e-Learning Ontario – Ontario Educational Resource Bank
Interactive Learning Math Resources - SECONDARY
Subject
Topic
Making Change
Jeopardy
MAT1L (Catholic): Unit 1 – Entire
Unit: Money Sense
MAT1L (Catholic): Unit 2 – Entire
Unit: Understanding and Using the
Metric System
MAT1L (Catholic): Unit 3 – Entire
Unit: Measurement of Length using
the Imperial System
MAT1L (Catholic): Unit 4 – Entire
Unit: Understanding and Applying
Perimeter, Area, and Volume
MAT 1L
MAT1L (Catholic): Unit 5 – Entire
Unit: Fractions and Percent
MAT1L (Catholic): Unit 6 – Entire
Unit: Ratio and Rate
MAT1L (Catholic): Unit 7 – Entire
Unit: Culminating Activity
MAT1L: Unit 6 - Entire Unit:
Culminating Activity - You be the
Boss!
Subject
Topic
Math Jeopardy
MFM 1P
Footprints
Basketball Drop
Description
In this activity, students will practice making change from various amounts of money. They will use the "counting
up" strategy to ensure that they are accurate.
This activity allows students to consolidate their understanding of perimeter, volume and area in a fun, Jeopardystyle game.
In this unit students will learn to read, write and understand money values using words, symbols, and numbers.
They will use estimation strategies to estimate amounts of money, and how much change they will get when they
buy something. They will learn and practice a method for making change. Finally, they will learn to solve
problems involving money by estimating and calculating the total cost of several items.
In this unit, you will use your skills to accurately measure and estimate lengths, mass and capacity using the
Metric system. You will use tape measures, rulers, web – sites and calculators to aid you in your measurement
calculations. This unit will require you to complete assignments in both the workplace and everyday-life
situations.
ELO #
ELO1142700
ELO1142740
ELO1144300
ELO1144800
In this unit, you will use your skills to accurately measure and estimate lengths using the Imperial system. You
will use tape measures, rulers and calculators to aid you in your measurement calculations.
ELO1143770
In this unit, you will use your skills to accurately measure and estimate perimeter, area and volume using the
Metric system.
ELO1144990
In this unit students will develop their understanding of fractions through the use of diagrams and interactive
elements. They will learn to add and subtract fractions using real-life models such as a clock, a ruler, and money
values. They will explore the relationship between fractions and decimals, which will lead into learning about
percent. In the final activity they will solve real life problems using fractions and percentages.
In this unit, you will learn to identify and use ratios and rates found in your everyday experiences. You will
develop skills in identifying and calculating equivalent ratios and use these skills to solve real-life problems. You
will learn to calculate important rates such as heart rate, speed, rate of pay and unit costs and use rates to solve
real-life problems.
In this unit, you will complete the Culminating Activity for this course. You will design, decorate and furnish your
dream bedroom. This project will include lots of choice in terms of choosing flooring, paint and bedroom
furniture. Along the way, you will determine the total cost for each item and keep track of it using a spreadsheet.
When your dream bedroom is complete, you will have a chance to reflect on your work and the amount of money
you “spent”!
In the culminating activity for this course, students pretend that they are entrepreneurs going through the process
of setting up a small business. This resource has also been developed for Grade 8 Mathematics. To make things
more manageable, the assignment is broken up into the five parts: research involving what it means to be an
entrepreneur, writing an application for a small business grant, creating and costing out a list of inventory for the
business, drawing to scale a floor plan of the business space that they have been awarded, and the calculation of
the total cost of renovating the business space.
Description
A math jeopardy-style quiz testing students on their knowledge regarding linear and non-linear
relationships, problem solving model, and statistics/sampling methods and terms. For 1 to 4 players.
Simulators that allow students to collect data for graphing and determining relationships without having to
use the actual objects. Great for students who might have missed data collection in class with their peers as
subjects.
ELO1144370
ELO1144420
ELO1144480
ELO1145840
ELO #
ELO1002842
ELO1002550
ELO1002555
MFM1P (Catholic): Unit 1 - Entire
Unit: Number Sense and Algebra
MFM1P (Catholic): Unit 2 - Entire
Unit: Linear Relations Introduction
MFM1P (Catholic): Unit 3:
Measurement and Geometry:
Introduction
Basketball Throw
Pizzazz!
Solve the Equation
Battleship
Subject
Topic
We're Going Batty
MPM 1D
MPM1D (Catholic): Unit 1 Entire Unit: Recap and Number
Sense
Unit for Number Sense and Algebra strand, contains 16 activities which develop skills in Proportional
Reasoning and Algebraic modelling. Activity 16 is the culminating activity which gives the students an
opportunity the apply all their learning in planning a 'virtual vacation.' A unit test also is included. among
other things, students should be encouraged to think reflectively and creatively to evaluate situations and
solve problems. Teachers using this resource are advised to ascertain the availability and suitability of the
recommended website(s)/hyperlink(s) beforehand. Teachers using this resource are advised to set up an ediscussion board in advance to substitute for the defunct drop-box feature in activities 6,8, and 11; should
they wish to administer these portions of these activities in an electronic learning environment.
This unit contains 24 activities and a unit test which collectively, develop the following set of expectations
for the Linear Relations strand: apply data-management techniques to investigate relationships between two
variables; determine the characteristics of linear relations; demonstrate an understanding of constant rate of
change and its connection to linear relations; connect various representations of a linear relation, and solve
problems sing the representations. TEMP EDIT NOTE: This resource may possibly need to be called back
from the repository, because of problems with hyperlinks in some activities.
This unit covers the following activities: Geometer's Sketch Pad, Greatest Area with a Fixed Perimeter,
Minimum Perimeter for a Given Area, Pythagorean Theorem, Perimeter and ARea of Composite Plane
Figures, Volume of Prisms, Volume of Cylinders, Volume of Pyramids and Cones, Volume of a Sphere,
Review of Geometric Concepts, Investigating Geometric Relationships, Interior and Exterior Angles of
Triangles, Interior and Exterior Angles of Quadrilaterals, Interior and Exterior Angles of Parallel Lines,
Diagonals Teachers using this resource are advised to ascertain the availability and suitability of the
recommended website(s)/hyperlink(s) beforehand.
