The Essential Skill of Mathematics Level 4 Developing Good
Problem-solving Tasks
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Goals Participants will Know how to select grade appropriate
mathematics objectives Know the key elements in a good mathematics
work sample Create a work sample that is complete and ready to
use
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The Essential Skill of Mathematics 3. Apply mathematics in a
variety of settings Interpret a situation and apply workable
mathematical concepts and strategies, using appropriate
technologies where applicable. Produce evidence, such as graphs,
data, or mathematical models, to obtain and verify a solution.
Communicate and defend the verified process and solution, using
pictures, symbols, models, narrative or other methods.
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Local Work Sample Scored using Official State Scoring Guide Two
Mathematics Work Samples Required Students must earn a score of 4
or higher in each dimension on each work sample
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Mathematics work samples may provide the opportunity that some
students need to show their math skills. Math Work Samples
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Most students need instruction and practice in completing
mathematics work samples Some students may need additional
instruction or targeted coaching to demonstrate proficiency in all
five dimensions Some students may need additional instruction to
reach high school level math standards Mathematics Work
Samples
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Instructional Continuum Whole group demonstration led by
teacher with some student input Whole group with lots of student
input Small group or pairs with reporting out and discussion/rework
opportunities Individual work with feedback
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Give feedback using scoring guide language regularly Use
scoring guide in class (student language version ok) Provide
scoring guide scores on all kinds of student work not just on
written responses to problem solving prompts Use the language of
the scoring guide often as an example of what is expected and how
the language of the scoring guide applies to their work
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Selecting Mathematics Topics and Objectives
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Sorting Activity Organize the 4 versions of the sample task
into any categories and in any manner you want. Be prepared to
report out your groups results as well as the reasoning behind your
categories.
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Guidelines for High School Mathematics Work Samples
Definitions, Requirements and Recommendations
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1.Select a Content Strand Algebra Geometry Statistics
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2.Select Content Standards Problem Solving Tasks need to be
tied to the standards Common Core State Standards or current
District/Oregon Standards
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Good tasks Tied to Standards Oregon or CCSS Tied to curriculum
and recent instruction
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Two types of tasks Stand alone Curriculum embedded
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Types of Tasks Curriculum Embedded Part of current unit of
study Real world connections especially to content area material
Stand Alone Ideally related to curriculum May be specifically
designed for Essential Skills proficiency
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3. Select a Context for Problem May be tied to real-life
applications of math Should be within students frame of
reference
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Elements of Good Tasks Thought-provoking Not routinely
practiced Not immediately solvable (solution at a glance) Clearly
worded
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Good tasks elicit responses that Can be scored on all
dimensions of the scoring guide Require the use of NCTM Process
Standards CCSS Math Practices Grade Level Appropriate Mathematics
Rich enough & complex enough when used for Essential Skills
proficiency
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ONE APPROACH Designing a Mathematics Problem Solving Task
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Heres how one person creates tasks the speedy way! Where to
find ideas? I think about a concept I will be working on in the
near future such as extending patterns
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Then I think about what students should be able to do What are
the VERBS in the standard(s) being addressed? For Example :
IDENTIFY patterns EXTEND patterns GENERALIZE patterns
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Then I think about problems I have seen previously TEXT BOOKS
PROBLEM BANKS NCTM resources Could I adjust any of these to fit my
needs?
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Then I think of a context for the problem Like LIKE I am
sitting on my boat reviewing state math problems and I really need
a break!!
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I decide to go paddle boarding.. After I am 30 meters from the
boat, I turn on my wrist GPS unit to track my progress so I can log
it in my exercise journal when I am done.
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After 3 minutes of steady paddling ( no falling in the water,
stopping to admire the pretty fish or having a speed boat go by and
knock me over with its wake) I am 69 meters from the boat.
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Where am I? At this rate, how far will I be from the boat in 15
minutes?
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Wow! I think I might have a problem-solving task! Next
Steps.....
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Confirm match to standards I check for a match. Later, I will
identify all the appropriate standards and achievement level
descriptors Since I started thinking about extending patterns, I am
pretty sure this idea meets several of the CCSS, but just to be
sure...
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Time to Edit!
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1. Read through and refine I AM SITTING ON MY BOAT REVIEWING
STATE MATH PROBLEMS AND I REALLY NEED A BREAK! TOO MANY WORDS Not
important to the task not something kids (or you) can relate
to
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More concise wording I decide to go paddle boarding. Joan is
paddle boarding. She is 30 meters from the shore. After I am 30
meters from the boat, I decide to turn on my wrist GPS unit.
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Continue Editing AFTER 3 MORE MINUTES OF STEADY PADDLING,( NO
FALLING IN THE WATER OR STOPPING TO ADMIRE THE PRETTY FISHES) I AM
JOAN IS A TOTAL OF 69 METERS FROM SHORE
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Clarify the Question How far will Joan be from shore after 15
more minutes of paddling?
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Now, work the problem! Find a solution Think about what kids
might do with this problem Ask colleagues to work the problem and
make suggestions REFINE SOME MORE.
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Then try it out with students!
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QUESTIONS TO ASK YOURSELF Does it really elicit the type of
responses you were hoping for? Could you extend it and/or adjust it
to meet needs of individual students? Are there multiple possible
approaches or entry levels to the problem? Could you use different
numbers (larger, smaller, decimals, fractions, etc.) and what
effect would that have on the problem?
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Give students feedback Give yourself more feedback Be nice to
yourself Fix it, and move on! Try It Again...
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If the task is rich enough to elicit scores across the full
spectrum of the scoring guide, If it can be identified as the
students own independent work, If it applies developmentally-
appropriate problem solving skills, And if its tied to grade level
standards... Remember
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Then it can be used as one of the two required work samples, to
fulfill the Mathematics Essential Skill requirement
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Lets Go on a Walk- about!
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Lets try it! Choose a standard Highlight the verbs Brainstorm
applications Draft a task Compare to the standard Do the task/have
colleagues do the task Predict what students might do Check to see
if expected responses could be scored in all dimension of the
scoring guide Revise until its ready for students
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Time to Share! Section 3
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Carousel Activity Place your groups problem solving task on the
table. Make sure the task and any graphics are clear and easy to
understand. Circulate among the tasks to give productive and
constructive feedback. Take 5 to 7 minutes to read and discuss each
task. Use the feedback form provided to share your thoughts with
the creator(s) of the task.
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Groups and individuals review feedback forms on their tasks
Read and discuss feedback from carousel activity Make any changes
adjustments to tasks based on this discussion or further thoughts
that have bubbled up while reviewing the tasks written by other
groups Provide Facilitator with a final version of your group
task
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Time to Debrief What did you learn? What support do you
need?
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Resources Oregon Department of Education
www.ode.state.or.us/go/worksamples Oregon Council of Teachers of
Mathematics http://www.octm.org/
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Future Work Sample Trainings Level 2 Introduction Dates: Level
3 In-Depth Training Dates: Contact Information: