Grade 6: "Free Little Library"
(From: OAME)
Embedded Files
(From: OAME)
On a computer? Click "file" then "make a copy" to save and make changes.
On an iPad? Select the 3 dots in the top right hand corner. "Share and Export" then "Make a Copy".
Content
Content
Big Idea: Using the process of mathematical modelling to solve a real-world problem, stocking a free “Little Library”. Students will make their own choices, assumptions and decisions as they develop a rating system to predict the likelihood a donated book will be read.
Big Idea: Using the process of mathematical modelling to solve a real-world problem, stocking a free “Little Library”. Students will make their own choices, assumptions and decisions as they develop a rating system to predict the likelihood a donated book will be read.
Expectations:
Expectations:
Algebra
C4. apply the process of mathematical modelling to represent, analyse, make predictions, and provide insight into real-life situations
Social Emotional Learning 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 recognize sources of stress and cope with challenges and build relationships and communicate effectively as they apply the mathematical processes of problem solving (develop, select, and apply problem-solving strategies) and reflecting (demonstrate that as they solve problems, they are pausing, looking back, and monitoring their thinking to help clarify their understanding), so they can work through challenging math problems, understanding that their resourcefulness in using various strategies to respond to stress is helping them build personal resilience, and so they can work collaboratively on math problems – expressing their thinking, listening to the thinking of others, and practising inclusivity – and in that way fostering healthy relationships.
Learning Goals
Learning Goals
We want students to...
We want students to...
to shift from finding an answer to a singular question to create a system that can be generalized and can be used with multiple situations.
tackle messy real-life problems and understand they may have several different solutions because there is not one answer that is 100% correct.
go back to reflect on our rating system and make alterations when we have additional information and/or a change in our thinking.
make choices, assumptions, and decisions as we make and use a rating system.
Success Criteria
Success Criteria
I can...
I can...
understand the difference between solving a question that only has a single correct answer and creating a system to address messy real-world problems.
explain the difference between what we call a “textbook question” and a real-world problem.
go back to reflect on my rating system and make changes when there is additional information and/or a change in my thinking.
explain my thinking behind the choices, assumptions and decisions I made while I developed my rating system.
Materials
Materials
Internet access
Computer and projection device
A number of books, perhaps in a box or container, that represent a variety of reading interests, genres, and age groups.
If you are unfamiliar with free little libraries this is a file with the link to the main site and photos of different types and designs.
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. This will also create a record of their work in order to communicate clearly with each other and the teacher.
Add a link to Part 1 - Background Information for Free Little Libraries in your virtual learning environment
Vocabulary
Vocabulary
Probability
Predictions
Rating Scale / Rating System
Assumptions
Mathematical Model
teacher background
teacher background
Students can start to experience the idea of rating.
If asked, some students would be able to say what makes a good shoe or a good friend. Providing experiences for students to realize there are characteristics of an item or idea that are important to them and other characteristics are not important to them will lead to the development of a rating system. A rating system, where we identify important characteristics to weigh and consider and eliminate other characteristics as we make choices and decisions, is a mathematical modelling process we use in real-life situations. When the predictions and decisions we make don’t turn out as expected, we return to analyze and assess the model we used to make those choices to adapt it to make better predictions going forward.
Pedagogy
Pedagogy
Understanding the situation
Understanding the situation
Students are shown a photo of a little library and given the chance to learn what it is.
Students need to decide what information they need to understand how a free little library operates. Some questions could be: What is a free little library? How many books can fit? Who uses this kind of library? Do you have to sign out books or just take them? How often do new books get introduced? and How do we tell people about the little library?
The messy real-world situation is:
Someone donated their free little library and a box of books to the school because they are moving away. We have been asked to continue to run the little library and I want it to be a success.
Part 3 - Understanding the Situation
Teacher Moves:
Ask questions such as What do you notice?; What do you wonder?; What are you curious about?; What do you know?; and What do you think this is used for? and record their thoughts. This will generate interest in this real-world problem.
The teacher asks: What information do you need to operate a successful free little library?
Record the students’ questions.
Use the recording tool to write students’ questions.
In this file, the author of the lesson plans to explain how the topic of a free little library was chosen and includes some excerpts from experts (and links to their sites) that assisted in the development of the math modelling lesson.
Resource A - Teacher to Teacher Notes
Analyze the situation
Analyze the situation
In a whole class discussion, students are asked, what do you look for in a book that you want to read?
