TEAM-Math and AMSTI Professional Mathematics Learning Communities

Building Classroom Discourse

Goals for Todayrsquos Session

To better understandbull How to analyze and organize student thinking

in order to promote discoursebull Teacher and student actions that support a

discourse-rich classroom environment

The Typical Math Classroom

Discussion in groupsbull What is the daily routine for the typical

mathematics classroombull What is the teacherrsquos role What is the

studentsrsquo rolebull What are the limitations of this organizationbull What might be an alternative approach

Discourse

bull What do we mean by ldquodiscourserdquoFrom Principles to Actionsbull Mathematical discourse includes the

purposeful exchange of ideas through classroom discussion as well as through other forms of verbal visual and written communication

Advantages

bull What are the advantages to a classroom that focuses on building student discourse

From Principles to Actionsbull The discourse in the mathematics classroom gives

students opportunities tondash share ideas and clarify understandings ndash construct convincing arguments regarding why and

how things work ndash develop a language for expressing mathematical ideas

andndash learn to see things from other perspectives

Phases of a Lesson

bull Launch ndash full group introduction to a worthwhile task

bull Explore ndash generally in small groupsbull Share and Summarize ndash full groupbull Applyextend ndash small groups or individually

Five Practicesfor effectively using student responses in classroom discourse

bull Anticipating student responses prior to the lesson bull Monitoring studentsrsquo work on and engagement with

the tasks bull Selecting particular students to present their

mathematical work bull Sequencing

1113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088studentsrsquo responses in a particular order for discussion

bull Connecting different studentsrsquo responses and connecting the responses to key mathematical ideas

The Candy Jar

bull Solve the problem in as many ways as you canbull Analyze the sample student solutionsbull Discuss the sequence in which you would have

students present their solutions

What Happenedhellipbull Mr Donnelly monitors his students as they work in

small groups on the Candy Jar task providing support as needed and taking note of their strategies

bull He decides to have the groups who created solutions B A and D present their work (in this order) since these groups used the strategies that he is targeting (ie scaling up scale factor and unit rate)

bull This sequencing reflects the sophistication and frequency of strategies (ie most groups used a version of the scaling up strategy and only one group used the unit rate strategy)

What Happenedhellipbull During the discussion Mr Donnelly asks the presenters to explain

what they did and why and he invites other students to consider whether the approach makes sense and to ask questions He makes a point of labeling each of the three strategies asking students which one is most efficient in solving this particular task and he poses questions that help students make connections among the strategies and with the key ideas that he is targeting

bull Specifically he wants students to see that the scale factor is the same as the number of entries in the table used for scaling up In other words it would take 20 candy jars with the same number of Jolly Ranchers and jawbreakers as the original jar to make the new candy jar Mr Donnelly then will have his students compare this result with the unit rate which is the factor that relates the number of Jolly Ranchers and the number of jawbreakers in each column of the table in solution 1 (eg 5 times 26 = 13 just as 55 times 26 = 143 just as 100 times 26 = 260)

What Happenedhellipbull Toward the end of the lesson Mr Donnelly places

solution C on the document camera in the classroom and asks students to decide whether or not this is a viable approach to solving the task and to justify their answers

bull Mr Donnelly gives the students five minutes to write a response and he collects their responses as they leave the room to go to the next class He expects their responses to give him some insight into whether they are coming to understand that for ratios to remain constant their numerators and denominators must grow at a rate that is multiplicative not additive

Teacher and Student Actions

bull Look at the chartndash How are the teacher and student actions

connectedndash Which of these do you experience on a consistent

basisndash Which of these are more challenging to do

bull What connections to the Standards for Mathematical Practice do the Student Actions suggest

• TEAM-Math and AMSTI Professional Mathematics Learning Communiti
• Goals for Todayrsquos Session
• The Typical Math Classroom
• Discourse
• Advantages
• Phases of a Lesson
• Five Practices for effectively using student responses in class
• The Candy Jar
• What Happenedhellip
• What Happenedhellip (2)
• What Happenedhellip (3)
• Teacher and Student Actions

Goals for Todayrsquos Session

To better understandbull How to analyze and organize student thinking

in order to promote discoursebull Teacher and student actions that support a

discourse-rich classroom environment

The Typical Math Classroom

Discussion in groupsbull What is the daily routine for the typical

mathematics classroombull What is the teacherrsquos role What is the

studentsrsquo rolebull What are the limitations of this organizationbull What might be an alternative approach

Discourse

bull What do we mean by ldquodiscourserdquoFrom Principles to Actionsbull Mathematical discourse includes the

purposeful exchange of ideas through classroom discussion as well as through other forms of verbal visual and written communication

Advantages

bull What are the advantages to a classroom that focuses on building student discourse

From Principles to Actionsbull The discourse in the mathematics classroom gives

students opportunities tondash share ideas and clarify understandings ndash construct convincing arguments regarding why and

how things work ndash develop a language for expressing mathematical ideas

andndash learn to see things from other perspectives

Phases of a Lesson

bull Launch ndash full group introduction to a worthwhile task

bull Explore ndash generally in small groupsbull Share and Summarize ndash full groupbull Applyextend ndash small groups or individually

Five Practicesfor effectively using student responses in classroom discourse

bull Anticipating student responses prior to the lesson bull Monitoring studentsrsquo work on and engagement with

the tasks bull Selecting particular students to present their

mathematical work bull Sequencing

1113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088studentsrsquo responses in a particular order for discussion

bull Connecting different studentsrsquo responses and connecting the responses to key mathematical ideas

The Candy Jar

bull Solve the problem in as many ways as you canbull Analyze the sample student solutionsbull Discuss the sequence in which you would have

students present their solutions

What Happenedhellipbull Mr Donnelly monitors his students as they work in

small groups on the Candy Jar task providing support as needed and taking note of their strategies

bull He decides to have the groups who created solutions B A and D present their work (in this order) since these groups used the strategies that he is targeting (ie scaling up scale factor and unit rate)

bull This sequencing reflects the sophistication and frequency of strategies (ie most groups used a version of the scaling up strategy and only one group used the unit rate strategy)

What Happenedhellipbull During the discussion Mr Donnelly asks the presenters to explain

what they did and why and he invites other students to consider whether the approach makes sense and to ask questions He makes a point of labeling each of the three strategies asking students which one is most efficient in solving this particular task and he poses questions that help students make connections among the strategies and with the key ideas that he is targeting

bull Specifically he wants students to see that the scale factor is the same as the number of entries in the table used for scaling up In other words it would take 20 candy jars with the same number of Jolly Ranchers and jawbreakers as the original jar to make the new candy jar Mr Donnelly then will have his students compare this result with the unit rate which is the factor that relates the number of Jolly Ranchers and the number of jawbreakers in each column of the table in solution 1 (eg 5 times 26 = 13 just as 55 times 26 = 143 just as 100 times 26 = 260)

What Happenedhellipbull Toward the end of the lesson Mr Donnelly places

solution C on the document camera in the classroom and asks students to decide whether or not this is a viable approach to solving the task and to justify their answers

bull Mr Donnelly gives the students five minutes to write a response and he collects their responses as they leave the room to go to the next class He expects their responses to give him some insight into whether they are coming to understand that for ratios to remain constant their numerators and denominators must grow at a rate that is multiplicative not additive

Teacher and Student Actions

bull Look at the chartndash How are the teacher and student actions

connectedndash Which of these do you experience on a consistent

basisndash Which of these are more challenging to do

bull What connections to the Standards for Mathematical Practice do the Student Actions suggest

• TEAM-Math and AMSTI Professional Mathematics Learning Communiti
• Goals for Todayrsquos Session
• The Typical Math Classroom
• Discourse
• Advantages
• Phases of a Lesson
• Five Practices for effectively using student responses in class
• The Candy Jar
• What Happenedhellip
• What Happenedhellip (2)
• What Happenedhellip (3)
• Teacher and Student Actions

The Typical Math Classroom

Discussion in groupsbull What is the daily routine for the typical

mathematics classroombull What is the teacherrsquos role What is the

studentsrsquo rolebull What are the limitations of this organizationbull What might be an alternative approach

Discourse

bull What do we mean by ldquodiscourserdquoFrom Principles to Actionsbull Mathematical discourse includes the

purposeful exchange of ideas through classroom discussion as well as through other forms of verbal visual and written communication

Advantages

bull What are the advantages to a classroom that focuses on building student discourse

From Principles to Actionsbull The discourse in the mathematics classroom gives

students opportunities tondash share ideas and clarify understandings ndash construct convincing arguments regarding why and

how things work ndash develop a language for expressing mathematical ideas

andndash learn to see things from other perspectives

Phases of a Lesson

bull Launch ndash full group introduction to a worthwhile task

bull Explore ndash generally in small groupsbull Share and Summarize ndash full groupbull Applyextend ndash small groups or individually

Five Practicesfor effectively using student responses in classroom discourse

bull Anticipating student responses prior to the lesson bull Monitoring studentsrsquo work on and engagement with

the tasks bull Selecting particular students to present their

mathematical work bull Sequencing

1113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088studentsrsquo responses in a particular order for discussion

bull Connecting different studentsrsquo responses and connecting the responses to key mathematical ideas

The Candy Jar

bull Solve the problem in as many ways as you canbull Analyze the sample student solutionsbull Discuss the sequence in which you would have

students present their solutions

What Happenedhellipbull Mr Donnelly monitors his students as they work in

small groups on the Candy Jar task providing support as needed and taking note of their strategies

bull He decides to have the groups who created solutions B A and D present their work (in this order) since these groups used the strategies that he is targeting (ie scaling up scale factor and unit rate)

bull This sequencing reflects the sophistication and frequency of strategies (ie most groups used a version of the scaling up strategy and only one group used the unit rate strategy)

What Happenedhellipbull During the discussion Mr Donnelly asks the presenters to explain

what they did and why and he invites other students to consider whether the approach makes sense and to ask questions He makes a point of labeling each of the three strategies asking students which one is most efficient in solving this particular task and he poses questions that help students make connections among the strategies and with the key ideas that he is targeting

bull Specifically he wants students to see that the scale factor is the same as the number of entries in the table used for scaling up In other words it would take 20 candy jars with the same number of Jolly Ranchers and jawbreakers as the original jar to make the new candy jar Mr Donnelly then will have his students compare this result with the unit rate which is the factor that relates the number of Jolly Ranchers and the number of jawbreakers in each column of the table in solution 1 (eg 5 times 26 = 13 just as 55 times 26 = 143 just as 100 times 26 = 260)

What Happenedhellipbull Toward the end of the lesson Mr Donnelly places

solution C on the document camera in the classroom and asks students to decide whether or not this is a viable approach to solving the task and to justify their answers

bull Mr Donnelly gives the students five minutes to write a response and he collects their responses as they leave the room to go to the next class He expects their responses to give him some insight into whether they are coming to understand that for ratios to remain constant their numerators and denominators must grow at a rate that is multiplicative not additive

Teacher and Student Actions

bull Look at the chartndash How are the teacher and student actions

connectedndash Which of these do you experience on a consistent

basisndash Which of these are more challenging to do

bull What connections to the Standards for Mathematical Practice do the Student Actions suggest

• TEAM-Math and AMSTI Professional Mathematics Learning Communiti
• Goals for Todayrsquos Session
• The Typical Math Classroom
• Discourse
• Advantages
• Phases of a Lesson
• Five Practices for effectively using student responses in class
• The Candy Jar
• What Happenedhellip
• What Happenedhellip (2)
• What Happenedhellip (3)
• Teacher and Student Actions

Discourse

bull What do we mean by ldquodiscourserdquoFrom Principles to Actionsbull Mathematical discourse includes the

purposeful exchange of ideas through classroom discussion as well as through other forms of verbal visual and written communication

Advantages

bull What are the advantages to a classroom that focuses on building student discourse

From Principles to Actionsbull The discourse in the mathematics classroom gives

students opportunities tondash share ideas and clarify understandings ndash construct convincing arguments regarding why and

how things work ndash develop a language for expressing mathematical ideas

andndash learn to see things from other perspectives

Phases of a Lesson

bull Launch ndash full group introduction to a worthwhile task

bull Explore ndash generally in small groupsbull Share and Summarize ndash full groupbull Applyextend ndash small groups or individually

Five Practicesfor effectively using student responses in classroom discourse

bull Anticipating student responses prior to the lesson bull Monitoring studentsrsquo work on and engagement with

the tasks bull Selecting particular students to present their

mathematical work bull Sequencing

1113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088studentsrsquo responses in a particular order for discussion

bull Connecting different studentsrsquo responses and connecting the responses to key mathematical ideas

The Candy Jar

bull Solve the problem in as many ways as you canbull Analyze the sample student solutionsbull Discuss the sequence in which you would have

students present their solutions

What Happenedhellipbull Mr Donnelly monitors his students as they work in

small groups on the Candy Jar task providing support as needed and taking note of their strategies

bull He decides to have the groups who created solutions B A and D present their work (in this order) since these groups used the strategies that he is targeting (ie scaling up scale factor and unit rate)

bull This sequencing reflects the sophistication and frequency of strategies (ie most groups used a version of the scaling up strategy and only one group used the unit rate strategy)

What Happenedhellipbull During the discussion Mr Donnelly asks the presenters to explain

what they did and why and he invites other students to consider whether the approach makes sense and to ask questions He makes a point of labeling each of the three strategies asking students which one is most efficient in solving this particular task and he poses questions that help students make connections among the strategies and with the key ideas that he is targeting

bull Specifically he wants students to see that the scale factor is the same as the number of entries in the table used for scaling up In other words it would take 20 candy jars with the same number of Jolly Ranchers and jawbreakers as the original jar to make the new candy jar Mr Donnelly then will have his students compare this result with the unit rate which is the factor that relates the number of Jolly Ranchers and the number of jawbreakers in each column of the table in solution 1 (eg 5 times 26 = 13 just as 55 times 26 = 143 just as 100 times 26 = 260)

What Happenedhellipbull Toward the end of the lesson Mr Donnelly places

solution C on the document camera in the classroom and asks students to decide whether or not this is a viable approach to solving the task and to justify their answers

bull Mr Donnelly gives the students five minutes to write a response and he collects their responses as they leave the room to go to the next class He expects their responses to give him some insight into whether they are coming to understand that for ratios to remain constant their numerators and denominators must grow at a rate that is multiplicative not additive

Teacher and Student Actions

bull Look at the chartndash How are the teacher and student actions

connectedndash Which of these do you experience on a consistent

basisndash Which of these are more challenging to do

bull What connections to the Standards for Mathematical Practice do the Student Actions suggest

• TEAM-Math and AMSTI Professional Mathematics Learning Communiti
• Goals for Todayrsquos Session
• The Typical Math Classroom
• Discourse
• Advantages
• Phases of a Lesson
• Five Practices for effectively using student responses in class
• The Candy Jar
• What Happenedhellip
• What Happenedhellip (2)
• What Happenedhellip (3)
• Teacher and Student Actions

Advantages

bull What are the advantages to a classroom that focuses on building student discourse

From Principles to Actionsbull The discourse in the mathematics classroom gives

students opportunities tondash share ideas and clarify understandings ndash construct convincing arguments regarding why and

how things work ndash develop a language for expressing mathematical ideas

andndash learn to see things from other perspectives

Phases of a Lesson

bull Launch ndash full group introduction to a worthwhile task

bull Explore ndash generally in small groupsbull Share and Summarize ndash full groupbull Applyextend ndash small groups or individually

Five Practicesfor effectively using student responses in classroom discourse

bull Anticipating student responses prior to the lesson bull Monitoring studentsrsquo work on and engagement with

the tasks bull Selecting particular students to present their

mathematical work bull Sequencing

1113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088studentsrsquo responses in a particular order for discussion

bull Connecting different studentsrsquo responses and connecting the responses to key mathematical ideas

