Introduction to Problem Solving Bank
The purpose of the Problem Solving Bank is to provide teachers with a resource to assist
in transitioning from teaching traditionally to teaching through problem solving and
inquiry utilizing the process standards and mathematical practices of problem solving,
communication, connection, reasoning and proof, and representation. This Problem
Solving Bank was created also to guide teachers in the process of how to create their own
worthwhile tasks that would specifically meet the needs of their students.
These problematic tasks were created by Rock Hill Schools Elementary teachers.
Teachers used the following guidelines to direct their collaborative thinking about how
students learn best using best teaching practices and standards.
These problem solving tasks are designed to:
 Determine the starting point for instruction
 Teach and develop mathematical concepts and understandings
 Re-enforce and clarify mathematical understandings
 Build new knowledge and understandings
 Encourage collaboration
 Enrich teaching and learning of integrated content
 Assess students’ thinking and understanding of math content and processes
 Encourage mathematical discourse
 Engage students and teachers in the learning process
 Assist students in making math connections with the world around them
 Inform student, teacher and parent of the learning progression
Before presenting the problem solving task, teachers must:
 Attend to the “Problem solving write-up Expectation”
 Know what it is that students are to gain an understanding of
 Solve the problem themselves and the tiers
 Predict how students might solve the problem
 Predict student questions and outcomes
 Modify problem, tiers, and/ or questions to meet the needs of their students
The “Problem solving write-up Expectation” format is on the following page and the
Math Workshop template is on the last page.
“The goal
for creating a mathematical environment
is to let all students believe
that they are the authors
of math ideas and logical arguments.”
John Van De Walle
Problem Solving Write up Expectation
(This is to accompany the Math Workshop Lesson Plan)
Lesson Title/ Key Concepts:
Essential Questions:
1.
2.
3.
Back ground knowledge needed:
(previous grade level)
Other Math Content embedded:
Other Content Integrated:
Overview/ briefing (for the teacher):
Problem:
Questions related to problem (Small group/ Whole group discussion)
1.
2.
3.
Tier question (review/ extension/ *challenge):
Tier question (review/ extension/ *challenge):
*Challenge—evidence of “4” on the report card
Possible ways to solve:
Enduring understanding:
(After having completed this task, what should student have an understanding of?)
How to Develop Problem Solving Tasks
(Collaboration is Key)
Step 1 – Decide on the math indicator/ standard
(Math concept is the idea that you want students to learn, not necessarily the skill)
(The best tasks will uncover skills through concepts.)
THINK: What mathematical “residue” or understanding do I want students to
walk away with after having completed the task?
What math concept(s) do I really want students to know?
Step 2 – What do students already know or need to know about the
indicator/ standard?
(Make sure the mathematics that has been identified in step one includes
something that is new or slightly unfamiliar to students)
*Mini Lesson could address what students need to know/ vocabulary to be
successful at solving the problem.
Step 3 --How does the “residue” apply to their daily lives? When would a person
use this or need this? What connections will students be able to make?
Create task!
Checklist
Will students believe this problem is realistic?
Will students build conceptual understanding from this task?
Do students need each other to work through this task? (apply process standards)
Does this task require higher level thinking?
Does this task align with what I want my students to be learning now?
Step 4 – Predict what will happen. Think about the strategies that the students might
use, be prepared to see students using strategies that you never considered.
Using the Math Workshop Lesson Plan Template:
Step 5 – Plan the mini lesson.
Step 6 – Plan Small group portion of the lesson.
Step 7 – Plan the after portion of the lesson.
LESSON TITLE:
SUGGESTED MATERIALS:
PROCESS INDICATORS ADDRESSED:
CONTENT INDICATORS ADDRESSED:
MINI LESSON
SMALL GROUP WORK
Plans for Differentiation:
WHOLE GROUP DISCUSSION