GEEM - Learning Situation

D1. Data Literacy

Manage, analyse, and use data to make convincing arguments and informed decisions, in various contexts drawn from real life.

Learning Situation 1: Handwashing Policy

Total duration: 3 to 5 days

Collecting data and modelling a real world problem, in this case, the time needed for handwashing for an entire class.

Overall and Specific Expectations
Algebra C2. Demonstrate an understanding of variables, expressions, equalities, and inequalities, and apply this understanding in various contexts. C2.3 Solve equations that involve multiple terms, whole numbers, and decimal numbers in various contexts, and verify solutions. C4. Apply the process of mathematical modelling to represent, analyse, make predictions, and provide insight into real-life situations. Number B2. Use knowledge of numbers and operations to solve mathematical problems encountered in everyday life. B2.1 Use the properties and order of operations, and the relationships between operations, to solve problems involving whole numbers, decimal numbers, fractions, ratios, rates, and percents, including those requiring multiple steps or multiple operations. Data D1. Manage, analyse, and use data to make convincing arguments and informed decisions, in various contexts drawn from real life. D1.2 Collect qualitative data and discrete and continuous quantitative data to answer questions of interest, and organize the sets of data as appropriate, including using percentages. Social Emotional Learning (SEL) Skills in Mathematics and the Mathematical Processes A1. Throughout this grade, in order to promote a positive identity as a math learner, to foster well-being and the ability to learn, build resilience, and thrive, students will apply, to the best of their ability, a variety of social-emotional learning skills to support their use of the mathematical processes and their learning in connection with the expectations in the other five strands of the mathematics curriculum. In this lesson, to the best of their ability, students will learn to develop self-awareness and a sense of identity and to think critically and creatively as they apply the mathematical processes reflecting (demonstrate that as they solve problems, they are pausing, looking back, and monitoring their thinking to help clarify their understanding) and representing (select from and create a variety of representations of mathematical ideas and apply them to solve problems) so they can see themselves as capable math learners, and strengthen their sense of ownership of their learning, as part of their emerging sense of identity and belonging and make connections between math and everyday contexts to help them to make informed judgements and decisions.

Overall and Specific Expectations

Algebra

C2. Demonstrate an understanding of variables, expressions, equalities, and inequalities, and apply this understanding in various contexts.

C2.3 Solve equations that involve multiple terms, whole numbers, and decimal numbers in various contexts, and verify solutions.

C4. Apply the process of mathematical modelling to represent, analyse, make predictions, and provide insight into real-life situations.

Number

B2. Use knowledge of numbers and operations to solve mathematical problems encountered in everyday life.

B2.1 Use the properties and order of operations, and the relationships between operations, to solve problems involving whole numbers, decimal numbers, fractions, ratios, rates, and percents, including those requiring multiple steps or multiple operations.

Data

D1. Manage, analyse, and use data to make convincing arguments and informed decisions, in various contexts drawn from real life.

D1.2 Collect qualitative data and discrete and continuous quantitative data to answer questions of interest, and organize the sets of data as appropriate, including using percentages.

Social Emotional Learning (SEL) Skills in Mathematics and the Mathematical Processes

A1. Throughout this grade, in order to promote a positive identity as a math learner, to foster well-being and the ability to learn, build resilience, and thrive, students will apply, to the best of their ability, a variety of social-emotional learning skills to support their use of the mathematical processes and their learning in connection with the expectations in the other five strands of the mathematics curriculum.

In this lesson, to the best of their ability, students will learn to develop self-awareness and a sense of identity and to think critically and creatively as they apply the mathematical processes reflecting (demonstrate that as they solve problems, they are pausing, looking back, and monitoring their thinking to help clarify their understanding) and representing (select from and create a variety of representations of mathematical ideas and apply them to solve problems) so they can see themselves as capable math learners, and strengthen their sense of ownership of their learning, as part of their emerging sense of identity and belonging and make connections between math and everyday contexts to help them to make informed judgements and decisions.

Learning Goals	Success Criteria	Prior Learning
We are learning how to use mathematical tools and processes to create a model that represents a real-life situation. We are learning how to write and solve equations. We are learning how to collect and organize discrete and continuous quantitative data to answer questions of interest and organize the sets of data as appropriate.	I can ask questions that help me to understand the situation. I can identify and apply mathematical concepts that help me to build and verify my mathematical model. I can communicate assumptions I’ve made and explain how they impact my model. I can write an equation using self-selected variables. I can solve equations involving multiple terms and verify my solutions. I can collect data through observation and organize the sets of data as appropriate.	In the past, students should have... Used the properties of operations to solve problems involving whole numbers, decimal numbers, ratios and percents. Solved equations that involve multiple terms and whole numbers and verified solutions. Determined the range as a measure of spread and the measures of central tendency for various data sets.

Learning Goals

Success Criteria

Prior Learning

We are learning how to use mathematical tools and processes to create a model that represents a real-life situation.

We are learning how to write and solve equations.

We are learning how to collect and organize discrete and continuous quantitative data to answer questions of interest and organize the sets of data as appropriate.

I can ask questions that help me to understand the situation.
I can identify and apply mathematical concepts that help me to build and verify my mathematical model.
I can communicate assumptions I’ve made and explain how they impact my model.
I can write an equation using self-selected variables.
I can solve equations involving multiple terms and verify my solutions.
I can collect data through observation and organize the sets of data as appropriate.

In the past, students should have...

Used the properties of operations to solve problems involving whole numbers, decimal numbers, ratios and percents.
Solved equations that involve multiple terms and whole numbers and verified solutions.
Determined the range as a measure of spread and the measures of central tendency for various data sets.

