Scope and Sequence
Mathematics, Grade 9
MTH1W1 (Grade 9 De-streamed)
NOTE
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| Question / Unit | Day | Lesson | Notes and Other Points for Discussion | Expectations Included | Links to Resources | Row Colour |
|---|---|---|---|---|---|---|
| Welcome to MTH1W1 | 1 | Non-Curricular Math Tasks • getting to know each other • establishing classroom norms • review of prerequisite skills | • ideally no homework assigned | A1, A2, AA1 | SAMPLE PROBLEMS BHNmath RESOURCES | 00000 |
| Welcome to MTH1W1 | 2 | Non-Curricular Math Tasks • getting to know each other • establishing classroom norms • review of prerequisite skills | • ideally no homework assigned | A1, A2, AA1 | SAMPLE PROBLEMS BHNmath RESOURCES | 00000 |
| Welcome to MTH1W1 | 3 | Non-Curricular Math Tasks • getting to know each other • establishing classroom norms • review of prerequisite skills | • ideally no homework assigned | A1, A2, AA1 | SAMPLE PROBLEMS BHNmath RESOURCES | 00000 |
| How can we represent it? | Ongoing | Tell a Story: Number Concept | • can be moved elsewhere | B1.1 | TOPIC IDEAS | 11111 |
| How can we represent it? | 1 | The 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 | B1.2 | BHNmath RESOURCES | 11111 |
| How can we represent it? | 2 | Representing 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, E1.3 | BHNmath RESOURCES | 11111 |
| How can we represent it? | 3 | Powers 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 | B2.1 | BHNmath RESOURCES | 11111 | |
| How can we represent it? | 4 | Algebraic 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, C1.5 | BHNmath RESOURCES | 11111 |
| How can we represent it? | 5 | Coding - 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, C2.3 | BHNmath RESOURCES | 11111 | |
| How can we represent it? | 6 | Infinity, 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, B1.3 | BHNmath RESOURCES | 11111 |
| How can we represent it? | 7 | Making Connections / Review / Assessment | Expectations covered throughout unit | 11111 | ||
| How can we represent it? | 8 | Making Connections / Review / Assessment | Expectations covered throughout unit | 11111 | ||
| When are different operations useful? | 1 | Adding and Subtracting Fractions and Mixed Numbers • adding and subtracting fractions and mixed numbers | • possible discussion of calculator's fraction button | B3.2, B3.3, B3.4, E1.3 | BHNmath RESOURCES | 22222 |
| When are different operations useful? | 2 | Multiplying 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 button | B3.2, B3.3, B3.4, E1.3 | BHNmath RESOURCES | 22222 |
| When are different operations useful? | 3 | Adding and Subtracting Monomials (Collecting Like Terms) • simplifying algebraic expressions • collecting like terms • equivalent algebraic expressions | C1.2, C1.3, C1.4 | BHNmath RESOURCES | 22222 | |
| When are different operations useful? | 4 | Adding and Subtracting Polynomials • adding and subtracting polynomials | C1.2, C1.4 | BHNmath RESOURCES | 22222 | |
| When are different operations useful? | 5 | Solving One-Step Equations • solving one-step equations without fraction coefficients • collecting like terms | C1.2, C1.3, C1.4, C1.5 | BHNmath RESOURCES | 22222 | |
| When are different operations useful? | 6 | Coding - Part 2 • data types (integer, floating point number and string) • user prompts • math library (for pi and square root) | C2.1, C2.2, C2.3 | BHNmath RESOURCES | 22222 | |
| When are different operations useful? | 7 | Making Connections / Review / Assessment | Expectations covered throughout unit | 22222 | ||
| When are different operations useful? | 8 | Making Connections / Review / Assessment | Expectations covered throughout unit | 22222 | ||
| How are things changing? | 1 | Talking About Change • dependent and independent variables • describing rates of change from graphs | C3.1, C3.3, C4.1 | BHNmath RESOURCES | 33333 | |
| How are things changing? | 2 | What 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, F1.2 | BHNmath RESOURCES | 33333 | |
| How are things changing? | 3 | A 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, C4.1 | BHNmath RESOURCES | 33333 | |
