
MTH1W - Mathematics
This course enables students to consolidate, and continue to develop, an understanding of mathematical concepts related to number sense and operations, algebra, measurement, geometry, data, probability, and financial literacy. Students will use mathematical processes, mathematical modelling, and coding to make sense of the mathematics they are learning and to apply their understanding to culturally responsive and relevant real-world situations. Students will continue to enhance their mathematical reasoning skills, including proportional reasoning, spatial reasoning, and algebraic reasoning, as they solve problems and communicate their thinking.
Department
Math
Development Date
2005
Course Title
Mathematics
Grade
09
Ministry Course Code
MTH1W
Prerequisite
None
Course Developer
The Educators Academy
Revision Date
2025
Course Reviser
The Educators Academy
Course Type
De-Streamed
Credit Value
01
Ministry Curriculum Policy Document
The Ontario Curriculum, Grades 9 and 10, 2005 (Revised)
Overall Curriculum Expectations
- A. Mathematical Thinking and Making Connections
- B. Number
- C. Algebra
- D. Data
- F. Financial Literacy
- E. Geometry and Measurement
A. Mathematical Thinking and Making Connections
A1. Mathematical Processes
i. Apply the mathematical processes to develop a conceptual understanding of, and procedural fluency with, the mathematics they are learning.
A2. Making Connections
i. Make connections between mathematics and various knowledge systems, their lived experiences, and various real-life applications of mathematics, including careers.
B. Number
B1. Development of Numbers and Number Sets
i. Demonstrate an understanding of the development and use of numbers, and make connections between sets of numbers.
B2. Powers
i. Represent numbers in various ways, evaluate powers, and simplify expressions by using the relationships between powers and their exponents.
B3. Number Sense and Operations
i. Apply an understanding of rational numbers, ratios, rates, percentages, and proportions in various mathematical contexts, and to solve problems.
C. Algebra
C1. Algebraic Expressions and Equations
i. Demonstrate an understanding of the development and use of algebraic concepts and of their connection to numbers, using various tools and representations.
C2. Coding
i. Apply coding skills to represent mathematical concepts and relationships dynamically, and to solve problems, in algebra and across the other strands.
C3. Applications of Relations
i. Represent and compare linear and non-linear relations that model real-life situations, and use these representations to make predictions.
C4. Characteristics of Relations
i. Demonstrate an understanding of the characteristics of various representations of linear and non-linear relations, using tools, including coding when appropriate.
D. Data
D1. Collection, Representation and Analysis of Data
i. Describe the collection and use of data, and represent and analyse data involving one and two variables.
D2. Mathematical Modelling
i. Apply the process of mathematical modelling, using data and mathematical concepts from other strands, to represent, analyse, make predictions, and provide insight into real-life situations.
F. Financial Literacy
F1. Financial Decisions
i. Demonstrate the knowledge and skills needed to make informed financial decisions.
E. Geometry and Measurement
E1. Geometric and Measurement Relations
i. Demonstrate an understanding of the development and use of geometric and measurement relationships, and apply these relationships to solve problems, including problems involving real-life situations.
Unit Outline
Units
Titles
Approx. Time
1
2
3
4
5
6
7
2 Hours
Total
110 Hours
Unit Description
- Unit 1: Mathematical Thinking and Making Connections (18 Hours)
- Unit 2: Number (18 Hours)
- Unit 3: Algebra (18 Hours)
- Unit 4: Data (18 Hours)
- Unit 5: Geometry and Measurement (18 Hours)
- Unit 6: Financial Literacy (18 Hours)
Unit 1: Mathematical Thinking and Making Connections (18 Hours)
Throughout the course, students apply the mathematical processes to develop conceptual understanding and procedural fluency while they engage in learning related to strands B through F. They also make connections between the mathematics they are learning and their lived experiences, various knowledge systems, and real-life applications, including employment and careers.
Unit 2: Number (18 Hours)
In this strand, students continue to make connections among various number systems, the cultural development of number concepts, and real-life applications. They will extend their learning about positive fractions, positive decimal numbers, and integers to work with negative fractions and negative decimal numbers. Students also extend their knowledge and skills related to percentages, ratios, rates, and proportions to make further connections to real life.
