1. Routines for Reasoning
Recognizing Repetition –
Visual Patterns

2. Instructional Discussion
Standard: 7.EE.1-2
SMPs: 8, 4, 2, 1, 6, 7
Learning Target: Students will deepen their understanding of connecting a visual representation with function notation during a process of generalizing a pattern.

3. Recognizing Repetition Routine Outline
IRMC Routines for Reasoning Action Research Project: Recognizing Repetition Routine
Teacher Name: wallin
Grade: 7
Date:
Standards Addressed: 7.EE.1-2
SMP Focus: 8, 4, 2, 1, 6, 7
Learning Target/Objective
Students will deepen their understanding of connecting a visual representation with function notation during a process of generalizing a pattern.
Task description with rationale
This lesson will present abstract algebraic functions in a meaningful way for students; through exploration of the patterns the students will develop a generalization that they can fully conceptualize based on the visual representation.
Recognizing Repetition Routine Outline
Routine Step
Planning Questions
Planning Notes
Launch
What are your thinking goals for this lesson?
Think about a problem like a mathematician.
What “Ask-Yourself Questions” will you give students?
What is staying the same each time?
What is changing each time?
What do I think the next example will look like?
Notice Repetition
What do you anticipate students will notice?
The number of blocks is increasing, there is one piece missing in the bottom left each time, there are always two “stacks” on the left and right side, etc.
How will you select pairs of students to share their noticing?
I will open up students to share all their noticing. I will record the student noticing for the group to see.
What sentence frames will you use?
I noticed ____________ stayed the same each time
I noticed ____________ changed each time
How will you manage the discussion?
I will try limit students from moving too far ahead of others with generalizations; I don’t want someone to simply state an answer – I want it to be in more general terms.
Generalize Repetition
What guiding questions will you use to support students as they generalize (Ask-Yourself Questions)?
How will you select pairs to present?
I will select a group who has good noticing, but not a generalization. I will see if the class, after hearing the group’s thinking can then generalize the task as a whole group. This is a divergent task (many possible solutions), so I will look for up to 3 different ways to solve. I may have groups create posters.
Discuss Generalizations
How will you determine the focus of the final discussion/select student work?
I would like to find two or three equivalent generalizations that the group can then discuss to see if these were equal.
How will use models or annotation to support discussion?
I will have the student posters from before and will move them side by side. I will try to bring out similarities between strategies. I will annotate how we could change one poster to be more like another.
“I notice ________ in his/her poster, which is like ________ in his/her poster”
Reflection on Student Thinking
What sentence frame will you use?
When looking for repetitions in a process, I learned to pay attention to _______________ because...”
What do you hope to learn from the student reflection?
I hope that students can see that the abstract expressions are created by decomposing visual representations – see it as less abstract. I also want students to see that divergent solutions can be equivalent and equally valid.

4. Recognizing Repetition
SMP Focus: Look for and express regularity in repeated reasoning
Noticing Repetition
Generalization
Essential Strategies
Ask-yourself questions
Four Rs: Repeat, Rephrase, Reword, Record

5. Purpose
Today we are going to use repetition in our reasoning to generalize a problem situation. We are going to notice how situations are changing and how they are staying the same to help us solve problems. We are going to talk to others to clarify our own thinking about the math problem.

6. Thinking Goals Think about a problem like a mathematician.
Thinking Questions:
What is staying the same each time?
What is changing each time?
What do I think the next example will look like?

7. “I noticed ___________ stayed the same each time.”
Figure 1
Figure 2
Figure 3
Figure 4
“I noticed ___________ stayed the same each time.”
“I noticed ___________ changed each time.”
pattern # 149

8. “We noticed __________, so they thought the next pattern would be…”
Figure 1
Figure 2
Figure 3
Figure 4
“We noticed __________, so they thought the next pattern would be…”
pattern # 149

9. Reflection
“When looking for repetitions in a process, I learned to pay attention to _______________ because...”