| How are things changing? | 4 | Connecting 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, C4.4 | BHNmath RESOURCES | 33333 | |
| How are things changing? | 5 | Solving Two-Step Equations • solving two-step equations without fraction coefficients • collecting like terms | B3.3, B3.5, C1.2, C1.3, C1.4, C1.5 | BHNmath RESOURCES | 33333 | |
| How are things changing? | 6 | Problem 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, C4.4 | BHNmath RESOURCES | 33333 | |
| How are things changing? | 7 | Coding - 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, C2.3 | BHNmath RESOURCES | 33333 |
| How are things changing? | 8 | Making Connections / Review / Assessment | Expectations covered throughout unit | 33333 | ||
| How are things changing? | 9 | Making Connections / Review / Assessment | Expectations covered throughout unit | 33333 | ||
| How can we describe it? | 1 | Working 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 C4.1 | BHNmath RESOURCES | 44444 |
| How can we describe it? | 2 | Slope • definition of slope • slope as rate of change | B3.3, B3.4, B3.5, C3.1, C4.1, | BHNmath RESOURCES | 44444 | |
| How can we describe it? | 3 | y = 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, C4.4 | BHNmath RESOURCES | 44444 | |
| How can we describe it? | 4 | Equations 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 form | B3.3, B3.4, B3.5, C3.1, C3.2, C3.3, C4.1, C4.2, C4.4 | BHNmath RESOURCES | 44444 |
| How can we describe it? | 5 | Equations of Lines Using Two Points • finding the equation of a line using two points on the line | • y=mx + b form | B3.3, B3.4, B3.5, C3.1, C3.2, C3.3, C4.1, C4.2, C4.4 | BHNmath RESOURCES | 44444 |
| How can we describe it? | 6 | Translations and Reflections of Lines • translating lines • reflecting lines | • mainly vertical translations and reflections | C3.1, C3.2, C3.3, C4.1, C4.2, C4.3, C4.4 | BHNmath RESOURCES | 44444 |
| How can we describe it? | 7 | Rotations of Lines • rotating lines • parallel and perpendicular lines | C3.1, C3.2, C3.3, C4.1, C4.2, C4.3, C4.4 | BHNmath RESOURCES | 44444 | |
| How can we describe it? | 8 | Equations 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=k | C3.1, C3.2, C4.1, C4.2, C4.4 | BHNmath RESOURCES | 44444 |
| How can we describe it? | 9 | Solving Equations with Variables on Both Sides • solving equations that have variables on both sides | B3.3, C1.2, C1.3, C1.4, C1.5, C3.3 | BHNmath RESOURCES | 44444 | |
| How can we describe it? | 10 | Making Connections / Review / Assessment | Expectations covered throughout unit | 44444 | ||
| How can we describe it? | 11 | Making Connections / Review / Assessment | Expectations covered throughout unit | 44444 | ||
| How can we make it simpler? | Ongoing | Tell a Story: Algebraic Concept | • can be moved elsewhere | C1.1 | TOPIC IDEAS | 55555 |
| How can we make it simpler? | 1 | Multiplying and Dividing Powers with the Same Base • multiplying and dividing powers with the same base • simplifying algebraic expressions | B2.2 | BHNmath RESOURCES | 55555 | |
| How can we make it simpler? | 2 | Powers of Powers, Products and Quotients • powers of powers, products and quotients • simplifying algebraic expressions | B2.2 | BHNmath RESOURCES | 55555 | |
| How can we make it simpler? | 3 | Multiplying 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, E1.3 | BHNmath RESOURCES | 55555 | |
| How can we make it simpler? | 4 | Multiplying Polynomials by Monomials (The Distributive Property) • multiplying polynomials by monomials (the distributive property) • simplifying algebraic expressions | B2.2, C1.2, C1.3, C1.4 | BHNmath RESOURCES | 55555 | |
| How can we make it simpler? | 5 | Solving 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, C1.5 | BHNmath RESOURCES | 55555 | |
| How can we make it simpler? | 6 | Relations 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) | C4.2 | BHNmath RESOURCES | 55555 |
| How can we make it simpler? | 7 | Making Connections / Review / Assessment | Expectations covered throughout unit | 55555 | ||