Students collect data to determine if there is a relationship between the height of a player and the number of
successful free throw shots out of a possible 10. There are 10 pictures different basketball players whose
individual heights are revealed to the students. When they click on the picture of a particular player, there
will be an animation of a basketball being shot by that player, towards a basket quickly 10 times. The
number of successful throws is shown in the table of values. -solving, time and resource management skills.
Interactive matching game with a cryptogram puzzle. Reviews expanded and simplified polynomial
expressions. Students match each simplified expression with its expanded counterpart. Once this stage is
successfully completed, they solve a cryptogram based on the results of the matches.
A matching game where students solve equations and match the correct solution with the matching
equation.
This multimedia interactive learning object is a game in which students must determine the location of the
all the battleships.
Description
An interactive activity in which the user can input a value for the slope (rate of change) in order
to see what happens to 1.finite differences in a table of values 2.the slope of the line
3.algebraically as the coefficient of x in the equation
This unit is meant to ease students back into mathematics. It is also meant to introduce extracurricular opportunities within the high school. Students will complete an introductory quiz to
see what they remember and what they need to refresh! Students will learn how to work with
integers as well as apply them to real life situations. They will learn the exponent laws, review
percents, ratios, and rates. There are two quizzes and one assignment to solidify their learning.
Students are able to explore all of these concepts using Algebra tiles and various links.
Opportunities for individual learning and group interaction through discussions are provided, so
that by the end of the unit, the students are prepared to complete both a formative and Summative
assessment on integers. Users should be aware that expectations.html may contain some
inaccuracies.
ELO1011220
ELO1011660
ELO1011720
ELO1030410
ELO1030620
ELO1084730
ELO1241280
ELO #
ELO1002655
ELO1105800
MPM1D (Catholic): Unit 2 Entire Unit: Algebra
MPM1D (Catholic): Unit 3 Entire Unit: Linear Relations
MPM1D (Catholic): Unit 4 Entire Unit: Analytical
Geometry
MPM1D (Catholic): Unit 5 Entire Unit: Measurement
MPM1D (Catholic): Unit 6 Entire Unit: Geometry
MPM1D (Catholic): Unit 7 Entire Unit: Culminating Task
Multiplying Powers
Subject
MAT 2L
In these activities, students will learn new algebra terminology. They will learn how to recognize
as well as manipulate different types of polynomials. Furthermore, students will delve into more
complex problem-solving situations involving real-life scenarios. Note: Users should be aware
that expectations.html may contain some inaccuracies.
Students gather, analyze, manipulate and display data to explore the characteristics of lines and
their corresponding equations. They make conjectures, conduct investigations based on realistic
situations and communicate their findings using a variety of technologies and models.
In this unit, students will continue work with linear relations. They will recognize how the degree
of the equation relates to whether a relationship is linear or non-linear.
In this unit, students are reintroduced to area, perimeter, surface area and volume. The
Pythagorean Theorem is also reviewed.
In this unit, students will investigate, discover and apply geometric relationships. Students will
examine properties of triangles and quadrilaterals and look for patterns that can be generalized
for all polygons. Students will use dynamic geometry software in their investigations.
This unit is the summative assessment for MPM1D. This assessment is worth 30% 0f the final
mark of the course. The assessment is divided into two parts: a performance task and a written
examination.
This secondary level resource can be used to help students understand the elements of exponents.
Students learn to add the exponents of like bases so as to express the base number as a single
power. Replay option calls up a new question.
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Topic
Description
ELO #
MAT2L (Catholic): Unit 1 Entire Unit: Money Cents
Students review and practice their skills in rounding dollar amounts and calculating change. They learn that monetary
amounts can be expressed in different ways. Students interpret the meaning of large amounts of money. They
develop everyday skills in working with money, such as estimating the cost of a purchase, and calculating taxes,
discounts and tips. They investigate possible part-time jobs and calculate possible incomes. Students complete an
assessment in which they plan a vacation with budget restrictions considering their income and spending habits.
ELO1149120
MAT2L (Catholic): Unit 2 Entire Unit: Measurement:
Metric vs. Imperial
This unit consists of activities in which students measure in both metric and imperial units. Students also calculate
area and perimeter. There are several multimedia components.
ELO1158640
MAT2L (Catholic): Unit 4 Entire Unit: Fractions, Ratios
and Rates - Oh My!
MAT2L (Catholic): Unit 5 Entire Unit: The Essential Event
In this unit, students extend their knowledge of proportional reasoning. Students have an opportunity to review and
practice converting between percents, fractions, and decimals. They determine the relationships between commonly
used equivalences between fractions and percentages and use these equivalences to solve real-world problems.
They create, read, and interpret circle graphs and discuss water use in Canada. Students write ratios to describe
everyday situations and analyze sets of ratios to determine whether or not they are proportional. Students create,
read, and interpret bar graphs and line graphs and identify misleading graphs. They complete a summative
assessment in which they analyze different types of graphs.
This unit consists of a quality assessment task with three main components. The first activity involves choosing a
charity and organizing a fundraiser. The second activity involves organizing the event, deciding on ticket prices, etc.
The third activity gets the students to create a scale diagram of the room in which they are holding their event. The
last activity is a final exam.
ELO1148920
ELO1158660
Many of the interactive resources for MAT 2L have been developed for MAT 1L and MAT 2L and can be found listed in the MAT 1L list.
