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.aspx?grade=1&grade=2

Shodor http://www.shodor.org/interactivate/activiti

es/

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