## Mathematics, Grade 9MTH1W1 (Grade 9 De-streamed)

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Question / UnitDayLessonNotes and Other Points for DiscussionExpectations IncludedLinks to ResourcesRow Colour
Welcome to MTH1W11Non-Curricular Math Tasks
• getting to know each other
• establishing classroom norms
• review of prerequisite skills
• ideally no homework assignedA1, A2, AA1SAMPLE PROBLEMS
BHNmath RESOURCES
00000
Welcome to MTH1W12Non-Curricular Math Tasks
• getting to know each other
• establishing classroom norms
• review of prerequisite skills
• ideally no homework assignedA1, A2, AA1SAMPLE PROBLEMS
BHNmath RESOURCES
00000
Welcome to MTH1W13Non-Curricular Math Tasks
• getting to know each other
• establishing classroom norms
• review of prerequisite skills
• ideally no homework assignedA1, A2, AA1SAMPLE PROBLEMS
BHNmath RESOURCES
00000
How can we represent it?OngoingTell a Story: Number Concept• can be moved elsewhereB1.1TOPIC IDEAS11111
How can we represent it?1The Numbers We Use: Sets and Subsets
• sets and subsets
• set notation
• review of the real number system
• origin of Hindu-Arabic numeral system and introduction of 0 (Brahmagupta)
• complex number system
• other number systems (binary, hexadecimal, etc.)
• Russell's Paradox
B1.2BHNmath RESOURCES11111
How can we represent it?2Representing and Comparing Fractions and Mixed Numbers
• representing fractions and mixed numbers
• comparing fractions and mixed numbers
• positive and negative fractions and mixed numbers
• relating unit fractions to other fractions
• converting between improper fractions and mixed numbers
• simplifying fractions
• use visual representations throughout lesson
• history of negatives (Chinese counting rods, Brahmagupta, etc.)
B3.2, B3.3, B3.4, E1.3BHNmath RESOURCES11111
How can we represent it?3Powers and Scientific Notation
• simplifying and evaluating numerical expressions involving powers
• relationship between the sign and size of an exponent and the value of a power
• definition of scientific notation
• switching between standard notation and scientific notation
• applications of scientific notation
• using patterning
B2.1BHNmath RESOURCES11111
How can we represent it?4Algebraic Expressions
• evaluating algebraic expressions at given values
• modelling with algebraic expressions
• algebraic expressions in equations
• inequalities on the number line (extension)
• history of algebra (Babylonians, "al-jabr", Muhammad ibn Mūsā al-Khwārizmī)C1.2, C1.5BHNmath RESOURCES11111
How can we represent it?5Coding - Part 1
• defining and using variables
• assigning values
• calculating values
• printing variables and strings
• rounding values
• using comments
• using programs to solve problems
C2.1, C2.2, C2.3BHNmath RESOURCES11111
How can we represent it?6Infinity, Limits and Density
• infinite sets and subsets
• patterns and number relationships to explain density, infinity and limits
• BEWARE - these concepts can quickly become very complicated (but also very interesting)
• keep lesson/discussions focused on big ideas
• no need to get too carried away with definitions, details and notation here
density property can be omitted entirely (it is not needed to address the concept of density)
• Zeno's Paradox
• history of ∞ (Anaximander, Euclid, Cantor, etc.)
