Session will be begin at 3:15 pm CCGPS Mathematics Unit-by-Unit Grade Level Webinar 4th Grade Unit 5: Fractions and Decimals November 14, 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.

Please provide feedback at the end of today’s session. Feedback helps us all to become better teachers and learners. Feedback helps as we develop the remaining unit-by-unit webinars. Please visit http://ccgpsmathematicsK-5.wikispaces.com/ to share your feedback. After reviewing the remaining units, please contact us with content area focus/format suggestions for future webinars. Turtle Gunn Toms– tgunn@doe.k12.ga.us Elementary Mathematics Specialist Feedback helps us all to become better- teachers, students, admin., everyone.

CCGPS Mathematics Unit-by-Unit Grade Level Webinar Fourth Grade Unit 5: Fractions and Decimals November 14, 2012 Turtle Toms– tgunn@doe.k12.ga.us Elementary Mathematics Specialist These materials are for nonprofit educational purposes only.  Any other use may constitute copyright infringement. Please enter into the chat window how many in your group, and where you are located. Thank you! Also, a big thank you to: Authors: Krystal Shaw Editor: Jenise Grundy, Mike Wiernicki Well done. Now I know you are out there, and capable of typing in answers…

Thank you for taking the time to join us in this discussion of Unit 5. Welcome! Thank you for taking the time to join us in this discussion of Unit 5. At the end of today’s session you should have at least 3 takeaways: What the research says about developing understanding. Ideas to support student and teacher understanding. Thank you so much for being here…

The intent of this webinar is to bring awareness to: the development of foundational fraction/decimal understanding. the mathematics of Unit 5. the underlying structure of a task. We will view task structure by looking at the culminating task for Unit 5 during this webinar. What’s the math

What’s Unit 5 all about? Decimal and fraction relationship Decimals and base ten understanding Fractions and decimal notation Adding fractions with denominators of 10 and 100 Comparing decimals Visual models

What should students bring from previous grades? Knowledge of fractions with denominators of 2,3,4, 5, 6, 8, 10, 12, 100 Familiarity with fraction notation Familiarity with fraction equivalence Knowledge of place value and base ten Understanding of money Familiarity with base ten models (base ten blocks, rekenrek, bead strings, ten frames, number line etc…) Understanding of operations with numbers

Here’s the skinny- The short version is happening right now. The long version is here: http://commoncoretools.me/wp-content/uploads/2012/02/ccss_progression_nf_35_2011_08_12.pdf And, I pushed it out.

What’s Unit 5 all about? Decimal and fraction relationship Decimal: Relating to or denoting a system of numbers and arithmetic based on the number ten, tenth parts, and powers of ten. (this is for you, not necessarily for kids) So, decimal as an adjective, is anything that is related to base ten. We have a base ten number system, or decimal system.

What’s Unit 5 all about? Decimals and base ten understanding What is “base ten”? 0 1 2 3 4 5 6 7 8 9 ? In our customary base-ten system, we have digits for the numbers zero through nine. We do not have a single-digit numeral for "ten". Yes, we write "10", but this stands for "1 ten and 0 ones". This is two digits; we have no single solitary digit that stands for "ten". Instead, when we need to count to one more than nine, we zero out the ones column and add one to the tens column. When we get too big in the tens column -- when we need one more than nine tens and nine ones ("99"), we zero out the tens and ones columns, and add one to the ten-times-ten, or hundreds, column. The next column is the ten-times-ten-times-ten, or thousands, column. And so forth, with each bigger column being ten times larger than the one before. We place digits in each column, telling us how many copies of that power of ten we need. The only reason base-ten math seems "natural" and the other bases don't is that you've been doing base-ten since you were a child. And (nearly) every civilization has used base-ten math probably for the simple reason that we have ten fingers. If instead we lived in a cartoon world, where we would have only four fingers on each hand (count them next time you're watching TV or reading the comics), then the "natural" base system would likely have been base-eight, or "octal". I found all of these words on the interweb… And as you all may have heard, computers use base-two, or binary.