Unit 3: Algebra (18 Hours)
In this strand, students continue to develop an understanding of algebra by making connections between algebra and numbers as they generalize relationships with algebraic expressions and equations. Students will extend and apply coding skills to dynamically represent situations, analyse mathematics concepts, and solve problems in various contexts. Students will be introduced to various representations of linear and non-linear relations that they will study in more depth in future secondary mathematics courses. Students develop an understanding of constant rate of change and initial values of linear relations, and solve related real-life problems.
Unit 4: Data (18 Hours)
In this strand, students extend their data literacy skills to examine the collection, representation, and use of data, as well as their implications in various contexts. Students consolidate and extend their understanding of data involving one and two variables and its connections to real life. Using data, students continue to apply the process of mathematical modelling to analyse real-life situations.
Unit 5: Geometry and Measurement (18 Hours)
In this strand, students make connections among various geometric properties and their real-life applications. Students analyse and create designs to extend their understanding of geometric relationships to include circle and triangle properties. Students solve problems using different units within and between various measurement systems, examine the relationships between the volume of cones and cylinders and of pyramids and prisms, and solve problems that involve the application of perimeter, area, surface area, and volume.
Unit 6: Financial Literacy (18 Hours)
In this strand, students analyse financial situations to explain how mathematics can be used to understand such situations and inform financial decisions. They extend their financial literacy knowledge to answer questions related to appreciation and depreciation, and explain how budgets can be modified based on changes in circumstances. Students compare the effects of different interest rates, down payments, and other factors associated with purchasing goods and services. Students use their learning from other strands to solve financial problems of interest.
Program Considerations
- Assessment and Evaluation
- Teaching & Learning Strategies
Assessemnt & Evaluation
The primary purpose of assessment and evaluation is to improve student learning. Information gathered through assessment helps teachers to determine students’ strengths and weaknesses in their achievement of the curriculum expectations in each course. This information also serves to guide teachers in adapting curriculum and instructional approaches to students’ needs and in assessing the overall effectiveness of programs and classroom practices.
For assessment and evaluation, we follow the Ministry of Education's Growing Success document, and by doing so will benefit the students both in the present and future. We designed assessments in such a way as to make it possible to gather and show evidence of learning in a variety of ways to gradually release responsibility to the students, and to give multiple and varied opportunities to reflect on learning and receive detailed feedback.
Assessment and evaluation will be based on the provincial curriculum expectations and the achievement levels outlined in this document. Growing Success articulates the vision the Ministry has for the purpose and structure of assessment and evaluation techniques.
In order to ensure that assessment and evaluation are valid and reliable and that they lead to the improvement of students’ learning, The Educators Academy’s assessment and evaluation strategies focus on:
- i. Address both what students learn and how well they learn.
- ii. Are varied in nature, administered over a period of time, and designed to provide opportunities for students to demonstrate the full range of their learning.
- iii. Are appropriate for the learning activities used, the purposes of instruction, and the needs and experiences of the students.
- iv. Are fair to all students.
- v. Accommodate students with special education needs, consistent with the strategies outlined in their Individual Education Plan and those who are learning the language of instruction (English or French).
- vi. Ensure that each student is given clear directions for improvement.
- vii. Promote students’ ability to assess their own learning and to set specific goals.
- viii. Include the use of samples of students’ work that provide evidence of their achievement.
- ix. Are communicated clearly to students and parents at the beginning of the school year and at other appropriate points (Parent Teacher Nights) throughout the school year.
The overall expectations are broad in nature, and the specific expectations define the particular content or scope of the knowledge and skills referred to in the overall expectations. Our teachers use their professional judgment to determine which specific expectations should be used to evaluate achievement of the overall expectations, and which ones will be covered in instruction and assessment (e.g., through direct observation) but not necessarily evaluated.
The assessment and evaluation strategy include diagnostic, formative and summative within the course and within each unit.
Assessment Strands:
The Educators Academy will ensure that student work is assessed and/or evaluated in a balanced manner with respect to the four categories, and that achievement of particular expectations is considered within the appropriate categories.
