How do you round numbers? It seems a very simple process, but reading the chief examiners' annual reports, this is not in fact the case. This series of handouts helps students become aware of how and when you should round and when you should use scientific notation.

Overview

Lesson 1: Scientific Notation / Answer

Lesson 2: Writing in Scientific Notation / Answer

Kahoot: Significant Figures and Rounding

In this set for DP Mathematics AI subtopic 1.2, students learn about sequences in general and then focus on arithmetic sequences. They earn the specific notation for arithmetic sequences, discover the formulae associated with this type of sequence themselves, and then apply the concepts and formulae to a wide variety of problems.

Overview

Teacher Notes / notes

Lesson 1: Arithmetic Sequences / Solution

Lesson 2: Basic Problem-Solving Solutions / Solution

Lesson 3: Real-World Application Problems / Solution

Lesson 4: Estimation and Sequences Solutions / Solution

In this DP Mathematics AI 1.3 set, students explore geometric sequences and follow an investigation allowing them to arrive at the formulae for geometric sequences themselves. This fun activity is based on an ancient exponential growth problem, which also has links to estimation and scientific notation. Then, a few sets of problems cover basic questions, real-world applications and sigma notation.

Overview

Teacher Notes / Notes

Lesson 1: Investigation / Solution

Lesson 2: Rice Activity / Solution

Lesson 3: Problem Solving / Solution

Lesson 4: Real-World Applications / Solution

Lesson 5: Sigma Notation Solutions / Solution

In this DP Mathematics AI 1.4 highly applicable subtopic, students will learn how geometric sequences extend into financial applications, specifically compound interest on savings, investments and loans. Notes on the basics of these concepts, a large set of exercises to practice their skills, interest activities and investigations are included. Students should observe multiple demonstrations that show the “power of compound interest.”

Overview / Notes

Lesson 1: Compound Interest Problem Solving / Solution / Calculator

Lesson 2: eInvestigation / Solution

Lesson 3: Futurama Interest

These DP Mathematics AI 1.5 materials contain some short explorations to help students discover the key exponent rules. These explorations are followed by questions designed to test their understanding and improve their problem-solving skills, with some scaffolding provided for those who need it. A short task is also included to help students establish the link between exponentials and logarithms.

Overview

Teacher Notes and Handout Solutions

Handouts: 1 / 2 / Ans / 3 / 4A / 4B / 5 / 6 / 7 / 8 / 9

In this DP Mathematics AI 1.7, there are two handouts that students can work through as a class or independently. The first deals with a business start-up and develops skills with the GDC. The second deals with a house mortgage, develops skills with the GDC, and extends skills at using and creating a spreadsheet with calculated columns. Each is meant to take one 80-minute class, and together they cover the entire sub-topic.

Overview

Lesson 1: Annuities (Teacher notes / Student)

Lesson 2: Amortization / Calculator

This DP Mathematics AI 1.8 set of materials explores the sum of infinite geometric sequences. Students work through short and extended response questions and complete a proof of the formula.

Overview

Lesson 1: Infinite Geometric Series Proof (Teacher / Student)

Lesson 2: Infinite Geometric Series Problems (Teacher / Student)

In the DP Mathematics AI 1.8 unit, the activities in this section are divided into two parts: Polynomial Equations and Systems of Linear Equations in up to Three Variables. Solving equations with the help of a graphic display calculator (GDC) is a fundamental technology skill of IB mathematics. This skill is often tested multiple times during the exams.

Overview

Lesson 1: Beyond the Quadratic Formula (Teacher / Student)

Lesson 2: Systems of Linear Equations up to Three Variables (Teacher / Student)

This DP Mathematics AI HL 1.9 subtopic continues the introduction to logarithms, where only the definition of a logarithm was given. Students learn three laws or rules of logarithms and then use and practice them in various ways. These widen the scope of the number of logarithms that can be evaluated and the number of log equations that can now be solved.

Overview

Subtopic Teacher Notes

Lesson 1: Basic Rules of Logarithms / Solution

Lesson 2: Log Rules Investigation

Lesson 3: Logarithms Green/Blue/Black / Solution

In this DP Mathematics AI 1.10 set, students will practice working with expressions and equations involving rational exponents in a (hopefully) fun way. As they come up with their answers, they unlock the punchlines to the math puns/jokes.

Overview

Lesson 1: Puzzle / Solution

This DP Mathematics AI AHL 1.11 investigation extends the geometric sequence concepts covered in 1.03 to find the sum of infinitely many terms. This goes into more profound aspects of “limits,” but the result is a relatively simple formula. Having a finite sum of infinitely many terms is surprising for many students.

Overview

Subtopic Notes

Lesson 1: Infinite Series Investigation / Solution

Lesson 2: Koch Snowflake Activity 

Lesson 3: Infinite Geometric Series General Exercises / Solution

This DP Mathematics AI AHL 1.12 set has two activities: 20 Questions to Become a Master and Unseen Roots of Some Parabolas. Activity 1 contains 20 different short-response (Paper 1 style) questions about the main parts of the content, ranging in difficulty. Activity 2 is a Paper 3 skill-builder activity requiring prolonged responses and sustained reasoning.

Overview

Lesson 1: 20 Questions to Become a Master ( A / B)

Lesson 2: Unseen Roots of Some Parabolas / Solution

In this DP Mathematics AI 1.13 set, students practice converting between different forms of complex numbers and then using these forms to multiply and divide easily. Students apply a real-life context for complex numbers and explore some ideas contained within electronics. Students also explore and discover the rules behind multiplication by complex numbers and find out the links between complex numbers and geometry.

Overview

Unit Plan

Lesson 1: Converting Complex Number Forms / Solution

Lesson 2: Electronics / Solution

Lesson 3: Geometrical Connections / Solution

In this DP Mathematics AI 1.14 unit, students investigate these three tasks designed to build an understanding of matrices and their applications. Students should be encouraged to compare and contrast matrix algebra with "normal" algebra as they work through the various tasks. In particular, the second task will allow students to check which algebraic properties (commutative, associative, etc.) still hold for matrix algebra.

Overview

Lesson 1: Operations with Matrices (Teacher / Student)

Lesson 2: Properties of Matrix Operations (Teacher / Student)

Lesson 3: Cryptography and Matrices (Teacher / Student)

In this DP Mathematics AI 1.15 teaching materials set, students explore two tasks designed to build an understanding of eigenvalues and eigenvectors. The first task helps students find and verify eigenvalues and eigenvectors for a given matrix and see their geometric interpretation. The second task allows students to apply their knowledge to determine Fibonacci numbers and the golden ratio using eigenvalues, eigenvectors and diagonalization of matrices.

Overview

Lesson 1: Intro to Eigenvalues and Eigenvectors / Solution

Lesson 2: Fibonacci and Eigenvalues / Solution