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 | 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 | 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 | 00000 | |
| How do these compare? | Ongoing | Tell a Story: Number Concept | • can be moved elsewhere | B1.1 | 11111 | |
| How do these compare? | 1 | 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 | 11111 | |
| How do these compare? | 2 | 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 | 11111 | |
| How do these compare? | 3 | 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 | 11111 | |
| How do these compare? | 4 | Algebraic Expressions • evaluating algebraic expressions at given values • modelling with algebraic expressions | • history of algebra (Babylonians, "al-jabr", Muhammad ibn Mūsā al-Khwārizmī) | C1.2, C1.5 | 11111 | |
| How do these compare? | 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 | 11111 | ||
| How do these compare? | 6 | Adding and Subtracting Monomials (Collecting Like Terms) • simplifying algebraic expressions • collecting like terms | C1.2, C1.3, C1.4 | 11111 | ||
| How do these compare? | 7 | One-Step Equations • solving one-step equations without fraction coefficients • collecting like terms | C1.2, C1.3, C1.4, C1.5 | 11111 | ||
| How do these compare? | 8 | 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 | 11111 | |
| How do these compare? | 9 | 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 | 11111 | |
| How do these compare? | 10 | Making Connections / Review / Assessment | Expectations covered throughout unit | 11111 | ||
| How do these compare? | 11 | Making Connections / Review / Assessment | Expectations covered throughout unit | 11111 | ||
| How are things changing? | Ongoing | Tell a Story: Algebraic Concept | • can be moved elsewhere | C1.1 | 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 | 22222 | ||
| 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 | 22222 | ||
| 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 | 22222 | ||
| How are things changing? | 4 | Connecting Representations • equations of the form y=start+rate*x • linear and non-linear relations | B3.3, B3.5, C3.1, C3.2, C3.3, C4.1, C4.4 | 22222 | ||
| How are things changing? | 5 | Adding and Subtracting Polynomials • adding and subtracting polynomials | C1.2, C1.4 | 22222 | ||
| How are things changing? | 6 | 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 | 22222 | ||
| How are things changing? | 7 | 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 | 22222 | ||
| How are things changing? | 8 | Making Connections / Review / Assessment | Expectations covered throughout unit | 22222 | ||
| How are things changing? | 9 | Making Connections / Review / Assessment | Expectations covered throughout unit | 22222 | ||
| How can we describe the space around us? | 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 | 33333 | |
| How can we describe the space around us? | 2 | Slope • definition of slope • slope as rate of change | B3.3, B3.4, B3.5, C3.1, C4.1, | 33333 | ||
| How can we describe the space around us? | 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 | 33333 | ||
| How can we describe the space around us? | 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 | 33333 | |
| How can we describe the space around us? | 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 | 33333 | |
| How can we describe the space around us? | 6 | Measurement Calculations • perimeter, area, surface area and volume | B3.5, E1.3, E1.4, E1.6 | 33333 | ||
| How can we describe the space around us? | 7 | 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, | 33333 | |
| How can we describe the space around us? | 8 | Geometric Relationships in Design • properties of triangles • properties of circles | E1.2, E1.5 | 33333 | ||
| How can we describe the space around us? | 9 | Making Connections / Review / Assessment | Expectations covered throughout unit | 33333 | ||
| How can we describe the space around us? | 10 | Making Connections / Review / Assessment | Expectations covered throughout unit | 33333 | ||
| How much is that? | 1 | 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 | 44444 | ||
| How much is that? | 2 | Multiplying and Dividing Powers with the Same Base • multiplying and dividing powers with the same base • simplifying algebraic expressions | B2.2 | 44444 | ||
| How much is that? | 3 | Powers of Powers, Products and Quotients • powers of powers, products and quotients • simplifying algebraic expressions | B2.2 | 44444 | ||
| How much is that? | 4 | 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 | 44444 | ||
| How much is that? | 5 | Equations with Variables on Both Sides • solving equations that have variables on both sides | B3.3, C1.2, C1.3, C1.4, C1.5 | 44444 | ||