Subject
MFM 2P
Topic
MFM2P: Unit 1 - Entire Unit:
Measurement and
Trigonometry
Description
In this unit of study students will investigate similar triangles, the trigonometry of right
triangles, and the measurement of three-dimensional figures. Teachers using this
resource are advised to ascertain the availability and suitability of the recommended
ELO #
ELO1021980
MFM2P: Unit 2 - Entire Unit:
Modelling Linear Relations
MFM2P: Unit 3 - Entire Unit:
Quadratic Relations in the
Form y=ax^2+bx+c
MFM2P: Unit 4 - Entire Unit:
Course Review and Course
Summative Assessment
Subject
Topic
MPM2D (Catholic): Unit 1 Entire Unit: Linear Systems
MPM2D (Catholic): Unit 2 Entire Unit: Analytic Geometry
MPM 2D
MPM2D (Catholic): Unit 3 Entire Unit: Properties of
Quadratic Relations
MPM2D (Catholic): Unit 4 Entire Unit: Applications of
Quadratic Relations
website(s)/hyperlink(s) beforehand.
In this unit students will investigate linear relations and extend their problem solving and
algebraic skills. Consists of 13 activities. Teachers using this resource are advised to
ascertain the availability and suitability of the recommended website(s)/hyperlink(s)
beforehand.
Unit consists of 11 activities. Students will investigate quadratic relations, by working
through the following: 1)Multiplying Two Binomials; 2)Common Factoring; 3)Factoring
Where Common Factoring is Not Possible; 4)Graph the Data and Curve of Best Fit for
Quadratics; 5)Investigation of a Quadratic Relation; 6)Second Differences; 7)Key
Features of a Parabola; 8)Graphical Representations Using Technology; 9)Finding xand y-intercepts; 10)Interpreting Quadratic Relations; 11)Experimental Data Involving
Quadratic Relations. Teachers using this resource are advised to ascertain the
availability and suitability of the recommended website(s)/hyperlink(s) beforehand.
In this unit, couched in the format of 'reality TV,' students use their knowledge from the
entire course to perform mathematical calculation tasks that people typically encounter
on an 'amazing race' tpye of trip around the world (i.e., currency conversion, time
differences, metric to imperial, volume of pyramids, distances, etc.). The ability to
choose options and exotic destinations adds interest to the tasks. Teachers using this
resource are advised to ascertain the availability and suitability of the recommended
website(s)/hyperlink(s) beforehand.
Description
Students will be introduced to a Peace and Development fundraising initiative which will
provide the context for using Linear Systems to solve problems. At the beginning of the unit,
they will complete an on-line tutorial for using Geometer's Sketchpad, a tool that can provide
graphical solutions for this unit and other units in this course. They will solve Linear Systems
algebraically and connect their solutions with graphical representations. Students will keep
their own notes in a journal which will be submitted periodically for assessment.
We will use analytical geometry to form a relationship between line segments, circles and
triangles. These shapes will also form the basis of some key formulas that are used in
calculations.
You will begin this unit by collecting and fitting data that is non-linear and then move into
graphing simple quadratic equations using appropriate technology. Through investigation,
you will learn some key features of parabolas. You will calculate the first and second
differences of quadratic equations. This leads to a study of some transformations of
quadratics and sketching by hand. You will learn to find the equation of a quadratic from a
graph. You will begin to explore the exponential function by comparing its graph to that of the
parabola. Throughout the unit, you will complete summary notes for each activity in
preparation for the summative test at the end of the unit.
The process of expanding and simplifying algebraic expressions is explored using
polynomial tiles. The exploration leads to the development of an algorithm that will permit
algebraic expansions to be performed more efficiently. The algorithm is reversed to introduce
the concept of factoring as well as the need for a variety of techniques of factoring. The
ability to express the same expression in different ways leads to the various forms in which a
quadratic relation may be written. Algebraic manipulation is used to change between forms
ELO1022630
ELO1024150
ELO1024560
ELO #
ELO1125550
ELO1126620
ELO1127680
ELO1126930
MPM2D (Catholic): Unit 5 Entire Unit: Similar Triangles
MPM2D (Catholic): Unit 6 Entire Unit: Trigonometry
MPM2D (Catholic): Unit 7 Entire Unit: Summative Activity
Subject
Topic
Working for your Money - Interactive
Quiz
You Auto Know Interactive Quiz
Personal Finance Terminology Interactive Quiz
MEL 3E
Making Change - Interactive Exercise
Travel Jeopardy
MEL3E (Catholic): Unit 2 - Entire
Unit: Hello, Good Buy!
of a quadratic relation. The graphical representation is connected to the various algebraic
representations of a quadratic relation. Interpreting the information from the graph introduces
the need to be able to solve quadratic equations. A variety of techniques to solve quadratic
equations are applied to a variety of situations that can be modeled by quadratic relations.
Students begin this unit with a diagnostic quiz on solving ratios which allows the teacher to
assess the level of mathematical knowledge. Students then undertake an investigation to
determine the basic properties of similar triangles. The study continues with a further look at
similar triangles, this time using different orientations and perspectives. The unit study then
moves into an activity on congruence versus similarity. Students learn how to solve for
unknown sides and angles in similar triangles. They further develop their skills with similar
triangles by examining the ratio of areas of similar triangles. Students apply their learning by
solving realistic problems with similar triangles. The unit concludes with a unit test.
Trigonometry is a branch of Mathematics that studies the relationship between sides and
angles in a triangle. This unit will focus on discovering some of these relationships and using
them as a method for finding the missing measurements of triangles. Surveyors, architects
and engineers, as well as navigators and astronomers to name but a few, use trigonometry
to find solutions to their problems.
This unit contains the summative evaluation for the course. The summative evaluation will
include "The Root of Fun" activity and a final exam. The Root of Fun activity has a focus of
the mathematics in a theme park. This exercise will be completed and then submitted. The
final exam will be written during a supervised time and will include concepts from the entire
course.
Description
Developed for use in MEL3E (Catholic). Also viable for use in MEL3S, BAN4E (both Catholic). This "drag and
drop" interactive quiz allows students to consolidate their learning about various terms related to work,
earnings, and deductions. Students should be encouraged to think creatively and reflectively; and as well to
think critically about the meaning and purpose of work.
Developed for use in MEL3E (Catholic). This interactive drag and drop quiz tests students' understanding of
terms associated with owning, leasing, or financing the purchase of an automobile. While essentially a 'fun
activity,' students should nonetheless be encouraged to reflect on accepting accountability for their own
actions; and as well, setting appropriate goals and priorities in school, work and personal life.
