CCGPS Mathematics Unit-by-Unit Grade Level Webinar Fifth Grade Unit 4: Adding, Subtracting, Multiplying and Dividing Fractions October 11, 2012 Session will be begin at 3:15 pm While you are waiting, please do the following: Configure your microphone and speakers by going to: Tools – Audio – Audio setup wizard Document downloads: When you are prompted to download a document, please choose or create the folder to which the document should be saved, so that you may retrieve it later.

CCGPS Mathematics Unit-by-Unit Grade Level Webinar Fifth Grade Unit 4: Adding, Subtracting, Multiplying and Dividing Fractions October 11, 2012 Turtle Toms– Elementary Mathematics Specialist These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.

Welcome!

Turtle Gunn Toms– Elementary Mathematics Specialist

Wiki Questions

Why are you doing a Unit 4 webinar now? We aren’t even done with unit 1.

Wiki Questions Why aren’t there answer keys? Has anyone at the state-level “dug in” and worked through the tasks as you are asking Georgia educators to do? Are these tasks vertically and horizontally aligned?

Wiki Questions What about homework and other resources? Where and what are teachers suppose to pull for those? Are the tasks supposed to go home? How are parents supposed to help their children without books or other resources? How are you letting districts know about changes in units?

TadWTadW Oct 5, :24 pm I have heard from Bill McCallum and Phil Daro that the CCSS does not discuss "simplifying" fractions because how we should use fractions depends on the contexts. In some instances, it may be useful to use the simplified form, but in other cases, a non- simplified form may be more informative. So, asking students to "simplify" a fraction without a context is meaningless - equivalent fractions are all equal and they represent the same number. In the same way, the Common Core does not specify that the "least common denominator" be used to add/subtract fractions. We just need a common unit…

Looked at LearnZillion yet?

Wiki Questions Do teachers have to complete all of the tasks? What about grades?

Wiki Questions What about students who are not progressing as they should using only the tasks? What about students with disabilities?

Need more? VandeWalle- ACTIVITIES AT A GLANCE

Wiki Questions What does mathematize mean? Do you understand what it is like to be in a classroom?

So, there are the answers.

We can’t change how people think by telling them what we think and we can’t change how people teach by telling them how to teach. They have to experience good teaching – first as a learner, then as a teacher. -a really smart person We can’t change how people think by telling them what we think and we can’t change how people teach by telling them how to teach. They have to experience good teaching – first as a learner, then as a teacher. -a really smart person

No support? On your own?

How can we get support? Collaboratively solve tasks and discuss.

Plan for the math by doing the math Learn alongside your learners

Learn alongside your learners

How can we get support? Inquire at a local college or university. Mathematicians are inexpensive! Some are free…

Does your district have a 10-15% ELL population?

Make time this year for the wiki and the webinars.

This is difficult.

But not impossible.

Sharing Candy Bars 5 th grade split into 4 groups. They shared candy bars as follows: 1 st group: 4 people shared 3 candy bars 2 nd group: 5 people shared 4 candy bars 3 rd group: 8 people shared 7 candy bars 4 th group: 5 people shared 3 candy bars Was this fair? Did people get different amounts?

What’s the big idea? Deepen understanding of what a fraction is. Deepen understanding of equivalency. Develop an understanding of fractions as units which can be “operated” upon. Deepen understanding of properties of operations. Use multiple models to represent operations with fractions. Standards for Mathematical Practice.

What about those transition standards? After your students do the first task from 5 th Unit 4, you may decide to go back and choose a few tasks from the 4 th grade Units (2, 3, and 4) to bridge understanding and address gaps. Suggestions: 4 th Unit 2- Fraction Kits, Equivalent Fractions, Making Fractions 4 th Unit 3- Sweet Fraction Bar, Rolling Fractions 4 th Unit 4- Bowl of Beans, Birthday Cookout

Big important ideas

Research - Communication The value of student interaction Challenges the teachers face in engaging students The teacher’s role Five strategies for encouraging high- quality student interaction 1.The use of rich math tasks 2.Justification of solutions 3.Students questioning one another 4.Use of wait time 5.Use of guidelines for Math Talk

Mathematical Communication The development of students’ mathematical communication shifts in precision and sophistication throughout the primary, junior and intermediate grades, yet the underlying characteristics remain applicable across all grades. CBS Mathematics

Mathematical Communication Mathematical communication is an essential process for learning mathematics because through communication, students reflect upon, clarify and expand their ideas and understanding of mathematical relationships and mathematical arguments. Ontario Ministry of Education

