The Big Ideas
Grade 9 Mathematics 1D1
Using your curriculum document:
http://edu.gov.on.ca/eng/curriculum/secondary/math.html
http://edu.gov.on.ca/eng/curriculum/secondary/math910curr.txt
The Place of Mathematics in the Curriculum
The secondary curriculum adopts a strong focus on the processes that
best enable students to understand mathematical concepts and learn
related skills. Attention to the mathematical processes is considered
to be essential to a balanced mathematics program. The seven
mathematical processes identified in this curriculum are problem
solving, reasoning and proving, reflecting, selecting tools and
computational strategies, connecting, representing, and communicating.
A balanced mathematics program at the secondary level includes the
development of algebraic skills. This curriculum has been designed to
equip students with the algebraic skills they need to understand other
aspects of mathematics that they are learning, to solve meaningful
problems, and to continue to meet with success as they study
mathematics in the future. The algebraic skills required in each course
have been carefully chosen to support the other topics included in the
course. Calculators and other appropriate technology will be used when
the primary purpose of a given activity is the development of concepts
or the solving of problems, or when situations arise in which
computation or symbolic manipulation is of secondary importance.
Academic courses develop students’ knowledge and skills through the
study of theory and abstract problems.
Strands in the Math Curriculum
The strands in the Grade 9 courses are designed to build on those in
Grade 8, while at the same time providing for growth in new directions
in high school.
1. Number Sense and Algebra
- builds on the Grade 8 Number Sense and Numeration strand and
parts of the Patterning and Algebra strand. It includes
expectations describing numeric skills that students are expected
to consolidate and apply, along with estimation and mental
computation skills, as they solve problems and learn new material
throughout the course. The strand includes the algebraic
knowledge and skills necessary for the study and application of
relations. In the Principles course, the strand covers the basic
exponent rules, manipulation of polynomials with up to two
variables, and the solving of first-degree equations.
2. Linear relations
- students develop initial understandings of the properties of
linear relations as they collect, organize, and interpret data
drawn from a variety of real-life situations (applying knowledge
gained in the Data Management strand of the elementary school
program) and create models for the data. Students then develop,
make connections among, and apply various representations of
linear relations and solve related problems.
3. Analytic Geometry
- students will extend the initial experiences of linear relations
into the abstract realm of equations in the
form y = mx + b, formulas, and problems.
4. Measurement and Geometry
- extends students’ understandings from Grade 8 to include the
measurement of composite two-dimensional shapes and the
development of formulas for, and applications of, additional
three-dimensional figures. Furthermore, in measurement, students
investigate the effect of varying dimensions (length and width)
on a measure such as area. Students in the Principles course
conduct similar investigations in connection with volume and
surface area. Examination of such relationships leads students to
make conclusions about shapes and figures. In geometry, the
knowledge students acquired in Grade 8 about the properties of
two-dimensional shapes is extended through investigations that
broaden their understanding of the relationships among the
properties.
Mathematical process expectations.
The mathematical processes are to be integrated into student learning
in all areas of this course.
Throughout this course, students will:
PROBLEM SOLVING
• 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;
REASONING AND PROVING
• develop and apply reasoning skills (e.g., recognition of
relationships, generalization through inductive reasoning, use of
counter-examples) to make mathematical conjectures, assess conjectures,
and justify conclusions, and plan and construct organized mathematical
arguments;
REFLECTING
• 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);
SELECTING TOOLS AND COMPUTATIONAL STRATEGIES
• select and use a variety of concrete, visual, and electronic learning
tools and appropriate computational strategies to investigate
mathematical ideas and to solve problems;
CONNECTING
• 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);
REPRESENTING
• 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;
COMMUNICATING
• communicate mathematical thinking orally, visually, and in writing,
using mathematical vocabulary and a variety of appropriate
representations, and observing mathematical conventions.
Principles of Mathematics, Grade 9, Academic (MPM1D)
This course enables students to develop an understanding of
mathematical concepts related to algebra, analytic geometry, and
measurement and geometry through investigation, the effective use of
technology, and abstract reasoning. Students will investigate
relationships, which they will then generalize as equations of lines,
and will determine the connections between different representations of
a linear relation. They will also explore relationships that emerge
from the measurement of three-dimensional figures and two-dimensional
shapes. Students will reason mathematically and communicate their
thinking as they solve multi-step problems.
1. Number Sense and Algebra
Overall Expectations
By the end of this course, students will:
• demonstrate an understanding of the exponent rules of multiplication
and division, and apply them to simplify expressions;
• manipulate numerical and polynomial expressions, and solve firstdegree equations.
2. Linear Relations
Overall Expectations
By the end of this course, students will:
• apply data-management techniques to investigate relationships
between two variables;
• demonstrate an understanding of the characteristics of a linear
relation;
• connect various representations of a linear relation.
3. Analytic Geometry
Overall Expectations
By the end of this course, students will:
• determine the relationship between the form of an equation and the
shape of its graph with respect to linearity and non-linearity;
• determine, through investigation, the properties of the slope and yintercept of a linear relation;
• solve problems involving linear relations.
4. Measurement and Geometry
Overall Expectations
By the end of this course, students will:
• determine, through investigation, the optimal values of various
measurements;
• solve problems involving the measurements of two-dimensional shapes
and the surface areas and volumes of three-dimensional figures;
• verify, through investigation facilitated by dynamic geometry
software, geometric properties and relationships involving twodimensional shapes, and apply the results to solving problems.