A Mathematics Blueprint: Designing a Comprehensive Mathematics Program

When designing a comprehensive mathematics program, it is important to understand the scope and sequence of curriculum mapping. I have come to understand that mathematics planning needs to consider: Big Ideas, Cross-Curricular Planning, Thoughtful and Clear Planning, and Day/Unit/Long-Range Plans. All of these components further need to be understood through a constructivist approach to learning. It is easy to convey this message to teachers, but it is still imperative that teachers
understand the practical application of these components to planning. Furthermore, in the 21st century, there are ways to tackle mathematics planning through the use of innovative digital technologies. The following post will describe the practical application of Big Ideas, Cross-Curricular Planning, Thoughtful and Clear Planning, and Day/Unit/Long-Range Plans.


The Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6: Number Sense and Numeration describes the Big Ideas as a lens (Ontario Ministry of Education, 2006). The following identifies what this lens can be used for in the classroom:

When I consider making instructional decisions or identifying prior learning, I immediately think of diagnostic assessment. Assessing what students already know in order to gauge their prior knowledge in a mathematics area is critical when focusing on Big Ideas. This will then elucidate to teachers a sense as to where to start for an upcoming lesson. One way that this can be achieved is through the formative assessment tool called Socrative. Socrative can be used as a polling tool where students can digitally respond to different types of questions (i.e., multiple choice, true/false, or short answer). The data can be collected to support instructional decisions, assess prior learning, and check for students' thinking and understanding in mathematics. Socrative also allows teachers to go in and provide feedback to students. It is a fantastic tool to foster a constructivist approach to teaching as students are the ones guiding the pace of learning. Click on the image below for a more in-depth post on Socrative: 


This is by far my favourite task while unit planning. I love making connections between subjects and seeing how mathematics especially can be made more relevant for students. Core to 21st century learning is making instructional activities more authentic and realistic for students. Just focusing on rote memorization and math facts are not enough. Mathematics should not be an isolated phenomenon. Cross-curricular planning can provide an opportunity for students to learn skills and meet expectations in more than one subject and within multiple settings (Ontario Ministry of Education, 2005). One way that I have really tried to enhance cross-curricular planning is through STEAM (Science; Technology; Engineering; The Arts; Mathematics). When considering the practical application of cross-curricular planning, I have found Education Closet to be very helpful. Education Closet supports the integration of The Arts into the STEAM model for education. There are a wide variety of lesson plans that enhance mathematics through The Arts. Click on the image below to view some great cross-curricular lesson plans:

I have also more recently been dabbling with a new model to cross-curricular learning through Innovation Stations. Essentially, it follows the same subjects embedded in STEAM, but the program, which can be purchased through TeachersPayTeachers, has different categories that are more inline with the focus on 21st century education. There are five stations, which include: The Arts, Engineering, Building, Coding, and Film Making. Here is a video to get a sense of what the program looks like: 

Some stations (i.e., engineering), can be linked to both Mathematics and the Science and Technology curriculum. When I initially decided to implement Innovation Stations, I sat down with the Instructional Coach in my board, and she made sure to emphasize the connections these stations have to the curriculum. I therefore made the curriculum connection chart below to hang-up and remind myself, my students, and administration of the value this program has and its effectiveness to connect to the Ontario curriculum. 

I have been struggling a little bit with the logistics of Innovation Stations, which mostly comes down to the time constraints I am limited to within Long-Term Occasional Positions. When I implemented this program, I had each station set-up, and students got to choose where they wanted to go. I let them choose their top 3 picks and then organized the groups based on that. I found this worked well, but because it was in grade 1, it was very busy having all of those stations set-up! Following constructivism, this approach to learning is very student-centered and allows for students to discover, create, and innovate using their own prior knowledge, strategies, and suggested materials. Here are some photos of what students were able to do during these Innovation Stations in Grade 1! 

Drawing using steps
Balanced Structures
Building Everyday Objects

When it comes to the 3-part lesson model, the one program/app that I have really been trying to integrate is SesameIO. The article posted in Professionally Speaking provides a fantastic overview of the 3-part lesson model. Using this model, I am going to try to explain how SesameIO can greatly enhance your planning and instruction. I find SesameIO always full of surprises and keeps coming in handy for more reasons than I can count! Usually I use SesameIO as a formative assessment tool while students are in the Working-On-It stage of the 3-part lesson. However, I have recently discovered its value during the Consolidation and Practice stage of the 3-part lesson. In SesameIO, I set-up individual profiles for all of my students. Myself and my students contribute to the documentation of their learning through pictures, videos, and text to demonstrate their thinking and learning during the Working-On-It stage. This is done using the Sesame SNAP app. I also will document students' learning during the first stage, Getting Started, as it provides me with some documentation of students' prior knowledge. I can use this to reflect on what my students know and need to know before they work on a problem. During the Working-On-It stage, students and myself then continue to document their learning. Once it is time for the Consolidation and Practice, I will pull SesameIO up on the SMART Board or LCD projector and display the work that has been tagged under the groups of students working together. When a group is presenting their work and strategies used, they can play back videos to demonstrate the process of their thinking and communicating that resulted in their final product. They can also use pictures to enhance their own verbal explanations. Following a constructivist approach to learning, students are able to learn from one another by sharing their strategies and visually depicting what they learned along the way. They can explain their whole process of thinking and communicating to teach other students. It supports a very student-centered approach to mathematics. What is also fantastic about this program is that teachers can embed rubrics or curriculum checklists. As I hear and see students make strides towards understanding curriculum expectations, I can check this expectation off the checklist within their profile. Overall, this app is a fantastic tool to use when planning the 3-part lesson in mathematics. Click on the Sesame SNAP app icon above to learn more about SesameIO.


As a teacher in the District School Board of Niagara (DSBN), we have been encouraged to focus our mathematics planning based on the DSBN Scope and Sequence Grade 1-8 Mathematics. Based on this long-range plan, I have utilized 21st century planning apps to support curriculum-mapping. Using the DSBN Scope and Sequence as a guide, I can integrate daily lessons, which follow the 3-part lesson model, into an app called Planboard. Planboard allows me to digitally embed Ontario curriculum expectations into my daily lesson plans. If I am following a lesson from an online resource like The Guide to Effective Instruction in Mathematics, I can attach the file I need inside my digital daybook. Click on the image below to learn more about Planboard as a means for long-range and daily planning:

Overall, it is imperative as educators that we think deeply about our mathematics program and how we are going to make it relevant, organized, hands-on, and enriched. The above resources hopefully demonstrated what the Big Ides, Cross-Curricular Planning, Thoughtful and Clear Planning, and Day/Unit/Long-Range Planning look like when practically applied in teaching. Happy planning!

Rochelle :)

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