Teacher Guide: Using This Curriculum

This comprehensive guide provides essential information for teachers implementing the 2023 Ontario De-streamed Grade 9 Mathematics curriculum (MTH1W). It explains the curriculum structure, instructional approaches, assessment strategies, and how to effectively use the weekly lesson plans to support all students in developing mathematical understanding and skills.

About the 2023 De-streamed Curriculum

The 2023 Ontario De-streamed Mathematics curriculum represents a significant shift in how Grade 9 mathematics is taught in Ontario schools. The new MTH1W course replaces the previous two-stream system of MPM1D (Academic) and MFM1P (Applied) courses.

Key Principles of De-streaming

High expectations for all students - The curriculum maintains rigorous standards while providing multiple pathways to success
Eliminates systemic barriers - Removes the early streaming that often limited students' future opportunities based on Grade 9 course selection
Values diversity and inclusion - Recognizes and celebrates the diverse backgrounds, experiences, and ways of knowing that students bring to mathematics
Emphasizes conceptual understanding and procedural fluency - Balances deep understanding of mathematical concepts with the ability to perform procedures accurately and efficiently
Promotes equity and access - Ensures all students have access to the same high-quality mathematics education regardless of their background or previous achievement

Curriculum Strands Explained

Strand AA Social-Emotional Learning (SEL) Skills in Mathematics

This strand focuses on developing social-emotional learning skills within mathematical contexts. SEL skills are integrated throughout instruction to support student well-being, positive learning environments, and mathematical identity development.

Important: SEL skills are developed and supported but are NOT assessed or evaluated as part of students' mathematics grades. The focus is on creating a supportive learning environment where all students can thrive.

Strand A Mathematical Thinking and Making Connections

This strand applies to all areas of course content and must be developed in conjunction with Strands B through F. It emphasizes:

Making connections between mathematical concepts and real-world contexts
Connecting mathematics to other disciplines and areas of study
Understanding relationships between different mathematical strands
Applying mathematical thinking to solve authentic problems
Developing mathematical reasoning and critical thinking skills

Assessment: This strand is assessed and evaluated throughout the course in conjunction with content from other strands.

Strand B Number

Covered in Weeks 1-3

This strand focuses on:

Development and use of numbers in various contexts
Connections between different sets of numbers (whole numbers, integers, rational numbers)
Operations with integers, fractions, and decimals
Exponents and scientific notation
Number sense and estimation strategies

Strand C Algebra

Covered in Weeks 4-6

This strand focuses on:

Algebraic expressions and equations
Linear and non-linear relations
Coding skills and computational thinking
Dynamic representations of mathematical relationships
Constant rate of change and initial values
Variables and their meanings in different contexts

Strand D Data

Covered in Weeks 10-13

This strand focuses on:

Data literacy skills for the 21st century
Collection, representation, and use of data
One-variable and two-variable data analysis
Mathematical modelling with data
Probability concepts and applications
Critical analysis of data and statistical claims

Strand E Geometry and Measurement

Covered in Weeks 7-9

This strand focuses on:

Geometric properties and relationships
Circle and triangle properties
Measurement systems and conversions
Perimeter, area, surface area, and volume
Spatial reasoning and visualization
Applications of geometry in real-world contexts

Strand F Financial Literacy

Covered in Weeks 14-15

This strand focuses on:

Financial situations and decision-making
Appreciation and depreciation of assets
Budgeting and budget modifications
Interest rates and their impact on purchasing decisions
Financial planning for future goals
Critical analysis of financial information and claims

Seven Mathematical Processes

The seven mathematical processes are interconnected and support effective mathematics learning. They should be integrated throughout instruction in all strands:

1. Problem Solving

Problem solving is central to doing mathematics and forms the foundation of mathematical instruction. Students develop critical thinking and mathematical reasoning by engaging with authentic, meaningful problems that require them to apply their knowledge in new contexts.

2. Reasoning and Proving

Students use their mathematical understanding to justify their thinking, form and test conjectures, and provide evidence for their solutions. This process helps students develop logical thinking and the ability to construct mathematical arguments.

3. Reflecting

Students monitor their own thought processes, consider the reasonableness of their answers, and develop metacognitive skills. Reflection helps students become more independent learners who can assess their own understanding and identify areas for improvement.

4. Connecting

Students understand relationships between different mathematical strands, link mathematics to other disciplines, and connect mathematical concepts to everyday life applications. Making connections helps students see mathematics as a coherent and useful body of knowledge.

