The following sample course plans should be considered with an understanding of the characteristics of an inclusive and identity affirming learning environment. There are two sample course plans offered below. One is organized by units and the other is based on a spiralling structure. These sample course plans are not meant to be prescriptive. There are other possible ways that learning can be organized to reflect different connections between the expectations of this course.

An approach organized by units highlights how expectations across strands can be combined to strengthen understanding. In this sample course plan, there are six units with suggested timing:

• Unit 1: Developing a Community of Learners and Making Connections with the Number Strand (20 – 25 hours)
• Unit 2: Making Connections with Data, Financial Literacy & Algebra (10 – 15 hours)
• Unit 3: Applications of Linear & Non-Linear Relations in Context (10 – 15 hours)
• Unit 4: Geometry and Measurement Relationships (15 – 20 hours)
• Unit 5: Representations of Linear and Non-Linear Relations (15 – 20 hours)
• Unit 6: Mathematical Modelling Process (10 – 15 hours)

The following units identify which overall expectations are included and what topics students are expected to learn. Note that expectation AA1 is to be included in classroom instruction, but not in assessment, evaluation, or reporting. In each unit, students will make connections to their lived experiences and various knowledge systems.

 Making connections with the Number Strand Expectations: AA1, A1, A2B1, B2, B3C2 Students will: apply the mathematical processes as they develop number sense and use it to solve problems in various contexts development & use of numbers number sets powers rational numbers applications of rational numbers, ratios, rates, percentages and proportions coding develop social emotional learning skills in context of their learning

 Making connections with data, financial literacy & algebra Expectations: AA1, A1, A2B3C1, C2D1F1 Students will: apply the mathematical processes as they develop an understanding of algebraic concepts in various contexts and by making connections to data and financial literacy concepts application of data representation & analysis of data financial decisions development & use of algebra algebra expressions & equations application of number operations coding develop social emotional learning skills in context of their learning

 Applications of linear & non-linear relations in context Expectations: AA1, A1, A2B2, B3C3E1F1 Students will: apply the mathematical processes as they develop an understanding of linear and non-linear relations in various contexts and by making connections to geometry & measurement and financial literacy concepts powers application of linear & non-linear relations geometric & measurement relationships financial decisions develop social emotional learning skills in context of their learning

 Geometry and measurement relationships Expectations: AA1, A1, A2B3,C2E1 Students will: apply the mathematical processes as they apply understanding of number concepts to solve problems involving geometry and measurement relationships applications of numbers geometric & measurement relationships coding develop social emotional learning skills in context of their learning

 Representations of linear & non-linear relations Expectations: AA1, A1, A2B3C1, C2, C4 Students will: apply the mathematical processes as they develop an understanding of the different characteristics of linear and non-linear relations and make connections between representations characteristics of linear & non-linear relations apply number operations apply understanding of algebraic expressions and equations coding develop social emotional learning skills in context of their learning

 Mathematical modelling process Expectations: AA1, A1, A2B3C1, C2D1, D2E1F1 Students will: apply the mathematical processes as they analyze real-life situations using the mathematical modelling process application of mathematical modelling application of number operations apply understanding of data involving one or two variables apply understanding of algebraic concepts and skills financial decisions coding develop social emotional learning skills in context of their learning

A spiraled or cycled approach focuses on introducing mathematical concepts and then revisiting and applying them in connection with other concepts throughout the course.

Students’ familiarity with math concepts can be assessed and addressed in an initial cycle. In subsequent cycles, students encounter these concepts again to strengthen their understanding and to make new connections with other concepts and between topics.

The video from High-Impact Instructional Practices in Mathematics resources provides more information on spiralling.

The plan outlined in the following table, identifies the four overall expectations that are taught in the context of all strands – AA1, A1, A2, and C2, with guiding questions to support planning throughout the course:

• How are social-emotional learning skills being incorporated into classroom instruction to foster a community of learners and to support all learners to build healthy mathematical identities?
• Which mathematical processes are students engaging with?
• What are the opportunities for the learning to be relevant to students?
• What are the opportunities for students to have choice in their learning?
• What are the opportunities for students to make connections to their lived experiences?
• What are the opportunities for students to learn about various knowledge systems?
• What are the opportunities for students to read, write, and alter code?

The spiralling structure in this sample course plan has four cycles:

• In Cycle 1 students are making connections to prior learning and are introduced to mathematical concepts from the course.
• In Cycle 2 students are introduced to mathematical concepts from the course and are applying mathematical concepts that were introduced in Cycle 1.
• In Cycle 3 students are introduced to mathematical concepts from the course and are applying mathematical concepts from Cycles 1 and 2.
• In Cycle 4 students are applying mathematical concepts from earlier cycles to consolidate their learning from the course.