| How can we make it simpler? | 8 | Making Connections / Review / Assessment | Expectations covered throughout unit | 55555 | ||
| How much is that? | Ongoing | Tell a Story: Geometric Concept or Measurement System | • can be moved elsewhere | E1.1 | TOPIC IDEAS | 66666 |
| How much is that? | 1 | Measurement Calculations in Two Dimensions • perimeter/circumference and area | B3.5, E1.3, E1.4, E1.6 | BHNmath RESOURCES | 66666 | |
| How much is that? | 2 | Sides 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 RESOURCES | 66666 |
| How much is that? | 3 | Angle Relationships • angle relationships involving polygons • angle relationships involving parallel and intersecting lines | C1.2, C1.5, E1.2 | BHNmath RESOURCES | 66666 | |
| How much is that? | 4 | Triangle and Circle Geometry • properties of triangles • properties of circles • geometric relationships in design | E1.2, E1.5 | BHNmath RESOURCES | 66666 | |
| How much is that? | 5 | Volume 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, E1.6 | BHNmath RESOURCES | 66666 | |
| How much is that? | 6 | Measurement Calculations in Three Dimensions • volume, surface area, perimeter/circumference, and area | B3.5, E1.3, E1.4, E1.5, E1.6 | BHNmath RESOURCES | 66666 | |
| How much is that? | 7 | Effects of Changing Dimensions • effect of changing one or more dimensions on perimeter/circumference, area, surface area, and volume | B3.5, E1.3, E1.4, E1.6 | BHNmath RESOURCES | 66666 | |
| How much is that? | 8 | Proportional 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, E1.3 | BHNmath RESOURCES | 66666 | |
| How much is that? | 9 | Coding - 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, C2.3 | BHNmath RESOURCES | 66666 |
| How much is that? | 10 | Making Connections / Review / Assessment | Expectations covered throughout unit | 66666 | ||
| How much is that? | 11 | Making Connections / Review / Assessment | Expectations covered throughout unit | 66666 | ||
| What's the cost? | 1 | Budget • creating and modifying budgets • fixed expenses and variable expenses • discretionary expenses and non-discretionary expenses • gross income and net income | F1.1, F1.4 | BHNmath RESOURCES | 77777 | |
| What's the cost? | 2 | Rates 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, F1.4 | BHNmath RESOURCES | 77777 | |
| What's the cost? | 3 | Appreciation and Depreciation • financial situations involving appreciation and depreciation • graphs related to appreciation and depreciation | C3.1, C3.2, C4.1, C4.4, F1.1, F1.2 | BHNmath RESOURCES | 77777 | |
| What's the cost? | 4 | Interest 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 formulas | B3.5, C3.1, C3.2, C4.1, F1.1, F1.2, F1.3 | BHNmath RESOURCES | 77777 |
| What's the cost? | 5 | Coding - Part 5 • coding for calculations involving interest | C2.1, C2.2, C2.3, F1.1, F1.2, F1.3 | BHNmath RESOURCES | 77777 | |
| What's the cost? | 6 | Making Connections / Review / Assessment | • possibly use a project for assessment/evaluation | Expectations covered throughout unit | 77777 | |
| What's the cost? | 7 | Making Connections / Review / Assessment | • possibly use a project for assessment/evaluation | Expectations covered throughout unit | 77777 | |
| What's the story? | 1 | Large 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, D2.1 | BHNmath RESOURCES | 88888 | |
| What's the story? | 2 | Single-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.) | D1.2 | BHNmath RESOURCES | 88888 | |
| What's the story? | 3 | Scatter 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, D1.3 | BHNmath RESOURCES | 88888 |
| What's the story? | 4 | Collecting and Analysing Data 1 | • possibly use a project for assessment/evaluation | C3.1, C4.1, D1.3, D2.2, D2.3, D2.4, D2.5 | 88888 | |
| What's the story? | 5 | Collecting and Analysing Data 2 | • possibly use a project for assessment/evaluation | C3.1, C4.1, D1.3, D2.2, D2.3, D2.4, D2.5 | 88888 | |
| What's the story? | 6 | Making Connections / Review / Assessment | Expectations covered throughout unit | 88888 | ||
| What's the story? | 7 | Making Connections / Review / Assessment | Expectations covered throughout unit | 88888 |