The Candy Jar

bull Solve the problem in as many ways as you canbull Analyze the sample student solutionsbull Discuss the sequence in which you would have

students present their solutions

What Happenedhellipbull Mr Donnelly monitors his students as they work in

small groups on the Candy Jar task providing support as needed and taking note of their strategies

bull He decides to have the groups who created solutions B A and D present their work (in this order) since these groups used the strategies that he is targeting (ie scaling up scale factor and unit rate)

bull This sequencing reflects the sophistication and frequency of strategies (ie most groups used a version of the scaling up strategy and only one group used the unit rate strategy)

What Happenedhellipbull During the discussion Mr Donnelly asks the presenters to explain

what they did and why and he invites other students to consider whether the approach makes sense and to ask questions He makes a point of labeling each of the three strategies asking students which one is most efficient in solving this particular task and he poses questions that help students make connections among the strategies and with the key ideas that he is targeting

bull Specifically he wants students to see that the scale factor is the same as the number of entries in the table used for scaling up In other words it would take 20 candy jars with the same number of Jolly Ranchers and jawbreakers as the original jar to make the new candy jar Mr Donnelly then will have his students compare this result with the unit rate which is the factor that relates the number of Jolly Ranchers and the number of jawbreakers in each column of the table in solution 1 (eg 5 times 26 = 13 just as 55 times 26 = 143 just as 100 times 26 = 260)

What Happenedhellipbull Toward the end of the lesson Mr Donnelly places

solution C on the document camera in the classroom and asks students to decide whether or not this is a viable approach to solving the task and to justify their answers

bull Mr Donnelly gives the students five minutes to write a response and he collects their responses as they leave the room to go to the next class He expects their responses to give him some insight into whether they are coming to understand that for ratios to remain constant their numerators and denominators must grow at a rate that is multiplicative not additive

Teacher and Student Actions

bull Look at the chartndash How are the teacher and student actions

connectedndash Which of these do you experience on a consistent

basisndash Which of these are more challenging to do

bull What connections to the Standards for Mathematical Practice do the Student Actions suggest

• TEAM-Math and AMSTI Professional Mathematics Learning Communiti
• Goals for Todayrsquos Session
• The Typical Math Classroom
• Discourse
• Advantages
• Phases of a Lesson
• Five Practices for effectively using student responses in class
• The Candy Jar
• What Happenedhellip
• What Happenedhellip (2)
• What Happenedhellip (3)
• Teacher and Student Actions

Phases of a Lesson

bull Launch ndash full group introduction to a worthwhile task

bull Explore ndash generally in small groupsbull Share and Summarize ndash full groupbull Applyextend ndash small groups or individually

Five Practicesfor effectively using student responses in classroom discourse

bull Anticipating student responses prior to the lesson bull Monitoring studentsrsquo work on and engagement with

the tasks bull Selecting particular students to present their

mathematical work bull Sequencing

1113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088studentsrsquo responses in a particular order for discussion

bull Connecting different studentsrsquo responses and connecting the responses to key mathematical ideas

The Candy Jar

bull Solve the problem in as many ways as you canbull Analyze the sample student solutionsbull Discuss the sequence in which you would have

students present their solutions

What Happenedhellipbull Mr Donnelly monitors his students as they work in

small groups on the Candy Jar task providing support as needed and taking note of their strategies

bull He decides to have the groups who created solutions B A and D present their work (in this order) since these groups used the strategies that he is targeting (ie scaling up scale factor and unit rate)

bull This sequencing reflects the sophistication and frequency of strategies (ie most groups used a version of the scaling up strategy and only one group used the unit rate strategy)

What Happenedhellipbull During the discussion Mr Donnelly asks the presenters to explain

what they did and why and he invites other students to consider whether the approach makes sense and to ask questions He makes a point of labeling each of the three strategies asking students which one is most efficient in solving this particular task and he poses questions that help students make connections among the strategies and with the key ideas that he is targeting

bull Specifically he wants students to see that the scale factor is the same as the number of entries in the table used for scaling up In other words it would take 20 candy jars with the same number of Jolly Ranchers and jawbreakers as the original jar to make the new candy jar Mr Donnelly then will have his students compare this result with the unit rate which is the factor that relates the number of Jolly Ranchers and the number of jawbreakers in each column of the table in solution 1 (eg 5 times 26 = 13 just as 55 times 26 = 143 just as 100 times 26 = 260)

