MTH1W.B: Number

MTH1W.B1: By the end of this course, students will: demonstrate an understanding of the development and use of numbers, and make connections between sets of numbers

3.1.2: Number Sets

MTH1W.B1.3: use patterns and number relationships to explain density, infinity, and limit as they relate to number sets

Treasure Hunter (Decimals on the Number Line)

MTH1W.B2: By the end of this course, students will: represent numbers in various ways, evaluate powers, and simplify expressions by using the relationships between powers and their exponents

3.2.1: Powers

MTH1W.B2.1: analyse, through the use of patterning, the relationship between the sign and size of an exponent and the value of a power, and use this relationship to express numbers in scientific notation and evaluate powers

Exponents and Power Rules
Number Systems

MTH1W.B2.2: analyse, through the use of patterning, the relationships between the exponents of powers and the operations with powers, and use these relationships to simplify numeric and algebraic expressions

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions

MTH1W.B3: By the end of this course, students will: apply an understanding of rational numbers, ratios, rates, percentages, and proportions, in various mathematical contexts, and to solve problems

3.3.1: Rational Numbers

MTH1W.B3.1: apply an understanding of integers to describe location, direction, amount, and changes in any of these, in various contexts

Adding and Subtracting Integers
Adding on the Number Line
Integers, Opposites, and Absolute Values

MTH1W.B3.2: apply an understanding of unit fractions and their relationship to other fractional amounts, in various contexts, including the use of measuring tools

Equivalent Fractions (Fraction Tiles)
Fraction Artist 1 (Area Models of Fractions)
Fraction Artist 2 (Area Models of Fractions)

MTH1W.B3.3: apply an understanding of integers to explain the effects that positive and negative signs have on the values of ratios, rates, fractions, and decimals, in various contexts

Adding on the Number Line
Rational Numbers, Opposites, and Absolute Values

3.3.2: Applications

MTH1W.B3.4: solve problems involving operations with positive and negative fractions and mixed numbers, including problems involving formulas, measurements, and linear relations, using technology when appropriate

Dividing Fractions
Dividing Mixed Numbers
Fractions with Unlike Denominators
Improper Fractions and Mixed Numbers
Multiplying Mixed Numbers

MTH1W.B3.5: pose and solve problems involving rates, percentages, and proportions in various contexts, including contexts connected to real-life applications of data, measurement, geometry, linear relations, and financial literacy

Estimating Population Size
Percent of Change
Percents and Proportions
Perimeters and Areas of Similar Figures
Proportions and Common Multipliers
Similarity in Right Triangles

MTH1W.C: Algebra

MTH1W.C1: By the end of this course, students will: demonstrate an understanding of the development and use of algebraic concepts and of their connection to numbers, using various tools and representations

4.1.2: Algebraic Expressions and Equations

MTH1W.C1.2: create algebraic expressions to generalize relationships expressed in words, numbers, and visual representations, in various contexts

Solving Equations by Graphing Each Side
Solving Equations on the Number Line
Using Algebraic Expressions

MTH1W.C1.3: compare algebraic expressions using concrete, numerical, graphical, and algebraic methods to identify those that are equivalent, and justify their choices

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II

MTH1W.C1.4: simplify algebraic expressions by applying properties of operations of numbers, using various representations and tools, in different contexts

Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

MTH1W.C1.5: create and solve equations for various contexts, and verify their solutions

Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations by Graphing Each Side
Solving Equations on the Number Line
Solving Two-Step Equations

MTH1W.C3: By the end of this course, students will: represent and compare linear and non-linear relations that model real-life situations, and use these representations to make predictions

4.3.1: Application of Linear and Non-Linear Relations

MTH1W.C3.1: compare the shapes of graphs of linear and non-linear relations to describe their rates of change, to make connections to growing and shrinking patterns, and to make predictions

Arithmetic and Geometric Sequences

MTH1W.C3.2: represent linear relations using concrete materials, tables of values, graphs, and equations, and make connections between the various representations to demonstrate an understanding of rates of change and initial values

Introduction to Functions
Linear Functions
Modeling One-Step Equations
Points, Lines, and Equations

MTH1W.C3.3: compare two linear relations of the form y = ax + b graphically and algebraically, and interpret the meaning of their point of intersection in terms of a given context

Solving Linear Systems (Slope-Intercept Form)

MTH1W.C4: By the end of this course, students will: demonstrate an understanding of the characteristics of various representations of linear and non-linear relations, using tools, including coding when appropriate

4.4.1: Characteristics of Linear and Non-Linear Relations

MTH1W.C4.1: compare characteristics of graphs, tables of values, and equations of linear and non-linear relations