5. Communicating

Students express their mathematical understanding using appropriate terminology, symbols, and representations. Communication can be oral, visual, written, or gestural, and helps students clarify their thinking while making their reasoning visible to others.

6. Representing

Students use tools, pictures, diagrams, graphs, tables, and other representations to model mathematical situations. They make connections among different representations and understand how each representation highlights different aspects of a mathematical concept.

7. Selecting Tools and Strategies

Students choose appropriate tools, technology, and problem-solving strategies for different mathematical tasks. This includes using manipulatives, digital tools, and various solution methods, developing flexibility in mathematical thinking.

Three-Part Lesson Structure

All lessons in this curriculum follow Ontario's recommended three-part lesson structure, which has been shown to be highly effective for mathematics instruction:

Part 1: Minds On

10-15 minutes

Purpose: Activate prior knowledge and engage students in the learning

Connect to previous learning and students' experiences
Introduce the learning goal and success criteria
Warm-up problems or mental math exercises
Connect to real-world contexts that are meaningful to students
Assess prior knowledge and identify potential misconceptions

Part 2: Action

40-50 minutes

Purpose: Students actively explore and develop understanding

Hands-on activities and mathematical investigations
Individual, pair, or group work with meaningful tasks
Use of manipulatives, tools, and technology
Mathematical discourse and collaboration among students
Teacher circulates, observes, asks probing questions, and provides support
Differentiated instruction to meet diverse learning needs

Part 3: Consolidation

10-15 minutes

Purpose: Synthesize learning and assess understanding

Class discussion and sharing of strategies
Summary of key concepts and big ideas
Exit cards or quick assessments to gauge understanding
Connection to future learning
Reflection on the learning process

Assessment Approaches

Assessment practices in this curriculum are based on Growing Success (2010), Ontario's assessment and evaluation policy. Assessment is integrated throughout instruction and serves multiple purposes:

Assessment FOR Learning (Formative Assessment)

Assessment for learning occurs during instruction and provides feedback to guide teaching and learning:

Ongoing observations during lessons
Questioning and mathematical discussions
Diagnostic assessments to identify prior knowledge and misconceptions
Formative feedback to guide instruction and student learning
Adjusting instruction based on student needs and understanding

Assessment AS Learning (Self and Peer Assessment)

Assessment as learning involves students in monitoring their own learning and setting goals:

Student self-assessment using success criteria
Peer assessment activities and feedback
Goal-setting and monitoring progress toward goals
Metacognitive skill development
Students taking ownership of their learning

Assessment OF Learning (Summative Assessment)

Assessment of learning occurs at the end of a period of learning and is used to make judgments about student achievement:

Quizzes and tests
Projects and presentations
Performance tasks
Portfolios of student work
Summative evaluations that inform report card grades

Four Achievement Categories

Student achievement is assessed across four categories:

Knowledge and Understanding - Understanding of mathematical terminology, concepts, and procedures
Thinking - Problem-solving skills, critical thinking, and mathematical reasoning
Communication - Expressing mathematical ideas clearly using appropriate representations and terminology
Application - Transfer of knowledge and skills to new contexts and real-world situations

Achievement Levels

Student performance is described using four levels:

Level 1 (50-59%) - Limited effectiveness in meeting expectations
Level 2 (60-69%) - Some effectiveness in meeting expectations
Level 3 (70-79%) - Considerable effectiveness in meeting expectations (Provincial standard)
Level 4 (80-100%) - High degree of effectiveness in meeting expectations

Note: Level 3 represents the provincial standard for student achievement. Students achieving at Level 3 are well prepared for further study in mathematics.

Differentiation and Inclusion

Universal Design for Learning (UDL)

UDL principles are embedded throughout the curriculum to ensure all students can access and engage with mathematical content:

Multiple means of engagement - Providing various ways to motivate and engage students
Multiple means of representation - Presenting information in different formats
Multiple means of action and expression - Allowing students to demonstrate learning in various ways
'Low floor, high ceiling' tasks - Activities that are accessible to all students but allow for extension
Flexible entry points - Tasks that students can approach at different levels of sophistication

Differentiated Instruction (DI)

Differentiated instruction is a student-centered approach that addresses varied readiness for learning:

Varies content (what students learn)
Varies process (how students learn)
Varies product (how students demonstrate learning)
Varies environment (the learning context)
Uses an asset-based approach focusing on student strengths

