*Algebraic ThinkingRelational Thinking

*Outcomes: *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

*Share T/F Number Talks:* Share in small group what you observed and discussed with your students using true/false number sentences.

*Understanding EqualityVideo 1.5*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?

*Equal Shmequal

*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

*Define relational thinking* 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

*Number Talk

*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

*Emma’s Problems

*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?

*Children’s Strategies

*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?

*Seesaw Problem*How do pictures support the relational thinking?

*What can the animals do to make the seesaw balance?

*Number Sentences -relational thinking*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

*Homework*Do the relational number talk with your students.