Exploring Mathematics Through Problem-Solving and Student Voice

Area(s) of Focus: math
Division(s): Primary, Junior
Level(s): Grade 1, Grade 2, Grade 3, Grade 4, Grade 5

Teacher resource of inquiry-based, open-ended mathematical problems that can be easily adapted to various grade levels. Three-part lesson plans are organized by grade and strand.

Our team created a teacher resource of inquiry-based, open-ended mathematical problems that can be easily adapted to various grade levels. The resource is organized by grade and by strand to support the expectations outlined in the Ontario Ministry of Education Mathematics Curriculum document. Problems are presented in the three-part lesson format. All lessons include: Minds-On, Working On It, Consolidation and Generalization. Some lessons include extension questions. Each problem encourages student voice and integrates the use of mathematical manipulatives.

Team Members

  • Shelby Monaco

    Toronto District School Board

  • Aileen Burke-Tsakmakas

    Toronto District School Board

  • Antonietta Scalzo

    Toronto District School Board

  • Lisa Bolduc

    Toronto District School Board

Professional Learning Goals

  • to enhance our own confidence in carrying out inquiry-based, open-ended mathematical programs
  • to develop a new and updated resource to support the professional learning goals in our school
  • to support the multiple intelligences and diversity of students in our every changing classrooms
  • to encourage student voice when solving mathematical problems
  • to collaborate and share resources and best practices with colleagues

Activities and Resources

Our team met several times to create three-part lessons and develop inquiry-based problems for students to solve. First, we referred to the mathematics continuum provided by our school board and the Ontario Curriculum Mathematics Document to determine the Big Ideas and curriculum expectations that we wanted to focus on. Then we began creating each lesson. We used a variety of resources to help us create the problems, including:

  • Nelson Mathematics resources (1-5)
  • Math Makes Sense resources (1-5)
  • Big Ideas from Dr. Small: Creating a Comfort Zone for Teaching Mathematics, Grades K-3 by Marian Small
  • Good Questions: Great Ways to Differentiate Mathematics Instruction by Marian Small
  • Making Math Meaningful To Canadian Students, K-8 by Marian Small
  • eqao.com

Unexpected Challenges

We found that the time frame was too short to create as many problems as we wanted to create and include technology. Therefore, we did not include the use of technology in our resource.

Enhancing Student Learning and Development

Students will engage in inquiry-based learning and will be exposed to open-ended mathematical problems throughout the year with the use of manipulatives. The questions will allow students to broaden their understanding and to demonstrate their knowledge of mathematical concepts by using multiple ways to solve problems and connecting these problems to real-world experiences. Teachers will use differentiated instruction and assessment to promote student voice. Students will improve their confidence and be more comfortable taking risks when solving mathematical problems. They will develop an understanding that there are multiple ways to solve mathematical problems.


We will share our resource by making it easily accessible and comprehensive. We will make it available online on our school Academic Workspace page so that teachers can easily modify it for their own use. We will also make our resource available in hard copy in the Math Room for teachers to sign out as needed. We will conduct Lunch and Learns to help promote and explain our resource.


Project Evaluation

The focus for Professional Learning Communities in our school this year was to plan and implement three-part lessons in mathematics. As a team, we were able to achieve our goal of developing a new and updated resource to support the professional learning goals in our school. Our resource includes inquiry-based, open-ended mathematical problems to support student voice, the multiple intelligences and the diversity of the students in our classrooms. Through this project, we were able to collaborate and share resources and best practices with our colleagues and enhance our own confidence in carrying out three-part lessons and inquiry-based, open-ended mathematical programs. Our resource will provide the teachers in our school with a framework to begin developing their own three-part lessons and inquiry-based, open-ended mathematical problems.

If we had more time, we would enhance our lessons and problems by including technology such as the Interactive White Board and software.


Resources Used


11 Plus for Parents, “Handling Data – Pictograms.” http://www.11plusforparents.co.uk/Maths/handling%20data%202.html. Accessed April 30, 2015. Electronic.

Adam, Carol et al. Nelson Mathematics 1-5. Canada: Thompson Canada Limited, 2004. Print.

All the Parts.

http://www.beaconlearningcenter.com/weblessons/alltheparts/default.htm Accessed May 13, 2015. Electronic.

Double Bar Graphs. 2015. http://www.ck12.org/book/CK-12-Middle-School-Math-Concepts-Grade-6/r4/section/2.12/. Accessed May 11, 2015. Electronic.

Education Quality and Accountability Office EQAO. 2015. http://www.eqao.com/categories/home.aspx?Lang=E. Accessed April 27, 2015. Electronic.

Graphs and Reading Data. http://ypccpod1.global2.vic.edu.au/links-for-        learning/graphs-and-reading-data/. Accessed May 1, 2015. Electronic.

IXL Learning, “Frequency Charts.” 2015. http://www.ixl.com/math/grade-        4/frequency-charts. Accessed May 12, 2015. Electronic.

Line Graph Practice. http://www.studyzone.org/testprep/math4/d/linegraph4p.cfm. Accessed May 14, 2014. Electronic.

Math Background, “Graphing Data: Overview.” 2015. http://www.eduplace.com/math/mw/background/2/03/te_2_03_overview.html. Accessed May 18, 2015. Electronic.

Mathematics K-12. “Teaching and Learning Expected Practice Series”. TDSB. 2011. http://www.annettestreetpublicschool.com/uploads/2/4/6/2/24625121/expected_practice_2012__math.pdf. Accessed May 27, 2015. Electronic.

Mighton, John et al. (2007). Jump Math Workbook 1 and 2. Canada. Print.

Peggy blog, Tally Chart Worksheet Generator. 2014. http://boratakann.blog.com/2014/07/20/tally-chart-worksheet-generator/. Accessed May 11, 2015. Electronic.

Problem Solving With Length, Money and Data. 2015. http://ps172grade2.blogspot.ca. Accessed May 14, 2015. Electronic.

“Reading Pictographs.” http://studyzone.org/testprep/math4/e/readpicto3p.cfm. Accessed May 7, 2015. Electronic.

Small, Marian. Making Math Meaningful to Canadian Students, K-8, Second Edition. United States of America: Nelson Education Ltd., 2013. Print.

Small, Marian. Good Questions: Great Ways to Differentiate Mathematics Instruction, Second Edition. New York: Teachers College Press, Columbia University, 2012. Print.

Tally Chart Worksheet. TutorVista.com. 2015. http://worksheets.tutorvista.com/tally-chart-worksheet.html. Accessed May 13, 2015. Electronic.

“Teaching Rocks!” 2012-2015. http://teachingrocks.ca/the-three-part-lesson-what-bansho/. Accessed May 26, 2015. Electronic.

The Ontario Curriculum, Grades 1-8. 2005 (Revised). http://www.edu.gov.on.ca/eng/curriculum/elementary/math18curr.pdf. Accessed April 27, 2015. Electronic.

Van de Walle, John A. and LouAnn H. Lovin. Teaching Student-Centered Mathematics, Grades K-3, Volume One. United States Of America: Rearson Education, Inc., 2006. Print.

Wesley, Addison et al. Math Makes Sense 1-5. Ontario: Pearson Education Canada, Inc., 2004. Print.