Support for Diverse Learners

English Language Learners (ELL)

Pre-teach key vocabulary with visual supports
Provide bilingual resources when available
Use gestures, demonstrations, and concrete materials
Allow use of translation tools
Pair with supportive peers for language modeling
Provide sentence frames for mathematical communication

Students with Special Education Needs

Provide accommodations as outlined in IEPs
Use assistive technology as appropriate
Offer alternative formats for instructions and materials
Provide one-on-one or small group support
Break tasks into smaller, manageable steps
Use visual schedules and graphic organizers

Indigenous Students

Include culturally relevant examples and contexts
Recognize and value Indigenous ways of knowing
Connect to Indigenous perspectives on mathematics
Create a culturally responsive learning environment

Gifted Students

Offer open-ended problems with multiple solution paths
Provide enrichment activities that deepen understanding
Encourage students to create their own problems
Connect to more advanced mathematical concepts
Allow independent exploration of topics of interest

Materials and Resources

Each lesson specifies required materials. Common resources used throughout the curriculum include:

Manipulatives and Concrete Materials

Algebra tiles for algebraic expressions and equations
Base-ten blocks for place value and operations
Fraction strips and circles for fraction concepts
Pattern blocks for geometry and patterns
Geometric solids for 3D geometry
Measuring tools (rulers, protractors, compasses)
Dice, coins, and spinners for probability
Real-world objects for hands-on activities

Technology and Digital Tools

Calculators (scientific or graphing)
Dynamic geometry software (e.g., GeoGebra)
Graphing tools and applications
Coding software for algebraic thinking
Statistical software for data analysis
Interactive whiteboards or projectors

Classroom Materials

Chart paper and markers for group work
Whiteboards and markers for individual practice
Grid paper and graph paper
Textbooks and workbooks
Visual aids and posters
Anchor charts for key concepts

Culturally Responsive and Relevant Pedagogy (CRRP)

Culturally responsive and relevant pedagogy is essential for creating an inclusive mathematics classroom where all students can succeed:

Key Elements of CRRP

Provide high-quality instruction emphasizing deep mathematical thinking for all students
Address issues of inequity and work to dismantle systemic barriers
Reflect on your own identities, biases, and assumptions
Learn about students' identities, lived experiences, and cultural backgrounds
Connect with cultural ways of knowing and problem-solving
Develop social consciousness and critical thinking about social issues
Value students' cultural backgrounds and competences as assets
Promote mathematical agency and investment in learning
Recognize multiple ways of knowing and approaching problems

How to Use the Weekly Lesson Plans

What Each Lesson Plan Includes

Curriculum strand and specific expectations
Clear learning goals and success criteria
Complete three-part lesson structure with timing
Teacher prompts and guiding questions
Real-world connections relevant to Grade 9 students
Hands-on activities and investigations
Assessment strategies (for, as, and of learning)
Required materials and resources list
Accommodations and modifications for diverse learners
Homework and practice assignments
Connection to future learning

Tips for Implementation

Review in advance - Read the lesson plan at least one day before teaching
Gather materials - Collect all required materials before the lesson begins
Adapt to your context - Modify activities based on your students' needs and interests
Use prompts as guides - Teacher prompts are suggestions, not scripts; adapt them to your teaching style
Encourage discourse - Promote mathematical discussions and multiple solution strategies
Create a safe environment - Foster a classroom where mistakes are valued as learning opportunities
Make connections - Link to students' lived experiences and cultural backgrounds
Assess continuously - Monitor understanding throughout the lesson and adjust as needed

Assessment Plan for the Semester

A balanced assessment plan includes multiple forms of assessment throughout the semester:

Weekly quizzes based on previous topics to reinforce learning
Mid-term project on algebra applications (after Week 6)
Final project focusing on an integrated topic across the semester
Ongoing formative assessment through observations and exit cards
Portfolio of student work samples demonstrating growth over time
Self and peer assessment opportunities throughout the course

Additional Resources and Support

Ontario Ministry of Education curriculum documents and support materials
Professional learning communities for mathematics teachers
Online resources and educational websites
Mathematics manipulative suppliers and catalogs
Professional development opportunities and workshops
Curriculum support from school board consultants
Mathematics education research and best practices

Ready to Start Teaching?

Explore the weekly lesson plans and begin implementing this comprehensive curriculum.

Start with Week 1 Browse All Lessons