This image summarizes the four main set operations. Union, intersection, difference, and complement. These concepts are applied in the World Cup Venn diagram below to classify countries based on their tournament performance.
Individual Geogebra Journal book
Need to add Illustration, Interactive Exercise, and/or an exploration based topic.
Table of Contents
- Sets
- 2026 Fifa World Cup: Sets Operations with Venn diagram
- Logic exercise for exploring logical statements
- Truth tables: Logical statements
- Factorials
- Understanding Factorials (n!)
- The division Algorithm
- Understanding the Division Algorithm
- Set Notation
- Set Notation Using Geogebra
- GCD AND LCM
- Greatest Common Divisor (GCD) and Least Common Multiple (LCM)
- Pascal's Triangle & Fibonacci project
- Fibonacci numbers and Pascal's Triangle
- Modular addition and multiplication
- Modular Addition and Multiplication
2026 Fifa World Cup: Sets Operations with Venn diagram
2026 Fifa World Cup: Illustrating set operations with Venn diagrams
Objective: This GeoGebra illustration demonstrates set operations using countries from the 2026 Fifa World Cup. The Venn diagram shows relationships between teams that qualified for the knockout stage, won their group, and finished the group stage undefeated. [br][br]Teachers can use this applet to introduce set operations such as unions, intersections, and complements by having students identify which countries belong to each region of the Venn diagram.
Set Definitions
Universal Set (U): All 48 countries that participated in the 2026 Fifa world cup.[br][br]Set A: Countries that qualified for the knockout stage. [br][br]Set B: Countries that won their group.[br][br]Set C: Countries that finished the group stage undefeated.[br][br]
Truth tables: Logical statements
Objective: Learn how truth tables determine the truth value of logical statements by exploring conjunction "And", disjunction "Or", negation "Not", implication "If.. Then". [br][br][br]P: It is raining.[br][br]Q: I bring an umbrella.
Description of Applet
This applet is showing a truth table for two propositions, P and Q. In this example, P represents "It is raining", and Q represents " I bring an umbrella." The table shows the truth values of not p and not p or q for every possible combination of truth values. It helps students understand how logical operators affect the truth of a statement. [br][br]Classroom use:[br][br]Students can use this applet to predict truth values of the logical expressions, and then compare their answers with the completed truth table.
Understanding Factorials (n!)
Objective: Learn how factorial notation is used to count arrangements and compute products of positive integers.
Factorials (n!)
Definition:[br]n! = n x (n - 1) x (n - 2) x (n - 3) x ...x 2 x 1 [br][br]Example: 3! = 3 x (3 - 1) x 1 = 6
Calculate the value of 5!
This applet introduces factorial notation and allows students to practice calculating factorials through a multiple-choice question.[br][br]Teachers can use this activity to introduce factorial notation and counting principles. Students solve the factorial problem and then review the explanation to reinforce their understanding. [br][br]How to use Applet?[br][br]1. Read the definition of a factorial. [br]2. Study the worked example. [br]3. Solve the multiple-choice question. [br]4. Check the explanation to verify your answer.
Explanation: [br]The correct answer is C. 120[br]5! = 5 x 4 x 3 x 2 x 1= 120 [br]or [br]5! = 5 x (5 - 1) x (5 - 2) x (5 - 3) x 1 = 120
Understanding the Division Algorithm
The Division Algorithm
The Division Algorithm: a = bq + r [br]where: [br]a = dividend [br]b = divisor [br]q = quotient [br]r = remainder with 0 less than or equal to r less than b [br]
Understanding the Division Algorithm
Objective: Learn how the Division Algorithm expresses a dividend as the product of a divisor and quotient plus a remainder. [br][br]Example [br]22 / 5[br][br]Dividend (a) = 22[br]Divisor (b) = 5[br]Quotient (q) = 4[br]Remainder (r) = 2[br][br]22 = 5 (4) + 2 [br]
Multiple Choice Question
Use the division Algorithm, what is the remainder when 23 is divided by 4?
Explanation: 23 = 4(5) + 3[br]The quotient is 5 and the remainder is 3. Therefore, C is the correct answer[br][br]This applet explains the Division algorithm by showing how a number can be divided into a quotient and a remainder. A worked example and a practice question is included to help students understand how the Division Algorithm works. [br][br]Classroom use: Students can use the activity to learn and practice the Division Algorithm. They can look at the example firs, solve the practice question, then check the explanation to see if they got the correct answer. This helps build their confidence.