What Happenedhellipbull Toward the end of the lesson Mr Donnelly places

solution C on the document camera in the classroom and asks students to decide whether or not this is a viable approach to solving the task and to justify their answers

bull Mr Donnelly gives the students five minutes to write a response and he collects their responses as they leave the room to go to the next class He expects their responses to give him some insight into whether they are coming to understand that for ratios to remain constant their numerators and denominators must grow at a rate that is multiplicative not additive

Teacher and Student Actions

bull Look at the chartndash How are the teacher and student actions

connectedndash Which of these do you experience on a consistent

basisndash Which of these are more challenging to do

bull What connections to the Standards for Mathematical Practice do the Student Actions suggest

• TEAM-Math and AMSTI Professional Mathematics Learning Communiti
• Goals for Todayrsquos Session
• The Typical Math Classroom
• Discourse
• Advantages
• Phases of a Lesson
• Five Practices for effectively using student responses in class
• The Candy Jar
• What Happenedhellip
• What Happenedhellip (2)
• What Happenedhellip (3)
• Teacher and Student Actions

Five Practicesfor effectively using student responses in classroom discourse

bull Anticipating student responses prior to the lesson bull Monitoring studentsrsquo work on and engagement with

the tasks bull Selecting particular students to present their

mathematical work bull Sequencing

1113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088111308811130881113088studentsrsquo responses in a particular order for discussion

bull Connecting different studentsrsquo responses and connecting the responses to key mathematical ideas

The Candy Jar

bull Solve the problem in as many ways as you canbull Analyze the sample student solutionsbull Discuss the sequence in which you would have

students present their solutions

What Happenedhellipbull Mr Donnelly monitors his students as they work in

small groups on the Candy Jar task providing support as needed and taking note of their strategies

bull He decides to have the groups who created solutions B A and D present their work (in this order) since these groups used the strategies that he is targeting (ie scaling up scale factor and unit rate)

bull This sequencing reflects the sophistication and frequency of strategies (ie most groups used a version of the scaling up strategy and only one group used the unit rate strategy)

What Happenedhellipbull During the discussion Mr Donnelly asks the presenters to explain

what they did and why and he invites other students to consider whether the approach makes sense and to ask questions He makes a point of labeling each of the three strategies asking students which one is most efficient in solving this particular task and he poses questions that help students make connections among the strategies and with the key ideas that he is targeting

bull Specifically he wants students to see that the scale factor is the same as the number of entries in the table used for scaling up In other words it would take 20 candy jars with the same number of Jolly Ranchers and jawbreakers as the original jar to make the new candy jar Mr Donnelly then will have his students compare this result with the unit rate which is the factor that relates the number of Jolly Ranchers and the number of jawbreakers in each column of the table in solution 1 (eg 5 times 26 = 13 just as 55 times 26 = 143 just as 100 times 26 = 260)

What Happenedhellipbull Toward the end of the lesson Mr Donnelly places

solution C on the document camera in the classroom and asks students to decide whether or not this is a viable approach to solving the task and to justify their answers

bull Mr Donnelly gives the students five minutes to write a response and he collects their responses as they leave the room to go to the next class He expects their responses to give him some insight into whether they are coming to understand that for ratios to remain constant their numerators and denominators must grow at a rate that is multiplicative not additive

Teacher and Student Actions

bull Look at the chartndash How are the teacher and student actions

connectedndash Which of these do you experience on a consistent

basisndash Which of these are more challenging to do

bull What connections to the Standards for Mathematical Practice do the Student Actions suggest

• TEAM-Math and AMSTI Professional Mathematics Learning Communiti
• Goals for Todayrsquos Session
• The Typical Math Classroom
• Discourse
• Advantages
• Phases of a Lesson
• Five Practices for effectively using student responses in class
• The Candy Jar
• What Happenedhellip
• What Happenedhellip (2)
• What Happenedhellip (3)
• Teacher and Student Actions

