Composing Problem Solving in
your Common Core Classroom
Presenters Jennifer Morris and Kristyl Nuckolls
jennifer_morris@upland.k12.ca.us
kristyl_nuckolls@upland.k12.ca.us
Problem Solving
What should it look like?
4 C’s of Common Core
●
Critical Thinking
●
Communication
●
Collaboration
●
Creativity and Innovation “Thinking outside the box”
What is Scaffolding?
●
●
Scaffolding is a
temporary structure
which provides help at
specific points in the
learning process.
It allows learners to
complete a task which
they would not be able to
accomplish without help.
Zone of Proximal Learning
Connect to prior knowledge
Entry activities
Exploration/Inquiry
Use visual aids
Chunk up the learning
Give time to talk
Encourage mathematical discussion
Out of reach
at the moment
Learns through
scaffolding
A bit difficult
Current
understanding.
Can work
Independently
Scaffolding Problem Solving?
WAYS TO SCAFFOLDING
● Clear Directions
WAYS NOT TO SCAFFOLDING
● Manipulatives
● Visuals
●
● Collaboration
●
● Hints/clues
● Modeled thinking
● Feedback
● Technology
● Question Stems/Prompts
●
●
●
Unclear problem to solve
Copying from the board
Making it “simple”
Modeling step by step
Memorization
Visual Scaffolding
Valentine's Day Cupcakes
Baldy View has 100 students in the fourth grade. A dad has volunteered to bake cupcakes for the
Valentine’s Day party. 37 of the 100 will be vanilla cupcakes. The remaining cupcakes will be
chocolate. What is the fraction and decimal for the chocolate cupcakes? With pictures, numbers
and words write a fraction and decimal for the chocolate cupcakes. Explain your answer.
Scaffolding with Manipulatives
Candy Combo Pack
CGI Direct
Modeling
The Willy Wonka Candy Factory has asked
you to make a candy combo pack to sell
at their new store. The combo pack will
have 10 pieces of candy. You can choose
between candy pumpkins and candy
corn. Mr. Wonka wants you to present all
the different combinations of candy
pumpkins and candy corn you can
package.
Child can use manipulatives to directly model the problem
Grade Level Specificity - Kinder
Candy Combo Pack
The Willy Wonka Candy Factory has
asked you to make a candy combo
pack to sell at their new store. The
combo pack will have 10 pieces of
candy. You can choose between
candy pumpkins and candy corn. Mr.
Wonka wants you to present 3
different combinations of candy
pumpkins and candy corn you can
package.
Collaborative Process
➢Review problem and
vocabulary together for
understanding
➢10 - 15 minutes
➢ independent
thinking/work time
➢Collaborating time
➢Everyone is responsible for
their paper
➢Teacher circulates the room
Leaves and Caterpillars
Performance Task
A fourth-grade class needs five
leaves each day to feed its 2
caterpillars.
●
How many leaves would they need
each day for 12 caterpillars?
●
Show how you solved this problem
with pictures, numbers or words.
Leaves and
Caterpillars
●
Research
● University of Nottingham
● University of California,
Berkeley
● Inside the Black Box Dylan
Williams
● McKinsey and Co. 2008
World’s Best Performing
Schools
5 Keys Strategies of Formative
Assessment
1.
Clarify, share and understand goals and criteria for learning.
2.
Engineer effective classroom discussion, questions and tasks.
3.
Provide feedback that moves learning forward.
4.
Activate students as owners of their own learning.
5.
Activating students as learning resources for one another.
Using Performance Tasks for Formative
Purposes
Problem Solving
Re-Engagement Model
● Give students the problem.
● Sort into 3 Groups Got it, Partially Got it, Didn’t get it
● Analyze Student Work for Common
Misconceptions
● Prepare Re-Engagement Lesson on Poster
● Re-Engage students incorporating class
discussion and collaboration
Place Value Task
•
•
•
They work independently
Formative Assessment tool
Depth of Knowledge piece
Re-Engagement Video
●Describe the components of the activity that supported students to work at
higher cognitive levels?
●How did the teacher facilitate deeper student thinking ?
●How would this model work in your classroom?
Re-Engagement Task
Student
Work
Re-engagement vs. Re-teaching
Cognitive Level is Higher
Cognitive Level is Lower
✓ Revisit student thinking
✓ Address conceptual
understanding
✓ Examine task from different
perspective
✓ Critique student
approaches/solutions to make
connections
✓ The entire class is engaged in the
math
✓ Teach the unit again
✓ Address basic skills that are
missing
✓ Do the same or similar problems
over
✓ Practice more to make sure
student learn the procedures
✓ Focus mostly on underachievers
Discussion Prompts
● How was the re-engagement activity
designed to differentiate instruction and
engagement?
● What were the core concepts the
students needed to learn and understand?
● How did the students communicate?
● How was the student work used to
deepen the understanding of the core
mathematical concepts?
General Scoring Principles
• Does the student work show more/less evidence of reasoning
and understanding?
• Anywhere on the student paper counts. (exception is when
wrong answer is designed)
• Only whole number points are awarded and partial credit only
when designated by rubric.
• Evidence is marked with symbols. The total is circled.
Candy Party
Performance Task
Candy Party Re-engagement
Name____________________________
Teacher___________________________
Candy Party
You are having a party and 36 friends have been invited. You surveyed the group and
found that 4/9 of them like Jolly Ranchers and 5/12 of them like Hershey Kisses .
You want to get the candy that is liked by most guests. Which candy would you buy
and why?
Pizza Party Re-engagement
Name____________________________
Teacher___________________________
Pizza Party
You are having a party and 24 friends have been invited. You surveyed the group and found that
5/6 of them like pepperoni pizza and 6/8 of them like cheese pizza. You want to get the
pizza that is liked by most guests. Which pizza would you buy and why?
Resources
Inside the black Box Article http://weaeducation.typepad.co.uk/files/blackbox-1.pdf
Best Performing Schools
http://mckinseyonsociety.com/downloads/reports/Education/Worlds_School_Systems_Final.pdf
Five Key Strategies of Formative Assessment
http://schools.nyc.gov/NR/rdonlyres/40877F5B-D6C0-4EB5-A5A45644A86CA523/0/Research_brief_04__Five_KeyStrategies.pdf
Tasks
http://www.insidemathematics.org/performance-assessment-tasks
http://www.noycefdn.org/mars2003.php
https://www.georgiastandards.org/standards/Pages/NETS-S-Performance-Tasks.aspx
http://www.livebinders.com/play/play_or_edit?id=330579
https://elementarymathematics.org/CMS_PERFORMANCE_TASKS.html
https://www.scoe.org/pub/htdocs/ccss-mathematics.html
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