# Mathematics (2020)

## The Program in Mathematics

#### Curriculum Expectations

*The Ontario Curriculum, Grades 1–8: Mathematics, 2020** *identifies the expectations for each grade and describes the knowledge, concepts, and skills that students are expected to acquire, demonstrate, and apply in their class work and activities, on tests, in demonstrations, and in various other activities on which their achievement is assessed and evaluated.

**Mandatory learning is described in the overall and specific expectations of the curriculum.**

Two sets of expectations – overall expectations and specific expectations – are listed for each *strand*, or broad area of the curriculum, in mathematics for Grades 1 to 8. The strands include Strand A and five strands, lettered B, C, D, E, and F. *Taken together, the overall and specific expectations represent the mandated curriculum*.

The *overall expectations *describe in general terms the knowledge, concepts, and skills that students are expected to demonstrate by the end of each grade. The *specific expectations *describe the expected knowledge, concepts, and skills in greater detail. The specific expectations are grouped under numbered subheadings, each of which indicates the strand and the overall expectation to which the group of specific expectations corresponds (e.g., “B2” indicates that the group relates to overall expectation 2 in strand B). This organization is not meant to imply that the expectations in any one group are achieved independently of the expectations in the other groups, nor is it intended to imply that learning the expectations happens in a linear, sequential way. The numbered headings are used merely as an organizational structure to help teachers focus on particular aspects of knowledge, concepts, and skills as they develop various lessons and learning activities for students. In the mathematics curriculum, strands B to F use additional subheadings within each group of expectations to identify the topics addressed in the strand.

In the mathematics curriculum, the overall expectations outline the fundamental knowledge, concepts, and skills that are required for engaging in appropriate mathematical situations in and out of the classroom at any grade or stage of development. For this reason, the overall expectations generally remain the same from Grades 1 to 8. The curriculum focuses on connecting, developing, reinforcing, and refining the knowledge, concepts, and skills that students acquire as they work towards meeting the overall expectations in the elementary school program. This approach reflects and accommodates the progressive nature of development of knowledge, concepts, and skills in mathematics learning.

The *specific expectations *reflect this progression in knowledge and skill development through changes in the wordings of the expectations and through the introduction of new expectations, where appropriate. The progression is captured by the increasing complexity of the pedagogical supports (see below) associated with most expectations and by the increasing specificity of mathematical relationships, the diversity of contexts in which the learning is applied, and the variety of opportunities presented for applying it. It should be noted that *all *the skills specified in the early grades continue to be developed and refined as students move through the grades, whether or not each of those skills continues to be explicitly required in an expectation.

There is an exception in Strand C: Algebra, where the overall expectation on mathematical modelling has no accompanying specific expectations. This is because mathematical modelling is an integrated process that is applied in various contexts, allowing students to extend and apply what they have learned in other strands. Students’ demonstration of the process of mathematical modelling, as they apply knowledge, concepts, and skills learned in other strands, is assessed and evaluated.

In addition to the expectations outlined within the other five strands, Strand A focuses on the development and application of social-emotional learning (SEL) skills while using mathematical processes. These skills support students’ understanding of mathematical knowledge, concepts, and skills and foster their overall well-being and ability to learn while helping them build resilience and thrive as mathematics learners. As they develop SEL skills, students demonstrate a greater ability to understand and apply the mathematical processes, which are critical to supporting learning in mathematics. In all grades of the mathematics program, the learning related to this strand takes place in the context of learning related to the other five strands and is assessed and evaluated within these contexts.

#### Examples, Key Concepts, and Sample Tasks

Specific expectations are accompanied by examples, key concepts, and/or sample tasks. These elements or “pedagogical supports” are intended to promote understanding of the intent of the specific expectations, and are offered as illustrations for teachers. *The pedagogical supports do not set out requirements for student learning; they are optional, not mandatory*.

The examples are meant to illustrate the intent of the expectation, illustrating the kind of knowledge or skill, the specific area of learning, the depth of learning, and/or the level of complexity that the expectation entails. The key concepts identify the central principles and mathematical ideas that underpin the learning in that specific expectation. The sample tasks have been developed to model appropriate practice for the grade. They provide possible learning activities for teachers to use with students and illustrate connections between the mathematical knowledge, concepts, and skills. Teachers can choose to draw on the sample tasks that are appropriate for their classrooms, or they may develop their own approaches that reflect a similar level of complexity. Whatever the specific ways in which the requirements outlined in the expectations are implemented in the classroom, they must, wherever possible, be inclusive and reflect the diversity of the student population and the population of the province. Teachers will notice that some of the sample tasks not only address the requirements of the expectation they are associated with but also incorporate mathematical concepts or skills described in expectations in other strands in the same grade.