Math for Teachers Course

Lesson 1 • Mathematical Reasoning and Proof

Introduces inductive and deductive reasoning, conjecture, and basic proof strategies. Develops logical thinking needed across all math domains.

Lesson 2 • Number Sense and Place Value

Explores whole numbers, place value structure, and magnitude comparison. Anchors later work in operations and algebraic reasoning.

Lesson 3 • Mathematical Communication

Covers precise vocabulary, notation, and written explanation in mathematics. Prepares teachers to set clear communication expectations for students.

Lesson 1 • Divisibility and Factors

Covers divisibility rules, prime factorisation, GCF, and LCM. Provides tools teachers need to explain fraction simplification and common denominators.

Lesson 2 • Number Theory Applications

Applies modular arithmetic, odd/even properties, and number patterns to problem solving. Strengthens teachers' ability to design rich number investigations.

Lesson 3 • Addition and Subtraction Concepts

Examines part-whole and comparison models for addition and subtraction. Connects concrete models to symbolic procedures for classroom instruction.

Lesson 4 • Multiplication and Division Concepts

Analyses equal-groups, array, and area models for multiplication and division. Builds the conceptual base for fraction and ratio work in later chapters.

Lesson 1 • Percent Concepts and Applications

Defines percent as a ratio per hundred and links it to fractions and decimals. Applies percent to real-world contexts teachers can use in lessons.

Lesson 2 • Decimal Representation and Operations

Connects decimals to place value and fraction equivalents, then extends to operations. Clarifies common errors such as misaligned decimal points.

Lesson 3 • Fraction Operations

Explains addition, subtraction, multiplication, and division of fractions with conceptual justification. Addresses why invert-and-multiply works using area and number line models.

Lesson 4 • Fraction Concepts and Models

Introduces part-whole, measurement, and quotient interpretations of fractions. Grounds instruction in multiple representations before moving to operations.

Lesson 1 • Ratio and Rate Concepts

Distinguishes ratios, rates, and unit rates using tables, graphs, and double number lines. Builds proportional reasoning as a foundation for linear functions.

Lesson 2 • Proportional Relationships

Identifies proportional relationships in tables, equations, and graphs. Connects the constant of proportionality to slope in linear functions.

Lesson 3 • Introduction to Variables and Expressions

Introduces variables as quantities that vary and builds expression-writing skills. Bridges arithmetic generalisations to formal algebraic notation.

Lesson 4 • Equations and Inequalities

Develops equation-solving strategies using balance, inverse operations, and properties of equality. Extends to one-variable inequalities and their graphical representation.

Lesson 1 • Linear Functions and Slope

Connects slope to rate of change and y-intercept to initial value in contextual problems. Builds fluency with slope-intercept, point-slope, and standard forms.

Lesson 2 • Systems of Linear Equations

Solves systems graphically, by substitution, and by elimination, connecting each method conceptually. Applies systems to real-world problems suitable for middle and high school classrooms.

Lesson 3 • Introduction to Nonlinear Functions

Contrasts linear and nonlinear functions using quadratic and exponential examples. Prepares teachers to help students recognise and describe nonlinear behaviour.

Lesson 4 • The Function Concept

Defines functions using mapping diagrams, tables, and graphs with emphasis on the vertical line test. Distinguishes functions from non-functions using concrete examples.

Lesson 1 • Coordinate Geometry

Applies the coordinate plane to compute distance, midpoint, and slope for geometric figures. Bridges algebra and geometry through proof and problem solving.

Lesson 2 • Geometric Figures and Properties

Classifies points, lines, angles, polygons, and circles using precise definitions. Establishes vocabulary and properties that underpin all geometric reasoning.

Lesson 3 • Volume and Capacity

Develops volume formulas for prisms, cylinders, pyramids, and spheres using unit-cube reasoning. Connects volume to capacity and real-world measurement contexts.

Lesson 4 • Transformations and Symmetry

Examines translations, reflections, rotations, and dilations on the coordinate plane. Connects transformations to congruence, similarity, and symmetry concepts.

Lesson 1 • Compound Events and Simulations

Applies counting principles, tree diagrams, and area models to compound probability. Uses simulations to connect experimental results to theoretical predictions.

Lesson 2 • Basic Probability Concepts

Defines probability, sample space, and events using experimental and theoretical approaches. Builds the foundation for compound events and simulations.

Lesson 3 • Measures of Centre and Spread

Computes and interprets mean, median, mode, range, IQR, and standard deviation. Connects choice of measure to data distribution shape.

Lesson 4 • Data Collection and Representation

Covers sampling methods, data types, and appropriate graphical displays for categorical and numerical data. Emphasizes choosing displays that reveal meaningful patterns.

Lesson 1 • Integers and the Real Number System

Extends the number system from rationals to irrationals and reals, clarifying the hierarchy. Addresses common student misconceptions about irrational numbers and square roots.

Lesson 2 • Vertical Alignment Across Grade Levels

Maps how key concepts develop from elementary through high school using learning progressions. Enables teachers to anticipate prerequisite gaps and plan instruction accordingly.

Lesson 3 • Algebraic Structures and Properties

Examines field properties, polynomial operations, and factoring as a unified algebraic system. Equips teachers to explain why algebraic rules hold rather than just how to apply them.

Lesson 4 • Connecting Mathematical Domains

Traces connections among number, algebra, geometry, and statistics through unifying themes. Helps teachers present mathematics as a coherent discipline rather than isolated topics.