CSRA-RESA October 1 st , 2014 by: graham fletcher email: gfletchy@gmail.com tweets: @gfletchy blogs: www.gfletchy.com slides and handouts: http://gfletchy.com/csra-resa/
• please silence all cell phones � � Housekeeping • be mindful when others were speaking • Restrooms � • Breaks � • Lunch • don't be selfish...if a great conversation is taking place at your table please be willing to share � � • using #CSRA-RESA
Broken Squares • Designate a shape keeper � • 6 congruent squares � • No shapes left over � • Everyone is encouraged to OFFER. No one may TAKE. They may ACCEPT a puzzle piece to use if OFFERED.
• What do you notice? � • What do you wonder?
Penny Cubed taken from Mike Wiernicki at http://mikewiernicki.com/2014/09/19/the-penny-cube/
What do you notice? What do you wonder? � Main question(s) � Estimation?
Denomination Penny Nickel Dime Quarter Dollar 6 inches Weight About 0.09 oz About 0.18 oz About 0.08 oz About 0.2 oz 6 inches Diameter 0.750 in 0.835 in 0.705 in. 0.955 in. 6 inches Act 2 Thickness About 0.06 in. About 0.08 in. About 0.05 in About 0.07 in.
Act 3: The Reveal
Penny Cubed 1.5: The Weight of it All? • How much does it weigh? � Penny Cube 2: Invasion of the Quarters! • Quarters would fit nicely in this cube as well. Which would you rather have, a cube of pennies or a cube of quarters? Act 4: The Sequel
Through the eyes of 5 th graders… last week!
Through the eyes of 5 th graders… last week!
“Algebrafy” the Mathematics � How much money could we fit in this room? � Can you find a rule that would tell us how much money could fit in any room? Act 4: The Sequel
Standards for Mathematical Practice Look at your SMP and create an anchor chart describing what it should/could look like in a 3rd-5th grade classroom. � Explain the standard using numbers, pictures and/or words to describe what it could look like. •what might the teacher be doing •examples of student thinking •types of tasks used (can you connect your SMP to Penny Cubed?)
What is mathematical modeling? • Put simply, mathematical modeling is the process of using mathematical tools and methods to ask and answer questions about real-world situations (Abrams 2012). � � • Is it a noun or is it a verb ?
decontextualize contextualized The sole use of manipulatives does not ensure that students are modeling mathematics. � � The model must be serving a context for students to be engaged in mathematical modeling.
The Condominium Problem • In a particular condominium community 2/3 of all of the men are married to 3/5 of all of the women. � • What fraction of the entire condominium community are married?
Three approaches to math instruction:
Level 1: "three step procedure" (the calculator) • provide no explanations • be very clear how to solve the problem • suggest that there will be more condo problems to practice for homework and you'll see this exact same type of problem on the Georgia Milestone Assessment • “Today we’re working on common numerator…here’s a problem”
Level 2: "this is how you" (the repeater) • teacher directed approach very conceptual • it is the teacher doing the thinking • students are only engaged in low level responses and their participation is dependent on their willingness to attend to your “wonderful” lecture.
Level 3: the questioner (the problem solver) • relentless questioning • know when to walk away AND be less helpful • student led discussions and strategies are shared • teacher leaves a trail of understanding
What happens if we do this? � What happens to the problem?
I have no idea making sense of the what I’m doing math and being able to apply it.
A Look Back We need to change � � 1995 TIMMS
TIMMS video take-aways: • 0:38- Seventy degrees. Go from there. Now you have supplementary angles, don't you? � • 1:43- Somebody just gave me the answer. � • 11:10- Okay, I know you don't like these protractors but- you use these because I want everybody to use the same one. � • 11:28- You know I am gonna give you plus or minus five degrees on a quiz, so don't worry about it. � • 17:00- All the rest are done the same way. Any questions? I’m curious to see, when you get down to number 37 and 38, you’re gonna have to think a little bit.
Looking Back Milestones Georgia We need to change � We need to change � � � � � � CCGPS 2014 1995 GPS (2003-2010) TIMMs Process Standards
How can we continue to promote and support best practice in our districts and schools? Hyper-focusing our attention on the Standards for Mathematical Practice (SMPs) � Teacher Student Task
Reflect: � • Using the SMP rubric, grade yourself on the last math lesson you taught. � Pitfalls • Focus on at least SMPs numbered 1, 2, 3, & 4 � • Share and discuss any ah-ha’s with your group or table
Has anything changed? • real-world link
• real-world link • how you model… (I show you)
• real-world link • how you model… (I’ll show you) • now you do it… (I’ll watch)
• real-world link • how you model… (I’ll show you) • now you do it… (I’ll watch) • guided practice
• real-world link • how you model… (I’ll show you) • now you do it… (I’ll watch) • practice some more • Independent practice • Wait for it…
• real-world link • how you model… (I’ll show you) • now you do it… (I’ll watch) • practice some more • by yourself now with the STEM and CCGPS connections
• real-world link • how you model… (I’ll show you) • now you do it… (I’ll watch) • guided practice • independent practice • H.O.T problems • test practice
• real-world link • how you model… (I’ll show you) • now you do it… (I’ll watch) • guided practice • independent practice • H.O.T problems • test practice • more extra practice
• real-world link • how you model… (I’ll show you) • now you do it… (I’ll watch) • guided practice • independent practice • H.O.T problems • test practice • more practice • more test practice • Common Core Review
4 pages = 35 problems …but only 2 of them are “Common Core” because the label said so
• real-world link • how you model… (I’ll show you) • now you do it… (I’ll watch) • guided practice • independent practice • H.O.T problems • test practice • more practice • more test practice • Common Core Review • NEED MORE PRACTICE? I’m not sure that students get excited about this!
I’m not suggesting….
How my fairy works…
How do we foster growth in our students perplexity fairy?
What do you need to know?
Food for thought • who usually asks all the math questions in class? � • who normally has all the information? � • who normally validates student answers? � How does this task align with the Standards for Mathematical Practice?
Division: one of the most difficult math concepts we teach in elementary school? • MCC4.NBT .6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
“Guzinta” is not a word
the Paper Cut taken from http://gfletchy.com/paper-cut/
Lunch
the Paper Cut taken from http://gfletchy.com/paper-cut/
Question: is the more white paper, colored paper, or is there an equal amount? 12 x 14 12 x 7
Solve without using any numbers or letters! WHAT’S UP DOG? � • A big dog weighs five times as much as a little dog. • The little dog weighs 2/3 as much as a medium-sized dog. • The medium-sized dog weighs 9 pounds more than the little dog. � How much does the big dog weigh?
How far apart are the exits on this freeway? � • Junction 90 • Jefferson Blvd?
Unit Fraction:
How students can model fractions:
Real Work Fake Fake Real World
CSRA-RESA October 1 st , 2014 by: graham fletcher email: gfletchy@gmail.com tweets: @gfletchy blogs: www.gfletchy.com slides and handouts: http://gfletchy.com/csra-resa/
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