HWDSB Math Strategy, Grade 2
HWDSB Math Strategy, Grade 2 Day 3 ~ Proportional Reasoning Blog - math.commons.hwdsb.on.ca Twitter - #hwdsbmathstrategy
Norms of Collaboration Presume positive intentions Promoting a spirit of inquiry Pausing Paraphrasing Probing Putting forward ideas Paying attention to self and others
AGENDA 1. Passport of Proportional Reasoning -Evidence of Student Learning 2. Examining Big Ideas 3. Reflection on Proportional Reasoning Focus 4. Exit Card
Help Us Clear Customs!
Getting Through Customs ● What’s an example of where we use proportional reasoning in the real world? ● What’s the difference between absolute and relative terms? ● What key concept is the basis for multiplication and our place value system?
Getting Through Customs ● Which concept involves thinking about how quantities relate, co-vary, or change together? ● Rational numbers are numbers that can be expressed as _____. ● Ability to use proportional relationships is a complex process that develops over an extended period of time. True or False?
Evidence of Learning •Sharing Evidence & Discussion •Recording in passport •Documentation posted on blog
Passport of Proportional Reasoning ● At your table groups, discuss the evidence of learning you brought for your marker students ● Focus for discussion might include: ○ What was your criteria for selecting students? ○ In what ways does this artifact provide evidence of the student’s growing understanding of proportional reasoning? ○ What strategies did you implement to move student understanding of proportional reasoning forward?
Why Does Professional Learning Matter So Much? What teachers are doing in classes with students on a daily basis has the greatest potential to influence the academic outcome for students, and the more challenged students are in social capital terms, the more true this is. ~Steven Katz, Intentional Interruptions
Big Ideas Big ideas are the enduring understandings that underpin the K-12 mathematics curricula. Each one is represented in many, if not all, grades. They are similar to the Mathematical Processes in that they are fundamental content concepts that repeatedly emerge and grow in the study of mathematics. ~Big Ideas and Questioning K-12: Proportional Reasoning
Why Big Ideas? Big ideas help us to ● prioritize and organize ● clarify aspects to focus on ● help build essential connections
Big Ideas are Everywhere!
Big Ideas in Proportional Reasoning
Connecting It All Together Student Work
TASK
Big Idea
Proportional Reasoning
BIN 5: The operations of addition, subtraction, multiplication, and division each hold the same fundamental meaning no matter the domain to which they are applied. The meanings of addition, subtraction, multiplication, and division hold true, regardless of the type of number being used.
What are some ways you could pack 32 cookies equally into bags. Show your work.
Questioning p. 14-15 & Task p.12-13
BIN 2:
Classifying numbers or numerical relationships provides information about the characteristics of the numbers or the relationship. Sometimes if you know a little about a number or relationship, you know more than you realize.
Fewer than 6 children equally share close to 26 treats. What do you know, for sure, about how many treats each child gets? Questioning p. 8-9 & Task p. 4-5
BIN 2 - Guiding Questions 1. What evidence is there that the student understands the big idea? 2. What evidence is there of proportional reasoning within the big idea? 3. What are the next steps for instruction?
Changing a Question... Fewer than 8 children equally share close to 100 treats. What do you know, for sure, about how many treats each gets? ➔ Fewer than 6 children equally share close to 26 treats. What do you know, for sure, about how many treats each child gets? ➔ 6 children equally share 26 treats. About how many treats does each child get?
Passport of Proportional Reasoning ● Find someone from another school that you haven’t talked to yet today. ● Take time to explore the artifacts that each of you brought. ● Discuss: ○ In what ways does this artifact provide evidence of the students’ growing understanding of proportional reasoning? ○ What changes in your instructional practice have you noticed as a result of this focus on proportional reasoning?
BIN 6: There are many algorithms for performing a given operation. You can add, subtract, multiply, or divide in more than one way.
What are all the different ways you can find the sum if you add 67 + 45?
Questioning p. 16-17 & Task p. 14-15
BIN 6 - Guiding Questions ● Anticipate student responses ● What models might students use? ● How does the task connect to the Big Idea and Proportional Reasoning?
Many Algorithms for Addition
Many Algorithms for Subtraction
BIN 4: Numbers are compared in many ways. Sometimes they are compared to each other; other times, they are compared to benchmark numbers. Numbers can be compared in different ways -- sometimes to each other and sometimes to benchmark numbers.
Compare the numbers 20 and 12. Represent your thinking.
Questioning p. 12-13 & Task p. 8-9
BIN 4 - Guiding Questions ● Anticipate student thinking and responses ● How could the student thinking relate to the big idea and proportional reasoning?
BIN 4 - Student Work Look at the student work on the table. ● What possible questions could you ask to further draw out the proportional reasoning? ● What mathematical vocabulary are the students’ using? ● What representations have they used?
Bin 4 - Next Step Choose a number for the second mark on the number line. Mark a third point on the line. Tell what number the point represents and explain your thinking. 0
The Number Line as a Thinking Tool Peterborough Lesson Study Team, Kindergarten to Grade Two
The Power of the Number Line
Resources
Next Steps... ● ● ● ●
visiting the blog (math.commons.hwdsb.on.ca) learning with the resources provided continuing your conversations connecting with instructional coach
Your Declaration!