Resources and Materials

Show Me the Science - Why Wash Your Hands? (Appendix 1) copies to distribute to students
The Process of Mathematical Modelling Schema (Appendix 2)
Stopwatch or other tool to measure time, such as a phone or online stopwatch, at least one
OntarioMath.Support Webinar 3 - Mathematical Modelling

For online/hybrid learning, small groups could be set up ahead of time. This could be facilitated via breakout rooms, depending on the different district conferencing tools used. In the breakout rooms, students could work together to generate questions and make assumptions. They could use a virtual whiteboard to support their discussions, such as shared slides, Google Jamboard, Microsoft Whiteboard, Padlet depending on district tools (recording tool). This will also create a record of their work in order to communicate clearly with each other and the teacher. For virtual manipulatives, students can use the mathies website.

If students need to collect data (for example, to time the time it takes for someone to wash their hands), they could do this at home with family members).

Upload copies of Appendix 1 and Appendix 2 ahead of time in your virtual learning environment (for example, Microsoft Teams, Google Classroom, D2L).

Learning and Teaching Activities

Understand the Situation

Student Moves	Teacher Moves
Students will generate questions about the situation that need answering. Students may generate questions as a whole class or as small groups of 3 - 4 students, then share, round-robin style, until all questions have been captured by the teacher. Use virtual breakout rooms and the recording tool.	The teacher will present the situation: In the late 1980's there was a film about a high-school student who has an uncanny skill at skipping classes and getting away with it. Intending to make one last duck-out before graduation he calls in sick, “borrows” a Ferrari, and embarks on a one-day journey through the streets of Chicago. On his trail is high school principal Rooney, who is determined to catch him in the act. (Google synopsis). The teacher will explain to students that in its day, this was a very popular movie and ask students to consider why it might have been so popular and to share their ideas.The teacher will explain that while our movie hero might have skipped school, there are many reasons students are absent from school. The teacher will ask students to identify some reasons they and other students might be absent from school and note the ideas on the board. The teacher will ask students to estimate the percentage of absences related to common contagious illnesses and explain that the incidence of these types of illnesses can be reduced through frequent and proper hand cleaning. The teacher will provide students with a copy of “Show Me the Science - Why Wash Your Hands?” and allow students time to read. The teacher will explain to students that schools are always looking to improve student health and learning. Preventing the spread of illnesses such as the cold and flu will keep kids and their families healthier and improve learning outcomes since absences will be reduced. The teacher will explain to students a school board is considering mandating scheduled hand cleaning several times a day. In order to better understand the impact of this policy, it wants to determine what percentage of instructional time would be lost due to this schedule. The teacher will capture student questions and listen for assumptions and misconceptions about the situation.
Opportunities for Differentiation Task could be simplified by asking students to create a model that predicts the time it takes for a class to wash their hands. Opportunities for Assessment (Observation and Conversation) Students are able to generate questions. Students identify and justify their assumptions.

Student Moves

Teacher Moves

Students will generate questions about the situation that need answering.

Students may generate questions as a whole class or as small groups of 3 - 4 students, then share, round-robin style, until all questions have been captured by the teacher.

Use virtual breakout rooms and the recording tool.

The teacher will present the situation:

In the late 1980's there was a film about a high-school student who has an uncanny skill at skipping classes and getting away with it. Intending to make one last duck-out before graduation he calls in sick, “borrows” a Ferrari, and embarks on a one-day journey through the streets of Chicago. On his trail is high school principal Rooney, who is determined to catch him in the act. (Google synopsis).

The teacher will explain to students that in its day, this was a very popular movie and ask students to consider why it might have been so popular and to share their ideas.The teacher will explain that while our movie hero might have skipped school, there are many reasons students are absent from school.

The teacher will ask students to identify some reasons they and other students might be absent from school and note the ideas on the board.

The teacher will ask students to estimate the percentage of absences related to common contagious illnesses and explain that the incidence of these types of illnesses can be reduced through frequent and proper hand cleaning.

The teacher will provide students with a copy of “Show Me the Science - Why Wash Your Hands?” and allow students time to read.

The teacher will explain to students that schools are always looking to improve student health and learning. Preventing the spread of illnesses such as the cold and flu will keep kids and their families healthier and improve learning outcomes since absences will be reduced.

The teacher will explain to students a school board is considering mandating scheduled hand cleaning several times a day. In order to better understand the impact of this policy, it wants to determine what percentage of instructional time would be lost due to this schedule.

The teacher will capture student questions and listen for assumptions and misconceptions about the situation.

Opportunities for Differentiation

Task could be simplified by asking students to create a model that predicts the time it takes for a class to wash their hands.

Opportunities for Assessment (Observation and Conversation)

Students are able to generate questions.
Students identify and justify their assumptions.

Analyse the Situation

Student Moves	Teacher Moves
With the teacher’s guidance, students will narrow down the initial list of questions. Use the recording tool to narrow down the list of questions. Of the questions that remain, students will brainstorm what information they have and what information they would need to be able to answer these questions.	The teacher will guide students in narrowing down the list of questions: Are some questions the same? Do some questions already have known answers? The teacher will help the students cull the list of questions so that only a few remain. For example: How much time does it take for one class to wash their hands? How much instructional time is there in a day? How many times should a class wash their hands in a day? The teacher will guide students in recognizing the many ways that mathematics can be used to enable us to better understand the situation. Can mathematics be used to gather information that we need? Can mathematics be used to analyse the information we have gathered? What quantities or measurements are required to answer the question? What quantities or measurements do we know? Which quantities or measurements will always stay the same (constant/invariant)? Which quantities or measurements could change (variable)? Can these take on any value, or is there a range of acceptable/realistic values within which these quantities or measurements must lie (constraints)? How could we get information about the quantities/measurements we don't know? Will we have to make any assumptions in order to proceed? For example: I assume it will take _ min. per student to wash their hands. I assume it would be better if we weren't all in a line. I assume that there will need to be some time between each student. I assume that students need to use a sink and not just hand sanitizer. I assume no instruction happens as students are washing hands.

Student Moves

Teacher Moves

With the teacher’s guidance, students will narrow down the initial list of questions.

Use the recording tool to narrow down the list of questions.

Of the questions that remain, students will brainstorm what information they have and what information they would need to be able to answer these questions.

