Undervisningsbeskrivelse
Stamoplysninger til brug ved prøver til gymnasiale uddannelser
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Termin(er)
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2024/25 - 2025/26
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Institution
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X - Ikast-Brande Gymnasium
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Fag og niveau
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Matematik -
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Lærer(e)
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Matthew Pilley
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Hold
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2024 MathAnSL/2 (1i MathAnSL/2, 2i MathAnSL/2)
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Oversigt over gennemførte undervisningsforløb
Beskrivelse af de enkelte undervisningsforløb (1 skema for hvert forløb)
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Titel
1
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Introduction
Unit: Sets and Venn Diagrams
Overview:
This unit provides an introduction to fundamental set theory and the use of Venn diagrams to represent relationships between sets. While HL students explore this content in greater depth, SL students will engage with key concepts in weekly lessons designed to build a foundational understanding. The unit supports the development of logical reasoning and visual representation skills.
Links to ATL Skills:
Thinking skills: Critical thinking through the classification and comparison of sets.
Communication skills: Using symbolic notation and diagrams to communicate mathematical relationships.
Links to TOK:
How do different systems of representation (such as symbolic language or diagrams) influence the way we think about mathematical relationships?
What does it mean for something to “belong” to a set — how do definitions shape knowledge in mathematics?
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Indhold
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Kernestof:
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Omfang
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Estimeret:
3,00 moduler
Dækker over:
4 moduler
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Særlige fokuspunkter
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- Almene (tværfaglige)
- Overskue og strukturere
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Væsentligste arbejdsformer
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Forelæsninger
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Gruppearbejde
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Lærerstyret undervisning
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Titel
2
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Core 1: Algebra & Functions
Unit: Straight Lines, Surds and Exponents, and Quadratic Equations
Chapters covered:
Chapter 1, Core: Straight Lines
Chapter 3, Core: Surds and Exponents
Chapter 4, Core: Quadratic Equations
Overview:
This unit covers three core algebraic topics from the Haese Mathematics Core textbook. Students explore straight-line equations and their graphical representations, manipulate surds and exponents, and learn to solve and apply quadratic equations. These skills provide a foundation for more advanced topics later in the course. The unit concludes with an assessment that contributes to the November progress grade.
Links to ATL Skills:
Thinking skills: Developing algebraic fluency and problem-solving strategies.
Self-management skills: Preparing for formal assessment and managing revision across multiple topics.
Links to TOK:
To what extent is mathematical knowledge “discovered” versus “invented”?
How do different forms of mathematical representation (graphs, symbols, equations) affect our understanding of abstract concepts?
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Indhold
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Kernestof:
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Omfang
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Estimeret:
12,00 moduler
Dækker over:
11 moduler
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Særlige fokuspunkter
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Væsentligste arbejdsformer
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Titel
3
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Core 2: Sequences & Intro to Trig & Geometry
Unit: Sequences & Series, Measurement, Trigonometry, and Points in Space
Chapters covered:
Chapter 5, Core: Sequences & Series
Chapter 6, Core: Measurement
Chapter 7, Core: Right-Angled Trigonometry
Chapter 8, Core: Non-Right-Angled Trigonometry
Chapter 9, Core: Points in Space
Overview:
This unit covers a broad set of mathematical tools and techniques from the Core Haese Mathematics textbook. Students begin with sequences and series, developing the ability to recognize patterns and model situations mathematically. Measurement concepts are reinforced through practical applications. Trigonometric techniques, both in right-angled and non-right-angled contexts, are introduced and extended. Finally, students explore three-dimensional space through points and vectors. Together, these topics support mathematical modeling and prepare students for future work with geometry and applications.
Links to ATL Skills:
Thinking skills: Applying mathematical concepts to model real-world problems.
Research skills: Investigating mathematical relationships through inquiry-based tasks.
Links to TOK:
How do mathematical models help us understand the physical world?
In what ways do the assumptions of mathematical models limit their usefulness in representing reality?
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Indhold
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Kernestof:
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Omfang
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Estimeret:
21,00 moduler
Dækker over:
15 moduler
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Særlige fokuspunkter
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Væsentligste arbejdsformer
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Titel
4
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Functions
Unit: Functions and Their Transformations
Chapters covered:
Chapter 2, AASL: Quadratic Functions
Chapter 3, AASL: Functions
Chapter 4, AASL: Transformations of Functions
Chapter 5, AASL: Exponential Functions
Chapter 6, AASL: Logarithmic Functions
Overview:
This unit focuses on the study of functions, transformations, and related families of curves, using the AASL Haese Mathematics textbook. Students review quadratic functions before moving into a broader investigation of function behavior, transformations, exponential functions, and logarithmic functions. Emphasis is placed on graphing, algebraic manipulation, and recognizing the underlying structures common to different types of functions. These topics are essential for developing a deep conceptual understanding of mathematical relationships and for preparing students for applications in modeling and analysis.
Links to ATL Skills:
Thinking skills: Recognizing patterns, analyzing functional behavior, and applying transformations.
Communication skills: Interpreting and expressing mathematical ideas graphically, symbolically, and verbally.
Links to TOK:
How do different representations of functions (graphs, equations, tables) influence the ways we understand mathematical relationships?
What is the role of abstraction in mathematical knowledge?