Developed for use in MEL3E (Catholic). Students learn some basic terminology of personal finance by using
this interactive checklist. It features a "drag and drop" fuction to match banking terms with appropriate
definitions. Students should be encouraged to integrate the teachings of their Catholic faith into their study of
personal finance. Specifically, they should be encouraged to make decisions in light of gospel values with an
informed moral conscience; adopts a holistic approach to life by integrating learning from various subject
areas and experience; and to set appropriate goals and priorities in school, work and personal life.
Developed for use in MEL3E (Catholic). This resource develops accuracy and resourcefulness when making
change for cash transactions in Canadian currency. Students practice calculating the correct amount of
change when receiving overpayment for retail merchandise. The specific mathematical calculation skills
include comprehension of unit, tens and hundreds; addition, subtraction, carrying-over/borrowing from units to
ten, tens to hundreds; and the meaning of decimals to the hundredth-division. Students should be encouraged
to think reflectively and creatively to evaluate situations and solve problems. Beyond this, they should also be
encouraged to see that in a culture that becomes increasingly commercialized, we are, more than ever, invited
to prayer and to worship. All this being said, students should especially be encouraged to apply the skills
learned in this resource toward employability, self-employment and entrepreneurship relative to Christian
vocation.
An interactive mix and match jeopardy game matching travel definitions with the appropriate terms.
Throughout this unit, students are involved in various investigations and activities that allow them to apply
responsible decision-making to purchasing situations. Students are given the opportunity to make correct
change, perform cost comparisons, and calculate discounts, sale prices, and taxes. Students also identify and
ELO1127040
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ELO1127170
ELO #
ELO1002483
ELO1002484
ELO1002549
ELO1002657
ELO1002718
ELO1022330
MEL3E (Catholic): Unit 3 - Entire
Unit: Bank On It
MEL3E (Catholic): Unit 4 - Entire
Unit: Making Your Money Work
MEL3E (Catholic): Unit 6 - Entire
Unit: You Auto Know
Subject
Topic
Transformation Time
Compound Interest
Imperial vs Metric System
Road Trip
MBF 3C
Sine and Cosine Law
MBF3C (Catholic): Unit 1 - Entire
Unit: Quadratic Relations
MBF3C (Catholic): Unit 2 - Entire
Unit: Data Management
MBF3C (Catholic): Unit 3 - Entire
Unit: Probability
compare various purchase plans. Technology is used to enhance student understanding. Students are
encouraged to utilize estimation to ensure that their calculated results are reasonable. Teachers using this
resource are advised to ascertain the availability and suitability of the recommended website(s)/hyperlink(s)
beforehand.
Developed for use in MEL3E (Catholic). In this unit, students explore the world of financial institutions as it
relates to saving their money. Particular emphasis is placed on simple and compound interest. Students
identify and investigate various financial services in the context of real-life situations. Applying appropriate
technology, students calculate investment growth, examine differences between simple interest and
compound interest, and compare savings alternatives. Students should be encouraged to think reflectively and
creatively to evaluate situations and solve problems; set appropriate goals and priorities in school, work and
personal life; examine and reflect on their personal values, abilities and aspirations influencing life's choices
and opportunities.
In this unit, students investigate different types of investment strategies and associated characteristics. Using
appropriate technology, they analyse expected growth of investments and their associated risks. The results of
this analysis enables students to make informed decisions regarding money management to optimize
investment opportunities.
Developed for use in MEL3E (Catholic). In this unit, students examine information and the costs involved in
obtaining a license. Comparisons of the cost of leasing a vehicle and buying a vehicle and buying a new
vehicle and buying a used vehicle will be conducted. Given several scenarios, students will make
recommendations regarding the best purchasing choice. Information will be gathered about insurance and
protecting yourself and your vehicle as well as the costs associated with keeping your car in good running
condition. The practical scenarios should encourage the students to think reflectively and creatively to
evaluate situations and solve problems; set appropriate goals and priorities in school, work and personal life;
and finally to examine and reflect on their personal values, abilities and aspirations influencing life's choices
and opportunities. Most importantly, they should understand that obtaining a license implies that they will
accept complete accountability for their own actions.
Description
This multimedia object shows students the effects of changing a, h, and k in a quadratic relation of the
form y = a(x – h)^2 + k. This learning object presents students with various examples of
transformations in a visual manner. Characteristics of the transformed functions are also illustrated.
Finally, this learning object will test their knowledge by matching equations to graphs and graphs to
equations.
This learning resource teaches students the compound interest formula in a step-by-step manner using
real-life financial examples. Students will learn how to calculate interest using a variety of compounding
periods.
This learning object will teach how to convert between the imperial and metric system as well as
illustrate which system is appropriate for various measurement examples.
This learning object teaches students the costs associated with owning a vehicle and compares buying
a new and used vehicle as well as the difference between buying and leasing.
This multimedia object demonstrates sine law and cosine law through animation. Students have the
opportunity to learn the formula in a visual manner and also have the opportunity to practice choosing
the correct law and using it to solve triangles.
This unit investigates the properties of quadratic equations. It looks at three ways to express a quadratic
equation and looks at transformations of quadratic equations.
In this unit, you will explore the applications of data management. You will learn how to properly collect,
organize, analyze and evaluate data. At the end of this unit, you will be expected to conduct your own
mini research experiment in which you will collect data from both primary and secondary sources.
In this unit, you will investigate probability, a branch of mathematics that tries to predict outcomes. You
will learn about theoretical and experimental probability as well as where we see probability in the world
around us. You will conduct several experiments and interpret their results. You will learn how
experimental probability has the tendency to approach the theoretical probability. You will also look at
how the media makes use of statistics. A summative task will involve the completion of a probability
experiment and comparing the results to the theoretical outcomes.