The teacher will guide students in narrowing down the list of questions:

Are some questions the same?
Do some questions already have known answers?

The teacher will help the students cull the list of questions so that only a few remain. For example:

How much time does it take for one class to wash their hands?
How much instructional time is there in a day?
How many times should a class wash their hands in a day?

The teacher will guide students in recognizing the many ways that mathematics can be used to enable us to better understand the situation.

Can mathematics be used to gather information that we need?
Can mathematics be used to analyse the information we have gathered?
What quantities or measurements are required to answer the question?
What quantities or measurements do we know?
Which quantities or measurements will always stay the same (constant/invariant)?
Which quantities or measurements could change (variable)? Can these take on any value, or is there a range of acceptable/realistic values within which these quantities or measurements must lie (constraints)?
How could we get information about the quantities/measurements we don't know?
Will we have to make any assumptions in order to proceed? For example:

I assume it will take _ min. per student to wash their hands.
I assume it would be better if we weren't all in a line.
I assume that there will need to be some time between each student.
I assume that students need to use a sink and not just hand sanitizer.
I assume no instruction happens as students are washing hands.

Create a Mathematical Model

Student Moves	Teacher Moves
Students will use mathematical tools to develop a plan to minimize classroom interruptions, while allowing ample time for each student to wash their hands. They will record all assumptions they are making. They will record all new information they have gathered and how they acquired that information. Students will mathematically justify all estimations and numerical values (either given, researched, or calculated) in their plan. Students' models will be useful to plan for minimized disruptions and predict how long these disruptions will take.	The teacher will look for any misconceptions. They will decide if any are common enough to call to the attention of the entire class, or they can be addressed individually or within the group. The teacher will look out for students who really need to revisit “understand the problem” or “analyse the situation” (Are students struggling with creating a plan because there is something about the situation that they do not fully understand? Are they struggling because they need to make an assumption to narrow down the problem? Did they make an unnecessary assumption that is preventing them from making a fulsome model?) The teacher will decide when would be a good time to have the groups share their progress. Examples of natural checkpoints Students have gathered data. Students have organized data. Students have created a first mathematical model. Use multiple rooms in your videoconferencing tool to have groups share their progress. As groups share their progress, the teacher will question students to help them to reflect on their strengths and their emotions. For example: What feelings came up as you were building your model? How did they change over time? What strength does each group member apply to the process? How did this help you to reach your objective? What was the most interesting part of the modelling process so far? Why?
Opportunities for Differentiation Students may observe someone or a class washing their hands before creating the model. Assist students in organizing their information, providing appropriate strategies or graphic organizers as necessary. Provide direct instruction, as necessary, on: Writing equations Using variables Calculating measures of central tendency Opportunities for Assessment (Observation and Conversation) Students effectively create a model by identifying needed information, using effective strategies and appropriate tools and making links to other situations and other math concepts. Students communicate their ideas and their reasoning clearly, using appropriate vocabulary. Students apply the following, as necessary and appropriate for their model: use the order of operations and the relationships between operations to solve problems including whole numbers, decimal numbers and percentages. solve equations that involve multiple terms. collect qualitative data and discrete and continuous quantitative data to answer questions of interest, and organize the sets of data.

Student Moves

Teacher Moves

Students will use mathematical tools to develop a plan to minimize classroom interruptions, while allowing ample time for each student to wash their hands.

They will record all assumptions they are making.

They will record all new information they have gathered and how they acquired that information.

Students will mathematically justify all estimations and numerical values (either given, researched, or calculated) in their plan.

Students' models will be useful to plan for minimized disruptions and predict how long these disruptions will take.

The teacher will look for any misconceptions. They will decide if any are common enough to call to the attention of the entire class, or they can be addressed individually or within the group.

The teacher will look out for students who really need to revisit “understand the problem” or “analyse the situation” (Are students struggling with creating a plan because there is something about the situation that they do not fully understand? Are they struggling because they need to make an assumption to narrow down the problem? Did they make an unnecessary assumption that is preventing them from making a fulsome model?)

The teacher will decide when would be a good time to have the groups share their progress.
Examples of natural checkpoints

Students have gathered data.
Students have organized data.
Students have created a first mathematical model.

Use multiple rooms in your videoconferencing tool to have groups share their progress.

As groups share their progress, the teacher will question students to help them to reflect on their strengths and their emotions. For example:

What feelings came up as you were building your model? How did they change over time?
What strength does each group member apply to the process? How did this help you to reach your objective?
What was the most interesting part of the modelling process so far? Why?

Opportunities for Differentiation

Students may observe someone or a class washing their hands before creating the model.

Assist students in organizing their information, providing appropriate strategies or graphic organizers as necessary. Provide direct instruction, as necessary, on:

Writing equations
Using variables
Calculating measures of central tendency

Opportunities for Assessment (Observation and Conversation)

Students effectively create a model by identifying needed information, using effective strategies and appropriate tools and making links to other situations and other math concepts.
Students communicate their ideas and their reasoning clearly, using appropriate vocabulary.
Students apply the following, as necessary and appropriate for their model:

use the order of operations and the relationships between operations to solve problems including whole numbers, decimal numbers and percentages.
solve equations that involve multiple terms.
collect qualitative data and discrete and continuous quantitative data to answer questions of interest, and organize the sets of data.