• Fibonacci Sequence and the Golden Ratio
B1.2, B1.3BHNmath RESOURCES11111
How can we represent it?7Making Connections / Review / AssessmentExpectations covered throughout unit11111
How can we represent it?8Making Connections / Review / AssessmentExpectations covered throughout unit11111
When are different operations useful?1Adding and Subtracting Fractions and Mixed Numbers
• adding and subtracting fractions and mixed numbers
• possible discussion of calculator's fraction buttonB3.2, B3.3, B3.4, E1.3BHNmath RESOURCES22222
When are different operations useful?2Multiplying and Dividing Fractions and Mixed Numbers
• multiplying and dividing fractions and mixed numbers
• powers of fractions and mixed numbers
• order of operations involving fractions and mixed numbers
• possible discussion of calculator's fraction buttonB3.2, B3.3, B3.4, E1.3BHNmath RESOURCES22222
When are different operations useful?3Adding and Subtracting Monomials (Collecting Like Terms)
• simplifying algebraic expressions
• collecting like terms
• equivalent algebraic expressions
C1.2, C1.3, C1.4BHNmath RESOURCES22222
When are different operations useful?4Adding and Subtracting Polynomials
• adding and subtracting polynomials
C1.2, C1.4BHNmath RESOURCES22222
When are different operations useful?5Solving One-Step Equations
• solving one-step equations without fraction coefficients
• collecting like terms
C1.2, C1.3, C1.4, C1.5BHNmath RESOURCES22222
When are different operations useful?6Coding - Part 2
• data types (integer, floating point number and string)
• user prompts
• math library (for pi and square root)
C2.1, C2.2, C2.3BHNmath RESOURCES22222
When are different operations useful?7Making Connections / Review / AssessmentExpectations covered throughout unit22222
When are different operations useful?8Making Connections / Review / AssessmentExpectations covered throughout unit22222
How are things changing?1Talking About Change
• dependent and independent variables
• describing rates of change from graphs
C3.1, C3.3, C4.1BHNmath RESOURCES33333
How are things changing?2What is a Linear Relation?
• characteristics of linear relations
• comparing graphs of linear and non-linear relations
• making tables of values from word descriptions
• making graphs from word descriptions
• linear and non-linear relations in real life
B3.3, B3.5, C3.2, C3.3, C4.1, F1.2BHNmath RESOURCES33333
How are things changing?3A Closer Look at Rate of Change
• finding rates from word descriptions
• finding rates from tables of values
• finding rates from graphs
• comparing rates of linear and non-linear relations
B3.3, B3.5, C3.1, C3.2, C3.3, C4.1BHNmath RESOURCES33333
How are things changing?4Connecting Representations
• equations of the form y=start+rate*x
• linear and non-linear relations
B3.3, B3.5, C1.5, C3.1, C3.2, C3.3, C4.1, C4.4BHNmath RESOURCES33333
How are things changing?5Solving Two-Step Equations
• solving two-step equations without fraction coefficients
• collecting like terms
B3.3, B3.5, C1.2, C1.3, C1.4, C1.5BHNmath RESOURCES33333
How are things changing?6Problem Solving with Linear Relations
• solving for the independent variable in the equation of a linear relation
• interpreting the point of intersection for two linear relations
B3.3, B3.5, C1.2, C1.3, C1.4, C1.5, C3.1, C3.2, C3.3, C4.1, C4.4BHNmath RESOURCES33333
How are things changing?7Coding - Part 3
for loops
while loops
• may require two days in computer lab
for loops in Python using range() function with only a single parameter, such as range(10)
• good lesson for introducing comparison operators (>, <, >=, <=, == , !=)
C2.1, C2.2, C2.3BHNmath RESOURCES33333
How are things changing?8Making Connections / Review / AssessmentExpectations covered throughout unit33333
How are things changing?9Making Connections / Review / AssessmentExpectations covered throughout unit33333
How can we describe it?1Working with Ordered Pairs
• Cartesian plane and Cartesian coordinates
• coordinates to describe location
• determining if a point satisfies a given linear or non-linear relation
• meaning of ordered pairs in different contexts
• identifying points of intersection
• other systems for defining location (longitude/latitude, polar coordinates,etc.)
