The Essential Skill of Mathematics
Level 4 – Developing Good Problem-solving Tasks
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
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.
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
Math Work Samples
Mathematics
work samples
may provide
the opportunity
that some
students need
to show their
math skills.
Mathematics Work Samples
• 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
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
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
Selecting
Mathematics
Topics and
Objectives
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
group’s results as well as the
reasoning behind your
categories.
Guidelines for High School
Mathematics Work Samples
Definitions, Requirements and Recommendations
1. Select a Content Strand
• Algebra
• Geometry
• Statistics
2. Select Content Standards
• Problem Solving Tasks need to
be tied to the standards
 Common Core State Standards
 or current District/Oregon Standards
Good tasks
• Tied to Standards
Oregon
or
CCSS
• Tied to curriculum and
recent instruction
Two types of tasks
• Stand alone
• Curriculum embedded
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
3. Select a Context for Problem
• May be tied to real-life
applications of math
• Should be within students’
frame of reference
Elements of Good Tasks
• Thought-provoking
• Not routinely practiced
• Not immediately solvable
(solution at a glance)
• Clearly worded
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
Designing a
Mathematics Problem
Solving Task
ONE APPROACH
Here’s how one person creates
tasks the speedy way!
Where to find ideas?
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
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?
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!!
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.
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.
Where am I?
• At this rate, how far will I be
from the boat in 15 minutes?
Wow! I think I might have
a problem-solving task!
Next Steps . . . . .
Confirm match to standards
I check for a match. Later, I will
identify all the appropriate standards
and achievement level descriptors
Time to Edit!
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
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.
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
Clarify the Question
How far will Joan be
from shore after 15 more
minutes of paddling?
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….
Then try it out with students!
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?
Try It Again . . .
• Give students
feedback
• Give yourself
more feedback
• Be nice to
yourself
• Fix it, and
move on!
Remember …

If the task is rich enough to elicit
scores across the full spectrum of
the scoring guide,

If it can be identified as the student’s
own independent work,

If it applies developmentallyappropriate problem solving skills,

And if it’s tied to grade level
standards . . .
Then it can be used as
one of the two required
work samples, to fulfill the
Mathematics Essential
Skill requirement
Let’s
Go on a
Walkabout!
Let’s 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 it’s ready for students
Time to Share!
Section 3
Carousel Activity
• Place your group’s 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.
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
Time to Debrief
• What did you learn?
• What support do you
need?
Resources
Oregon Department of Education
www.ode.state.or.us/go/worksamples
Oregon Council of Teachers of
Mathematics
http://www.octm.org/
Future Work
Sample Trainings
• Level 2 Introduction
 Dates:
• Level 3 In-Depth Training
 Dates:
Contact Information: