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By: Marcy Myers. Developing Math Tasks. http://answergarden.ch/view/63462. Answer Garden. Performance Tasks. - PowerPoint PPT Presentation
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DEVELOPING MATH TASKSBy: Marcy Myers
ANSWER GARDEN
http://answergarden.ch/view/63462
Performance Tasks
DEFINITION OF PERFORMANCE TASK
Performance tasks challenge students to apply their knowledge and skills to respond to complex real-world problems. They can best be described as collections of questions and activities that are coherently connected to a single theme or scenario. These activities are meant to measure capacities such as depth of understanding, writing and research skills, and complex analysis, which cannot be adequately assessed with traditional assessment questions. (Smarter Balanced, 2012)
DEPTH OF KNOWLEDGE (RIGOR)
Retrieved from: Smarter Balanced
TYPE I: TASKS ASSESSING CONCEPTS, SKILLS AND PROCEDURES
Type I tasks include a balance of conceptual understanding, fluency, and application. These tasks can involve any or all mathematical practice standards.
TYPE II: TASKS ASSESSING EXPRESSING MATHEMATICAL REASONING
Type II tasks call for written arguments/justifications, critique of reasoning, or precision in mathematical statements (MP. 3, 6). These tasks can also involve other mathematical practice standards.
TYPE III: TASKS ASSESSING MODELING / APPLICATIONS
Type III tasks call for modeling/application in a real-world context or scenario (MP.4) and can also involve other mathematical practice standards.
COMMON CORE
Standards Mathematical Practices (Begin Here)
1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning
KEYS TO PERFORMANCE TASKS
Begin with Real World and use factual data
Then move to abstract or symbolic Do not use distracting graphs, pictures,
etc. Non Math vocabulary 1 grade level
below
CREATING THE TASKS
Concise Questions Time for Exploration
creating conjectures and understanding perplexity or wonder
• Photos or videos are useful
IMPLEMENTATION OF MATH TASKS
Allow time for Communication MP 3 Construct viable arguments and critique the reasoning of others
Develop roles in small group (facilitator, recorder, manager, reporter)
Allow think time begin with individual time Anticipate Questions
Group asks question guide thinking “no answers” Set Clear Expectations (consistent) Some problems short (opener type) Open with a literacy passage to introduce
DEVELOPING A TASK
Task Name Grade Level Task Description Standards Mathematical Practices Create a Rubric or Scoring
BRAIN STORM
What standard are you trying to address? What are some real life situations for this
age group that is relevant? Cell Phones/Mobile devices Games Sports Music Downloads Ask for a survey at beginning of year what
they enjoy.
DO YOU WANT TO HAVE A PARTY?
The staff decided to get
16 hot dogs for the party
of 10.
How many are needed for 100 people and1000
people if using the same proportion of
Hot dogs per person?
What is a statement that you can make on how to calculate the number of hot
dogs?
What if you had only 5 people?
Write another math question using this
information.
BEGINNING OF YEAR TASK EXAMPLE
What do you see?
BEGINNING OF YEAR TASK EXAMPLE
Now what do you notice?
4
10
19
BEGINNING OF YEAR TASK EXAMPLE
What do you see on this picture?
1 4
10
17 19
BEGINNING OF YEAR TASK EXAMPLE
What do you think?
1 4
10
17 19
25
BEGINNING OF YEAR TASK EXAMPLE
Now ask them how much they think these items might cost for 1 student?
BEGINNING OF YEAR TASK EXAMPLE
Now ask them how much do these items cost for 1 student based on the information provided?
How much would these supplies cost for our class? How did you calculate that?
Notebook: $1.00Pack of Paper: $0.50Colored Pencils: $1.50Scissors: $2.00Eraser: $1.00Ruler: $0.50Pack of Pencils: $0.50 Folders: $3.00
BEGINNING OF YEAR TASK EXAMPLE
How much would these supplies cost for 10 students?How much would these supplies cost for 100 students?How much would these supplies cost for 500 students?