The purpose of the achievement chart is to:
- provide a common framework that encompasses the curriculum expectations for all courses outlined in this document;
- guide the development of quality assessment tasks and tools (including rubrics);
- help teachers to plan instruction for learning;
- assist teachers in providing meaningful feedback to students;
- provide various categories and criteria with which to assess and evaluate student learning.
Evaluation and Reporting of Students' Achievements by Report Cards
Student achievement is communicated formally to students and parents by means of the Provincial Report Card. The report card provides a record of the student's achievement of the curriculum expectations in every course, at particular points in the school year or semester, in the form of a percentage grade. Report cards are issued upon completion of the course. Each report card will focus on related aspects of student achievement. The percentage grade will represent the quality of the student's overall achievement of the expectations for the course and will reflect the corresponding level of achievement. The Educators Academy will record a final grade for every course, and a credit is granted for the course in which the student's grade is 50% or higher.
- Seventy per cent of the grade will be based on evaluations conducted throughout the course. This portion of the grade should reflect the student's most consistent level of achievement throughout the course, although special consideration should be given to more recent evidence of achievement.
- Thirty per cent of the grade will be based on a final evaluation in the form of an examination, performance, essay, and/or other method of evaluation suitable to the course content and administered towards the end of the course.
Final Assessment and Evaluation = 100%
The teacher will also provide written comments concerning the student's strengths, areas for improvement, and next steps (E–Excellent, G–Good, S–Satisfactory, N–Needs Improvement). The report card will indicate whether an OSSD credit has been earned or not. Upon completion of a course, The Educators Academy will send a copy of the report card back to the student's home school where the course will be added to the ongoing list of courses on the student's Ontario Student Transcript. The report card will also be sent to the student's home address for parents' communication.
Teaching & Learning Strategies
To make new learning more accessible to students, The Educators Academy’s teachers draw upon the knowledge and skills students have acquired in previous years – in other words, they help to activate prior mathematical knowledge. It is important to assess where students are in their mathematical growth and to bring them forward in their learning. The aim of this course is to help students use the language of mathematics skillfully, confidently and flexibly, a wide variety of instructional strategies are used to provide learning opportunities to accommodate a variety of learning styles, interests and ability levels.
For mathematical processes, some teaching and learning strategies used are:
- i. Communicating: To improve student success there will be several opportunities for students to share their understanding both in oral as well as written form.
- ii. The use of technological tools and software (e.g., graphing software, dynamic geometry software, the Internet, spreadsheets, and multimedia) in activities, demonstrations, and investigations to facilitate the exploration and understanding of mathematical concepts;
- iii. Learning Goals and Success Criteria is explained to the students before starting any unit, task or activity.
- iv. Problem solving: Scaffolding of knowledge, detecting patterns, making and justifying conjectures, guiding students as they apply their chosen strategy, directing students to use multiple strategies to solve the same problem, when appropriate, recognizing, encouraging, and applauding perseverance, discussing the relative merits of different strategies for specific types of problems.
- v. Reasoning and proving: Asking questions that get students to hypothesize, providing students with one or more numerical examples that parallel these with the generalization and describing their thinking in more detail.
- vi. Reflecting: Modeling the reflective process, asking students how they know.
- vii. Selecting Tools and Computational Strategies: Modeling the use of tools and having students use technology to help solve problems.
- viii. Connecting: Activating prior knowledge when introducing a new concept in order to make a smooth connection between previous learning and new concepts, and introducing skills in context to make connections between particular manipulations and problems that require them.
- ix. Representing: Modeling various ways to demonstrate understanding, posing questions that require students to use different representations as they are working at each level of conceptual development - concrete, visual or symbolic, allowing individual students the time they need to solidify their understanding at each conceptual stage.
- x. Group Work: Working cooperatively in groups reduces isolation and provides students with opportunities to share ideas and communicate their thinking in a supportive environment as they work together towards a common goal.
- xi. Comparison and evaluation of written work is very important in this course. This course focuses on giving many examples of correct work, and helping students build the skills needed to peer-correct and self correct.
- xii. Oral presentations are a good tool for learning. Students can learn from one another, and from their teacher. Charts and graphs are used to present effective learning opportunities of concepts and skills to different students.