Mathematical Habits of Mind Webinar Series

1. Mathematical Habits of Mind Webinar Series Practices 3 and 4 Presented by Tammy Tucker and Jill Savage

2. Questions from 1st Webinar • Practices 1 & 2 • Find the webinars and the PowerPoint slides on the WV TREE under Professional Learning • Math WebinarPresentation • Science Integration WebinarPresentation

3. Mathematical Practices 3 and 4 Construct viable arguments and critique the reasoning of others. Model with mathematics.

26. Model With Mathematics • What does Modeling with Mathematics mean?   • Modeling with Mathematics doesn’t quite mean pull out the manipulatives.  This habit is meant for teachers to  create problem solving experiences for students that they will encounter in real life.

29. Concrete manipulatives.  

30. Here students are using semi – concrete and abstract manipulatives.  

31. Our goal is move away from the manipulatives.  We want to be able to solve problems by using only the abstract numbers.    38 + 53 = ?  

32. 24 + 30 =  24 + 29 =   25 + 31 =   25 x 2 =   25 x 4 =   25 x 6 =   Number Talks has students use prior knowledge.

33. Use of prior knowledge. • Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to use tools such as diagrams, two-way tables, graphs, flowcharts and formulas. • Jo Boaler – Mathematical Mindsets

34. Rich Mathematical Task • If I have to put 2/3 cups of flour in the recipe and I need to double the recipe, how many times do I need  to fill a 1/3 measuring cup to put enough flour in the doubled recipe? 

35. How would you solve this problem?  Start by using concrete manipulatives • If I have to put 2/3 cups of flour in the recipe and I need to double the recipe, how many times do I need  to fill a 1/3 measuring cup to put enough flour in the doubled recipe?

36. Next, use semi – abstract manipulatives. • If I have to put 2/3 cups of flour in the recipe and I need to double the recipe, how many times do I need  to fill a 1/3 measuring cup to put enough flour in the doubled recipe? 

37. This problem is a good way to explain mixed numbers. • If I have to put 2/3 cups of flour in the recipe and I need to double the recipe, how many times do I need  to fill a 1/3 measuring cup to put enough flour in the doubled recipe?  

38. We want our students to be life long problem solvers.   • Which cell phone data and calling package is the best buy? • What time do I need to wake up for school to get dressed and be there fifteen minutes early? • If I can only spend 25% of my income on renting a house, how much money do I need to make to rent a house that is $500 a month? $600? $900? • How could you create a floor plan for a house with 1428 square feet? • If a certain medicine is shown to be effective 33% of the time, should it be used to treat an illness?

39. Problem Solvers In early grades, this might be as simple as writing an addition equation to describe a situation.   In middle grades, a student might analyze a problem in the community.  

40. By high school, a student might use geometry to design a building, or use proportional reasoning to determine which cell phone plan is the most economical.  

41. Modeling With Mathematics • Modeling with mathematics and showing the progression of using concrete, semi – concrete and eventually asbstract manipulatives, students will have a better understand of how to solve problems.  

42. Sources • Mathematical Mindsets - Jo Boaler • http://www.corestandards.org/Math/Practice/MP4/ • https://learningbridges.com/NewsletterArticle.aspx?ArticleID=33

43. Questions? • Next Webinar in the series will highlight Mathematical Habits of Mind practices 5 and 6. • The Webinar will be held on January 19. • Click here to join the Mathematical Habits of Mind Practices 5 & 6 Skype Meeting