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Cuisenaire Rods Exploration - St. Charles School - 6/22/22

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Cuisenaire Rods Exploration - St. Charles School - 6/22/22

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Why is it important for children to construct their own fraction kit rather than just purchase the ready-made version?

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Cuisenaire Rod Number Line Task - Group 4

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Cuisenaire Rod Number Line Task - Group 4

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Group4_PartitioningNumberLines_SSFS_StCharles_062222

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Cuisenaire Rod Number Line Task - Group 3

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Cuisenaire Rod Number Line Task - Group 3

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Group3_PartitioningNumberLines_SSFS_StCharles_062222

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Cuisenaire Rod Number Line Task - Group 2

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Cuisenaire Rod Number Line Task - Group 2

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Group2_PartitioningNumberLines_SSFS_StCharles_062222

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Cuisenaire Rod Number Line Task - Group 1

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Cuisenaire Rod Number Line Task - Group 1

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Group1_PartitioningNumberLines_SSFS_StCharles_062222

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How do the tools in this task, including discourse, support student understanding and sense-making?

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What challenges do fractions on a number line present to students?

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How is reasoning about fractions on a number line different than reasoning about part and whole? How are they the same?

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How did the teacher facilitate the discussion in a way that was supportive of students’ learning?

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What did the students’ strategies indicate that they knew about fractions?

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TALK MOVES: A TEACHER'S GUIDE / Video Clip 4D: Fraction Number Line

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How do sentence stems support student learning?

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How do you currently use sentence stems?

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Which 1 or 2 Talk Moves do you want to be more intentional about using?

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Which Talk Moves do you use most frequently?

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WhichIsABetterChoiceTask_SSFS_StCharles_062222

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How do the grades 4 and 5 standards connect to the grade 3 standards?

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What do the grade 3 standards mean?

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Communicating About Fractions on a Number Line

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Communicating About Fractions on a Number Line

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Cuisenaire Rod Measurement Task (GROUP 4)

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Cuisenaire Rod Measurement Task (GROUP 4)

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MeasurementTask_Group4_SSFS_StCharles_062222

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Cuisenaire Rod Measurement Task (GROUP 3)

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Cuisenaire Rod Measurement Task (GROUP 3)

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MeasurementTask_Group3_SSFS_StCharles_062222

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Cuisenaire Rod Measurement Task (GROUP 2)

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Cuisenaire Rod Measurement Task (GROUP 2)

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MeasurementTask_Group2_SSFS_StCharles_062222

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How does this experience differ from a more traditional approach to helping students understand fraction equivalency?

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What new ideas about fraction equivalency do you have as a result of engaging in this task?

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How does this measurement activity help students make sense of fraction equivalency?

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What important ideas about measurement did this task cause you to think about?

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What important ideas about fractions did this task cause you to think about?

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Cuisenaire Rod Measurement Task (GROUP 1)

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Cuisenaire Rod Measurement Task (GROUP 1)

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MeasurementTask_Group1_SSFS_StCharles_062222

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Unit of measure = Brown rod

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In your exploration, what relationships did you notice with the rods?

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Explore our Cuisenaire environment, or scroll down for some instructions.

Click to reveal a short video which explains how to use the Cuisenaire environment.

Alternatively, here are some instructions.

Click on the coloured circles to choose a Cuisenaire rod. Drag it wherever you like on the background.
You can rotate a rod by clicking to select it, then clicking on the 'Rotate' button.
You can move any rod by dragging or you can select a rod and use the arrows.

To delete a rod, drag it to the bin. You can clear all the rods by pressing the 'Clear rods' button.
You can turn the grid and labels on and off using the purple buttons.
Use the + and - buttons to zoom in and out.
You can save your table of rods and load one that you have saved using the 'Save' and 'Load' buttons.

'Prefabs' gives you a selection of ready-made arrangements.
'Activities' offers you a selection of tasks to explore.
'Collaborate' allows you to set up or join a shared table.
'Hide' moves the menu out of the way to give you more space.

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An environment which simulates working with Cuisenaire rods.

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How have you connected instruction about fractions and measurement in the past?

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GroundingReflections_MeaningsOfFractions_StCharles_062222

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Session Code:  449677
Instructor:  Katie Talbot

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What questions do you still have?

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Identify 2 actions that you plan to take related to choosing tasks for your students.

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What ideas from this session are most important to you?

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How did these experiences help you make sense of elements of these standards?

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Drag out the fraction bars you want to use when you play.

Click "Split Tiles" so that you can separate the pieces.

Use the Uniform Spinner and make sure it has 6 equal parts.

