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# Exploring Fractions

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• We see and talk about fractions everyday. We may say that we need a half a dozen eggs or please cut me a piece of the pie. Mom can I please get those new shoes…they are half price!Gas has gone up to \$102.9! Learning about fractions extends students’ understanding of our numeration system. While whole numbers represent quantities of whole units, fractions signify parts of whole units or parts of sets.Instruction should emphasize the meaning of fractions before any abstract rules are introduced. Meaningful concepts are developed when students represent fraction quantities in various contexts, using a variety of materials. Through these experiences, students learn to see fractions as useful and helpful numbers.
• Learning about fractions extends students’ understanding of our numeration system. While whole numbers represent quantities of whole units, fractions signify parts of whole units or parts of sets.Instruction should emphasize the meaning of fractions before any abstract rules are introduced. Meaningful concepts are developed when students represent fraction quantities in various contexts, using a variety of materials. Through these experiences, students learn to see fractions as useful and helpful numbers. Using the materials in front of you, make a fraction and talk to your partner what the numerator and denominator represent.How could you use the number line to explain one whole . What would the spaces represent inbetween the numbers on a number line.
• Students need to understand that for any particular fractional part:the whole is composed of the appropriate number of parts (e.g., for &quot;thirds&quot;, the whole is made up of three parts)each part is equal in size.Examples and Non-ExamplesTo help students understand key ideas about fractions as parts of a whole, display some examples and non-examples of fractional parts. The following shapes are divided into parts. Which parts are fifths? Why are the parts fifths?
• Tangram activity
• A numerical benchmark refers to a number to which other numbers can be related. For example, 100 is a whole number benchmark to which students can compare other numbers (e.g., 98 is a little less than 100, 52 is about one half of 100, 205 is a little more than 2 hundreds).Relating fractions less than 1 to the benchmarks of 0, 1/2, and 1 helps to provide a sense of their relative size. Students should learn to recognize that fractions such as 1/8 and 2/12 represent small quantities, and are close to 0 because there are few fractional parts compared to the whole. On the other hand, fractions such as 7/8 and 10/12 are close to 1 (the whole). Since 1/2 is a common fraction (the first fraction children learn), it is sometimes helpful to relate other fractions to 1/2 in order to describe their size (e.g., 2/5 is close to 1/2).As you explore fractions ask students is this fraction more or less than one half?Fraction models such as fraction circles and fraction strips can be used to demonstrate the proximity of fractions to the benchmarks of 0, 1/2, and 1.As students’ ability to conceptualize the size of fractions grows, they will be able to use reasoning to think about the proximity of fractions to the benchmarks.Relating Fractions to Benchmarks.
• ½ is another name for 2/4 since the same part of the whole is represented in both fractions.
• In the primary grades, students develop a sense of whole number quantities, initially of numbers less than 10, and later, of multi-digit numbers. Instruction in the junior grades needs to help students further develop their sense of number quantity, by exploring the “howmuchness” of fractions through concrete materials and diagrams. While many students gain an understanding of one half through everyday experiences, they may be unsure of quantities represented by other fractions.Learning activities that involve students in modeling fractions, exploring part-whole relationships, and relating fractions to the benchmarks of 0, 1/2, and 1 help them understand fraction quantities.
• Model : Counting and Trading ActivitiesWhen students count fourths and fifths, as they did in the video, they learn that:four fourths make one whole, and five fifths also make one wholefourths are larger than fifths because it takes fewer fourths than fifths to make one whole.Learning activities should include opportunities to count fractional quantities greater than one whole. This gives students experience in representing improper fractions concretely and allows them to observe the relationship between improper fractions and the whole.