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Indhold
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Kernestof:
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Omfang
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Estimeret:
Ikke angivet
Dækker over:
32 moduler
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Særlige fokuspunkter
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Væsentligste arbejdsformer
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Titel
5
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Statistics & Probability
Unit: Probability and Statistics
Chapters covered:
Chapter 10, Core: Probability
Chapter 11, Core: Sampling and Data
Chapter 12, Core: Statistics
Chapter 19, AASL: Bivariate Statistics
Overview:
This unit develops students’ understanding of probability and statistics, using both the Core and AASL Haese Mathematics textbooks. Topics include the fundamental principles of probability, methods of sampling, data collection, and analysis. Students also learn how to interpret and display statistical information through measures of central tendency, variation, and graphical techniques. Bivariate statistics is introduced to explore relationships between two variables. Throughout the unit, students work with real-world contexts, supporting the application of statistical methods to practical situations.
Links to ATL Skills:
Research skills: Collecting, organizing, and analyzing data to draw conclusions.
Thinking skills: Interpreting data critically, identifying patterns and trends, and assessing reliability.
Links to TOK:
How can statistics be used to inform — or mislead — our understanding of the world?
What are the ethical implications of data collection and statistical analysis?
How does uncertainty affect knowledge in the field of statistics?
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Indhold
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Kernestof:
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Omfang
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Estimeret:
Ikke angivet
Dækker over:
12 moduler
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Særlige fokuspunkter
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Væsentligste arbejdsformer
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Titel
6
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Trig 2
Unit: Trigonometric Functions and Identities
Chapters covered:
Chapter 7, AASL: Radians
Chapter 8, AASL: Unit Circle and Periodic Functions
Chapter 9, AASL: Trigonometric Identities
Overview:
This unit explores trigonometric functions and their properties, using Chapters 7–9 of the AASL Haese Mathematics textbook. Students begin by developing fluency with radian measure and the unit circle, then extend their understanding to periodic functions and key trigonometric identities. Emphasis is placed on using these tools to model cyclical behavior and solve a variety of problems. These skills will serve as a foundation for future applications in both pure and applied mathematics.
Links to ATL Skills:
Thinking skills: Applying conceptual understanding to solve unfamiliar problems; manipulating algebraic expressions.
Communication skills: Expressing mathematical ideas using multiple forms of representation.
Links to TOK:
How does the concept of periodicity help us model real-world phenomena?
In what ways does mathematical abstraction (such as radians or the unit circle) contribute to or limit understanding?
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Indhold
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Kernestof:
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Omfang
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Estimeret:
14,00 moduler
Dækker over:
12 moduler
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Særlige fokuspunkter
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Væsentligste arbejdsformer
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Titel
7
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Binomial Theorem
Unit: Binomial Distributions
Chapters covered:
Chapter 1, AASL: Binomial Distributions
Overview:
This short but important unit focuses on understanding binomial distributions and their applications. Over three lessons, students will first unpack the key ideas and assumptions behind binomial models, then apply these to real-world scenarios. The unit concludes with focused practice on IB exam-style questions, as binomial distributions are a common topic in IB assessments.
Links to ATL Skills:
Thinking skills: Applying probability models to practical problems; analyzing assumptions and limitations.
Research skills: Interpreting results and drawing conclusions from statistical data.
Links to TOK:
How do probabilistic models influence our expectations of real-world events?
What are the strengths and limitations of representing uncertainty mathematically?
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Indhold
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Kernestof:
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Omfang
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Estimeret:
3,00 moduler
Dækker over:
3 moduler
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Særlige fokuspunkter
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Væsentligste arbejdsformer
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Titel
8
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Derivative Calculus
Unit: Differential Calculus
Chapters covered:
Chapter 12, AASL: Rules of Differentiation
Chapter 13, AASL: Properties of Curves
Chapter 14, AASL: Applications of Differentiation
Overview:
This unit introduces the key concepts and techniques of differential calculus using Chapters 12–14 of the AASL Haese Mathematics textbook. Students begin by exploring the concept of the derivative and its interpretation, followed by learning the formal rules of differentiation. The unit then focuses on using calculus to analyze the properties of curves and apply differentiation to practical problems, including optimization and rates of change. These topics develop both conceptual understanding and technical proficiency, laying a foundation for further study of calculus.
Links to ATL Skills:
Thinking skills: Analyzing mathematical change and behavior; applying calculus to real-world contexts.
Communication skills: Interpreting graphical and algebraic representations of change.
Links to TOK:
How does calculus allow us to describe and understand dynamic processes?
To what extent do mathematical models based on calculus accurately reflect the real world?
Just let me know when you’re ready with the next one!
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Indhold
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Kernestof:
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Omfang
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Estimeret:
26,00 moduler
Dækker over:
20 moduler
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Særlige fokuspunkter
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Væsentligste arbejdsformer
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Titel
9
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Integral Calculus
Unit: Integral Calculus and Applications
Chapters covered:
Chapter 15, AASL: Introduction to Integration
Chapter 16, AASL: Techniques for Integration
Chapter 17, AASL: Definite Integrals
Chapter 18, AASL: Kinematics
Overview:
This unit introduces the fundamental concepts of integral calculus. Students begin by exploring the concept of integration and develop technical proficiency in a range of integration techniques. The unit then extends to the application of definite integrals to solve problems involving areas and accumulations. Finally, students apply integral calculus to kinematics, deepening their understanding of motion and rates of change. These chapters support students in building both conceptual and practical mastery of calculus.
Links to ATL Skills:
Thinking skills: Understanding and modeling dynamic processes; solving complex problems using integration.
Communication skills: Translating between graphical, symbolic, and contextual representations.
Links to TOK:
How does calculus extend our ability to model continuous change in the physical world?
In what ways does mathematical abstraction contribute to — or limit — our understanding of motion and change?
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Indhold
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Kernestof:
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Omfang
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Estimeret:
Ikke angivet
Dækker over:
19 moduler
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Særlige fokuspunkter
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Væsentligste arbejdsformer
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