ELO1022390
ELO1022370
ELO1022420
ELO #
ELO1150710
ELO1150720
ELO1150730
ELO1150770
ELO1150780
ELO1221780
ELO1221870
ELO1221940
MBF3C (Catholic): Unit 4 - Entire
Unit: Personal Finance
MBF3C (Catholic): Unit 5 - Entire
Unit: Exponential Relations
MBF3C (Catholic): Unit 6 - Entire
Unit: Trigonometry
MBF3C (Catholic): Unit 7 - Entire
Unit: Geometry
MBF3C (Catholic): Unit 8 - Entire
Unit: Culminating Course Activities
Subject
Topic
Functions and Applications
Glossary
The Function Machine
Leak
Exploring Exponential Functions
Quadratic Transformations
MCF 3M
Just Chillin
Keep on Rollin
Quadratic Mini-Golf Game
MCF3M (Catholic): Unit 1 - Entire
Unit: Quadratic Functions
In this unit, students become familiar with both simple and compound interest. They will learn how
interest can be earned through various investments and how interest must be paid for borrowing
money. Students become aware, through investigation, of the factors that affect the final amount of
money that is available at the end of an investment period. A research activity allows students to learn
about the investment possibilities available through a few major banks in Canada. Students investigate
the different credit cards, as well as the interest rates, any fees, and other incentives associated with
these credit cards. Students also practice determining the amount of interest that is owed if a credit card
bill is not paid off entirely on the payment date. An investigation into the costs of owning and operating a
vehicle is also explored.
In this unit, students will learn about Exponential Relations. They will learn how to use exponent laws to
simplify algebraic expressions and how to graph both increasing and decreasing exponential functions.
Students will learn about real-life applications of exponential growth and decay and will apply their
knowledge to solving problems.
This unit will review how to solve right angled triangles using the primary trigonometric ratios. You will
also learn how to solve for angles and sides on triangles that are not right angled using the sine law and
cosine law. All of these concepts will then be practiced in real- world applications.
This unit investigates geometry and explores the different occupations associated with it. Students will
also investigate the different ways a three-dimensional shape can be represented.
In this unit, you will be asked to demonstrate your learning in this course in a final culminating task as
well as final examination. The culminating activity is divided into two segments: Part 1 covers concepts
in the first two strands, Mathematical Models and Personal Finance. Part 2 covers concepts in the final
two strands, Geometry and Trigonometry and Data Management. The final exam contains a multiple
choice section, a true and false section, and a section where you are asked to show the full solution.
The exam is contained in the documents folder of Activity 2. This folder cannot be accessed by
previewing the activity online. You will need to download it to your computer.
Description
This glossary provides a list of definitions for terms used with the course MCF3M (Functions and
Applications).
In this activity you will see how the function machine will generate the range of a function for a
given domain. This will be demonstrated through tables of values, data sets, mapping diagrams or
graphs.
This simulation collects and graphs data which is quadratic in nature. The demonstration
simulates water leaking from a cylinder and records the volume remaining at each time interval.
This activity explores the graph of the basic exponential function and determines the
characteristics of a transformed exponential function. This includes direction of opening, yintercept, domain and range.
In this activity, users will describe the transformations of a quadratic function in vertex form and
will summarize the role of each parameter in the equation.
This activity plots the graph of an exponential function. The participant will answer questions
about the graph given its equation. The participant will be required to interpret the parts of the
equation of the curve.
This activity simulates the rolling of 100 dice and removing all the 1's that have appeared. The
remaining dice are rolled again and the 1's are removed again. The process is repeated 20 times
or until no dice are remaining. The number of trials and the number of dice remaining are
recorded in a table. This data is then graphed and analyzed.
This resource simulates the putt of a golf ball as a quadratic function. The objective is to
determine the equation of the quadratic from the vertex given and the point given.
This unit introduces the concept of a function, including function notation, and domain and range.
There is an emphasis on relating the numerical, algebraic, and graphical representations of
functions. Techniques for solving quadratic equations and graphing quadratic functions are
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ELO #
ELO1079490
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ELO1104500
MCF3M (Catholic): Unit 2 - Entire
Unit: Exponential Functions
MCF3M (Catholic): Unit 3 - Entire
Unit: Trigonometric Functions
MCF3M (Catholic): Unit 4 - Entire
Unit: Culminating Task
Subject
Topic
Math Jeopardy: Functions
Functions and their Inverses
MCR 3U
MCR3U (Catholic): Unit 1 Entire Unit: Discrete
Functions
MCR3U (Catholic): Unit 2 Entire Unit: Functions
MCR3U (Catholic): Unit 3 Entire Unit: Quadratics and
studied extensively. Applications of quadratic functions including data collection and modeling with
technology are woven throughout the unit.
This unit reviews the rules for working with integral and rational exponents and explores the
concept of exponential growth and decay. The concept of graphing exponential functions is
introduced by completing table of values and discovering similarities and differences between
quadratic, exponential, and linear functions. Real life situations that generate exponential graphs
or functions will also be covered. Financial planning will be investigated with a focus upon simple
interest, compound interest and annuities and their relation to the exponential function.
Problems will be solved using the sine and cosine laws. The periodic nature of sinusoidal waves
will be investigated. This will be extended and used to model real-world problems. This resource is
best viewed with Internet Explorer. Teachers using this resource are advised to ascertain the
availability and suitability of the recommended website(s)/hyperlink(s) beforehand. The quiz
mentioned in Activity 2 is not included in the resource. Teachers should be prepared to be asked
by students about these. For Activity 6 and Activity 14, teachers are advised to look in the folder
for each respective activity for quiz(s) and test(s) mentioned in the activity.
This is a summative assessment that evaluates the properties and applications of various
relationships. Students will work independently to integrate mathematical skills, knowledge, and
applications from many areas of the Functions and Applications course. This culminating task
called the “Functional Fairground” should be completed independently with the use of a computer
and/or calculator. Students should review/study all of your course notes and examples before the
culminating task and their final exam. The final exam is in the docs folder.
Description
The purpose of this object is for students to have fun with some mathematical terms.