Then they use some of the ideas generated from a whole class discussion on characteristics or ideas about books and/or add their own characteristics to make an individualized list.
Students will analyze the list and make choices about the items on the list. These choices might involve: How many items will they use to decide if a book is suitable for them? Which items from the list will they select and which ones will they eliminate? Of the items selected, which are ‘must-haves’? which ones are they ambivalent about? which ones would be an ‘added bonus’ or a minor annoyance?
Link for examples of possible student lists and summary of possible lesson:
Teacher Moves:
The teacher scribes the characteristics of ideal books and/or the ideas about books in a whole class discussion.
The teacher provides a worksheet table for students to record items from the class list and/or add their own items as they make a ranked list for, What makes a good book for me to read?
The teacher moderates the whole class discussions as students present their lists of criteria and explain the thinking behind their choices. The teacher should make sure the students understand they are making assumptions about how others choose books, not just their own choices in their explanations to the rest of the class.
In a virtual environment, it may be difficult to have this discussion with the whole class. Use virtual breakout rooms for students to meet with their peers. Students use the recording tool to collaborate and make assumptions.
After recapping the task events, the teacher describes the next step - to create a rating system that could be used to predict if a book should be part of the class little library.
create a mathematical model
create a mathematical model
Using the criteria students chose previously, students develop a model that would help them predict how likely they would read a book if it was in a little library.
Part 5 - Create a Mathematical Model
Teacher Moves:
The teacher guides the students’ choices regarding the weighting of the criteria in their list by suggesting possible scenarios for them to think through their decisions.
The teacher moderates the whole class discussions as students present their rating systems and explain the thinking behind their choices.
After recapping the task events, the teacher describes the next step - using actual books with the rating systems.
Students use a shared document to collaborate, develop a model, and share it with the teacher and the group.
analyze and assess the model
analyze and assess the model
A student example first mentioned in Analyze the Situation and used to create a rating system in Create a Mathematical Model is testing out two books. It can be used as an example with your students as a whole class discussion to decide what if any changes are needed for the system. Then the systems created by your students can be discussed.
Next, in small groups the students use their rating systems on the same book, looking for ways to combine their individual rating systems to one that represents the group.
Part 6 - Analyze and Assess the Model
Teacher Moves:
Teacher has a box of books for students to rate a book with their rating system (their mathematical model) and reflect on the results. If the results are unexpected and puzzling, the teacher guides their students to analyze and assess the system (model) and adapt it
to improve the predictability of the system with other books.
Students working from home will use the model to rate books they have at home. Alternatively, they could rate e-books they borrow from their public library.
Working with small groups the teacher guides the class to identify common criteria from individual rating systems to develop a class rating system. As books are donated, the rating system predicts the likelihood the book will be selected and read from the little library. The development of an inventory system (Consolidation of Learning) will provide information for students to further analyze and assess the class rating system.
consolidation
consolidation
If your students decide to make their own little library what might they do to open it up to the rest of the school? What will they adjust in the rating system for this new set of little library customers? How will they keep track of the books?
Students assess their own progress by reflecting on Learning Goal statements:
I can understand the difference between solving a question that only has a single correct answer and creating a system to address messy real-world problems; I can explain the difference between what we call a “textbook question” and a real-world problem; I can go back to reflect on my rating system and make changes when there is additional information and/or a change in my thinking’ and I can explain my thinking behind the choices, assumptions and decisions I made while I developed my rating system.
Part 7 - Consolidation - The Real-World Running of a Little Library
Differentiation:
Arrange for students to work in small groups that suit their individual needs.
Teacher Moves:
The choice to create a real little library in a school will require a long term commitment on the part of the teacher and students. It will require establishing routines to maintain the library with students in your class and establishing routines with the school for the use of a little library. Additional information for a teacher to consider for moving forward is in Part 7 file.
extenstions / next steps
extenstions / next steps
Students could write a letter to the previous owners of the little library and report the progress.
Students could develop instructions for students in another school who want to have their own little library.
Ideas for advertising and promoting the little library are included. Finally, what does the idea of “success” mean for a little library and suggestions for your students to tackle the messy real-world problem of how many books fit in a little library.
Assessment Opportunities
Assessment Opportunities
A series of questions to ask as you observe students as they develop a rating system, explain the system to others and work in small groups.
Resource B - Questions to Guide Teacher Observations
Each part of the lesson plan has possible questions a teacher can use to guide their students’ learning. This file copies them into one place.
Page updated
Report abuse