Analyse and Assess the Model

Student Moves	Teacher Moves
Students will use their model to predict the number of minutes it will take their class to wash their hands. A member of each group will write the answer on a sticky-note and place their sticky-notes in ascending order on the board. Students describe their models to the class, including any assumptions they’ve made. Students play-out a handwashing break. Students discuss, in their groups, the difference between their calculation and the experiential result. Students evaluate the accuracy of their model. Did our assumptions make sense? Did we miss important pieces to consider? Students can modify their model, given the new information. Students will reflect on, be prepared to justify and present their opinion on the board policy based on the information provided by their model.	The teacher will ask students to use their model to determine the number of minutes they predict the class will take to wash their hands. The teacher will guide a discussion as to why there might be differences in the predictions. The teacher will ask students to present their models. The teacher will guide students in identifying similarities and differences between the models and any assumptions that have been made. The teacher will guide the group through a handwashing break, timing the experience and present the time to students. Students at home can play out a handwashing break with their family members to test out the model. The teacher will help students to develop their presentation. What mathematical tools did you use, and how did they help solve the problem? Are there situations where your solution wouldn’t work or your model wouldn’t apply? Describe these. What changes would you need to make to your model so that it could be applied to more situations? If you had more time, what else might you do?
Opportunities for Assessment (Observation/Conversation) Students evaluate the accuracy of their model. Students modify their model to better represent new information. Opportunities for Assessment (Production) Students develop and present an opinion using mathematical arguments based on their mathematical models. Students demonstrate an understanding of mathematical modelling, including its limits.

Student Moves

Teacher Moves

Students will use their model to predict the number of minutes it will take their class to wash their hands.

A member of each group will write the answer on a sticky-note and place their sticky-notes in ascending order on the board.

Students describe their models to the class, including any assumptions they’ve made.

Students play-out a handwashing break.

Students discuss, in their groups, the difference between their calculation and the experiential result.

Students evaluate the accuracy of their model.

Did our assumptions make sense?
Did we miss important pieces to consider?

Students can modify their model, given the new information.

Students will reflect on, be prepared to justify and present their opinion on the board policy based on the information provided by their model.

The teacher will ask students to use their model to determine the number of minutes they predict the class will take to wash their hands.

The teacher will guide a discussion as to why there might be differences in the predictions.

The teacher will ask students to present their models.

The teacher will guide students in identifying similarities and differences between the models and any assumptions that have been made.

The teacher will guide the group through a handwashing break, timing the experience and present the time to students.

Students at home can play out a handwashing break with their family members to test out the model.

The teacher will help students to develop their presentation.

What mathematical tools did you use, and how did they help solve the problem?
Are there situations where your solution wouldn’t work or your model wouldn’t apply? Describe these.
What changes would you need to make to your model so that it could be applied to more situations?
If you had more time, what else might you do?

Opportunities for Assessment (Observation/Conversation)

Students evaluate the accuracy of their model.
Students modify their model to better represent new information.

Opportunities for Assessment (Production)

Students develop and present an opinion using mathematical arguments based on their mathematical models.
Students demonstrate an understanding of mathematical modelling, including its limits.

Consolidation of Learning

Student Moves	Teacher Moves
Students will explain their model and present their opinions on the board policy based on the information provided by their model. Use your videoconferencing tool to have groups explain their model. With the teacher’s support, students will identify any commonalities among the presentations. With the teacher’s support, students will reflect on the process of mathematical modelling and contribute their ideas to the development of a classroom Process of Mathematical Modelling schema.	The teacher will note and summarize all the mathematics that was developed during the previous parts of the lesson, including the student's reflections on the mathematical modelling process. The teacher will present the students with the Process of Mathematical Modelling schema (Appendix 2) and ask them to what degree it represents the process they undertook. The teacher will further students' reflections on the mathematical process by asking questions, such as: What is important about this process? In what way are assumptions key to an effective model? To what extent was our model helpful? Allow students to add their own ideas, questions and reminders to the schema.

Student Moves

Teacher Moves

Students will explain their model and present their opinions on the board policy based on the information provided by their model.

Use your videoconferencing tool to have groups explain their model.

With the teacher’s support, students will identify any commonalities among the presentations.

With the teacher’s support, students will reflect on the process of mathematical modelling and contribute their ideas to the development of a classroom Process of Mathematical Modelling schema.

The teacher will note and summarize all the mathematics that was developed during the previous parts of the lesson, including the student's reflections on the mathematical modelling process.

The teacher will present the students with the Process of Mathematical Modelling schema (Appendix 2) and ask them to what degree it represents the process they undertook.

The teacher will further students' reflections on the mathematical process by asking questions, such as:

What is important about this process?
In what way are assumptions key to an effective model?
To what extent was our model helpful?

Allow students to add their own ideas, questions and reminders to the schema.

Further Consolidation – Next Steps for Students and Teachers

Students may be given the opportunity to revise their mathematical models after the whole class has completed their presentations and feedback has been shared.

If possible, the teacher will allow students to repeat the “predict and verify” process with other classes in the school.

Students collect and share the data needed to make a prediction using their model (ex., the number of students in the class, the distance from the washroom, etc.)
Students use the data to make predictions based on their model.
Students (individually, as a small group or whole class) observe the class washing their hands, note their observations and time the experience.
Students share data as necessary.
Students compare their predicted time to the actual time.
As a group, students discuss the accuracy of their models. Allow students to continue to modify their models based on new information.

Source: OAME (Lesson Plan and Evaluation - Handwashing Policy - Google Documents).

Learning Situation 2: Forest in Crisis

Total duration: Over several days

Mathematical Modelling and our forests.