| How much is that? | 6 | Coding 1 | C2.1, C2.2, C2.3 | 44444 | ||
| How much is that? | 7 | Coding 2 | C2.1, C2.2, C2.3 | 44444 | ||
| How much is that? | 8 | Making Connections / Review / Assessment | Expectations covered throughout unit | 44444 | ||
| How much is that? | 9 | Making Connections / Review / Assessment | Expectations covered throughout unit | 44444 | ||
| Scaling and splitting: How much now? | Ongoing | Tell a Story: Geometric Concept or Measurement System | • can be moved elsewhere | E1.1 | 55555 | |
| Scaling and splitting: How much now? | 1 | 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 | 55555 | ||
| Scaling and splitting: How much now? | 2 | 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 | 55555 | ||
| Scaling and splitting: How much now? | 3 | 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 | 55555 | ||
| Scaling and splitting: How much now? | 4 | Proportions and Percentages • solving problems involving proportions and percentages • using and comparing different measurement systems (imperial, metric, etc.) • converting within a measurement system and between measurement systems | B3.5, E1.3 | 55555 | ||
| Scaling and splitting: How much now? | 5 | Rates and Proportional Relationships • solving problems involving rates and proportional relationships • conditions for a linear relation to be proportional | B3.5, C3.1, C3.2, C3.3, C4.1, C4.4 | 55555 | ||
| Scaling and splitting: How much now? | 6 | Coding 3 | C2.1, C2.2, C2.3 | 55555 | ||
| Scaling and splitting: How much now? | 7 | Making Connections / Review / Assessment | Expectations covered throughout unit | 55555 | ||
| Scaling and splitting: How much now? | 8 | Making Connections / Review / Assessment | Expectations covered throughout unit | 55555 | ||
| When are different operations useful? | 1 | Equations of Lines in Other Forms • lines of the form x+y=k x-y=k, ax+by=k • graphing lines using intercepts • rearranging equations into the form y=mx+b | C3.1, C3.2, C4.1, C4.2, C4.4 | 66666 | ||
| When are different operations useful? | 2 | Equations vs. Inequalities | C3.1, C3.2, C4.1, C4.2, C4.4 | 66666 | ||
| When are different operations useful? | 3 | Reflections and Translations of y=ax | C3.1, C3.2, C3.3, C4.1, C4.2, C4.3, C4.4 | 66666 | ||
| When are different operations useful? | 4 | Rotations of y=ax • parallel and perpendicular slopes | C3.1, C3.2, C3.3, C4.1, C4.2, C4.3, C4.4 | 66666 | ||
| When are different operations useful? | 5 | Graphing Relations of the Form xy=k | C4.2 | 66666 | ||
| When are different operations useful? | 6 | Coding 4 | C2.1, C2.2, C2.3 | 66666 | ||
| When are different operations useful? | 7 | Making Connections / Review / Assessment | Expectations covered throughout unit | 66666 | ||
| When are different operations useful? | 8 | Making Connections / Review / Assessment | Expectations covered throughout unit | 66666 | ||
| How can we make predictions and decide? | 1 | Making Financial Decisions • factors to consider | F1.1 | 77777 | ||
| How can we make predictions and decide? | 2 | Appreciation and Depreciation | F1.2 | 77777 | ||
| How can we make predictions and decide? | 3 | Interest | F1.2, F1.3 | 77777 | ||
| How can we make predictions and decide? | 4 | Budget | F1.4 | 77777 | ||
| How can we make predictions and decide? | 5 | Coding 5 | C2.1, C2.2, C2.3 | 77777 | ||
| How can we make predictions and decide? | 6 | Making Connections / Review / Assessment | Expectations covered throughout unit | 77777 | ||
| How can we make predictions and decide? | 7 | Making Connections / Review / Assessment | Expectations covered throughout unit | 77777 | ||
| What's the story? | 1 | Data and Modelling • working with large amounts of data (context, challlenges, resources, etc.) • value of mathematical modelling | D1.1, D2.1 | 88888 | ||
| What's the story? | 2 | Single-Variable Data | D1.2 | 88888 | ||
| What's the story? | 3 | Scatter Plots and Correlation 1 • using technology • regression models | C3.1, C4.1, D1.3 | 88888 | ||
| What's the story? | 4 | Scatter Plots and Correlation 2 • using technology • regression models | C3.1, C4.1, D1.3 | 88888 | ||
| What's the story? | 5 | Collecting and Analysing Data 1 | • project for assessment? | C3.1, C4.1, D1.3, D2.2, D2.3, D2.4, D2.5 | 88888 | |
| What's the story? | 6 | Collecting and Analysing Data 2 | • project for assessment? | C3.1, C4.1, D1.3, D2.2, D2.3, D2.4, D2.5 | 88888 | |
| What's the story? | 7 | Coding 6 | C2.1, C2.2, C2.3 | 88888 | ||
| What's the story? | 8 | Making Connections / Review / Assessment | Expectations covered throughout unit | 88888 | ||
| What's the story? | 9 | Making Connections / Review / Assessment | Expectations covered throughout unit | 88888 |