1. Routines for Reasoning
Recognizing Repetition –
Pattern Block Fractions

2. Learning Target/Objective
IRMC Routines for Reasoning Action Research Project: Recognizing Repetition Routine
Teacher Name: wallin
Grade: 4
Date:
Standards Addressed:
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. We will connect visual pattern to fraction operations
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. Some students will benefit from having pattern blocks avaialbe.
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?
Students will struggle to see anything that is staying the same each time, but they will discuss what is changing. Using pattern blocks students will have a better idea that we are increasing by two rhombuses (2/3) each time.
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 to 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)?
What do I think the next example will look like? How can we decompose the hexagons to better understand this problem? Can you use numbers to show how the pattern is growing?
How will you select pairs to present?
I will select a group who has good noticing, and who have connected the visual to fractions. If there is no one, then I will choose a group that has successfully completed pattern 5 and I will press them to discuss how they made their decisions. I will then use that to annotate the fractions on the image.
Discuss Generalizations
How will you determine the focus of the final discussion/select student work?
I would like to focus on mixed number and improper fractions. I have slide 7 of my PowerPoint to emphasize this fact. We can label each pattern on the board – showing how the two are equivalent. I want to build confidence with fractions.
How will use models or annotation to support discussion?
We will use the PowerPoint slides and the pattern blocks to show the fraction idea. We will write on the board over the PowerPoint slides or we will use an Elmo to project and annotate on the paper for the whole class to see.
“We noticed __________, so they thought the next pattern would be…”
Reflection on Student Thinking
What sentence frame will you use?
“Looking for what changes and what stays the same in a pattern helps me to…”
What do you hope to learn from the student reflection?
I hope that students can see the power of using visual models for understanding fractions and I hope they discuss how they could see the equivalence between the mixed number and the improper fraction visualizations by the end of the class.

3. 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.

4. 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?

5. 1) 2) 3) 4) “I noticed ___________ stayed the same each time.”
“I noticed ___________ changed each time.” 2) 3) 4)

6. 1)
“We noticed __________, so they thought the next pattern would be…” 2) 5) 3) 4)

7. “They noticed ___________ stayed the same each time.”
“They noticed ___________ changed each time.”

8. Reflection
“Looking for what changes and what stays the same in a pattern helps me to…”