Overall and Specific Expectations
Algebra C4. Apply the process of mathematical modelling to represent, analyse, make predictions, and provide insight into real-life situations. Data D1. Manage, analyse, and use data to make convincing arguments and informed decisions, in various contexts drawn from real life. D1.2 Collect qualitative data and discrete and continuous quantitative data to answer questions of interest, and organize the sets of data as appropriate, including using percentages. Social-Emotional Learning Skills in Mathematics and the Mathematical Processes A1. Throughout this grade, in order to promote a positive identity as a math learn, to foster well-being and the ability to learn, build resilience, and thrive, students will apply, to the best of their ability, a variety of social-emotional learning skills to support their use of the mathematical processes and their learning in connection with the expectations in the other five strands of the mathematics curriculum. In this lesson, to the best of their ability, students will learn to maintain positive motivation and perseverance and think creatively and critically as they apply the mathematical processes reasoning and proving (develop and apply reasoning skills to justify thinking, make and investigate conjectures, and construct and defend arguments), reflecting (demonstrate that as they solve problems, they are pausing, looking back, and monitoring their thinking to help clarify their understanding (for example, by comparing and adjusting strategies used, by explaining why they think their results are reasonable, by recording their thinking in a math journal)) and representing (select from and create a variety of representations of mathematical ideas (for example, representations involving physical models, pictures, numbers, variables, graphs) and apply them to solve problems) so they can recognize that testing out different approaches to problems and learning from mistakes is an important part of the learning process, and is aided by a sense of optimism and hope, and so they can make connections between math and everyday contexts to help them make informed judgements and decisions. Geography - Natural Resources Around the World: Use and Sustainability B1. Analyse aspects of the extraction/ harvesting and use of natural resources in different regions of the world, and assess ways of preserving these resources. B1.1 Analyse interrelationships between the location/accessibility, mode of extraction/harvesting, and use of various natural resources. B2. Use the geographic inquiry process to investigate issues related to the impact of the extraction/ harvesting and/or use of natural resources around the world from a geographic perspective. B2.1 Formulate questions to guide investigations into issues related to the impact of the extraction/harvesting and/or use of natural resources around the world from a geographic perspective.

Overall and Specific Expectations

Algebra

C4. Apply the process of mathematical modelling to represent, analyse, make predictions, and provide insight into real-life situations.

Data

D1. Manage, analyse, and use data to make convincing arguments and informed decisions, in various contexts drawn from real life.

D1.2 Collect qualitative data and discrete and continuous quantitative data to answer questions of interest, and organize the sets of data as appropriate, including using percentages.

Social-Emotional Learning Skills in Mathematics and the Mathematical Processes

A1. Throughout this grade, in order to promote a positive identity as a math learn, to foster well-being and the ability to learn, build resilience, and thrive, students will apply, to the best of their ability, a variety of social-emotional learning skills to support their use of the mathematical processes and their learning in connection with the expectations in the other five strands of the mathematics curriculum.

In this lesson, to the best of their ability, students will learn to maintain positive motivation and perseverance and think creatively and critically as they apply the mathematical processes reasoning and proving (develop and apply reasoning skills to justify thinking, make and investigate conjectures, and construct and defend arguments), reflecting (demonstrate that as they solve problems, they are pausing, looking back, and monitoring their thinking to help clarify their understanding (for example, by comparing and adjusting strategies used, by explaining why they think their results are reasonable, by recording their thinking in a math journal)) and representing (select from and create a variety of representations of mathematical ideas (for example, representations involving physical models, pictures, numbers, variables, graphs) and apply them to solve problems) so they can recognize that testing out different approaches to problems and learning from mistakes is an important part of the learning process, and is aided by a sense of optimism and hope, and so they can make connections between math and everyday contexts to help them make informed judgements and decisions.

Geography - Natural Resources Around the World: Use and Sustainability

B1. Analyse aspects of the extraction/ harvesting and use of natural resources in different regions of the world, and assess ways of preserving these resources.

B1.1 Analyse interrelationships between the location/accessibility, mode of extraction/harvesting, and use of various natural resources.

B2. Use the geographic inquiry process to investigate issues related to the impact of the extraction/ harvesting and/or use of natural resources around the world from a geographic perspective.

B2.1 Formulate questions to guide investigations into issues related to the impact of the extraction/harvesting and/or use of natural resources around the world from a geographic perspective.

Learning goals	Success Criteria	Prior Learning
We are learning... to apply the process of mathematical modelling to analyse data and make decisions. to create a model that can be used to predict the point at which we will no longer have enough forestry products to meet our needs.	I can... make and evaluate assumptions in order to create a list of useful research questions for my model. collect and organize data related to the impact of the use of forestry products. use my model to identify a point in time when the demand for forestry products will overtake the available supply. reflect on the effectiveness of my model by comparing it to other models. reflect on the impact my assumptions made on my model. By adding these success criteria to your virtual learning platform (Google Classroom, D2L, …), you can share these success criteria with students who are in virtual classrooms so they can refer to them and assess their progress.	As part of their learning in Grade 7 geography, students will understand the ways in which people extract and use natural resources, and some of the potential social, economic, political and environmental consequences.

Learning goals

Success Criteria

Prior Learning

We are learning...

to apply the process of mathematical modelling to analyse data and make decisions.
to create a model that can be used to predict the point at which we will no longer have enough forestry products to meet our needs.

I can...

make and evaluate assumptions in order to create a list of useful research questions for my model.
collect and organize data related to the impact of the use of forestry products.
use my model to identify a point in time when the demand for forestry products will overtake the available supply.
reflect on the effectiveness of my model by comparing it to other models.
reflect on the impact my assumptions made on my model.

By adding these success criteria to your virtual learning platform (Google Classroom, D2L, …), you can share these success criteria with students who are in virtual classrooms so they can refer to them and assess their progress.

As part of their learning in Grade 7 geography, students will understand the ways in which people extract and use natural resources, and some of the potential social, economic, political and environmental consequences.

Resources and Materials

Laptops / chromebooks in order to conduct their research
Canadian Forest Service Statistical Data

Share these resources with students who are learning remotely as slides of pdfs by posting them to your virtual learning platform.

