Introduction

Welcome to our mathematics class!

Mathematics is all around us and can be noticed in our lives every day. Carpenters, game designers, electricians, and engineers use it in their careers.

Math encompasses many ideas and topics that will be explored in this course.

Notebook

Notebook icon

Throughout this course, you will use a notebook to keep track of what you're learning. This could be a physical paper notebook, or a digital file.

Use your notebook to respond to prompts like this one, and refer back to it when preparing for assignments, quizzes, and your final test.

Begin by making a list of the first five to seven mathematical ideas or topics that you can recall from the mathematics you have studied before. Choose one or two that invoked curiosity, frustration, or joy.

Write a paragraph sharing your memories of that moment of strong emotion when learning or doing mathematics.

The following prompts might help:

  • What was it about the topics that made you feel curiosity, frustration or joy?
  • Describe the activity you were doing that caused those feelings.
  • Were you learning as an individual or in a group? How did learning this way affect your feelings when you were engaged in this topic of mathematics?

As you navigate through this course, you may wish to access resources that can help to enhance your learning.

One of the additional supports that you have in this course to help you with a more personalized math learning experience is Mathify. Mathify is your online personal math mentor. Mathify connects you with an Ontario certified math teacher online, to help you better understand how to solve math problems. It’s all done on a shared whiteboard where you communicate with your tutor via texting and/or audio chat. You can open a whiteboard at any time and use it as a workspace. Then, you can invite the tutor of your choice to your whiteboard when you need help or would like confirmation that you are on the right track.

If you are new to Mathify, take the time right now to get registered and explore this service and the hours that tutors are available. You will require an Ontario Education Number (OEN) and e-mail address.

Note: Mathify is for learners in Ontario.

Acknowledgements (Opens in new window)

Finding a quarter

To “quarter” something means to partition or divide it into four equal pieces. A “quarter” means one-fourth of a whole.

Try it!

Try it!

Access the following printable document Finding a quarter to complete the activity. Use the document as you work through the following questions.

  1. Can you shade in exactly 1 4 of the following square? How do you know you are right?

    A square that is cut into four equal sized squares

2. Does your square appear similar to the following?

Suggested answers like this one are present throughout the course. A suggested answer is just that - a suggestion. If you came up with a different answer, compare it carefully and thoughtfully to the suggested answer. How different is it? Does it still show all of the expected knowledge? If so, you're succeeding and can proceed. If it's still different, take a moment to think about the problem again. What other information can you gather?

3. Can you challenge yourself to shade in 1 4 of the square again, but try to do a shading that no one else would think of?

Student responsibilities

Course completion

Throughout this course you will be asked to demonstrate your learning in several ways, including but not limited to the following:

  • solving problems in graded assignments
  • completing a final test at the end of the course

Notebook

Notebook icon

Access the following printable document Quarter the t-shape to complete the activity.

Shade the t-shape so that exactly 1/4 of the shape is shaded in. Try to be as creative as possible. Try to create a design that nobody else would think of.

Image of plus sign being made with five squares

Source:

Dekker, T. & Querelle, N. (2002). Great Assessment Problems. Utrecht, The Netherlands: Freudenthal Institute.

Connecting to transferable skills

Transferable skills icon

Recently, Ontario worked with other provinces in Canada to outline a set of competencies that are requirements to thrive. Ontario then developed its transferable skills framework as a set of skills for students to develop over time. These competencies are ones that are important to have in order to be successful in today’s world.

Read through the framework and the student look-fors (Opens in new window). Copy this document into your notes - you'll refer to it in each unit.


Definition

Critical thinking and problem solving involve examining complex issues and problems from a variety of different points of view in order to make informed judgments and decisions. Learning is deeper when the experiences are meaningful, real-world, and authentic.

Look fors

Students consistently:

  • solve meaningful, real-life problems;
  • take steps to organize, design, and manage projects using inquiry processes;
  • analyze information to make informed decisions;
  • see patterns, make connections, and transfer learning from one situation to another;
  • see the connections between social, economic, and ecological systems.


