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Effective Instruction in Mathematics for the Junior learner Number Sense and Numeration

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Minds On Exploring BIG IDEAS Draw as many demonstrations pictures or figures as you can of 2/5

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5 Big Ideas In the junior division students understanding of fractions become broader in their variety of meaning and representation. There are 5 Big Ideas for fractions.

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Just a part of a fraction Introduce yourself to anyone at your table you do not know In your group, make a list of the following: 3 or 4 things that might be true of nearly all of us 3 or 4 things that might be true of nearly half of us 3 or 4 things that might be true of nearly none of us. Be prepared to share

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Mathematical Principles Connecting mathematics to a real world context.

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Scavenger Hunt Using Volume 1: The Big Ideas in Number Sense and Numeration, Grades 4 to 6. Explore: What are the 5 Big Ideas The importance of learning big ideas; Characteristics of student learning as they relate to big ideas; and Instructional strategies to big ideas

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Fractions & Big Ideas Fractions can represent parts of regions, parts of sets, parts of measures, division or ratio. A fraction is not meaningful without knowing what the whole is. Renaming fractions is often the key to comparing them or computing with them. Ever fraction can be renamed in an infinite number of ways. There are multiple models and/or procedures for comparing and computing with fractions, just as there are with whole numbers. Operations with fractions have the same meanings as operations with whole numbers, even though the algorithms differ.

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Promote the belief that all students have learned some mathematics through their lived experiences in the world and that the math classroom is one where students bring that thinking to their work.

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Principles Underlying Effective Mathematics Instruction Foster Positive Mathematical Attitudes Focus on Conceptual Understanding Involve Students Actively in Their Learning Acknowledge and Utilize Students’ Prior Knowledge Provide Developmentally Appropriate Learning Tasks Respect How Each Student Learns Provide a Culture and Climate for Learning Recognize the Importance of Metacognition Focus on the Significant Mathematical Concepts (“Big Ideas”) Diversity and Effective Instruction

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To sum it up! By organizing content around KEY IDEAS, teachers can teach more effectively, but, most importantly, students can make connections between seemingly isolated topics that help them learn new mathematical ideas. There are a number of mathematical processes that can and should be developed no matter what content is being taught. Problem solving, communication, and reasoning

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e-workshop The eWorkshop site can be accessed at: http://www.eworkshop.on.ca/edu/core.cfm

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eworkshop.on.ca The eworkshop.on.ca is a portal with free access to resources specifically crafted for Ontario educators seeking to improve their skills and knowledge. Its user-friendly websites and e- learning modules, which provide comprehensive information and learning situations, cover portions of the Ontario elementary literacy and numeracy curriculum, as well as some of the Ministry of Education policies. The Learning Modules are subdivided into Literacy and Numeracy. They are further subdivided by division with respect to Primary and Junior and the units of study taught within the divisions.

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Module on Fractions The overview section on “Fractions” leads you through an introduction, the importance of the strand, Big Ideas in Number Sense and Numeracy, and “What You Will Learn”. The “Tell Me” section on “Fractions” leads you through an exercise on Fractional meanings, Fraction Quantity, and Fraction Symbols. There are sub-groupings that are further subdivided to lead you through a sub- group with the aid of informational prompts and videos.

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Module on Fractions The “Show Me” section on “Fractions” leads you through an introduction, The Lesson, and Lesson Summary. The lesson section is subdivided to address Getting Started, Working On It, and Reflecting and Connecting. The “Let Me Try” section on “Fractions” leads you through sub-sections on Introduction, Acquiring of Learning Materials, Planning Learning Activities and Learning More About Teaching Fractions. The sections are further subdivided to address specific needs for each section such as Planning template to assist in lesson preparation..

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Think about it..... In table teams. Answer the following question: “How might the use of this site improve/influence your teaching of this concept” Be prepared to share with the larger group

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References “ A Guide to Effective Instruction in Mathematics Kindergarten to Grade 6. Vol 1. Retrieved July 11, 2008 from www.eworkshop.on.ca National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. Reston, VA: Author. “ Number Sense and Numeration, Grades 4-6. Vol 1 The Big Ideas. Retrieved July 11, 2008 from www.eworkshop.on.ca “ Number Sense and Numeration, Grades 4-6. Vol 5 Fractions. Retrieved July 11, 2008 from www.eworkshop.on.ca Van De Walle, John. Elementary and Middle School Mathematics, New York, Allyn and Bacon 2000 Small, Marian. Making Math Meaningful. Toronto, Nelson Education 2008.

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