• map projections
B3.1, B3.5, C3.1, C3.2, C3.3 C4.1BHNmath RESOURCES44444
How can we describe it?2Slope
• definition of slope
• slope as rate of change
B3.3, B3.4, B3.5, C3.1, C4.1,BHNmath RESOURCES44444
How can we describe it?3y = mx + b Form for the Equation of a Line
• identifying slopes and y-intercepts of lines
• using slopes and y-intercepts to graph lines
• equations of lines using slopes and y-intercepts
B3.3, B3.4, B3.5, C3.1, C3.2, C3.3, C4.1, C4.4BHNmath RESOURCES44444
How can we describe it?4Equations of Lines Using Slope and a Point
• finding the equation of a line using its slope and a point on the line
• horizontal and vertical lines
y=mx + b formB3.3, B3.4, B3.5, C3.1, C3.2, C3.3, C4.1, C4.2, C4.4BHNmath RESOURCES44444
How can we describe it?5Equations of Lines Using Two Points
• finding the equation of a line using two points on the line
y=mx + b formB3.3, B3.4, B3.5, C3.1, C3.2, C3.3, C4.1, C4.2, C4.4BHNmath RESOURCES44444
How can we describe it?6Translations and Reflections of Lines
• translating lines
• reflecting lines
• mainly vertical translations and reflectionsC3.1, C3.2, C3.3, C4.1, C4.2, C4.3, C4.4BHNmath RESOURCES44444
How can we describe it?7Rotations of Lines
• rotating lines
• parallel and perpendicular lines
C3.1, C3.2, C3.3, C4.1, C4.2, C4.3, C4.4BHNmath RESOURCES44444
How can we describe it?8Equations Versus Inequalities
• graphing linear equations and inequalities from algebraic representations of various forms
• graphing lines using intercepts
• lines with equations of the form y=k, x=k, y=mx+b, x+y=k, x-y=k, ax+by=kC3.1, C3.2, C4.1, C4.2, C4.4BHNmath RESOURCES44444
How can we describe it?9Solving Equations with Variables on Both Sides
• solving equations that have variables on both sides
B3.3, C1.2, C1.3, C1.4, C1.5, C3.3BHNmath RESOURCES44444
How can we describe it?10Making Connections / Review / AssessmentExpectations covered throughout unit44444
How can we describe it?11Making Connections / Review / AssessmentExpectations covered throughout unit44444
How can we make it simpler?OngoingTell a Story: Algebraic Concept• can be moved elsewhereC1.1TOPIC IDEAS55555
How can we make it simpler?1Multiplying and Dividing Powers with the Same Base
• multiplying and dividing powers with the same base
• simplifying algebraic expressions
B2.2BHNmath RESOURCES55555
How can we make it simpler?2Powers of Powers, Products and Quotients
• powers of powers, products and quotients
• simplifying algebraic expressions
B2.2BHNmath RESOURCES55555
How can we make it simpler?3Multiplying and Dividing Monomials
• multiplying and dividing monomials
• laws of exponents
• simplifying algebraic expressions
• converting area and volume measurements
B2.2, C1.2, C1.3, C1.4, C1.5, E1.3BHNmath RESOURCES55555
How can we make it simpler?4Multiplying Polynomials by Monomials (The Distributive Property)
• multiplying polynomials by monomials (the distributive property)
• simplifying algebraic expressions
B2.2, C1.2, C1.3, C1.4BHNmath RESOURCES55555
How can we make it simpler?5Solving Equations Involving Fractions and/or Distribution
• solving equations involving fractions
• solving equations involving the distributive property
B3.3, B3.4, C1.2, C1.3, C1.4, C1.5BHNmath RESOURCES55555
How can we make it simpler?6Relations of the Form xy=k
• graphing relations of the form xy=k and their associated inequalities
• no need to dedicate much time to this topic (to be honest, I really don't know why it even shows up in this course)C4.2BHNmath RESOURCES55555
How can we make it simpler?7Making Connections / Review / AssessmentExpectations covered throughout unit55555
How can we make it simpler?8Making Connections / Review / AssessmentExpectations covered throughout unit55555
How much is that?OngoingTell a Story: Geometric Concept or Measurement System• can be moved elsewhereE1.1TOPIC IDEAS66666
How much is that?1Measurement Calculations in Two Dimensions
• perimeter/circumference and area
B3.5, E1.3, E1.4, E1.6BHNmath RESOURCES66666
How much is that?2Sides of Right Triangles
• side-length relationship for right triangles
• solving problems using the side-length relationship for right triangles
• origin of the “Pythagorean Theorem”
• Babylonian origin of "Pythagorean Theorem"E1.3, E1.5,BHNmath RESOURCES66666
How much is that?3Angle Relationships
• angle relationships involving polygons
• angle relationships involving parallel and intersecting lines
C1.2, C1.5, E1.2BHNmath RESOURCES66666
How much is that?4Triangle and Circle Geometry
• properties of triangles
• properties of circles
• geometric relationships in design
E1.2, E1.5BHNmath RESOURCES66666
How much is that?5Volume Relationships
• review of meaning of volume
• calculating and comparing volumes
• relationship between volumes of prisms and pyramids
• relationship between volumes of cylinders and cones
B3.5, C1.5, E1.3, E1.4, E1.6BHNmath RESOURCES66666
How much is that?6Measurement Calculations in Three Dimensions
• volume, surface area, perimeter/circumference, and area
B3.5, E1.3, E1.4, E1.5, E1.6BHNmath RESOURCES66666
How much is that?7Effects of Changing Dimensions
• effect of changing one or more dimensions on perimeter/circumference, area, surface area, and volume
B3.5, E1.3, E1.4, E1.6BHNmath RESOURCES66666
How much is that?8Proportional Relationships and Conversions
• solving problems involving proportional relationships
• using and comparing different measurement systems (metric, imperial, etc.)