Set Notation Using Geogebra
Objective: Students will learn how to read and write set notation and identify common set operations using mathematical notation. [br][br]Sets are collections of distinct objects. [br]Student will use the examples below to practice reading mathematical notation. [br][br]Example sets: A = {1, 2, 3, 4, 5} B = {3, 4, 5, 6, 7}[br]
Answers to problems
Question 1 answer: A intersect B is {3, 4, 5} [br][br]Question 2 answer: A union B {1, 2, 3, 4, 5, 6, 7}[br][br]Question 3 answer: The difference between A - B is {1, 2}[br][br][br]This Applet is an interactive exercise that helps students practice set notation. It uses two examples sets and asks students to find the intersection, union and difference between the sets. The activity helps students become more familiar with common symbols used in discrete mathematics. [br][br][br]This activity can be used in a classroom after students learn the basic of sets. Students can work through the three questions on their own or with a partner and then compare their answers. It is a simple way to practice reading and using set notation before moving on to more challenging problems.
Greatest Common Divisor (GCD) and Least Common Multiple (LCM)
Interactive exercise
Objective: Students will practice finding the Greatest Common Divisor (GCD) and the Least common Multiple (LCM) of two numbers. [br][br]The greatest common Divisor (GCD) is the largest number that divides two numbers evenly. The Least Common Multiple (LCM) is the smallest positive number that both numbers share as a multiple. [br][br]EXAMPLE NUMBER 24 AND 36 [br][br]1) Find the GCD of 24 and 36.[br]Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24[br]Factors of 36 is = 1, 2, 3, 4, 6, 9, 12, 18, 36[br][br]Answer is 12[br][br]2) Find the LCM of 24 and 36.[br][br]Multiples of 24: 24, 48, 72, 96, 120, ....[br]Multiples of 36: 36, 72, 108, 144, ...[br][br]Answer is 72[br][br]
What is the Greatest Common Divisor (GCD) of 10 and 12?[br]
What is the Least Common Multiple (LCM) of 15 and 20?[br]
What is the Greatest Common Divisor (GCD) of 24 and 36?[br]
This applet is an interactive exercise that helps students practice finding the Greatest Common Divisor (GCD) and the Least Common Multiple (LCM) of two numbers. [br]Students solve each problem and compare their answers to strengthen their understanding of these concepts. [br][br][br]This activity can be used to after introducing GCD and LCM in class. Students can complete the questions independently or work with a partner to explain how they found each answer. The activity reinforces problem-solving skills and prepares students for more advanced number theory topics.
Fibonacci numbers and Pascal's Triangle
Use the Fibonacci above to answer the questions below. Remember that each number is found by adding the two numbers before it.
What is the next number in the Fibonacci sequence?[br]0, 1, 1, 2, 3, 5, 8, 13, ?
What number is missing?[br]0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ?, 89....
Which rule describes the Fibonacci sequence?
Pascal's Triangle
Use the Pascal's Triangle above to answer the following questions below. Remember that each number inside the triangle is found by adding the two numbers directly above it. [br]
What number is missing from this row of Pascal's Triangle?[br]1, 5, 10, ?, 5, 1
What is the next row after [br]1, 3, 3, 1?
Description of the Applet:[br][br]This interactive exercise helps students understand Fibonacci numbers and Pascal’s Triangle. The pictures show the patterns, and the questions allow students to practice what they learned.[br][br]Classroom use:[br][br]This activity can be used to introduce or review Fibonacci numbers and Pascal’s Triangle. Students can look at the examples and answer the questions to check their understanding.[br][br]What the Applet does is give students a visual of both concepts and multiple-choice questions to practice. It helps students recognize how the numbers are created and identify patterns.[br]
Modular Addition and Multiplication
Modular arithmetic is based on the remainder after division. To solve each problem, first add or multiply the numbers, then divide by the modulus and find the remainder.[br][br]For example: 17 (mod 5) =2 [br]it is because when we do 17/5 it leaves a remainder of 2. [br][br][br]
What is 7 + 8 (mod 5) ?
Multiplication
What is 4 x 5 (mod 6) ?
Addition
What is 9 + 7 (mod 6)
This applet helps students practice modular addition and multiplication using a picture and interactive questions. It shows how to find the remainder and understand modular arithmetic.[br][br]Classroom use:[br][br]This activity can be used in class to introduce or review modular arithmetic. Students can use the picture to understand the concept and answer the questions to check their understanding.[br]