Learning and Teaching Activities

Understand the Situation

Student Moves	Teacher Moves
Within the context of their learning in geography about natural resources and the ways in which people extract and use forestry products, the teacher will pose the following problem: At the current rate of deforestation in Canada, at what point will we no longer have enough forestry products to meet our needs? Students will be placed in small flexible groups and given the task of trying to figure out what they need to know in order to solve this problem. The teacher consolidates the students’ ideas into a larger list of what they might need to know in order to solve this problem. Anticipated responses include: How many hectares of trees do we have? How much lumber do we harvest per year? Is the amount of lumber we harvest increasing or holding steady? Are there places in Canada where we cannot harvest trees? How many hectares of trees are lost each year due to forest fires? What is the reforestation rate?	The teacher circulates to observe the students and address any misconceptions about the problem. In order to facilitate their problem solving, the teacher can ask: How do we know deforestation is a concern? How could we prove that deforestation is a concern? Why might some people (for example, governments, everyday citizens) not be concerned at this time? What kinds of information will you need in order to solve this problem?
Opportunities for Differentiation Complete in pairs rather than small groups. Provide students with some of the questions that might need to be answered to solve the problem to help get them started. Provide students with the sources for conducting their research. Provide students with graphic organizers for recording and organizing their research. Scaffold the research process using the gradual release of responsibility. Assist students in differentiating between relevant and extraneous information. Opportunities for Assessment Assessment for Learning (Observations and Conversations) Ability to make assumptions in order to create a list of useful research questions. Ability to reflect on and prioritize their questions. Ability to research in order to collect and organize relevant data. Opportunity for Assessment and Differentiation At any point in this lesson during which in-school students are collaborating, at-home students can be placed in small groups by assigning them to break out rooms. Provide a sharing option so that students can capture their thinking and share it with the in-school class and the teacher (for example, Google slides, Padlet, Jamboard, or voice recording). Pop into the breakout rooms to listen for any misconceptions that may be surfacing. Make note of any interesting ideas that you might hear that can be shared with the in-school students to support the remote students to feel part of the discussion.

Student Moves

Teacher Moves

Within the context of their learning in geography about natural resources and the ways in which people extract and use forestry products, the teacher will pose the following problem:

At the current rate of deforestation in Canada, at what point will we no longer have enough forestry products to meet our needs?

Students will be placed in small flexible groups and given the task of trying to figure out what they need to know in order to solve this problem.

The teacher consolidates the students’ ideas into a larger list of what they might need to know in order to solve this problem. Anticipated responses include:

How many hectares of trees do we have?
How much lumber do we harvest per year?
Is the amount of lumber we harvest increasing or holding steady?
Are there places in Canada where we cannot harvest trees?
How many hectares of trees are lost each year due to forest fires?
What is the reforestation rate?

The teacher circulates to observe the students and address any misconceptions about the problem. In order to facilitate their problem solving, the teacher can ask:

How do we know deforestation is a concern?
How could we prove that deforestation is a concern?
Why might some people (for example, governments, everyday citizens) not be concerned at this time?
What kinds of information will you need in order to solve this problem?

Opportunities for Differentiation

Complete in pairs rather than small groups.
Provide students with some of the questions that might need to be answered to solve the problem to help get them started.
Provide students with the sources for conducting their research.
Provide students with graphic organizers for recording and organizing their research.
Scaffold the research process using the gradual release of responsibility.
Assist students in differentiating between relevant and extraneous information.

Opportunities for Assessment

Assessment for Learning (Observations and Conversations)

Ability to make assumptions in order to create a list of useful research questions.
Ability to reflect on and prioritize their questions.
Ability to research in order to collect and organize relevant data.

Opportunity for Assessment and Differentiation

At any point in this lesson during which in-school students are collaborating, at-home students can be placed in small groups by assigning them to break out rooms. Provide a sharing option so that students can capture their thinking and share it with the in-school class and the teacher (for example, Google slides, Padlet, Jamboard, or voice recording).

Pop into the breakout rooms to listen for any misconceptions that may be surfacing. Make note of any interesting ideas that you might hear that can be shared with the in-school students to support the remote students to feel part of the discussion.

Analyse the Situation

Student Moves	Teacher Moves
Students return to their small groups with the list generated by the whole class and are given the following task: Determine which of the questions can be researched. Identify which of the questions would be most useful in helping to solve the problem. Order your list of questions according to their usefulness in solving the problem, in order to allow for focused and timely research. Once each group has generated and prioritized their list of questions, they are given multiple periods, either during math or geography, or both, to research and gather the data to answer their questions. Canadian Forest Service Statistical Data	The teacher moves about the room to support each small group in identifying which questions are the most useful for solving the problem. The teacher might ask: Which of these questions do you need answered in order to find the point at which our supply of forestry products will not be able to meet our demand? Which of these answers would be the most helpful in solving this problem? Which of these questions will best help you determine how our needs of forestry products might change over time? Which questions might be most effective in helping you determine how accessible forestry products will be over time? The teacher will also help students determine how they could research to find the required data. The teacher might ask: Where could you find the answers to these questions? How will you know your information is reliable? During the research periods, it is important that the teacher is conferencing with and checking-in on each group frequently in order to ensure that their research is focused and that the data they are gathering is relevant and reliable. The teacher circulates to observe the groups and guide them in reflecting on their data for the purpose of determining which data they are going to use to make their model. The teacher helps the students identify which data is not helpful for solving the problem and guides them in removing extraneous information in order to make their model more manageable. The teacher might ask: Which information does not help us determine when our need for forestry products will overtake our supply? Which information can help us answer this question? What quantities or measurements are remaining constant? Which quantities are changing? What is the rate at which they are changing? How do these quantities or rates of change help us determine a point at which our supply of forestry products will be overtaken by our need for these products? Ultimately, the teacher poses the following question to each group: How can we use mathematics and the data you have gathered to find the point at which we will no longer have enough forestry products in Canada to meet our needs? How can we use a graphic to determine when the demand will overtake the supply?
Opportunities for Differentiation Differentiate by interest by grouping students according to the criteria they find most important in solving the problem. Groups share back their findings with the whole class. Opportunities for Assessment (Observations and Conversations) Ability to reflect on the relevance and usefulness of their data. A student working from home might benefit from creating a record/journal of what they did, using words, sketches, photographs, screen captures, and numbers to help them describe their process.

Student Moves

Teacher Moves

Students return to their small groups with the list generated by the whole class and are given the following task:

Determine which of the questions can be researched.
Identify which of the questions would be most useful in helping to solve the problem.
Order your list of questions according to their usefulness in solving the problem, in order to allow for focused and timely research.

