Grade 7 & 8 Mathematics

The Grade 7 & 8 mathematics curriculum at CanKnow really includes all topics in mathematics typically encountered up to and including the age of about 13, or an Ontario Grade 8 level. Choose this subject if you are working on Grade 7 or 8 math, or if you are struggling with any basic mathematical concepts. Details of the Grade 7 and 8 math curriculum in Ontario can be found here: https://www.ontario.ca/page/new-math-curriculum-grades-1-8#grade8

• Rational versus irrational numbers, rounding, comparison
• Arithmetic with whole numbers, decimals, fractions
• Ratio & proportion, converting among fractions, decimals, percentages
• Order of operations, basic algebra, collecting like terms, evaluating algebraic expressions
• Introduction to coding
• Introduction to probability, statistics and data visualization
• 2-D and 3-D geometric shapes, their properties, and calculating length, area, surface area volume
• Cartesian coordinate system, graphing points, lines, shapes
• Transformations, scaling
• Metric system
• Basics of financial math

Grade 9 Math

The overall aim of the Grade 9 mathematics course in Ontario is to ensure that all students can access any secondary mathematics course they need in order to pursue future studies and careers that are of interest to them. Choose Grade 9 Math if you are in Grade 9 math or if you are struggling with any of the topics listed below. Details of the Ontario Grade 9 Math curriculum can be found here: https://www.dcp.edu.gov.on.ca/en/curriculum/secondary-mathematics/courses/mth1w/elements-of-the-grade-9-mathematics-course#expectations.

• Number sets – Whole, Integer, Rational, Irrational, Real
• Powers/Exponents, Scientific notation
• Arithmetic and Geometric sequences, written as algebraic expressions
• Applications, measuring, metric system, converting among measurement systems
• Development and use of algebra, evaluating more complex algebraic expressions and solving more complex equations, absolute value
• Coding
• Application of linear and non-linear (specifically xy=k) relations
• Characteristics of linear and non-linear relations
• Graphing linear equations where slope is 0, 1, infinity, or any real number, transformations of linear equations
• Solving systems of linear equations by graphing
• Data collection, sampling, concept of bias
• Representation and analysis of data using box-and-whisker plots, scatter plots, bar and line graphs, histograms, pie/circle charts, stem-and-leaf plots
• Introduction to mathematical modelling
• Circles: Area, circumference, radius and diameter, central angles, chords, tangents, sectors
• Triangles: angle sum, right triangles, Pythagoras, area
• Volume and surface area of prisms, pyramids, cones, cylinders
• Scale drawings, similar shapes, are, perimeter, volume, changes in scale
• Estimating measurements, converting between metric and imperial measurements
• Financial decisions, use of graphs in finance, interest rates, markup, discount, profit, loss, budgeting

Grade 10 Math

Mathematics at the Grade 10 level in Ontario comprises the following topics:

• Quadratic relations and their applications
• Solving linear systems, applications of linear systems
• Properties of geometric figures using analytic geometry
• Similar triangles, trigonometry of right and acute triangles
• Measurement of three-dimensional figures

Join this session if you are in Grade 10 math in Ontario or if you are struggling with any of these concepts.

Grade 11 Math

There are several mathematics courses at the Grade 11 level in Ontario. Choose this subject if you are in any Grade 11 course in Ontario, if you are in “Mathematics for Work and Everyday Life, Grade 12, Workplace (MEL4E)” in Ontario, or if you are struggling with any of the following topics:

• Linear and quadratic relations
• Properties of discrete and continuous functions
• Trigonometric and exponential functions
• Applications of functions, inverse functions
• Equivalent algebraic expressions
• Modelling real-world situations with linear, quadratic, trigonometric, and exponential functions
• Data collection, analysis, evaluating data involving one variable, probability and statistics
• Applications of geometry and trigonometry
• Simple and compound interest in saving, investing, and borrowing
• Problems associated with earning money, budgeting, paying taxes, and making purchases, costs of transportation and travel in a variety of situations
• Using proportional reasoning; estimating and measuring; and applying geometric concepts to create designs

Grade 12 Math

Again, there are many mathematics courses at the Grade 12 level in Ontario. Choose this option if you are in any Grade 12 course in Ontario EXCEPT “Mathematics for Work and Everyday Life, Grade 12, Workplace (MEL4E)” or if you are struggling with any of the following topics:

• Properties and applications of polynomial, exponential, rational, logarithmic, and trigonometric functions
• Techniques for combining functions; simplifying expressions
• Problems involving geometric and algebraic representations of vectors and representations of lines and planes in three-dimensional space
• Understanding of rates of change to include the derivatives of polynomial, sinusoidal, exponential, rational, and radical functions
• Applications of algebra, trigonometry, vectors, and geometry
• Mathematics as it relates to managing data; organizing and analyzing large amounts of information
• Problems involving probability and statistics
• Financial problems connected with annuities, budgets, and renting or owning accommodation

Science (Grades 7 - 10)

Choose this option if you are in any science course in middle school or high school other than upper year high school chemistry, physics or biology.

Grade 11-12 Science

Choose this option if you are studying chemistry, physics or biology in high school. Note that some sessions are listed as Grade 11-12 Science, while others may specify the individual sciences.

English as a Second Language

Choose this subject if you are in middle school or high school and you need help with English because it is not your mother tongue.

French as a Second language

Choose this subject if you are in middle school or high school and you need help with French. 

English Language, Literature and Creative Writing

You can choose this subject if you need help with your English coursework in middle school or high school. This option is not meant to support learning English as a second language.