The Candy Jar

bull Solve the problem in as many ways as you canbull Analyze the sample student solutionsbull Discuss the sequence in which you would have

students present their solutions

What Happenedhellipbull Mr Donnelly monitors his students as they work in

small groups on the Candy Jar task providing support as needed and taking note of their strategies

bull He decides to have the groups who created solutions B A and D present their work (in this order) since these groups used the strategies that he is targeting (ie scaling up scale factor and unit rate)

bull This sequencing reflects the sophistication and frequency of strategies (ie most groups used a version of the scaling up strategy and only one group used the unit rate strategy)

What Happenedhellipbull During the discussion Mr Donnelly asks the presenters to explain

what they did and why and he invites other students to consider whether the approach makes sense and to ask questions He makes a point of labeling each of the three strategies asking students which one is most efficient in solving this particular task and he poses questions that help students make connections among the strategies and with the key ideas that he is targeting

bull Specifically he wants students to see that the scale factor is the same as the number of entries in the table used for scaling up In other words it would take 20 candy jars with the same number of Jolly Ranchers and jawbreakers as the original jar to make the new candy jar Mr Donnelly then will have his students compare this result with the unit rate which is the factor that relates the number of Jolly Ranchers and the number of jawbreakers in each column of the table in solution 1 (eg 5 times 26 = 13 just as 55 times 26 = 143 just as 100 times 26 = 260)

What Happenedhellipbull Toward the end of the lesson Mr Donnelly places

solution C on the document camera in the classroom and asks students to decide whether or not this is a viable approach to solving the task and to justify their answers

bull Mr Donnelly gives the students five minutes to write a response and he collects their responses as they leave the room to go to the next class He expects their responses to give him some insight into whether they are coming to understand that for ratios to remain constant their numerators and denominators must grow at a rate that is multiplicative not additive

Teacher and Student Actions

bull Look at the chartndash How are the teacher and student actions

connectedndash Which of these do you experience on a consistent

basisndash Which of these are more challenging to do

bull What connections to the Standards for Mathematical Practice do the Student Actions suggest

• TEAM-Math and AMSTI Professional Mathematics Learning Communiti
• Goals for Todayrsquos Session
• The Typical Math Classroom
• Discourse
• Advantages
• Phases of a Lesson
• Five Practices for effectively using student responses in class
• The Candy Jar
• What Happenedhellip
• What Happenedhellip (2)
• What Happenedhellip (3)
• Teacher and Student Actions

What Happenedhellipbull Mr Donnelly monitors his students as they work in

small groups on the Candy Jar task providing support as needed and taking note of their strategies

bull He decides to have the groups who created solutions B A and D present their work (in this order) since these groups used the strategies that he is targeting (ie scaling up scale factor and unit rate)

bull This sequencing reflects the sophistication and frequency of strategies (ie most groups used a version of the scaling up strategy and only one group used the unit rate strategy)

What Happenedhellipbull During the discussion Mr Donnelly asks the presenters to explain

what they did and why and he invites other students to consider whether the approach makes sense and to ask questions He makes a point of labeling each of the three strategies asking students which one is most efficient in solving this particular task and he poses questions that help students make connections among the strategies and with the key ideas that he is targeting

bull Specifically he wants students to see that the scale factor is the same as the number of entries in the table used for scaling up In other words it would take 20 candy jars with the same number of Jolly Ranchers and jawbreakers as the original jar to make the new candy jar Mr Donnelly then will have his students compare this result with the unit rate which is the factor that relates the number of Jolly Ranchers and the number of jawbreakers in each column of the table in solution 1 (eg 5 times 26 = 13 just as 55 times 26 = 143 just as 100 times 26 = 260)

What Happenedhellipbull Toward the end of the lesson Mr Donnelly places

solution C on the document camera in the classroom and asks students to decide whether or not this is a viable approach to solving the task and to justify their answers

bull Mr Donnelly gives the students five minutes to write a response and he collects their responses as they leave the room to go to the next class He expects their responses to give him some insight into whether they are coming to understand that for ratios to remain constant their numerators and denominators must grow at a rate that is multiplicative not additive