Once each group has generated and prioritized their list of questions, they are given multiple periods, either during math or geography, or both, to research and gather the data to answer their questions.

Canadian Forest Service Statistical Data

The teacher moves about the room to support each small group in identifying which questions are the most useful for solving the problem.

The teacher might ask:

Which of these questions do you need answered in order to find the point at which our supply of forestry products will not be able to meet our demand?
Which of these answers would be the most helpful in solving this problem?
Which of these questions will best help you determine how our needs of forestry products might change over time?
Which questions might be most effective in helping you determine how accessible forestry products will be over time?

The teacher will also help students determine how they could research to find the required data.

The teacher might ask:

Where could you find the answers to these questions?
How will you know your information is reliable?

During the research periods, it is important that the teacher is conferencing with and checking-in on each group frequently in order to ensure that their research is focused and that the data they are gathering is relevant and reliable.

The teacher circulates to observe the groups and guide them in reflecting on their data for the purpose of determining which data they are going to use to make their model. The teacher helps the students identify which data is not helpful for solving the problem and guides them in removing extraneous information in order to make their model more manageable.

The teacher might ask:

Which information does not help us determine when our need for forestry products will overtake our supply?
Which information can help us answer this question?
What quantities or measurements are remaining constant? Which quantities are changing? What is the rate at which they are changing? How do these quantities or rates of change help us determine a point at which our supply of forestry products will be overtaken by our need for these products?

Ultimately, the teacher poses the following question to each group:

How can we use mathematics and the data you have gathered to find the point at which we will no longer have enough forestry products in Canada to meet our needs?
How can we use a graphic to determine when the demand will overtake the supply?

Opportunities for Differentiation

Differentiate by interest by grouping students according to the criteria they find most important in solving the problem. Groups share back their findings with the whole class.

Opportunities for Assessment (Observations and Conversations)

Ability to reflect on the relevance and usefulness of their data.

A student working from home might benefit from creating a record/journal of what they did, using words, sketches, photographs, screen captures, and numbers to help them describe their process.

Create a Mathematical Model

Student Moves	Teacher Moves
The students work in their groups to create a model using their data that will determine when the demand for Canadian forestry products will overtake the available supply. Students’ choice of graphic representations may include: a number line; a double-bar graph; a double-line graph; an equation.	The teacher moves about the room to observe and guide small group discussions through questioning: Which graphic representation have you selected for your model? How could you visually represent any equations you have created? Have you accounted for any rates that may change over time? (e.g. an increasing population would account for an increase in the demand for forestry products; increasing wildfire rates would have an impact on the available supply). The teacher identifies any groups or individual students who are still struggling with understanding the problem or who are struggling with creating a model to determine the point at which we will no longer have enough forestry products to meet our needs. The teacher addresses misconceptions and provides clarification as needed.
Opportunities for Differentiation Complete in pairs rather than small groups. The teacher could direct the prioritization of the data or provide the data to be used to develop the model. Opportunities for Assessment (Observations and Conversations) Use of representations to solve the problem. Ability to reflect on the impact of their assumptions and the usefulness of their data. Ability to test out different approaches to solving the problem. Understanding of the impact of various rates on the point at which the demand for forestry products will overtake the available supply. Capture the students’ work so that they can be shared with students who are learning remotely.

Student Moves

Teacher Moves

The students work in their groups to create a model using their data that will determine when the demand for Canadian forestry products will overtake the available supply.

Students’ choice of graphic representations may include:

a number line;
a double-bar graph;
a double-line graph;
an equation.

The teacher moves about the room to observe and guide small group discussions through questioning:

Which graphic representation have you selected for your model?
How could you visually represent any equations you have created?
Have you accounted for any rates that may change over time? (e.g. an increasing population would account for an increase in the demand for forestry products; increasing wildfire rates would have an impact on the available supply).

The teacher identifies any groups or individual students who are still struggling with understanding the problem or who are struggling with creating a model to determine the point at which we will no longer have enough forestry products to meet our needs.

The teacher addresses misconceptions and provides clarification as needed.

Opportunities for Differentiation

Complete in pairs rather than small groups.
The teacher could direct the prioritization of the data or provide the data to be used to develop the model.

Opportunities for Assessment (Observations and Conversations)

Use of representations to solve the problem.
Ability to reflect on the impact of their assumptions and the usefulness of their data.
Ability to test out different approaches to solving the problem.
Understanding of the impact of various rates on the point at which the demand for forestry products will overtake the available supply.

Capture the students’ work so that they can be shared with students who are learning remotely.

Analyse and Assess the Model

Student Moves	Teacher Moves
In their small groups or individually in their Math Journal, the students will reflect on their models and the assumptions they made when creating their models. They will reflect on the following questions: Does their model provide a point at which the demand for Canadian forestry products will no longer meet our needs? Is the point in time identified by their model reasonable? Could their model be applied to the issue of extraction / harvesting of other natural resources? Why or why not? The teacher will select certain groups or individual students to share portions of their reflections with the whole group in order to move the learning forward. For instance, the teacher will have different groups present the year that their models generated in order to demonstrate and debrief the impact of different assumptions on the specific years generated by the models. In particular, the teacher will select groups to share their models in order to demonstrate the impact that realistic assumptions, such as the increased rate of wildfires or population growth, would have on the year(s) identified as the point at which the available forestry products would no longer meet the need for such products.	The teacher moves about the room to observe and guide the students’ reflections through questioning: Which of your assumptions were correct? Which of your assumptions had the biggest impact on your model? Did you recognize the fact that rates will change over time? (e.g. increasing population will impact the rate at which forestry products are used; as a natural resource becomes more limited, the rate of usage changes as people find alternative sources or the cost of the resource increases, etc.) What impact did/would these changed rates have on the point in time generated by your model? What were the most important factors that led to your choice of year?
Opportunities for Differentiation Math Journals or Think/Pair/Share to reflect on the models. Guiding questions provided to direct the groups’ reflections. Opportunities for Assessment Assessment as Learning - Personal Reflections (Math Journal) Ability to reflect on the impact their assumptions had on the effectiveness of their model. Ability to reflect on the similarities and differences between their model and those of their classmates in order to further improve the effectiveness of their own model. Assessment for Learning - Personal Reflections (Math Journal, Class Discussions) Ability to reflect on the impact their assumptions had on the effectiveness of their model. Ability to reflect on the effectiveness of their model.