Social Sciences

Choose this option if you are in secondary school and you need help with any of the social sciences, such as Economics, Geography, History, Law, Political Science, Psychology, or Sociology.

Essay Writing

Choose this topic if you are in any secondary education and you need help with writing an essay for any of your courses. 

Group Project - Science or Group Project - Arts or Social Sciences

If you are working on group projects, you may find it beneficial for all members of your group to register for the same session. You can then work online with your group and get help from a teacher. There are Breakout Rooms called Project Rooms as well as separate tutoring sessions designed for this purpose.

Math for College

Choose this option if you are in any finance, business, healthcare or trades program in a public or private college and you are struggling with any aspect of mathematics. If you are in a degree program and you are struggling with university-level mathematics, choose the relevant math course.

Calculus

Choose this session if you are in any college or university calculus course, or if you are struggling with any of the following topics:

• Limits and continuity
• Derivatives: definition and basic rules
• Derivatives: chain rule and other advanced topics
• Applications of derivatives
• Analyzing functions
• Integrals
• Differential equations
• Applications of integrals

Probability and Statistics

Choose this option if you are in any college or university probability or statistics course, or if you are struggling with any of the following topics:

• Descriptive Statistics:
  • Measures of central tendency (mean, median, mode)
  • Measures of dispersion (range, variance, standard deviation)
  • Percentiles and quartiles
• Probability:
  • Basic probability rules and axioms
  • Probability distributions (discrete and continuous)
  • Conditional probability and independence
  • Bayes' theorem
• Random Variables:
  • Discrete and continuous random variables
  • Probability mass functions (PMFs) and probability density functions (PDFs)
  • Cumulative distribution functions (CDFs)
  • Expected value and variance of a random variable
  • Linearity of expectation
• Sampling Distributions:
  • Sampling from populations
  • Sampling distribution of the sample mean and proportion
• Inferential Statistics:
  • Confidence intervals
  • Hypothesis testing
  • Type I and Type II errors
  • Power of a test
• Regression and Correlation:
  • Simple linear regression
  • Multiple regression
  • Correlation coefficient
• Analysis of Variance (ANOVA):
  • One-way ANOVA
  • Two-way ANOVA
• Non-parametric Statistics:
  • Mann-Whitney U test
  • Wilcoxon signed-rank test
  • Kruskal-Wallis test
• Probability Distributions:
  • Binomial distribution
  • Poisson distribution
  • Normal distribution
  • Exponential distribution
• Statistical Software:
  • Introduction to statistical software (e.g., R, Python, SAS)
  • Data visualization and analysis
• Advanced Topics:
  • Maximum likelihood estimation
  • Bayesian statistics
  • Multivariate analysis
  • Time series analysis

Linear Algebra

Choose this subject if you are in any college or university linear course, or if you are struggling with any of the following topics:

• Vectors and Vector Spaces:
  • Definition of vectors
  • Vector operations (addition, scalar multiplication)
  • Linear combinations
  • Span of vectors
  • Subspaces
• Matrices:
  • Matrix representation
  • Matrix operations (addition, multiplication)
  • Transpose of a matrix
  • Determinants
  • Inverse matrices
• Systems of Linear Equations:
  • Gaussian elimination
  • Row echelon form and reduced row echelon form
  • Solutions to systems of linear equations
  • Homogeneous and nonhomogeneous systems
• Eigenvalues and Eigenvectors:
  • Eigenvalues and eigenvectors of a matrix
  • Diagonalization of matrices
  • Characteristic polynomial
• Linear Transformations:
  • Definition of linear transformations
  • Kernel and image (range) of a linear transformation
  • Rank-nullity theorem
• Inner Product Spaces:
  • Dot product
  • Norms and inner products
  • Orthogonality
  • Gram-Schmidt process
• Orthogonalization and Orthogonal Diagonalization:
  • Orthogonal matrices
  • QR factorization
  • Orthogonal diagonalization of symmetric matrices
• Applications:
  • Least squares approximation
  • Markov chains
  • Linear programming
  • Principal component analysis
• Abstract Vector Spaces:
  • Generalization of vector spaces
  • Dual spaces
  • Dual bases
• Singular Value Decomposition (SVD):
  • Decomposition of a matrix into singular values and singular vectors
  • Applications in data compression and dimensionality reduction

Python Programming

Choose this option if you are struggling with programming in Python.

Data Visualization

If you are learning Power BI or Tableau and need some help, this session is for you.

Advanced Math

Choose this option if you are struggling with any upper level university math course, such as Analysis, Algebra, Topology, Number Theory, etc...

Economics

Choose this option if you are struggling with any college or university economics course.

Essay Writing

Choose this topic if you are in university or any post-secondary education and you need help with writing an essay for any of your courses. 

Job Search

Choose this option if you are looking for a job and need help with writing a resume, modifying it to match a job description, writing a cover letter, developing a video application, or even looking for a job. 

Project Management

If you need help studying for your PMP or PRINCE2 exam, or putting together your portfolio for certification, or if you are trying to manage a project and need help, or if you are simply interested in learning how to manage projects, this is the right session for you.

Proposal Management

If you are writing a proposal and need help, or if you want to learn how to write proposals, choose this option.

Data Science

Choose this topic if you are struggling with any concept in Data Analysis or Data Science. Topics may include, but are not limited to, the following:

• Data Extraction, Data Transformation, Extract/Load/Transform, SQL
• Data Analysis, Statistics
• Data Visualization, Power BI, Tableau
• Machine Learning
• Natural Language Processing
• Data Management
• Data Governance