for her dining room table.

She. 6 or 6 So, the fraction 5 30 is really the whole number 6. Notice that a whole number can always be written as a fraction with a denominator of 1.

e.g. 10 = 1 10 3. Mixed Numbers A mixed number is a combination of a whole number and a common fraction. e.g. 2 5 3 (two and three-fifths) 27 9 2 (twenty-seven and two-ninths) 9 6 3 = 9 2 1 (always.

For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷.

So another way of thinking about it is that 8/3 divided by 1/3 is the same thing as 8/3 times 3. And we could either write it like this. We could write times 3 like that. Or, if we want to write 3 as a fraction, we know that 3 is the same thing as 3/1. And we already know how to multiply fractions.

Multiply the numerators. 8 times 3. Fractions as Division CCSS Math NFB.3 asks students to interpret fractions as division of the numerator by the denominator. This activity helps students to work with that idea.

Students will find this center area engaging as they match improper fractions to their equal mixed number. In this fraction division activity, 7th graders find the reciprocals for the first twelve problems.

In this second set, students find the quotient for each fraction division problem. Math in English Skills VIII Exercise Book For Students 3rd - 6th. For some learners, fractions are the bane of fifth- and sixth-grade existence. Use this. Adaptations and updates to IM 6–8 Math are copyright by Illustrative Mathematics, and are licensed under the Creative Commons Attribution International License (CC BY ).

Adaptations to add additional English language learner supports are copyright by Open Up Resources, and are licensed under the Creative Commons Attribution. 6th grade multiplication and division worksheets, including multiplying in parts, multiplying in columns, division with remainders, long division and missing factor, divisor or.

On right, On right, Tyler's diagram and equation. 6 equal parts labeled 2. Total, Equation 6 times blank = How do you think Clare and Tyler thought about $$12\div 6$$.

Explain what each diagram and the parts of each equation could mean about the situation with the bags of almonds. Make sure to include the meaning of the missing number. Fractions as division Anyone who has studied secondary school mathematics would probably be comfortable with the convention of ' a over b ' meaning ' a divided by b '.

That is, $$\frac{a}{b}$$ = a ÷ b. The fraction symbol here can be interpreted as division. And looking at this diagram right here, it made complete sense. If you started with 3 wholes, and you want to divide it into 4 equal groups, one group, two groups, three groups, four groups, each group is going to have 3/4 in it.

The most sophisticated part of the study of fractions occurs naturally in grades 6 and 7, where the concept of fraction division is fully explained. Division is the foundation on which the concepts of percent, ratio, and rate are built. Needless to say, it is the latter concepts that play a dominant role in applications.

The discus. Fractions domain, to multiply and divide fractions. Key developments in grade 5 include connecting fractions to division (B.3), multiplying a whole number or a fraction by a fraction (B.4), and understanding multiplication as scaling (B.5) in preparation for ratios and proportional relationships, which is introduced in grade 6.Fractions are divisions (5th grade math) We study the concept that a whole-number division problem, such as 21 ÷ 5, can be solved by writing it as a fraction.

In other words, the answer to 21 ÷ 5 IS the fraction 21/5. I justify that by solving a few division problems with the help of a visual model.Section 2. Multiple Interpretations of Fractions Clarke and Roche () encourage educators to place a greater emphasis on the various meanings of fractions during instruction in order to improve students’ understanding of fraction.

Within North American education, fraction learning is.