In each cycle, expectations are grouped into three clusters based on their connections. For some clusters, other possible connections are also identified as in Cycle 1 – cluster 1: when students research about number a number concept like the golden ratio, they may also see the connections to geometry and measurement where the golden ratio can be seen in the geometric design of certain plants.

#### Spiralling Course Plan (MTH1W)

 Overall AA1: Social Emotional Learning Skills (SELs)How are social-emotional learning skills being incorporated into classroom instruction to foster a community of learners and to support all learners to build healthy mathematical identities? Overall A1 and A2: Mathematical Thinking and Making ConnectionsWhich mathematical processes are students engaging with?What are the opportunities for the learning to be relevant to students?What are the opportunities for students to have choice in their learning?What are the opportunities for students to make connections to their lived experiences?What are the opportunities for students to make connections to learn various knowledge systems? Overall C2: CodingWhat are the opportunities for students to read, write, and alter code? Cycle 1 Connections to prior learning and introduction to mathematical concepts from the course. Cycle 2 Introduction to mathematical concepts from the course and applications of mathematical concepts from Cycle 1. Cycle 3 Introduction to mathematical concepts from the course and applications of mathematical concepts from Cycles 1 and 2. Cycle 4 Consolidation of mathematical concepts from the course. Cluster 1: Types of Numbers and Applications of Integers in Real Life Students will: research a number concept make connections between different types of numbers solve problems involving integers B1.1, B1.2, B3.1 Possible connections to B1.3, E1.1 Cluster 1: Relationship of Numbers and their Application in Measurement Systems Students will: develop an understanding of density, infinity and limit apply an understanding of positive fractions solve problems involving different measurement systems B1.3, B3.2, B3.4, E1.3 Possible connection to E1.1 Cluster 1: Geometric Designs and Measurement Problems Students will: research a geometric concept or a measurement system apply understanding of solving equations and operations with positive rational numbers when solving problems involving geometric designs and measurements E1.1, C1.5, B3.4, E1.2, E1.5, E1.6 Cluster 1: Application of Number and Algebra to Solve Problems Students will: pose and solve problems involving rates, percentages, and proportions and make connections to financial literacy simplify numeric expressions, involving rational bases and integral exponents solve problems involving the simplification of algebraic expressions and the solving of equations with rational numbers solve problems involving measurement B3.5, F1.3, B2.1, B2.2, C1.4, C1.5, E1.4 Possible connection to E1.3 Cluster 2: Relations in Real life Students will: create algebraic expressions to generalize relationships solve equations involving integers represent linear relations that model real-life situations, and solve related problems make connections to proportional relationships make connections to financial literacy C1.2, C1.5, C3.2, B3.1, B3.5, F1.1 Cluster 2: Patterning and Applications of Linear and Non-Linear Relations Students will: develop an understanding of powers with integral bases and exponents and make connections to algebraic expressions compare and simplify algebraic expressions compare the shapes of graphs of linear and non-linear relations that model real-life situations, and make connections to powers make connections to appreciation and depreciation B2.1, B2.2, C1.3, C1.4, C3.1 F1.2 Possible connection to C1.5 Cluster 2: Characteristics of Linear and Non-Linear Relations Students will: research an algebraic concept solve real-life problems involving pairs of linear relations compare characteristics of linear and non-linear relations determine the equations of lines solve problems involving rational numbers, including those involving linear relations C1.1, C3.3, C4.1, C4.4, B3.3, B3.4 Cluster 2: Connections Between Various Relations Students will: graph equations that have been defined as well as their associated inequalities translate the line defined by y = ax represent and analyse data involving two-variables C4.2, C4.3, D1.3 Possible connection to C4.4 Cluster 3: Real-life Applications of Data Students will: develop an understanding of big data analyse data involving one-variable connected to financial literacy apply operations of integers and decimal numbers D1.1, D1.2, F1.1, B3.1 Possible connection to B3.5 Cluster 3: Data and Mathematical Modelling Students will: represent and analyse data involving one-variable and apply proportional reasoning identify examples of mathematical modelling used in real-life apply an understanding of operations to modify budgets displayed in various ways, including in a circle graph, and in a spreadsheet apply the process of mathematical modelling to solve a problem of interest related to data involving one-variable D2.1, B3.5, D2.2, D2.3, D2.4, D2.5 Cluster 3: Mathematical Modelling Students will: apply the process of mathematical modelling to solve a problem of interest related to measurement and/or linear relations D2.2, D2.3, D2.4, D2.5 Possible connections to E1.4, C3.2, C3.3 Cluster 3: Mathematical Modelling Students will: apply the process of mathematical modelling to solve a problem of interest, applying their understanding of the mathematical concepts in the course D2.2, D2.3, D2.4, D2.5 Suggested Timing:20 – 25 hours Suggested Timing:25 – 30 hours Suggested Timing:25 – 30 hours Suggested Timing:20 – 25 hours

Note: This sample course plan is not meant to be prescriptive and may be modified based on other possible connections among the expectations. 