What is Base Ten? 4.NBT.1 Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division. This standard calls for students to extend their understanding of place value related to multiplying and dividing by multiples of 10. In this standard, students should reason about the magnitude of digits in a number. Students should be given opportunities to reason and analyze the relationships of numbers that they are working with. In the base-ten system, the value of each place is 10 times the value of the place to the immediate right. Because of this, multiplying by 10 yields a product I n which each digit of the multiplicand is shifted one place to the left. (Progressions for the CCSSM; Number and Operation in Base Ten, CCSS Writing Team, April 2011, page 12) From another progression, the one for Number and Operation in Base Ten

Activate your Brain This is what 5th graders will do with what 4th graders learn. So, what is 10 to the first power? 10 The second power? 10x10 oh, 100, oh, 2 zeros! The third power? 10x10x10 oh, 1000, oh, 3 zeros! And so on- the magic of powers of ten continue. If we were using 2 instead of starting with ten, we’d have powers of two. Chew on that tonight, and figure out how to write numbers using only 0 and 1 to represent any number in base two…What patterns do you see? Once you’ve dialed that, go for base 7, or whatever your favorite number is. In base 16, I’m only 38! Love it. Prize to the first person to figure out how old I really am…

Activate your Brain So- when we think about the unit cube magnified and broken into smaller units (yes, they could get infinitely smaller!) we can see the flat representing one tenth of the cube- 10 to the negative 1, or .1, and the rod representing 1 hundredth of the cube- 10 to the negative 2, or .01, and so on… Yes, nice visual for kids- I like to have them imagine themselves shrinking to be able to see the unit cube looking like a thousand cube. Then we switch to the thousand cube as representing one and start breaking it down… Later, in 8th grade, students represent these numbers using negative exponents! You’ve laid the foundation here with a different representation, and hopefully a visual representation for the same numbers. 6th grade teachers should link back to powers of ten when they begin to discuss exponents for any whole number.

Visual Representations A major task for any student engaged in problem solving is to translate the quantitative information in a problem into a symbolic equation (an arithmetic/algebraic statement) necessary for solving the problem. Students who learn to visually represent the mathematical information in problems prior to writing an equation are more effective at problem solving. What Works Clearing House http://ies.ed.gov/ncee/wwc/PracticeGuide.aspx?sid=16 Just some research to back up the use of strong visuals…

Visual Representations Visual representations help students solve problems by linking the relationships between quantities in the problem with the mathematical operations needed to solve the problem. Visual representations include tables, graphs, number lines, and diagrams such as strip diagrams, percent bars, and schematic diagrams. What Works Clearing House http://ies.ed.gov/ncee/wwc/PracticeGuide.aspx?sid=16 I would add manipulatives to this list.

Visual Representations Recommendations by WWC to assist students in their development and use of visual representations: Select visual representations that are appropriate for students and the problems they are solving. Use think-alouds and discussions to teach students how to represent problems visually. Show students how to convert the visually represented information into mathematical notation. What Works Clearing House http://ies.ed.gov/ncee/wwc/PracticeGuide.aspx?sid=16 I would also allow students to choose, as they often have an alternative solution path.

What’s Unit 5 all about? Fractions and decimal notation So, now we understand that decimals are just another way to represent a fractional part of a whole number. Fractions are units that can be operated on.

What’s Unit 5 all about? Adding fractions with denominators of 10 and 100 Once students understand the idea of unitizing, then addition is much easier to visualize, estimate, and complete.

What’s Unit 5 all about? Comparing decimals Relating different fraction models to decimals

What’s Unit 5 all about? Comparing decimals

What’s Unit 5 all about? Visual models- Yep. I think we get this now.

Culminating Task: Cell Phone Plans Students demonstrating their understanding of the ideas in this unit. Ability to connect ideas, construct and defend arguments, organize thinking…. Allows for multiple entry points, and student choice.

Culminating Task: Cell Phone Plans It is time for McKinley to purchase a new cell phone. With so many new phones and so many companies, McKinley has a lot to consider before she purchases her phone. Read all the information she has gathered below and help her decide which plan is best! Rank the three plans according to which you think is the best deal and be prepared to defend your thinking! Use math words, numbers, models, and symbols to explain your thinking! McKinley’s Usual Phone Usage Per Month 300 minutes of talk time 200 texts 200 megabytes of data What is the goal of this task? How can you structure the task so that it works for your classroom?

200 minutes free (2/10 of a dollar per minute after that) Phone Company Monthly Fee Talk Time Texts Data Usage Cecelia’s Cells $30 200 minutes free (2/10 of a dollar per minute after that) 100 texts free (10 texts per dollar after that) 50 megabytes free (2/100 of a dollar per megabyte after that) Matt’s Mobiles None 5/100 of a dollar per minute 25/100 of a dollar per text 1/10 of a dollar per megabyte Phyllis’s Phones $ 15 200 minutes free (1/10 of a dollar per minute after that) 150 texts free (2/10 of a dollar per text after that) 150 megabytes free (2/10 of a dollar after that)

What’s the goal of this task? What might you add? Cell Phone Plans What’s the goal of this task? What might you add? How might you increase student choice/entry points? Students demonstrating their understanding of the ideas in this unit. Ability to connect ideas, construct and defend arguments, organize thinking…. Allows for multiple entry points, and student choice about how to represent their thinking.

