Implementing “Common” Tasks in a Traditional Classroom
A Problem A Day
Easing into the Common Core
Jillian Riehl
Teacher @ Flintridge Preparatory School
Masters Student @ California State University, Northridge
La Canada, CA
Systems of Equations
Solve the following system algebraically:
3𝑦 = 𝑥 − 2𝑦 − 1
3𝑥 = 2𝑥 − 𝑦 − 1
From Algebra & Trigonometry Structure & Method, Book 2. McDougall Littell, Page 129, #25
Systems of Equations
A-CED 4: This problem could be used in Math 1 (Algebra I) or Math 3 (Algebra II)
FOUND: illustrativemathematics.org
What Was My Plan?
Use one “Common Core” problem per day
that addresses at least 2 standards for mathematical practice
Step 1: Map Out Your Curriculum Pathway
I decided to follow the progression of my Algebra II textbook
since my school has not changed our math curriculum.
Websites with progression suggestions for Common Core Math I, Math II, and Math III can be found in your supplement
Step 2: Get A “Common Core” Problem For
Each Day
What makes a “Common Core” problem:
• SHORT: 10-20 minutes long INCLUDING a final discussion
• BUT NOT TOO SHORT: Students should have to consider what is being
asked and discuss the problem with a classmate
• MULTIPLE APPROACHES: Students are encouraged (and applauded)
for finding a new method.
• PRACTICE STANDARDS: Problems must meet at least 2
What Do I Mean by Get?
• Find a problem online
• http://www.illustrativemathematics.org/standards/hs
• http://map.mathshell.org/materials/stds.php?id=1190#standard1201
• Rewrite a textbook problem
Using www.IllustrativeMathematics.org
Using http://map.mathshell.org/
How to Write a Good Problem
when you can’t find what you’re looking for
Use a published
problem as a
template &
insert your
content!
http://www.smarterbalanced.org/
Sample Items
Systems of Equations
Solve the following system algebraically:
3𝑦 = 𝑥 − 2𝑦 − 1
3𝑥 = 2𝑥 − 𝑦 − 1
From Algebra & Trigonometry Structure & Method, Book 2. McDougall Littell, Page 129, #25
Systems of Equations
A-CED 4: This problem could be used in Math 1 (Algebra I) or Math 3 (Algebra II)
Practice Standards Addressed:
FOUND: illustrativemathematics.org
Problem Set #1
Systems of Equations
Work with your neighbor.
Look for multiple approaches for finding the
solution. Then determine which practice
standard(s) each problem addresses. Be prepared to
justify your choices!
Debrief
Methods and Standards
What Do You Do When Kids Resist?
• Your thoughts?
• Break the challenge down into easier problems
• Do it regularly so they get used to the format
• Test out the problem with friendly numbers
• Be ok with discomfort!
After 2 Months…
Test Scores
Average for all of my Algebra II classes on the Chapter 2 & 3 Test
2009: 89%
2010: 90%
2011: 89%
2012: 88%
2013: 93%
The Students Weigh In…
Phase
Section C
Section D
How bored were you in class?
Possible score is between 1 and 4 points (4 is very bored)
On the first day of school
Q: How bored have you been
historically in math class?
2.076
2.7222
After 3 weeks where BOTH
CLASSES did a Common Core
problem each day
1.6428
1.4444
After 3 weeks where NO CLASSES
got Common Core problems
1.788
1.833
After 3 weeks where ONLY
SECTION C did a Common Core
problem each day
1.412
1.7
Student Feedback After First 3 Weeks
where both classes had Common Core problems
“I find your teaching methods really different yet fun. I'm used to listening to boring lectures all day, but in your
class that rarely happens. You give us challenging yet fun problems to work on by ourselves
or with a partner. You give us a chance to go to the front of the class and teach what we learned”
“I like the format, it is nice to learn with word
problems”
“I think your class is great. I like how we use math to calculate real life problems, not just the
normal math in the book. I also like how we have partners and how we do lots of group work. I
think that really helps. When
I do not get a problem, I can talk it
out with my partner”
Student Feedback After Next 3 Weeks
where neither class had Common Core problems
“I don't really remember doing anything very interesting in the past
couple of weeks. The challenge problems made it fun before, but we didn't do any of those.”
“This last section had to do simplifying and factoring variables and equations and such and
therefore there wasn't much connection to everyday life and a lot was
just review so only some of it was truly challenging but you made it really fun and
interesting and I enjoyed all of it.”
“I still don't understand when I will
in my everyday life outside of class”
ever graph an inequality
Student Feedback After Final 3 Weeks
where ONLY section C had challenge problems
“I like how we find
every possible way to solve a problem.” –Section C
“I like the asking
"why.”” – Section C
“I like the amount of participation the whole class has in general. Everyone gets a chance
to
try, think about and learn the concepts…” –Section C
“I liked when we worked on the challenge problems! Bring them back!” – Sect. D
How Do You Get Started?
Know your curriculum pathway
Get problems to match up with each lesson
Overwhelmed? Start small – even one problem per week is good!
References
Material:
• www.illustrativemathmatics.org
• http://map.mathshell.org/
Comics:
• larrycuban.wordpress.com
• www.Someecards.com
• www.weareteachers.com
Radical Expressions
Simplify:
From Algebra & Trigonometry Structure & Method, Book 2. McDougall Littell, Page 268, #10
Radical Expressions
N-RN 2: This topic will now be covered in Math 2 (Geometry)
Practice Standards Addressed:
Without using a calculator, put the expressions in order
from least to greatest
9 270 4 3 3
96 50
3
,
,
, 135, 32,
,
5
6
3 49
12