This DP Mathematics AI 3.3 set has three activities. The first activity focuses specifically on bearing problems and their real-life applications. The second activity covers the concepts of applying sine rule and Pythagorean rule in different situations, angle of elevation and depressions. The third activity covers the concepts of applying 3D trigonometry and Pythagorean rule in different situations.  

Overview

Lesson 1: Bearing Problems and the Princes’ Islands of Istanbul / Solution

Lesson 2: The Master of Trigonometry—Archerfish / Solution

Lesson 3: Secrets of the Great Pyramid of Giza / Solution

The DP Mathematics 3.4 subtopic on sectors of circles begins with an engaging Desmos activity. After investigating the formula for the area of a sector, students use it in application-style scenarios. Students find arc lengths and areas and use the formulae given in the formula booklet to find other variables. For HL students, this subtopic may be taught concurrently with subtopic 3.7.

Overview

Lesson 1: The Area Is / Solution

Lesson 2: Arcs and Sectors Applications / Solution

Lesson 3: Goal Free Problem / Solution

This DP Mathematics AI 3.5 set directs students to explore a perpendicular bisector's properties and the method to calculate its equation on the analytic plane. First, the PowerPoint file “Perpendicular Bisectors” will be used as a cognitive activator. It aims to create an understanding of a perpendicular bisector and how it can be used in real life. Then, students are directed to construct the perpendicular bisector using the dynamic geometry software GeoGebra.

Overview

Lesson 1: Constructing the Perpendicular Bisector of a Line Segment (Teacher / Student)

Lesson 2: Finding the Equation of the Perpendicular Bisector of a Line (Teacher / Student)

This DP Mathematics AI 3.6 teaching materials set is designed to enhance understanding and applications of Voronoi diagrams. These six learning activities demonstrate how Voronoi diagrams can be used in various real-world scenarios, from weather prediction to emergency response time. There are also activities to review perpendicular bisectors.  

Overview

Teacher Notes: Unit prep

Lesson 1: Definition of a Voronoi Diagram (Teacher / Student)

Lesson 2: Constructing Simple Voronoi Diagrams

Lesson 3: Using the Power Algorithms

Lesson 4: Predicting from Voronoi Diagrams

Lesson 5: Response Times and Voronoi Diagrams

Lesson 6: Rain Prediction and Voronoi Diagrams

Lesson 7: Review Activity

These DP Mathematics AI HL 3.7 teaching materials introduce students to the concept of a radian, building on prior knowledge of working with sectors and arcs of a circle using radian measures. Once students understand why we use a radian measure as a more intuitive measure of an angle, they discover a direct application to finding the area and arc of a sector by using the formulae where the angle is in radians.

Overview / Notes

Lesson 1: Radian Measure Exercises / Solution / Teacher Guidance

This DP Mathematics AI HL 3.8 activity consists of Handout 1 on Rectangular or Trapezoidal Mini Garden Design and Handout 2 on Designing a Motif Using the Sine-Ambiguous Case. In this set, students learn how to use trigonometric equations in architectural design and art by going beyond the classical patterns. For the first time, students learn the basics of three-dimensional graphic drawing step by step. It ignites the creativity of students who will do IA.

Overview

Lesson 1: Rectangular or Trapezoidal Mini-Garden Design / Solution

Lesson 2: Designing Motifs by Using the Sine-Ambiguous Case / Solution

These DP Mathematics AHL 3.9 teaching materials include two tasks designed to build an understanding of transformations with matrices. The first task helps build knowledge of basic transformations using matrices and area in terms of the determinant of the matrix. The second task allows students to apply their knowledge to create the Pythagorean tree fractal and analyse branches of the tree using combinations of matrix transformations.

Overview

Lesson 1: Matrix Transformations / Solution

Lesson 2: Pythagorean Trees / Solution

This DP Mathematics AI 3.10 resource provides brief notes and questions to familiarise students with vectors, scalars and rescaling vectors. It includes links to online resources such as videos and GeoGebra animations. Students should use such resources to better visualize the various vector concepts.

Overview

Lesson 1: Introduction to Vectors / Solution

This DP Mathematics AI HL 3.11 set has two activities: In 15 Questions to Become a Master, there are 15 different Paper 1-style short-response questions about vector equations of a line in 2 and 3D. The Six Different Lines Pop-Up Quiz is a 2-page pop-up quiz that measures students’ ability to form equations and comment on these equations by using the given initial conditions and hints given in the questions.

Overview

Lesson 1: 15 Questions to Become a Master / Solution

Lesson 2: Six Different Lines Pop Up Quiz / Solution

In this DP Mathematics AL HL 3.12 set, students explore the link between motion in 2 and 3 dimensions and vectors. Students will explore a projectile motion investigation, apply variable motion to Lissajous Curves, and model drone flight. Content covered includes vector applications to kinematics, modelling linear motion with constant velocity in two and three dimensions and motion with variable velocity in two dimensions.

Overview

Lesson 1: Flying Drones / Solution

Lesson 2: Lissajous Curves / Solution

Lesson 3: Projectile Motion Investigation / Solution

This DP Mathematics AI HL 3.13 resource provides brief notes and questions to familiarise students with two types of vector products. It includes links to online resources such as videos and GeoGebra animations. Students should use such resources to better visualize the various vector concepts. The resource also includes a small selection of questions that are woven into the notes. Students can discuss those in pairs or small groups.

Overview

Lesson 1: Dot and Cross Products / Solution

In this DP Mathematics AI HL 3.14 unit, the first two tasks introduce the vocabulary and most used diagrams in graph theory, which is the study of graphs that have been drawn to represent relationships between two or more objects. A worksheet is provided to give students different contexts to draw specific graphs or diagrams. A graph in this context is made up of vertices which are connected by two vertices asymmetrically. Graphs are one of the principal objects of study in discrete mathematics.

Overview

Unit Plan: Graph Theory Introduction

Lesson 1: Graph Theory Terminology / Solution

Lesson 2: Graph Theory Worksheet / Solution

Lesson 3: The Handshake Problem

This DP Mathematics AI AHL 3.15 set builds on the unit started in AHL 3.14. Two handouts allow the student to practice walks and weighted graphs. Matrices are also used in this topic as another form to represent data. Finally, students they can explore as a research assignment. For related work, continue this unit in AHL 3.16.

Overview

Lesson 1: Walks Worksheet (Teacher / Student)

Lesson 2: Weighted Adjacency Tables (Teacher / Student)

Lesson 3: How Google's PageRank Algorithm Works (Teacher / Student)

In this DP Mathematics AI HL 3.16 unit, students encounter discrete mathematics, often an unfamiliar topic to many of them. After learning the properties of Eulerian trails and circuits, plus Hamiltonian paths and cycles, they can apply their knowledge to real-life problems, such as the Königsberg Bridge, Chinese Postman and Travelling Salesman problems.

Overview

Lesson 1: Eulerian Trails / Solution

Lesson 2: Hamiltonian Paths / Solution

Lesson 3: The Chinese Postman / Solution

Lesson 4: The Königsberg Bridge Problem / Solution