Student Moves

Teacher Moves

In their small groups or individually in their Math Journal, the students will reflect on their models and the assumptions they made when creating their models. They will reflect on the following questions:

Does their model provide a point at which the demand for Canadian forestry products will no longer meet our needs?
Is the point in time identified by their model reasonable?
Could their model be applied to the issue of extraction / harvesting of other natural resources? Why or why not?

The teacher will select certain groups or individual students to share portions of their reflections with the whole group in order to move the learning forward. For instance, the teacher will have different groups present the year that their models generated in order to demonstrate and debrief the impact of different assumptions on the specific years generated by the models. In particular, the teacher will select groups to share their models in order to demonstrate the impact that realistic assumptions, such as the increased rate of wildfires or population growth, would have on the year(s) identified as the point at which the available forestry products would no longer meet the need for such products.

The teacher moves about the room to observe and guide the students’ reflections through questioning:

Which of your assumptions were correct?
Which of your assumptions had the biggest impact on your model?
Did you recognize the fact that rates will change over time? (e.g. increasing population will impact the rate at which forestry products are used; as a natural resource becomes more limited, the rate of usage changes as people find alternative sources or the cost of the resource increases, etc.)
What impact did/would these changed rates have on the point in time generated by your model?
What were the most important factors that led to your choice of year?

Opportunities for Differentiation

Math Journals or Think/Pair/Share to reflect on the models.
Guiding questions provided to direct the groups’ reflections.

Opportunities for Assessment
Assessment as Learning - Personal Reflections (Math Journal)

Ability to reflect on the impact their assumptions had on the effectiveness of their model.
Ability to reflect on the similarities and differences between their model and those of their classmates in order to further improve the effectiveness of their own model.

Assessment for Learning - Personal Reflections (Math Journal, Class Discussions)

Ability to reflect on the impact their assumptions had on the effectiveness of their model.
Ability to reflect on the effectiveness of their model.

Consolidation of Learning

Student Moves	Teacher Moves
The students present their models and explain how they used mathematics to determine a year in response to the problem. As these models would be generating predictive data, the students would be unable to test them. The teacher would lead a class discussion on what students might see happening in the real world that would lead to the need to readjust their models. For example, if the Canadian government imposed a tax on the use of forestry products or the rate of wildfires increased at an unprecedented rate, the models would have to be adjusted to account for these factors. As a class, the students reflect on which model they think best represents what would actually happen. In their small groups or as a whole class, the students reflect on the process of mathematical learning, why we engage in mathematical modelling and what they learned about themselves as mathematicians and about the issue of deforestation.	The teacher helps students see the commonalities amongst the various groups’ models through questioning: What similarities did we see between the different models? What differences did we see between the models? What impact did different assumptions have on the years that were generated by the models? Which model do you think most closely represents the modelling that would take place in real life? Why? How can you tell? The teacher helps students reflect on the process of mathematical modelling by posing reflective questions such as: Why do we use mathematical modelling? How does mathematical modelling help us understand issues or solve problems? What was the benefit of having each group share their models and their reflections? What challenges did you face throughout the process? How did you respond to these challenges? What different approaches did you try throughout the process? Which ones were the most effective? Why? What did you learn about yourself as a mathematician? (for example, in terms of solving problems, thinking creatively, representing your thinking, etc.)
Opportunities for Assessment (Assessment of Learning) Understanding of the mathematical modelling process, including the impact of assumptions on the effectiveness of a model, as evidenced through the students’ individual reflections in their Math Journal and their contributions to the class discussion.

Student Moves

Teacher Moves

The students present their models and explain how they used mathematics to determine a year in response to the problem. As these models would be generating predictive data, the students would be unable to test them. The teacher would lead a class discussion on what students might see happening in the real world that would lead to the need to readjust their models. For example, if the Canadian government imposed a tax on the use of forestry products or the rate of wildfires increased at an unprecedented rate, the models would have to be adjusted to account for these factors.

As a class, the students reflect on which model they think best represents what would actually happen.

In their small groups or as a whole class, the students reflect on the process of mathematical learning, why we engage in mathematical modelling and what they learned about themselves as mathematicians and about the issue of deforestation.

The teacher helps students see the commonalities amongst the various groups’ models through questioning:

What similarities did we see between the different models?
What differences did we see between the models?
What impact did different assumptions have on the years that were generated by the models?
Which model do you think most closely represents the modelling that would take place in real life? Why? How can you tell?

The teacher helps students reflect on the process of mathematical modelling by posing reflective questions such as:

Why do we use mathematical modelling? How does mathematical modelling help us understand issues or solve problems?
What was the benefit of having each group share their models and their reflections?
What challenges did you face throughout the process? How did you respond to these challenges?
What different approaches did you try throughout the process? Which ones were the most effective? Why?
What did you learn about yourself as a mathematician? (for example, in terms of solving problems, thinking creatively, representing your thinking, etc.)

Opportunities for Assessment (Assessment of Learning)

Understanding of the mathematical modelling process, including the impact of assumptions on the effectiveness of a model, as evidenced through the students’ individual reflections in their Math Journal and their contributions to the class discussion.

Further Consolidation – Next Steps for students and teachers

Students may be given the opportunity to revise their mathematical models after the whole class has completed their presentations and feedback has been shared.

Students may repeat the mathematical modelling process in order to address another issue with respect to the extraction or harvesting of natural resources.

Source: OAME (Lesson and Assessment Plan - Forests in Crisis - Google Documents).