Culminating Task: Cell Phone Plans How can you structure the task so that it works for your classroom? Intro task- start with task and create a rubric. Edit task if necessary to better fit your students. Students work independently while you circulate and ask questions, take notes Set benchmarks along the way to keep students moving forward, help kids to organize their workflow Classroom work area? Models? How to make this work? Time after other work is done, tools available for student use, work during a few class sessions- some tasks just take longer.

Culminating Task: Cell Phone Plans Refer students back to rubric all along the way to help kids to organize their thinking and improve their work. Choose strategically which student ideas offer opportunities for “mid-stream minilessons”. Question more than you answer. Listen more than you talk. If you are recording your thinking, you are modeling your expectation for them. Presentations? Could they be shared with others outside the classroom? Inviting in outside guests/experts is a great way to bring relevance to the task. Administrators, parents, school staff, outside experts can be given a rubric and score student work. This is very motivating for students, and a great way to help parents and administrators see what’s going on in mathematics. You can provide a cheat sheet for parents for the content portion of the presentations. Divide and conquer.

Looking at a Task: https://www.teachingchannel.org/videos/elementary-math-lesson-plan?fd=1 Great video of a fourth grade teacher whose class is playing a fractions and decimals game. All of the resources are shared on the website. Watch if there is time.

Horizontal and vertical connections Strategies apply everywhere, in multiple contexts Integration of content areas ensures connections and relational thinking Multiple steps builds understanding and deeper thinking Work the culminating task collaboratively with colleagues so you know where your kids need to go, and what they might have difficulty with Journaling helps with all of these- particularly with multi-step situations- keeping track of what you are doing is an essential skill for mathematicians.

How might a rubric be made by your students? Different criteria- you can choose! Standards (for sure) Student behavior How could you help students incorporate specific content understanding?

Interested? http://www.teachervision.fen.com/teaching-methods-and-management/rubrics/4586.html http://faculty.mwsu.edu/west/maryann.coe/coe/Projects/epaper/rubrics.htm http://sblc.registereastconn.org/greatrubrics.pdf http://www.schrockguide.net/assessment-and-rubrics.html http://www.scholastic.com/teachers/article/making-most-rubrics

Effective Feedback Sharing thinking The most powerful use of feedback would be during a whole class discussion/sharing time or midstream minilesson, when student work is shared. Teachers should choose student work which will give the most bang for the buck, or which serves as an entry point for strategy development. Ask the student (gently) to explain their thinking. Having students explain and share their thinking is the best avenue to understanding what they know. When looking at student work, or working with students, put your questions and observations on sticky notes so that they can carry on working. I also don’t allow students to erase- the erasures remove evidence of growth, evidence of misconceptions. Instead, have them circle the work they’d like to erase, and write nearby- “I changed my plan/thinking.”

Culmination of the unit, not the grade. It’s important to remember that while this is a culminating task, it is not the culmination of fourth grade, and as such, is not summative. Collaborative teacher discussion of student work on this task is a perfect opportunity to collect information to continue to guide students in development of deep and useful understanding, based on the understanding and misunderstandings evidenced. It isn’t over just because Unit 5 is over. Continue to use ideas developed in this unit during number talks, mathematized daily life, books you read, etc…

Food for thought: From a math coach friend… “I’ve learned a lot from watching good teachers.  The most important thing I’ve learned:  adopt the mantra “Just the answer isn’t good enough.”  I watched teachers transform passive students into thinkers because of this simple idea.  This expectation, that a teacher sets at any point in the year, opens up doors to all of the SMP’s (not every one every day – but many every day).  In those classes, because “just the answer isn’t good enough,” kids made sense of the mathematics they were doing, reasoned to justify that their answer was correct, critiqued their work and others’, used tools and made models of the mathematics that was happening, used some measure of precision as they explained their thinking, and sometimes found structure (even a few teachers found this) in their own repeated reasoning.”  From a math coach friend… From a math coach friend- I modified a bit- added the word JUST, because it could be misleading. Thanks, friend.

Thank You. Please visit http://ccgpsmathematicsK-5. wikispaces Thank You! Please visit http://ccgpsmathematicsK-5.wikispaces.com/ to provide us with your feedback! Turtle Gunn Toms Program Specialist (K-5) tgunn@doe.k12.ga.us These materials are for nonprofit educational purposes only.  Any other use may constitute copyright infringement. Join the listserve! join-mathematics-k-5@list.doe.k12.ga.us Follow on Twitter! Follow @GaDOEMath Follow @turtletoms (yep, I’m tweeting math resources in a very informal manner) Join and participate in the wiki Follow on Twitter.