• converting within a measurement system and between measurement systems
• conditions for a linear relation to be proportional
B3.5, C3.1, C3.2, C3.3, C4.1, C4.4, E1.3BHNmath RESOURCES66666
How much is that?9Coding - Part 4
if statements
if…else statements
• nested if…else statements
if…else if…else statements
• may require two days in computer lab
• may need to discuss/review comparison operators (>, <, >=, <=, == , !=)
C2.1, C2.2, C2.3BHNmath RESOURCES66666
How much is that?10Making Connections / Review / AssessmentExpectations covered throughout unit66666
How much is that?11Making Connections / Review / AssessmentExpectations covered throughout unit66666
What's the cost?1Budget
• creating and modifying budgets
• fixed expenses and variable expenses
• discretionary expenses and non-discretionary expenses
• gross income and net income
F1.1, F1.4BHNmath RESOURCES77777
What's the cost?2Rates and Percentages
• solving problems involving rates and percentages
• rates and percentages in financial decision making
B3.5, C3.1, C3.2, C3.3, C4.1, C4.4, E1.3, E1.4, F1.1, F1.4BHNmath RESOURCES77777
What's the cost?3Appreciation and Depreciation
• financial situations involving appreciation and depreciation
• graphs related to appreciation and depreciation
C3.1, C3.2, C4.1, C4.4, F1.1, F1.2BHNmath RESOURCES77777
What's the cost?4Interest and Borrowing
• the cost of borrowing
• simple interest and compound interest
• comparing effects of different interest types/rates, borrowing times and down payment amounts
• can be taught with or without the use of formulasB3.5, C3.1, C3.2, C4.1, F1.1, F1.2, F1.3BHNmath RESOURCES77777
What's the cost?5Coding - Part 5
• coding for calculations involving interest
C2.1, C2.2, C2.3, F1.1, F1.2, F1.3BHNmath RESOURCES77777
What's the cost?6Making Connections / Review / Assessment• possibly use a project for assessment/evaluationExpectations covered throughout unit77777
What's the cost?7Making Connections / Review / Assessment• possibly use a project for assessment/evaluationExpectations covered throughout unit77777
What's the story?1Large Amounts of Data
• large amounts of data in the real world
• benefits and challenges associated with the use of large amounts of data
D1.1, D2.1BHNmath RESOURCES88888
What's the story?2Single-Variable Data
• measures of central tendency (mean, median and mode)
• measures of spread (range, interquartile range)
• representations of single-variable data (box plots, histograms, bar graphs, circle graphs, etc.)
D1.2BHNmath RESOURCES88888
What's the story?3Scatter Plots and Mathematical Modelling
• scatter plots and regression using technology
• correlation
• outliers
• interpolation and extrapolation
• discuss shapes of regression models (no need to go into great detail about the characteristics of the functions)
• no need to cover how correlation coefficient is calculated
C3.1, C4.1, D1.3BHNmath RESOURCES88888
What's the story?4Collecting and Analysing Data 1• possibly use a project for assessment/evaluationC3.1, C4.1, D1.3, D2.2, D2.3, D2.4, D2.588888
What's the story?5Collecting and Analysing Data 2• possibly use a project for assessment/evaluationC3.1, C4.1, D1.3, D2.2, D2.3, D2.4, D2.588888
What's the story?6Making Connections / Review / AssessmentExpectations covered throughout unit88888
What's the story?7Making Connections / Review / AssessmentExpectations covered throughout unit88888