Linear Functions

MTH1W.C4.2: graph relations represented as algebraic equations of the forms x = k, y = k, x + y = k, x – y = k, ax + by = k, and xy = k, and their associated inequalities, where a, b, and k are constants, to identify various characteristics and the points and/or regions defined by these equations and inequalities

Linear Inequalities in Two Variables
Slope-Intercept Form of a Line
Standard Form of a Line

MTH1W.C4.3: translate, reflect, and rotate lines defined by y = ax, where a is a constant, and describe how each transformation affects the graphs and equations of the defined lines

Point-Slope Form of a Line
Slope-Intercept Form of a Line

MTH1W.C4.4: determine the equations of lines from graphs, tables of values, and concrete representations of linear relations by making connections between rates of change and slopes, and between initial values and y-intercepts, and use these equations to solve problems

Slope-Intercept Form of a Line
Standard Form of a Line

MTH1W.D: Data

MTH1W.D1: By the end of this course, students will: describe the collection and use of data, and represent and analyse data involving one and two variables

5.1.1: Application of Data

MTH1W.D1.1: identify a current context involving a large amount of data, and describe potential implications and consequences of its collection, storage, representation, and use

Polling: City
Polling: Neighborhood
Populations and Samples

5.1.2: Representation and Analysis of Data

MTH1W.D1.2: represent and statistically analyse data from a real-life situation involving a single variable in various ways, including the use of quartile values and box plots

Box-and-Whisker Plots
Histograms
Stem-and-Leaf Plots

MTH1W.D1.3: create a scatter plot to represent the relationship between two variables, determine the correlation between these variables by testing different regression models using technology, and use a model to make predictions when appropriate

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots

MTH1W.D2: By the end of this course, students will: apply the process of mathematical modelling, using data and mathematical concepts from other strands, to represent, analyse, make predictions, and provide insight into real-life situations

5.2.2: Process of Mathematical Modelling

MTH1W.D2.2: identify a question of interest requiring the collection and analysis of data, and identify the information needed to answer the question

Estimating Population Size
Polling: Neighborhood
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

MTH1W.D2.3: create a plan to collect the necessary data on the question of interest from an appropriate source, identify assumptions, identify what may vary and what may remain the same in the situation, and then carry out the plan

Estimating Population Size
Polling: Neighborhood
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

MTH1W.D2.4: determine ways to display and analyse the data in order to create a mathematical model to answer the original question of interest, taking into account the nature of the data, the context, and the assumptions made

Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

MTH1W.D2.5: report how the model can be used to answer the question of interest, how well the model fits the context, potential limitations of the model, and what predictions can be made based on the model

Estimating Population Size
Polling: City
Polling: Neighborhood
Reaction Time 2 (Graphs and Statistics)

MTH1W.E: Geometry and Measurement

MTH1W.E1: By the end of this course, students will: demonstrate an understanding of the development and use of geometric and measurement relationships, and apply these relationships to solve problems, including problems involving real-life situations

6.1.1: Geometric and Measurement Relationships

MTH1W.E1.2: create and analyse designs involving geometric relationships and circle and triangle properties, using various tools

Holiday Snowflake Designer
Quilting Bee (Symmetry)

MTH1W.E1.3: solve problems involving different units within a measurement system and between measurement systems, including those from various cultures or communities, using various representations and technology, when appropriate

Unit Conversions
Unit Conversions 2 - Scientific Notation and Significant Digits

MTH1W.E1.4: show how changing one or more dimensions of a two-dimensional shape and a three-dimensional object affects perimeter/circumference, area, surface area, and volume, using technology when appropriate

Area of Parallelograms
Area of Triangles
Circumference and Area of Circles
Perimeter and Area of Rectangles
Prisms and Cylinders
Pyramids and Cones
Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

MTH1W.E1.5: solve problems involving the side-length relationship for right triangles in real-life situations, including problems that involve composite shapes

Pythagorean Theorem
Pythagorean Theorem with a Geoboard

MTH1W.E1.6: solve problems using the relationships between the volume of prisms and pyramids and between the volume of cylinders and cones, involving various units of measure

Prisms and Cylinders
Pyramids and Cones

MTH1W.F: Financial Literacy

MTH1W.F1: By the end of this course, students will: demonstrate the knowledge and skills needed to make informed financial decisions

7.1.1: Financial Decisions

MTH1W.F1.3: compare the effects that different interest rates, lengths of borrowing time, ways in which interest is calculated, and amounts of down payments have on the overall costs associated with purchasing goods or services, using appropriate tools

Compound Interest