Students will practice defining terms while playing jeopardy. Game is interactive, from
one to four players. Teen-like avatars with changing facial expressions engage student
interest. While essentially a fun activity, students should be encouraged toward
excellence, originality, and integrity in their own work and to support these qualities in
the work of others. As well, they should respect the rights, responsibilities and
contributions of self and others.
The purpose of this object is for students to consolidate their knowledge of the graphs of
functions and their inverses and also with equations of functions and their inverses.
Students should be encouraged to think reflectively and creatively in their approach to
problem solving.
Discrete Functions covers topics on patterns, arithmetic and geometric sequences and
series and then moves into financial math. Simple interest, compound interest, present
value, amount of an annuity and present value of an annuity are all covered as
applications of financial math. Students will use Nelson and McGraw-Hill Ryerson
textbooks to complete the assignments.
The 10 activities of this unit on Functions cover topics that include defining a function,
function notation, domain and range, the inverse of a function, simplifying polynomials,
rational expressions, adding and subtracting rational expressions and radicals. Activity
10 is the culminating task that requires students to code a function for 9-digit Canadian
social insurance numbers.
This unit 3 covers topics on quadratics, extreme values in functions and solving
quadratics by completing the square and linear-quadratic systems. Transformations
ELO1104520
ELO1104530
ELO1104540
ELO #
ELO1031060
ELO1031070
ELO1047040
ELO1047850
ELO1047060
Transformations
MCR3U (Catholic): Unit 4 Entire Unit: Exponential
Function
MCR3U (Catholic): Unit 5 Entire Unit: Trigonometric
Functions
MCR3U (Catholic): Unit 6 Entire Unit: Course
Culminating Assignment and
Final Examination
Subject
Topic
MEL4E (Catholic): Unit
1 - Entire Unit:
Interpreting and
Displaying Data
MEL
4E
MEL4E (Catholic): Unit
2 - Entire Unit:
Investigating
Probability
MEL4E (Catholic): Unit
3 - Entire Unit: All
About Income Tax
involving translations, stretches and compressions or shrinks are also covered. Students
will need Nelson and McGraw-Hill Ryerson textbooks to complete the assignments.
Unit 4: Exponential Function covers topics on integral and rational exponents,
exponential growth and decay, graphing exponential functions and transformations of
the exponential function. Students should be encouraged to think reflectively and
creatively in their approaches to problem-solving.
Trigonometric Functions will cover topics on trigonometric ratios and applications of
trigonometry. Identities and special triangles along with transformations, sketches and
applications of sinusoidal functions are also covered in this unit. Teachers using this
resource are advised to ascertain the availability and suitability of the recommended
website(s)/hyperlink(s) beforehand.
"Activity 1" is the sole activity that comprises all of "Unit 6." In this activity, students will
complete a culminating project. In the culminating project, there are two situations: one
dealing with counting toothpicks and the other dealing with a Ferris wheel. The ultimate
goal in each situation is to model the situation with the appropriate function. As well,
they will write the final examination for the course. The exam is not included, so
teachers will need to procure a viable examination from outside this resource
beforehand. Students should be encouraged to think reflectively and creatively to
evaluate situations and solve problems; and as well, achieve excellence, originality, and
integrity in their own work and support these qualities in the work of others.
Description
In this unit, students will investigate methods of collecting data from
primary and secondary sources and displaying it using a variety of
charts and graphs. They will learn how to analyze and interpret
graphs, differentiate between graphs that accurately display the
data and those that do not, use QuattroPro, WordPerfect and
Fathom to create charts and determine why data is important in the
workplace and in everyday life.
Students investigate probability through various activities such as
simulations, games, journals and discussions. Community issues
involving probability are examined and students are challenged to
create a game involving probability as part of their summative
assessment.
This unit focuses on the process of filing an income tax return, with
emphasis on the differences in Total Income, Net Income and
Taxable Income. The various deductions that can be claimed and
how they effect the income tax paid are explored. Methods of filing
an income tax return are investigated.
ELO1048200
ELO1047070
ELO1048410
ELO #
ELO1180200
ELO1188710
ELO1145020
MEL4E (Catholic): Unit
4 - Entire Unit: What
Does it Cost to Live
Here?
MEL4E (Catholic): Unit
5 - Entire Unit:
Designing Budgets
MEL4E (Catholic): Unit
6 - Entire Unit:
Applications of
Measurement
Subject
Topic
MAP4C (Catholic): Unit 1 Entire Unit: Statistics
MAP4C (Catholic): Unit 2 Entire Unit: Statistics and
Graphical Models
MAP 4C
MAP4C (Catholic): Unit 3 Entire Unit: Exponential
Computations & Equations and
Annuities
MAP4C (Catholic): Unit 4 Entire Unit: Personal Finance
MAP4C (Catholic): Unit 5 Entire Unit: Measurement and
Geometry
This unit explores the factors involved in deciding whether to rent or
buy accommodation. The advantages and disadvantages of renting
and owning your own accommodation along with associated costs
of each choice are investigated.
In this activity, the components of a personal budget are identified,
including the differences between fixed and variable expenses and
discretionary and non-discretionary expenses. The process of
making necessary adjustments to budgets as expenses changed is
also explored.
Mathematics can be very useful in the design of many items that
are used in everyday life. This unit will introduce students to some
of the concepts in design, including angles, area, perimeter, and
volume. They will use this knowledge to design and build scale
models and plan different renovations. This unit is very practical for
real-world experiences.
Description
This unit introduces students to data gathering techniques such as stratified sampling,
random sampling and systematic sampling. Students learn how these techniques are applied
in everyday situations that require population sampling. They will also investigate how to
evaluate statistics that appear in media.
This unit investigates how two-variable data is interpreted both algebraically and
graphically. Technology is used to determine if there is a relationship between the two
variables, and if it exists the strength of that relationship.
In this unit, students will be expanding their skills using the basic exponential equations and
exponent laws. Rational and negative exponents will be investigated and reviewed. Towards
the end of this unit they will apply this knowledge to real-world situations, including
mortgages and annuities. To conclude this unit they will look into the practical applications
and the jobs that relate to this material.
