Breakout 4a: Questioning, listening, and responding to elicit/promote
students’ mathematical thinking
Time Bar:
MO: 40
AC: 50
CO: 15
Action!
Materials
 Base 10 materials
 Linking Cubes
Practice questioning and listening strategies that evoke and expose
 Square Tiles
thinking
 Algebra Tiles
Reflect on the role of the teacher and the role of the students in a learning  Graph Paper
 Card Stock (6)
community
 Math Process Posters
Make connections between number sense, fractions, and algebra
Use the area mode to explore part to whole relationships and support math  Sticky Notes
 Chart Paper, Markers
reasoning
 Math Talk Research
Article
 Video Camera
 BLM 4.1 (1/group)
 BLM 4.2 (1/group)
Learning Goals
1.
2.
3.
4.
Minds On…
9-12 Breakout
Whole Group  Watch videos, and listen for: (20 min)
Watch Jerry Sienfeld teaching History video(Questioning, Responding)
Watch a video of Math Talk in action
Q.What are the key differences between these two classes? Consider the role of the
teacher and the role of the students (turn and talk)
Individual  Reflection (15 min)
Read Math Talk Learning Community research synopsis – highlight ideas – selfassess (turn and talk)
Q. Where does listening fit in? (Anchor Chart - Role of Listening in a Learning
Community, put on learning wall)
Groups of 4  Frayer Model (10 min)
Participants create Frayer model for Interpretive Listening, put on learning wall
(Characteristics, Examples (responses, question stems), Non-examples (responses,
question stems), Definition)
Teacher led Introduction (10 min)
Introduce Goals for the activity:
1. To understand how work with fractions supports algebraic reasoning.
2. To explore fraction meanings through the area model
3. To practice interpretive listening and responding as students and teachers
Introduce ideas and terms: unit fraction, relational thinking, distributive property,
area model
Groups of 4  Teacher/Student Simulation (10min + 25 min)
Ask for volunteers to be the teachers (each group needs 1 teacher)
1.Intro (10 minutes)
- One facilitator takes “teachers” to another room and review activity, learning
goals, possible “student” thinking (see BLM 4a.2)
-Other facilitator leads “students” in the creation of a set of stems to be used
during their upcoming “Math Talk” session.
2.Groups work on the Activity (BLM4a.1) while “teachers” circulate and use
interpretive listening, questioning, and responding to move towards learning goals.
- Teachers confer to advise each other on responses / questions / prompts
Teacher  Consolidate Math Learning (10 minutes)
– teacher pulls samples from the class and consolidates key ideas on an anchor
Consolidate chart (BLM4a.3) OR Gallery Walk
Debrief
Individual Exit Card (5 minutes)
-How did it feel being a student? A teacher?
- When it comes to Math Talk, what is your next step?
Draw out key
characteristics – shift
from teacher to student
1)
Questioning
2)
Explaining thinking
3)
Source of
Mathematical Ideas
4)
Responsibility for
Learning
Use SelfAssessment anchors
learning in personal
context
The goal is to practice
interpretive listening and
questioning from the
perspective of the
learner (student) and
the teacher through an
learning experience.
The area model is used
to represent fraction as
linear measure, part to
whole, and operator
Videotape group
work / math talk to
personalize learning in
later sessions and for
use on learning wall
Collect exit cards
and collate feedback.
Summarize key points
and display in class
4a.1: Activity: Making Connections
Student Copy
Learning Goals:




Model and decompose whole numbers, fractions and algebraic expressions
Engage in algebraic thinking and reasoning
Use manipulatives as thinking tools
Make connections between whole numbers, fractions, and algebra
Instructions: Work through the following questions as a group.
Do not rush – you do not need to finish all of the questions.
Record your thinking on chart paper.
Listen to each other and build on each other’s ideas.
Thinking Tools: Base 10 blocks, algebra tiles, cubalinks or square tiles, graph paper
1. Represent 144 using the base 10 blocks. Show several different arrangements.
Write equivalent expressions that reflect these arrangements.
2. Now suppose the big square represents 1.
What do your arrangements illustrate?
3. Now suppose the big square represents x2.
What do your arrangements represent?
4a.2: Activity: Making Connections
Teacher Copy
Learning Goals:




Model and decompose whole numbers, fractions and algebraic expressions
Engage in algebraic thinking and reasoning
Use manipulatives as thinking tools
Make connections between whole numbers, fractions, and algebra
Key Ideas:
Arrangements represent expressions
Equivalent expressions
Distribute Property
Area model for multiplication – looking at dimensions (length x width = area)
Redefining the whole
Connecting fraction meanings : operator, linear measure, part to whole (area)
Instructions: Work through the following questions as a group.
Do not rush – you do not need to finish all of the questions.
Record your thinking on chart paper.
Listen to each other and build on each other’s ideas.
Thinking Tools: Base 10 blocks, algebra tiles, cubalinks or square tiles, graph paper
1. Represent 144 using the base 10 blocks. Show several different arrangements.
Write equivalent expressions that reflect these arrangements.
ex. 100 + (4 x 10) + 4 = (14 x 10) + 4 = 12 x 12 = (10 x 10) + 2(10 x 2) + 4
 Encourage connections between “groups of” and “dimensions”
(ex. 40 is 4 groups of 10, or 4 by 10)
 Encourage many arrangements / expressions
 Encourage the creation of a square to represent the
square number. (12 x 12)
 Encourage the four parts of the multiplication
144 = (10 x 10) + 2(10 x 2) + 4
4a.2 (continued)
2. Now suppose the big square represents 1.
What do your arrangements illustrate?







We are now redefining the whole
Smallest square is .01 or 1/100 of the whole
Row of 10 is 0.1 or 1/10 of the whole
Encourage use of decimal and fraction notation (10ths, 100ths)
Encourage the creation of a square 1 and 1/5 by 1 and 1/5 (1.2 x 1.2)
1/10 of 1/10 same as 1/10 by 1/10  move to dimensions
Encourage the four parts of the multiplication with decimals and fractions
3. Now suppose the big square represents x2.
What do your arrangements represent?
 Introduce algebra tiles, and encourage connections
4a.3: Possible Anchor Chart : Algebraic Reasoning through Area Models
Distributive Property – Whole Numbers
Distributive Property – Fractions and Decimals
Distributive Property – Binomials