Use the pen tool to label the sections with 1/2, 1/4, 1/4, 1/8, 1/8, and 1/8.  (This will act as your fraction dice.)

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Polypad - Virtual Manipulatives - Mathigon

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Virtual manipulatives, dynamic geometry, graph plotting, data science and more: explore the ultimate mathematical playground!

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What are the aspects of understanding fractions that the fraction kit helps students to make sense of, rather than teaching by telling?

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Note: Be sure to uncheck "Show Fractions" before starting the lesson.  This will give you and students the chance to name the fractions together.

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FractionNameChart_FractionKit_SSFS_StCharles_062222

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What are key understandings that we want students to have around the standards?

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Making Sense of Fractional Values with a Fraction Kit

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Making Sense of Fractional Values with a Fraction Kit

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How does careful selection of numbers and combinations support the mathematical understanding and development of fractions?

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How might different shapes (squares or rectangles) impact students' thinking and strategies?

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What challenges might the numbers of cookies and children present for students when solving the problem?

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SharingCookies_SummaryDiscussion_StCharles_062222

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SharingCookies_Group3_StCharles_062222

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The version of the browser you are using is no longer supported. Please upgrade to a supported browser. Dismiss

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SharingCookies_Group2_StCharles_062222

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The version of the browser you are using is no longer supported. Please upgrade to a supported browser. Dismiss

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SharingCookies_Group1_StCharles_062222

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The version of the browser you are using is no longer supported. Please upgrade to a supported browser. Dismiss

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Extending Children's Mathematics: Fractions and Decimals

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Extending Children's Mathematics: Fractions and Decimals

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Innovations In Cognitively Guided Instruction

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.

Special Offer: Save 30% off our list price automatically when you buy 15 or more.

"With the collaboration of a number of dedicated teachers and their students, Susan Empson and Linda Levi have produced a volume that is faithful to the basic principles of CGI while at the same time covering new ground with insight and innovation."
-Thomas P. Carpenter

This highly anticipated follow-up volume to the landmark Fractions remain one of the key stumbling blocks in math education, and here Empson and Levi lay a foundation for understanding fractions and decimals in ways that build conceptual learning. They show 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. Just as they did in Children's Mathematics: Cognitively Guided Instruction addresses the urgent need to help teachers understand and teach fraction concepts. Children's Mathematics and Thinking Mathematically, Empson and Levi provide important insights into children's thinking and alternative approaches to solving problems. Three themes appear throughout the book:

building meaning for fractions and decimals through discussing and solving word problems

the progression of children's strategies for solving fraction word problems and equations from direct modeling through relational thinking

designing instruction that capitalizes on students' relational thinking strategies to integrate algebra into teaching and learning fractions.

With illuminating examples of student work, classroom vignettes, "Teacher Commentaries" from the field, sample problems and instructional guides provided in each chapter, you'll have all the tools you need to teach fractions and decimals with understanding and confidence.

(click any section below to continue reading)

Contents

Introduction: Issues in Learning Fractions and Decimals: Rethinking Our Approach
1. Equal Sharing Problems and Children's Strategies for Solving Them
2. From the Classroom: Getting Started with Fractions
3. Multiple Groups problems and Children's Strategies for Solving Them
4. Relational Thinking: Connecting Fractions and Algebra
5. From the Classroom: Making Relational Thinking Explicit
6. Understanding Fraction Equivalence and Order
7. Understanding Decimals
8. Understanding Operations on Fractions and Decimals
9. The Long View: Learning to Use Children's Thinking to Guide Instruction

Reviews

This book is enthusiastically recommended to my colleagues and curriculum coordinator, and it is recommended with equal enthusiasm to the readers of Mathematics Teaching in the Middle School.
--reviewer, Mathematics Teaching in the Middle School

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Extending Children's Mathematics: Fractions & Decimals

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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. Special Offer: Save 30% off our list price automatically when you buy 15 or more.

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Keep a record of the number of cookies and the number of people the cookies were shared with.

Consider where you might pause in the read aloud and what questions you might ask students when you pause.

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Read Aloud: The Doorbell Rang by Pat Hutchins

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Read Aloud: The Doorbell Rang by Pat Hutchins

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The Doorbell Rang | Division Children's Books Read Aloud – Milk and Cookies Story Time

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What experiences would teachers want to be sure to include in their instruction?

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What would children need to do to be able to show that they can demonstrate these grade-level standards?

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GroundingQuestions-Fractions_SSFS_St Charles_062222

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01 MSJP-7869_Standards for Mathematical Content Fractions 1-5 handout