“Which comes first,
creating or reasoning?”
Jenny Ray, Kentucky Department of Education
Professional Growth and Effectiveness Specialist
Professional Development
Learning Targets
 I can explain what it means to teach to the standards, as
opposed to teaching the topics of the standards.
 I can compare and make connections between the A-CED
and A-REI standards.
Two Minute Review
A-CED and A-REI Standards
 Please take one minute to re-
familiarize yourself with the
standards we will be considering in
this session.
 Highlight, underline, or use your
own language in the margins to
remind yourself of the ‘content’ of
these specific standards: A-CED 2, 3,
4 and A-REI 5, 6
Video of Teaching
Solving Systems of Linear Equations
 Make note of the standards that are being taught as you
watch this 5-minute video clip:
Five minutes to share your thoughts…
 Share your thoughts/insights on the standards being taught
with a table partner, then with others at your table.
 Choose someone to share out from your table with the
group.
Working through a task…
 Everyone should have a copy of “Cash Box” from Illustrative
Mathematics.
 INDEPENDENTLY, please brainstorm what you know and
some solution strategies. (You will have time to work with
others, but for now, please just work on your own.)
 Now, share your ideas with a partner at your table. Begin to
formulate a way to solve the problem.
 Be ready to share with your group how you solved the
problem.
Whole Group Discussion
 What was different about this task and typical problems that
students solve when learning to solve systems of equations?
 What was different about your experience as a learner, in this
task, than perhaps how you learned to solve ‘word problems’
in high school?
 What Standards for Mathematical Practice did you exemplify
in your experience today?
Modeling a Formative
Assessment Lesson
Solving Linear Equations in Two Variables
Notebooks and Pens
 Read through the questions and try to answer them as
carefully as you can.
 Please work independently for 10 minutes.
Cash Registers Task—Independent Work
 Count off 1-?
 Go to that numbered table to complete the individual task.
 Spend about 10 minutes working through the task on your
own at your table. Do not discuss with others at your table,
yet.
Cash Registers—Small Groups
 Now, go back to your original seat and compare your solution
method with others at your table.
 Work together in your groups to produce an answer together
that is better than your individual ones.
Comparing Different Approaches
 Examining Student Work Samples
 Whole-Class Discussion
Improving Notebooks and Pens
 This would be the next lesson, if there is not time during the
original lesson.
 Look at your original responses and think about what you
have learned this lesson.
 Using what you have learned, try to improve your work.
Review the Targets
Professional Development
Learning Targets
 I can explain what it means to teach to the standards, as
opposed to teaching the topics of the standards.
 I can compare and make connections between the A-CED
and A-REI standards.
RESOURCES
 www.Jennyray.net —You can find this PPT and other
resources on the Math Resources tab
 http://www.illustrativemathematics.org/ Also on website,
above, under the Math Links tab. This site offers many rich
tasks that are correlated to CCSSM
 http://map.mathshell.org/materials/lessons.php