Mathematical Communication Developing effective mathematical communication Categories of mathematical communication Organizing students to think, talk, and write Updating the three-part problem-solving lesson  Gallery Walk  Math Congress  Bansho (Board Writing)

Mathematical Communication “Because mathematics is so often conveyed in symbols, oral and written, communication about mathematical ideas is not always recognized as an important part of mathematics education. Students do not necessarily talk about mathematics naturally; teachers need to help them learn how to do so.” Cobb, Wood, & Yackel

Mathematical Communication “The role of the teacher during whole-class discussion is to develop and to build on the personal and collective sense- making of students rather than to simply sanction particular approaches as being correct or demonstrate procedures for solving predictable tasks.” Stein, Engle, Smith, & Hughes

Mathematical Communication When teacher talk dominates whole-class discussion, students tend to rely on teachers to be the expert, rather than learning that they can work out their own solutions and learn from other students. CBS Mathematics

o Imitative Bad Math?

o Passive/receptive Bad Math?

o Minimal student explanations, comparisons Bad Math?

Passive Active

Transmission Challenging

Recipe for Success

How do students learn math?

Misconceptions Understandings Pre- Assessment Feedback Discussion Explanations Collaborative Task Improvement Deeper Understanding Post- Assessment

Misconceptions Understandings Pre- Assessment Feedback Discussion Explanations Collaborative Task Improvement Deeper Understanding Post- Assessment Hmmm..All three are communication

Worthwhile Task fractions

Worthwhile Task Teacher sets up the task…how? Supports include…what ? Suggestion included….what? Student ideas emerge, take form, and are shared….how? Conjectures are made and explored, and evolve into strategies…how? Strategies become retrievable practices…how? The plenary discussion at the end helps to cement these ideas….how and why?

How are Number Talks Useful? From Math Solutions Want more?

Number Talk Who does the math thinking during the number talk? What specific mathematics do the students demonstrate they understand? What does the teacher do to support the student discourse? What recording techniques might the teacher employ that supported learning in the class?

Assessment?

Mathematical Communication Tips on Getting Started 1.Organizing the classroom learning environment 2.Preparing yourself mathematically 3.Coordinating student discussion and analysis of solutions

Sharing Candy Bars 5 th grade split into 4 groups. They shared candy bars as follows: 1 st group: 4 people shared 3 candy bars 2 nd group: 5 people shared 4 candy bars 3 rd group: 8 people shared 7 candy bars 4 th group: 5 people shared 3 candy bars Was this fair? Did people get different amounts?

Sharing Candy Bars Students do not necessarily talk about mathematics naturally; teachers need to help them learn how to do so. The role of the teacher during whole-class discussion is to develop and the build on the personal and collective sense-making of students. …learning that they can work out their own solutions and learn from other students.

How do teachers change practice?

Resource List The following list is provided as a sample of available resources and is for informational purposes only. It is your responsibility to investigate them to determine their value and appropriateness for your district. GaDOE does not endorse or recommend the purchase of or use of any particular resource.

Resources Books  Van De Walle and Lovin, Teaching Student- Centered Mathematics, K-3 and 3-5  Parrish, Number Talks  Fosnot and Dolk, Young Mathematicians at Work  Shumway, Number Sense Routines  Wedekind, Math Exchanges

Resources Common Core Resources  SEDL videos -  Illustrative Mathematics -  Dana Center's CCSS Toolbox -  Arizona DOE - practices/mathematics-standards/ practices/mathematics-standards/  Inside Mathematics-  Common Core Standards -  Tools for the Common Core Standards -  Phil Daro talks about the Common Core Mathematics Standards  Progressions-

Resources Professional Learning Resources  Inside Mathematics-  Edutopia –  Teaching Channel -  Annenberg Learner - Assessment Resources  DANA Center-  MARS -  MAP -  PARCC -

A little something extra: Instead of 30 minutes of television tonight, watch this: _more_than_fun_it_s_vital.html Fifth Grade resources : LearnZillion- Vocabulary cards- pushed out to you, and posted on the wiki

Shaky foundations…

“ It ain’t what people don’t know that hurts them. It’s what they do know that ain’t so.” Will Rogers “ It ain’t what people don’t know that hurts them. It’s what they do know that ain’t so.” Will Rogers

Thank You! Please visit to provide us with your feedback! Turtle Gunn Toms Program Specialist (K-5) These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement. Join the listserve! Follow on Twitter! (yep, I’m tweeting math resources in a very informal manner)