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Algebraic Thinking Relational Thinking. Develop an understanding of the concept of relational thinking. Consider how to encourage students to develop and engage in relational thinking. Develop an understanding of the basic properties of number operations . Outcomes: .

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## Algebraic Thinking Relational Thinking

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**Develop an understanding of the concept of relational**thinking. • Consider how to encourage students to develop and engage in relational thinking. • Develop an understanding of the basic properties of number operations Outcomes:**Share in small group what you observed and discussed with**your students using true/false number sentences. Share T/F Number Talks:**Talk about teacher decisions**• Why were certain number sentences particularly good? • What number sentences might you have added to help out? • How does the sequence build understanding? Understanding EqualityVideo 1.5**Literature in math**• http://sdcounts.tie.wikispaces.net/Thinking+Mathematically+-+Integrating+Arithmetic+and+Algebra • Pan Balances at Illuminations • http://illuminations.nctm.org/activitydetail.aspx?id=33 Equal Shmequal**More of Heidi’s Developing Number Sense and Relational**Thinking Article • What is the difference between calculating an answer on both sides of the equation and looking for the relation between the numbers and not finding the solutions? Define relational thinking**Introduction to Relational Thinking**• Find 3 ways to solve these problems • Think beyond arithmetic • Think about relationships of numbers Define relational thinking**Video clip 2.2**• Develop a definition of relational thinking • Think about the video and the article • Work in groups to develop a definition of relational thinking Define relational thinking**37+56=39+54**• 33-27=34-26 • 5x84=10x42 • 64/14=32/28 Think mentally about each of these problems and how you can use relational thinking to determine if each is true or false Number Talk**Video 2.1**• Write down the strategy used after each problem. • Why were these number sentences particularly useful? • What other paths could you take? • How can we encourage children to look for relationships? Emma’s Problems**Video 2.4**• How did each child solve the problem? • What does each child understand? • What problem would you pose next to these children? • What properties are these children using? Children’s Strategies**How do pictures support the relational thinking?**• What can the animals do to make the seesaw balance? Seesaw Problem**Grade level groups**• Use both T/F and open sentences • Use more complex relationships for older students but not tricky computations • Post the number sentences • Explain why you selected those sentences – What relationships do you want them to see? • Helpful website for grades 3-8 – http://www.sandi.net/site/Default.aspx?PageID=1286 Number Sentences -relational thinking

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