Teacher and Student Actions

bull Look at the chartndash How are the teacher and student actions

connectedndash Which of these do you experience on a consistent

basisndash Which of these are more challenging to do

bull What connections to the Standards for Mathematical Practice do the Student Actions suggest

• TEAM-Math and AMSTI Professional Mathematics Learning Communiti
• Goals for Todayrsquos Session
• The Typical Math Classroom
• Discourse
• Advantages
• Phases of a Lesson
• Five Practices for effectively using student responses in class
• The Candy Jar
• What Happenedhellip
• What Happenedhellip (2)
• What Happenedhellip (3)
• Teacher and Student Actions

What Happenedhellipbull During the discussion Mr Donnelly asks the presenters to explain

what they did and why and he invites other students to consider whether the approach makes sense and to ask questions He makes a point of labeling each of the three strategies asking students which one is most efficient in solving this particular task and he poses questions that help students make connections among the strategies and with the key ideas that he is targeting

bull Specifically he wants students to see that the scale factor is the same as the number of entries in the table used for scaling up In other words it would take 20 candy jars with the same number of Jolly Ranchers and jawbreakers as the original jar to make the new candy jar Mr Donnelly then will have his students compare this result with the unit rate which is the factor that relates the number of Jolly Ranchers and the number of jawbreakers in each column of the table in solution 1 (eg 5 times 26 = 13 just as 55 times 26 = 143 just as 100 times 26 = 260)

What Happenedhellipbull Toward the end of the lesson Mr Donnelly places

solution C on the document camera in the classroom and asks students to decide whether or not this is a viable approach to solving the task and to justify their answers

bull Mr Donnelly gives the students five minutes to write a response and he collects their responses as they leave the room to go to the next class He expects their responses to give him some insight into whether they are coming to understand that for ratios to remain constant their numerators and denominators must grow at a rate that is multiplicative not additive

Teacher and Student Actions

bull Look at the chartndash How are the teacher and student actions

connectedndash Which of these do you experience on a consistent

basisndash Which of these are more challenging to do

bull What connections to the Standards for Mathematical Practice do the Student Actions suggest

• TEAM-Math and AMSTI Professional Mathematics Learning Communiti
• Goals for Todayrsquos Session
• The Typical Math Classroom
• Discourse
• Advantages
• Phases of a Lesson
• Five Practices for effectively using student responses in class
• The Candy Jar
• What Happenedhellip
• What Happenedhellip (2)
• What Happenedhellip (3)
• Teacher and Student Actions

What Happenedhellipbull Toward the end of the lesson Mr Donnelly places

solution C on the document camera in the classroom and asks students to decide whether or not this is a viable approach to solving the task and to justify their answers

bull Mr Donnelly gives the students five minutes to write a response and he collects their responses as they leave the room to go to the next class He expects their responses to give him some insight into whether they are coming to understand that for ratios to remain constant their numerators and denominators must grow at a rate that is multiplicative not additive

Teacher and Student Actions

bull Look at the chartndash How are the teacher and student actions

connectedndash Which of these do you experience on a consistent

basisndash Which of these are more challenging to do

bull What connections to the Standards for Mathematical Practice do the Student Actions suggest

• TEAM-Math and AMSTI Professional Mathematics Learning Communiti
• Goals for Todayrsquos Session
• The Typical Math Classroom
• Discourse
• Advantages
• Phases of a Lesson
• Five Practices for effectively using student responses in class
• The Candy Jar
• What Happenedhellip
• What Happenedhellip (2)
• What Happenedhellip (3)
• Teacher and Student Actions

Teacher and Student Actions

bull Look at the chartndash How are the teacher and student actions

connectedndash Which of these do you experience on a consistent

basisndash Which of these are more challenging to do

bull What connections to the Standards for Mathematical Practice do the Student Actions suggest

• TEAM-Math and AMSTI Professional Mathematics Learning Communiti
• Goals for Todayrsquos Session
• The Typical Math Classroom
• Discourse
• Advantages
• Phases of a Lesson
• Five Practices for effectively using student responses in class
• The Candy Jar
• What Happenedhellip
• What Happenedhellip (2)
• What Happenedhellip (3)
• Teacher and Student Actions