How did you calculate each of the above?
Notebook: $1.00Pack of Paper: $0.50Colored Pencils: $1.50Scissors: $2.00Eraser: $1.00Ruler: $0.50Pack of Pencils: $0.50 Folders: $3.00
BEGINNING OF THE YEAR TASK
This could be appropriate for any grade one way to make it accessible for a 1st grader is to change it to just calculating how much the supplies are that are dollar amounts.
Then focus on 1 item that might be $1.00 to find how much for 10 students or the class question.
You might want to give them actual play money to represent the money.
Technology In Math
5 QUESTIONS TO ASK FOR TOOL SELECTION
Does the tool provide a meaningful model to support the mathematics?
Does the tool extend students’ thinking and support their learning of the given mathematical topic?
Is the tool necessary? Is the tool easy to use? Does the tool provide support for students
to engage in and solve a problem?
VIRTUAL MANIPULATIVES
Virtual Manipulative Library http://nlvm.usu.edu/en/nav/vlibrary.html
Illuminations http://illuminations.nctm.org/Activities.asp
x?grade=1&grade=2 Shodor
http://www.shodor.org/interactivate/activities/
APPS FOR IPADS
Close to 20, 100, 1000 (from pearson) Wings (see quick images and
comparing) Brainbow (fun for teachers and
challenging) Hungry Fish (good for
addition/subtraction starts off easy and gets challenging)
Hands On Equations Math Kid (very basic addition,
subtraction, multiplication, and division)
Math and Literacy
MATH AND LITERACY
Meaningful and has purpose Read Alouds, small group reads Teach how to write in math
Begin Day 1 Model
MATH LITERATURE
http://teacher.scholastic.com/products/math-concepts-skills/math-reads/webinar.htm Webinar from Marilyn Burns
http://teacher.scholastic.com/products/math-concepts-skills/math-reads/math-books-topics.htm List of books from Math Reads by grade
level http://www.slideshare.net/ismes/one-is-a-s
nail-ten-is-a-crab This is the book Marilyn uses
Balanced Math
BALANCED MATHKEY IS STANDARDS BASED AND STUDENT CENTERED
Mental Math (5-7 minutes) Today’s Number On carpet Not writing down possibly
Math Review (5-7 minutes) Lesson (10-15 minutes)
Whole group Problem solving
Flexible Groups (50-60 minutes) Individuals Technology (computers, smart board, Ipad, etc.) Groups of no more than 4 Key is students need to have direction!!!!!!
Closure (5-7 minutes) Bring students back to carpet Journal Writing
WHAT NOW
Establish Procedures or routines Accountability (students) Data Driven Instruction
(MAPs, anecdotal notes, observations, common assessments)
References
REFERENCE PAGE Blomberg, A. (May, 2013). Math Tasks in a Common Core
Curriculum Alignment. Master's Paper for University of Wisconsin. Retrieved from
minds.wisconsin.edu/bitstream/handle/1793/65896/AdamBlomberg.pdf?sequence=1
Rothman, R. (July/August 2012). Nine Ways the Common Core Will Change Classroom Practice. Harvard Education Letter. Retrieved from:
http://hepg.org/hel/article/543
Ramirez, G. Gunderson, E.A., Levine, S.C., Beilock, S.L. Math Anxiety and Working Memory in Elementary School. Journal of Cognition and Development. Retrieved from
http://home.uchicago.edu/~lizgunderson/Publications/Ramirez%20et%20al%20%28in%20press%29%20-%20math%20anxiety.pdf
FEW IMPORTANT INFORMATION
CMS Math- https://elementarymathematics.org/
Marcy’s Wiki- http://marcymyers.cmswiki.wikispaces.net/
My Blog- http://mmyers44.weebly.com/blog.html
Pearson for investigations- https://www.pearsonsuccessnet.com/snpapp/login/login.jsp?showLoginPage=true