ENG1D, English, Grade 9, Academic
This course enables students to develop an understanding of mathematical concepts related to introductory algebra, proportional reasoning, and measurement and geometry through investigation, the effective use of technology, and hands-on activities. Students will investigate real-life examples to develop various representations of linear relations, and will determine the connections between the representations. They will also explore certain relationships that emerge from the measurement of three-dimensional figures and two-dimensional shapes. Students will consolidate their mathematical skills as they solve problems and communicate their thinking.
Department
English
Development Date
2023
Course Title
ENG1D, English, Grade 9, Academic
Grade
09
Ministry Course Code
ENG1D
Prerequisite
None
Course Developer
The Educators Academy
Revision Date
2025
Course Reviser
The Educators Academy
Course Type
Applied
Credit Value
01
Ministry Curriculum Policy Document
The Ontario Curriculum, grades 9 and 10, 2005 (Revised)
Overall Curriculum Expectations
- English Process Expectations
- Number Sense and Algebra
- Linear Relations
- Measurement and Geometry
English Process Expectations
i. develop, select, apply, and compare a variety of problem-solving strategies as they pose and solve problems and conduct investigations, to help deepen their mathematical understanding;
ii. develop and apply reasoning skills (e.g., recognition of relationships, generalization through inductive reasoning, use of counter-examples) to make mathematical conjectures,
iii. assess conjectures, and justify conclusions, and plan and construct organized mathematical arguments;
iv. demonstrate that they are reflecting on and monitoring their thinking to help clarify their understanding as they complete an investigation or solve a problem (e.g., by assessing the effectiveness of strategies and processes used, by proposing alternative approaches, by judging the reasonableness of results, by verifying solutions);
v. select and use a variety of concrete, visual, and electronic learning tools and appropriate computational strategies to investigate mathematical ideas and to solve problems;
vi. make connections among mathematical concepts and procedures, and relate mathematical ideas to situations or phenomena drawn from other contexts (e.g., other curriculum areas, daily life, current events, art and culture, sports);
vii. create a variety of representations of mathematical ideas (e.g., numeric, geometric, algebraic, graphical, pictorial representations; onscreen dynamic representations), connect and compare them, and select and apply the appropriate representations to solve problems;
viii. communicate mathematical thinking orally, visually, and in writing, using mathematical vocabulary and a variety of appropriate representations, and observing mathematical conventions.
Number Sense and Algebra
i. solve problems involving proportional reasoning;
ii. simplify numerical and polynomial expressions in one variable, and solve simple first-degree equations.
Linear Relations
i. apply data-management techniques to investigate relationships between two variables;
ii. determine the characteristics of linear relations;
iii. demonstrate an understanding of constant rate of change and its connection to linear relations;
iv. connect various representations of a linear relation, and solve problems using the representations.
Measurement and Geometry
i. determine, through investigation, the optimal values of various measurements of rectangles;
ii. solve problems involving the measurements of two-dimensional shapes and the surface areas and volumes of three-dimensional figures;
iii. determine, through investigation facilitated by dynamic geometry software, geometric properties and relationships involving two-dimensional shapes, and apply the results to solving problems.
Unit Outline
#
Unit
Approx. Time
1
Number Sense and Algebra
36 Hours
2
Linear Relations
36 Hours
3
Measurement and Geometry
36 Hours
4
Final Examination
3 Hours
5
Total
110 Hours
Unit Description
- Unit 1: Number Sense and Algebra (36 Hours)
- Unit 2: Linear Relations (35 Hours)
- Unit 3: Measurement and Geometry (36 Hours)
Unit 1: Number Sense and Algebra (36 Hours)
In this unit, students will review the major concepts that are necessary for success in the rest of the course. Fundamental training includes developing a strong number sense, reviewing order of operations, and understanding the concepts surrounding decimals, fractions, ratios and proportions.
Unit 2: Linear Relations (35 Hours)
In this unit, students will investigate by developing strategies to solve linear equations. Data numbers and figures that are used to describe and make sense of the world around us - are only useful if they can be organized, analyzed and presented in ways that make sense to ourselves and each other. This unit is about using mathematical and graphical tools to understand data. Understanding of statistics and proportionality will be developed. Learning to recognize and manipulate linear relationships, and to extrapolate and interpolate data based upon pre-existing data, are also investigated. Simple algebra to describe graphs will be introduced. Building upon the algebra developed earlier in this unit, students will learn to solve simple linear equations. Adding and subtracting polynomials and the distributive law will be introduced and practiced.
Multi-step equations will be examined. By the end of the unit, students will have experience translating written words into mathematical equations, and vice-versa. Based upon the understandings of linear equations developed in Unit, the concepts of slope, rates of change are introduced and we investigate how these ideas relate to practical relations such as distance-time relationships. The techniques and uses of finding the point of intersection of two lines on a graph will be studied.
Unit 3: Measurement and Geometry (36 Hours)
In this unit, Students will demonstrate an understanding of the physical and mathematical properties of a variety of two- and three-dimensional shapes will be considered. Building on ideas of proportionality developed earlier, the relationships between distance, area and volume will be examined. Techniques for optimization design will be discussed. Essential knowledge in many trades, Pythagorean Theorem and Parallel Line Theorem will be studied in detail.
Program Considerations
- Assessment and Evaluation
- Teaching & Learning Strategies
Assessment and 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:
- Address both what students learn and how well they learn;
- 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;
- Are appropriate for the learning activities used, the purposes of instruction, and the needs and experiences of the students;
- Are fair to all students;
- 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)
- Ensure that each student is given clear directions for improvement;
- Promote students' ability to assess their own learning and to set specific goals;
- Include the use of samples of students' work that provide evidence of their achievement;
- 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.
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.
Evaluation Instruments/ Strategies
| Rubrics | Observation |
| Checklist | Project Work |
| Peer | Interviewing |
| Self | Researching |
| Group | Conferencing |
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:
- Communicating:
To improve student success there will be several opportunities for students to share their understanding both in oral as well as written form. - 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. - 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. - Reflecting:
Modeling the reflective process, asking students how they know. - Selecting Tools and Computational Strategies: Modeling the use of tools and having students use technology to help solve problems.
- 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. - 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. - 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.