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: . - PowerPoint PPT Presentation
Algebraic Thinking Equality
Algebraic ThinkingRelational Thinking
Put credit forms on the table1Outcomes: 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 1.5Talk about teacher decisionsWhy were certain number sentences particularly good?What number sentences might you have added to help out?How does the sequence build understanding?
4Equal ShmequalLiterature in math http://sdcounts.tie.wikispaces.net/Thinking+Mathematically+-+Integrating+Arithmetic+and+Algebra
Pan Balances at Illuminationshttp://illuminations.nctm.org/activitydetail.aspx?id=33Share the Math Literature document on the SD Counts Wiki. Share the interactive pan balances for use in the classroom from Illuminations
5Define relational thinkingMore of Heidis Developing Number Sense and Relational Thinking ArticleWhat 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? Small Group then big ideas large group6Define relational thinkingIntroduction to Relational ThinkingFind 3 ways to solve these problemsThink beyond arithmeticThink about relationships of numbersSmall Group then big ideas large group7Define relational thinkingVideo clip 2.2
Develop a definition of relational thinking Think about the video and the articleWork in groups to develop a definition of relational thinkingSmall Group then big ideas large group8Number Talk37+56=39+54
64/14=32/28Think mentally about each of these problems and how you can use relational thinking to determine if each is true or falseEmmas ProblemsVideo 2.1Write 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?Small Group then big ideas large group10Childrens StrategiesVideo 2.4How 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?Small Group then big ideas large group11Seesaw ProblemHow do pictures support the relational thinking?What can the animals do to make the seesaw balance?
Small Group then big ideas large group12Number Sentences -relational thinkingGrade level groupsUse both T/F and open sentencesUse more complex relationships for older students but not tricky computationsPost the number sentencesExplain 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=1286Small Group then big ideas large group13HomeworkDo the relational number talk with your students.
Large group revisions on chart paper14