This unit provides students with the opportunity to investigate the advantages and
disadvantages of renting a home versus buying a home. The unit concludes by examining the
practical applications of personal finances and careers related to this material.
Throughout this unit students will be able to bring together previous knowledge and new
knowledge of shapes and measurements that surround them. They will soon be able to
determine the area, surface area and volume of many different shapes that are often used in
real world scenarios everyday. At the end of this unit they will finish by understanding how
they can maximize volume while minimizing surface area. This is usually very important so
that containers can hold as much material as possible while spending as little as possible on
ELO1144760
ELO1145050
ELO1189300
ELO #
ELO1146480
ELO1146580
ELO1187580
ELO1187570
ELO1187560
MAP4C (Catholic): Unit 6 Entire Unit: Trigonometry
MAP4C (Catholic): Unit 7 Entire Unit: Summative
Assessment
Subject
Topic
MCT4C (Catholic): Unit 1 Entire Unit: Exponential
Functions
MCT4C (Catholic): Unit 2 Entire Unit: Polynomial
Functions
MCT 4C
MCT4C (Catholic): Unit 3 Entire Unit: Polynomial
Equations
MCT4C (Catholic): Unit 4 Entire Unit: Trigonometric
Functions
MCT4C (Catholic): Unit 5 Entire Unit: Applications of
Trig Ratios and Vectors
MCT4C (Catholic): Unit 6 Entire Unit: Measurement
and Geometry
MCT4C (Catholic): Unit 7 Entire Unit: Summative Unit
the materials that make the container.
In this unit, students expand their skills using the basic trigonometric ratios and cosine and
sine laws. Acute angles will be reviewed and then extended into the uncharted territory of
the obtuse angle. Practical applications and the jobs that involve trigonometry are
investigated.
Using the knowledge and skills that students have developed throughout the units in this
course, they will conduct a variety of tasks. These tasks will include: accessing and
generating graphical output of data from Statistics Canada; solving real-world applications
of the sine and cosine laws; researching and calculating the monthly costs of a mortgage for
a new home; solving real-world applications of measurement and geometry; applying data
management techniques to analyze a relationship.
Description
This unit will enable students to extend their knowledge of exponential functions.
Students will investigate and apply properties of the exponential function. Students will
represent this function numerically, graphically, and algebraically. They will also
develop facility in simplifying expressions and solving equations in order to solve
problems that address applications of real world problems. Students will reason
mathematically and communicate their thinking as they solve multi-step problems. This
unit will assist in preparing students for a variety of college technology programs.
This unit enables students to extend their knowledge of functions. Students will
investigate and apply properties of polynomial functions, continue to represent functions
numerically, graphically and algebraically and solve problems modeled by polynomial
functions.
This unit provides students with opportunities to solve polynomial equations by
factoring. As well, students will connect algebraic and graphical models of polynomial
expressions.
In this unit students will be learning about trigonometric functions and their
applications. They will be asked to look for connections between the following
information: graph, table of values, equation and trig ratio. Once they have consolidated
their knowledge they will be looking at how these models exist in the real world.
In this unit students will be working through activities involving the sine and cosine law.
Also, they will be working through some introductory activities involving vectors.
This is the entire unit for the measurement and geometry strand. Students will solve
problems involving metric and imperial measurements arising from a variety of realworld applications.
This summative unit contains three parts. A review activity, an exam and a summative
task. The summative task will allow students a brief examination of the impact they
have on the world around them. Students will learn what an ‘environmental footprint’ is
and will then see how mathematics fits into the real world involving this issue. The final
ELO1146650
ELO1216530
ELO #
ELO1164270
ELO1151880
ELO1182140
ELO1167780
ELO1167850
ELO1187610
ELO1189090
exam is a paper and pencil test that will cover exponential, trigonometric and
polynomial functions as well as geometry and measurement applications. It is a
knowledge- and application-based assessment.
Subject
MCV
4U
Topic
Vector Connector:
MCV4U (Catholic)
Geometric Algebraic
Vector Conversion:
MCV4U (Catholic)
Identifying
Derivatives: MCV4U
(Catholic)
Projections of
Algebraic Vectors:
MCV4U (Catholic)
Plotting Points Lines
Planes 3D: MCV4U
(Catholic)
Computing
Derivatives: MCV4U
(Catholic)
Rates of Change:
MCV4U (Catholic)
Description
Students identify equivalent, parallel and equal magnitude
vectors using this interactive quiz.
ELO #
ELO1080060
Convert vectors from one form to another (algebraic and
geometric).
ELO1081440
This applet graphs functions and its derivatives by plotting
points generated from the slope of its tangent.
ELO1081460
This applet shows how to calculate the projection of one vector
ELO1084130
onto another with a review of dot product.
This activity requires students be able to plot 3D planes, lines,
points and vectors and rotate their view in real time by clicking
and dragging the mouse.
ELO1090060
This is a set of multiple choice questions dealing with
derivative rules.
ELO1090670
Students are given a polynomial function and asked to identify
the max/min positions and the intervals of positive and
negative rates of change.
ELO1104000
The Ministry of Education (e-Learning Ontario) course is also available for MCV 4U. Go to “Browse by
Curriculum”, enter Grade 12, MCV 4U, type “entire unit” in the grey keyword search box and then click the
Keyword Search button.
Subject
Topic
MDM4U (Catholic): Unit 1 Entire Unit: Solving Probability
Problems Involving Discrete
Sample Spaces
MDM4U (Catholic): Unit 2 Entire Unit: Solving Problems
Using Counting Principles
MDM4U (Catholic): Unit 3 Entire Unit: Analyzing One
Variable Data Sets
MDM4U (Catholic): Unit 4 Entire Unit: Analyzing Two
Variable Data
MDM 4U
MDM4U (Catholic): Unit 5 Entire Unit: Understanding
Probability Distributions for
Discrete Random Variables
MDM4U (Catholic): Unit 6 Entire Unit: Understanding
Probability Distributions for
Continuous Random Variables
MDM4U (Catholic): Unit 7 Entire Unit: Culminating Data
Management Investigation /
Description
In this unit, students will investigate different methods to determine the probability of future
events. When we use methods to measure this likelihood, we are using concepts in the
branch of mathematics known as probability and combinatorics. Some tools that will help
students to categorize the given information are Venn diagrams and tree diagrams. Using
these visual displays, students will determine the probability that various events will occur.