Definition

Innovation, creativity, and entrepreneurship involve the ability to turn ideas into action to meet the needs of a community. The ability to contribute new-to-the-world thinking and solutions to solve complex problems involves leadership, risk taking, and independent/unconventional thinking. Experimenting with new strategies, techniques, and perspectives through research is part of this skill set.

Look fors

Students consistently:

  • formulate insightful questions to generate opinions;
  • take risks in thinking; experiment to find new ways of doing things;
  • demonstrate leadership in a range of creative projects;
  • motivate others in an ethical and entrepreneurial spirit.


Definition

Self-directed learning means: becoming aware and demonstrating ownership in your learning. Belief in your ability to learn (growth mindset), combined with strategies for planning, monitoring, and reflecting on your past, present, and future goals promote lifelong learning, well-being, and adaptability in an ever-changing world.

Look fors

Students consistently:

  • are aware of how they learn best;
  • ask for support when needed;
  • set goals and make a plan to achieve their goals;
  • practice new skills they want to improve;
  • reflect on their own learning to determine strengths;
  • learn to adapt to change and become resilient in the face of adversity;
  • become managers of different aspects of their lives to enhance their health and overall well being.


Definition

Collaboration involves participating ethically and effectively in teams. Being versatile across different situations, roles, groups, and perspectives allows you to co-construct knowledge, meaning, content, and learn from, and with others in physical and online spaces.

Look fors

Students consistently:

  • participate in teams in respectful and positive ways;
  • learn from others; contribute to the learning of others;
  • assume various roles on a team as needed, being respectful of a diversity of perspectives, including Indigenous ways of knowing;
  • address disagreements and manage conflict in sensitive and constructive ways;
  • network with a variety of people and groups on an ongoing basis.


Definition

Communication involves receiving and expressing meaning (e.g., reading and writing, viewing and creating, listening and speaking) in different contexts and with different audiences and purposes. Effective communication increasingly involves understanding both local and global perspectives, including using a variety of media appropriately, responsibly, and safely with regard to your digital footprint.

Look fors

Students consistently:

  • communicate effectively in a variety of media;
  • use digital tools appropriately to create a positive digital footprint;
  • listen to understand;
  • ask effective questions;
  • understand the cultural importance of language.


Definition

Global citizenship and sustainability involve understanding diverse worldviews and perspectives in order to address political, ecological, social, and economic issues that are crucial to living in a sustainable world. Being aware of what it means to be an engaged citizen and how the appreciation for the diversity of people and perspectives contributes to a sustainable world are part of this skill set.

Look fors

Students consistently:

  • take actions and make responsible decisions to support the quality of life for all;
  • understand the histories, knowledge, contributions, and inherent rights of Indigenous people;
  • recognize discrimination and work to promote the principles of equity;
  • contribute to their local and global community;
  • participate in an inclusive, accountable, sustainable, and ethical manner, both in groups and in online networks.


Definition

Digital literacy involves the ability to solve problems using technology in a safe, legal, and ethically responsible manner. Digitally literate students recognize the rights and responsibilities, as well as the opportunities, that come with living, learning, and working in an interconnected digital world.

Look fors

Students consistently:

  • select and use appropriate digital tools to collaborate, communicate, create, innovate, and solve problems;
  • use technology in a way that is consistent with supporting their mental health and well-being;
  • use digital tools effectively to solve problems and inform decisions;
  • demonstrate a willingness and confidence to explore new or unfamiliar digital tools and emerging technologies;
  • manage their digital footprint by engaging in social media and online communities respectfully, inclusively, safely, legally, and ethically.

The transferable skills described in these videos have been adapted from the ministry‘s definitions and descriptions that are available for viewing on the Ministry of Education‘s Curriculum and Resources site: Transferable skills(Opens in a new window)

Note the indicators that you think you will develop in this course. At the end of the course you will reflect on your development of these skills.

As you continue through this unit and the rest of the course, keep your notebook updated and be mindful of opportunities to apply and develop transferable skills.

Culminating assignment

At the end of this course, you will complete and submit a culminating assignment that includes tasks from various units. Keep the culminating assignment in mind as you progress through the course. Take a moment to review the culminating activity description(Opens in new window) now, and while you do not have to complete any of the tasks now, you should think about them.