Thank You!
Norms of Collaboration Presume positive intentions Promoting a spirit of inquiry Pausing Paraphrasing Probing Putting forward ideas Paying attention to self and others
AGENDA 1. Passport of Proportional Reasoning -Evidence of Student Learning 2. Examining Big Ideas 3. Reflection on Proportional Reasoning Focus 4. Exit Card
Help Us Clear Customs!
Getting Through Customs ● What’s an example of where we use proportional reasoning in the real world? ● What’s the difference between absolute and relative terms? ● What key concept is the basis for multiplication and our place value system?
Getting Through Customs ● Which concept involves thinking about how quantities relate, co-vary, or change together? ● Rational numbers are numbers that can be expressed as _____. ● Ability to use proportional relationships is a complex process that develops over an extended period of time. True or False?
Evidence of Learning •Sharing Evidence & Discussion •Recording in passport •Documentation posted on blog
Passport of Proportional Reasoning ● At your table groups, discuss the evidence of learning you brought for your marker students ● Focus for discussion might include: ○ What was your criteria for selecting students? ○ In what ways does this artifact provide evidence of the student’s growing understanding of proportional reasoning? ○ What strategies did you implement to move student understanding of proportional reasoning forward?
Why Does Professional Learning Matter So Much? What teachers are doing in classes with students on a daily basis has the greatest potential to influence the academic outcome for students, and the more challenged students are in social capital terms, the more true this is. ~Steven Katz, Intentional Interruptions
Big Ideas Big ideas are the enduring understandings that underpin the K-12 mathematics curricula. Each one is represented in many, if not all, grades. They are similar to the Mathematical Processes in that they are fundamental content concepts that repeatedly emerge and grow in the study of mathematics. ~Big Ideas and Questioning K-12: Proportional Reasoning
Why Big Ideas? Big ideas help us to ● prioritize and organize ● clarify aspects to focus on ● help build essential connections
Big Ideas are Everywhere!
Big Ideas in Proportional Reasoning
Connecting It All Together Student Work
TASK
Big Idea
Proportional Reasoning
BIN 5: The operations of addition, subtraction, multiplication, and division each hold the same fundamental meaning no matter the domain to which they are applied. The meanings of addition, subtraction, multiplication, and division hold true, regardless of the type of number being used.
What are some ways you could pack 32 cookies equally into bags. Show your work.
Questioning p. 14-15 & Task p.12-13
BIN 2:
Classifying numbers or numerical relationships provides information about the characteristics of the numbers or the relationship. Sometimes if you know a little about a number or relationship, you know more than you realize.
Fewer than 6 children equally share close to 26 treats. What do you know, for sure, about how many treats each child gets? Questioning p. 8-9 & Task p. 4-5
BIN 2 - Guiding Questions 1. What evidence is there that the student understands the big idea? 2. What evidence is there of proportional reasoning within the big idea? 3. What are the next steps for instruction?
Changing a Question... Fewer than 8 children equally share close to 100 treats. What do you know, for sure, about how many treats each gets? ➔ Fewer than 6 children equally share close to 26 treats. What do you know, for sure, about how many treats each child gets? ➔ 6 children equally share 26 treats. About how many treats does each child get?
Passport of Proportional Reasoning ● Find someone from another school that you haven’t talked to yet today. ● Take time to explore the artifacts that each of you brought. ● Discuss: ○ In what ways does this artifact provide evidence of the students’ growing understanding of proportional reasoning? ○ What changes in your instructional practice have you noticed as a result of this focus on proportional reasoning?
BIN 6: There are many algorithms for performing a given operation. You can add, subtract, multiply, or divide in more than one way.
What are all the different ways you can find the sum if you add 67 + 45?
Questioning p. 16-17 & Task p. 14-15
BIN 6 - Guiding Questions ● Anticipate student responses ● What models might students use? ● How does the task connect to the Big Idea and Proportional Reasoning?
Many Algorithms for Addition
Many Algorithms for Subtraction
BIN 4: Numbers are compared in many ways. Sometimes they are compared to each other; other times, they are compared to benchmark numbers. Numbers can be compared in different ways -- sometimes to each other and sometimes to benchmark numbers.
Compare the numbers 20 and 12. Represent your thinking.
Questioning p. 12-13 & Task p. 8-9
BIN 4 - Guiding Questions ● Anticipate student thinking and responses ● How could the student thinking relate to the big idea and proportional reasoning?
BIN 4 - Student Work Look at the student work on the table. ● What possible questions could you ask to further draw out the proportional reasoning? ● What mathematical vocabulary are the students’ using? ● What representations have they used?
Bin 4 - Next Step Choose a number for the second mark on the number line. Mark a third point on the line. Tell what number the point represents and explain your thinking. 0
The Number Line as a Thinking Tool Peterborough Lesson Study Team, Kindergarten to Grade Two
The Power of the Number Line
Resources
Next Steps... ● ● ● ●
visiting the blog (math.commons.hwdsb.on.ca) learning with the resources provided continuing your conversations connecting with instructional coach
Your Declaration!
Thank You!