In this unit, students build on their knowledge of probability concepts to tackle more complex
problems. They are introduced to several new methods for counting arrangements and
groups. These methods will simplify the process by which we evaluate the probability of an
event occurring.
In this unit, students will learn many of the methods and principles used in statistics to collect
reliable information. Since decisions are made based on this type of information, they will
learn how data can be misrepresented and result in bias, which deteriorates the reliability of
the conclusions made from the data that was collected. Furthermore, they will discover
several ways of presenting the data graphically which are very informative when used
appropriately. Finally, they will learn how to calculate various statistical measurements that
can be used to describe data that has been collected.
Data analysis introduces statistics as a problem-solving process. In this unit, you will build
your skills through the investigation of different ways to organize, represent, describe and
analyze data. Through practical examples, you will come to understand the concepts of
correlation between two variables, the effect of sampling techniques and bias, the
implications of cause-and-effect relationships, as well as the investigation of the validity of
statistics and statistical applications.
We deal with probabilities frequently in our every day lives. In this unit we will be revisiting
the concept of probability but with a different approach. Rather than simply focusing on a
single probability, we will be considering all possible outcomes that could occur. We will be
using tables, charts and graph to analyze these probabilities. We will be investigating the
properties of discrete random variables (ones that can only assume a unique value for each
outcome). We will also be introduced to the concept of expected value for an event. This unit
focuses on the distinction between independent trials and dependent trials. We need to know
whether the occurrence of one outcome has an effect on future outcomes.
In this section of the course, we will investigate probability distributions for continuous
random variables. In particular, we will focus on the normal distribution. The normal
distribution is one of the most important and most widely-used distributions in statistical
analysis. Furthermore, you will come to understand the concepts of continuous probability
distributions, make connections to discrete probability distributions, determine standard
deviations, describe key features of the normal distribution, as well as solve related problems
from a variety of applications. Note: In activity 3, links to Frontenac News have been moved
to: http://www.frontenacnews.ca
In this unit, students are to successfully complete the culminating project outlined in the
Culminating Data Management Investigation strand. They will engage in several activities in
which they apply several of the techniques/tools of the course to answer significant
questions. Students should be aware that their reports are to be assessed for their
ELO #
ELO1153020
ELO1153110
ELO1144740
ELO1144880
ELO1157160
ELO1144970
ELO1157170
Subject
Final Exam
mathematical validity. The mathematical content of the report should be substantial. This
project is the students' opportunity to demonstrate their understanding of the skills and
concepts of this course in an integrated approach. This unit will conclude with the final
examination.
Topic
Radian Measure: An Interactive
Approach: MHF4U (Catholic)
Description
This learning object demonstrates the relationship between degree and radian measures and
how to find and solve problems in radian measure.
A visual representation of the definition of a logarithm and an investigation of the laws of
logarithms.
This lesson provides an activity to graphically illustrate the solution to polynomial inequalities.
Students then practice solving and verifying their solutions.
This activity demonstrates the effects of combining two functions on the characteristics the
compound function.
This learning object examines the characteristics of polynomial functions. In this interactive
model, students can look at: roots or zeros of a function; intervals of increase and decrease
of a function; relative maximum and minimum points; the end behaviour of a function. Each
characteristic has a link to take the student to a page where more detailed information about
that characteristic of the function is given.
This learning object looks at the similarities and differences between various types of
functions.
This interactive object allows students to choose various characteristics of complex rational
functions. The characteristics include: horizontal and vertical asymptotes; intervals of
increase and decrease; domain and range. With each of these characteristics, students can
choose a particular characteristic and they will be linked to another page where a more
detailed description of that characteristic is illustrated.
This object analyzes rational functions and develops skills for graphing these functions using
critical characteristics of the equations.
Log Laws: MHF4U (Catholic)
Polynomial Inequalities: MHF4U
(Catholic)
Investigating Compound
Functions: MHF4U (Catholic)
Characteristics of Polynomials:
MHF4U (Catholic)
Comparison of Functions:
MHF4U (Catholic)
Rational Function
Characteristics: MHF4U
(Catholic)
MHF 4U
Rational Functions Curve
Sketching: MHF4U (Catholic)
Complex Rational Functions
Curve Sketching: MHF4U
(Catholic)
Applications of Logs
Exponentials and Logarithms
Functions: An Interactive
Approach: MHF4U (Catholic)
Division of Polynomials: MHF4U
(Catholic)
Finite Differences: MHF4U
(Catholic)
Transformations of Logarithms:
MHF4U (Catholic)
Graphing Trig: MHF4U
(Catholic)
Investigating Instantaneous
Rates Of Change: MHF4U
(Catholic)
ELO #
ELO1079570
ELO1087850
ELO1088070
ELO1088090
ELO1090640
ELO1090690
ELO1090720
ELO1090750
This activity shows the visual representations of complex rational function graphs.
ELO1090770
This resource applies mathematics to investigate real-world situations involving exponential
growth and decay using exponents and logarithms.
ELO1090800
In this lesson students can watch an animation of how to divide a polynomial by a binomial.
Demonstrations show both long division and synthetic division.
An investigation of the finite differences in linear, quadratic, cubic, quartic polynomial
functions.
This learning object shows the parameters of a logarithmic function and how it behaves
when one of the parameters is changed.
ELO1093620
ELO1098300
ELO1098320
This activity is a visual representation of the six trig functions and identify their key features.
ELO1098700
This learning object investigates the relationship between average and instantaneous rates
of change.
ELO1099000
The Ministry of Education (e-Learning Ontario) course is also available for MCV 4U. Go to “Browse by Curriculum”, enter Grade 12, MCV 4U, type “entire unit” in the
grey keyword search box and then click the Keyword Search button.