• IntroductionLet’s look at a lesson based on a problem in which different numbers of pizzas need to be shared equally by different-sized groups of campers. The lesson highlights several fraction concepts:a whole can be divided into different-sized partsthe size of different fractional parts can be compareddivision can involve partitioning quantities into fractional parts.The lesson demonstrates how to introduce students to the problem-solving task, how to engage them in the problem, and how to help them reflect on what they have learned.The LessonThe problem-solving lesson featured in the video clips has three sections:Getting Started – The teacher explains the problem and prepares the students for the problem-solving activity.Working on It – The teacher provides an opportunity for the students to solve the problem. During this stage of the lesson, the teacher observes the students as they work, and poses questions that help the students clarify their thinking.Reflecting and Connecting – To conclude the lesson, the teacher asks the students to explain how they solved the problem. The teacher encourages the students to think about and share what they learned through the problem-solving activity.
• ### Exploring Fractions

1. 1. Exploring Fractions<br />Susan Muir <br />K-4 Math Coach<br />January 29th , 2010<br />
2. 2. Discuss with your elbow partner, instances in your professional life where “one half” has significance.<br />Instructional Strategies: Accessing Prior Knowledge through Connections<br /> The Meaning of One Half<br />
3. 3. <ul><li>What is a Fraction?
4. 4. Fraction Principles- Exploration and Discussion
5. 5. Fraction Quantity
6. 6. Exploring Part-Whole Relationships
7. 7. Let’s Experience a Problem
8. 8. Where Do I Go From Here?</li></ul>Agenda<br />
9. 9. Fractions are used frequently in real life situations.<br />Fractions are all Around Us<br />
10. 10. 1.A fraction has a numerator and a denominator.<br /><ul><li>The denominator tells the total number of equal parts in a whole, and the numerator tells the number of parts accounted for.</li></ul> Fraction of a Set<br />3 of the 4 balls are soccer balls.3/4 are soccer balls.<br />Fraction Principles<br />
11. 11. 2.You have to know what the whole is to say what the fraction is.<br /><ul><li>Fractions represent parts of the whole.
12. 12. As the whole changes, so does the fraction.</li></ul>Fraction Principles<br />
13. 13. 3. The equal parts into which the whole is divided are equal but do not have to be identical.<br />4. Fraction parts do not have to be adjacent.<br />Fraction Principles<br />
14. 14. 5. The parts of a set or group do not have to be identical.<br />6. If the numerator and denominator of a fraction are equal, the fraction represents one whole, or 1. Therefore the whole number can be represented as fractions.<br /><ul><li>2/2, 3/3, 4/4, and so on.</li></ul>Fraction Principles<br />
15. 15. 7. Fractions have more than one name.<br />8. Fractions with a numerator greater than their denominator are greater than 1.<br /><ul><li>7/4 is greater than 1</li></ul>Fraction Principles<br />
16. 16. Fraction Quantity<br />Area Models<br />Set Models<br />Linear Models<br />
17. 17. Exploring Part Whole Relationships<br />Counting Activities<br />Trading Activities<br />Find the Whole/Part/Fraction<br />
18. 18. Three Part Lesson Model<br /><ul><li>Before- Gains Background Knowledge
19. 19. During-Explore Activity
20. 20. After- Show and Share/ Connect and Reflect</li></ul> Let’s Experience a Problem<br />
21. 21. <ul><li>Learning Materials</li></ul>http://hoodamath.com/games/fractioneaters.php<br />fraction game<br />http://nces.ed.gov/nceskids/createagraph/<br />graph maker<br />http://themathworksheetsite.com/numline.html<br />Number line generator<br />http://www.mrnussbaum.com/tonyfraction.htm<br />Pizza Shop ( Michelle Morley’s Website)<br />http://www.curriculumsupport.education.nsw.gov.au/secondary/mathematics/years7_10/teaching/frac.htm<br />Fraction website with printable resources- using pattern blocks to teach fractions<br /><ul><li>http://www.eworkshop.on.ca/edu/core.cfm
22. 22. Ontario Online Teaching Resource
23. 23. Planning Outcome-based Lessons
24. 24. Learning More About Teaching Fractions</li></ul> Workshop Wednesdays<br /> Where Do I Go From Here?<br />