1. Contemplate then Calculate
Hmmm…
Contemplate then Calculate
An Instructional Routine
Prompting Structural Thinking (MP7)
Experience and Reflect

2. Contemplate then Calculate
Hmmm…
Contemplate then Calculate
WHAT: Practice looking for shortcuts to find values for variables.
WHY: to “think like mathematicians” and find shortcuts using mathematical structure.

3. Contemplate then Calculate
Hmmm…
Contemplate then Calculate
Notice
Find Calculation Shortcut
Share and Study Shortcuts
Reflect on Learning

4. What do you notice?
About to project a task; your job is to contemplate – notice – SEE.
Pencils down. This is not the time to begin working on the task.
I’m only going to project the task for about 3 seconds.

5. What do you notice?
About to project a task; your job is to contemplate – notice – SEE.
Pencils down. This is not the time to begin working on the task.
I’m only going to project the task for about 3 seconds.

6. What do you notice?
About to project a task; your job is to contemplate – notice – SEE.
Pencils down. This is not the time to begin working on the task.
I’m only going to project the task for about 3 seconds.

7. Share
I noticed…
What did you notice?

8. Find Calculation Shortcut Find Calculation Shortcut
“In your head”
Find the value quickly with the fewest calculations
Explain why your shortcut works.
Use what you noticed. Use what you know about numbers and operations
PAIR NO PENCILs. Reason it out.
P – 1-2 min

9. Find Calculation Shortcut Find Calculation Shortcut
“In your head”
Find the value quickly with the fewest calculations
Explain why your shortcut works.
Use what you noticed. Use what you know about numbers and operations
PAIR NO PENCILs. Reason it out.
P – 1-2 min

10. Share and Study Shortcuts
Presenter
We noticed… so we…
We knew… so we…
Our shortcut works because…
Audience
They noticed… so they…
They knew… so they…
Their shortcut works because…
CHUNK (any grouping, associative property of addition)
CHANGE sub to adding a negative in order to use associative and commutative property of addition. Change the order (commutative property of +)
Connect mult to addition

11. Reflect on Learning
The next time I will _____________________ before I calculate because _______________ ______________________________________
Paying attention to _____________________ is helpful because ______________________ ______________________________________
Reflection Write-Pair Share

12. Credits for Contemplate then Calculate
This routine was developed by Amy Lucenta and Grace Kelemanik. They have also developed many other instructional routines that can be found in their book, Routines for Reasoning.
This routine was presented to me through New Visions and David Wees.

13. Unpacking Contemplate then Calculate
Turn and Talk: What is interesting/different about this routine? What role could it play in your classroom?
How I Use It:
To build problem solving and generate a variety of strategies developed genuinely by the students
To introduce a new strategy (such as zero product property, as long you think a student will genuinely develop it) and compare it to old strategies to highlight the new strategy’s strengths.
To help students practice low-stakes conversation and collaboration

14. What Contemplate then Calculates are out there?
There’s a whole library of Contemplate then Calculates:
There is also a second instructional routine called “Connecting Representations” where students develop connections between two different representations of a single concept (For instance, students might connect recursive function notation to tables). Activities for both Contemplate then Calculate and Connecting Representations can be found on the link above.