Out Of The Box Thinking Through Mathematics
Free Online Course by IIT Madras Pravartak Technologies Foundation.
Certification Exam registration closes on 7th November, 2024.
Certification Exam is on 22nd December, 2024.
Levels Of OOBT
Level - 1: Eligibility – (School Class 5 and above)
Level - 3: Eligibility – (School Class 9 and above)
Level - 2: Eligibility – (School Class 7 and above)
Level - 4: Eligibility – (School Class 11 and above)
By serving in this pivotal role, an OOBT SPOC plays a crucial part in fostering innovative thinking, enhancing student performance, and building a bridge between the educational institution and IIT Madras.
Out of the Box Thinking through (OOBT)
Mathematics
About the Course by Prof. V. Kamakoti, Director, IIT Madras
Process
Apart from recorded lecture sessions, each level provides periodic assignments and answers.
Eligibility
Familiarity with basic concepts and ready mindset for learning non-routine problem-solving skills.
By serving in this pivotal role, an OOBT SPOC plays a crucial part in fostering innovative thinking, enhancing student performance, and building a bridge between the educational institution and IIT Madras.
Registration & Certification
- Course is free online.
- Course Registration will be open for each level every year.
- Recorded lectures are posted every week during the ten-week course.
- Students should go through the lectures before practicing the assignments posted biweekly.
- Students desiring certification must opt for the final exam during the Exam Registration process that carries a nominal fee.
- Final exam will be a proctored one and conducted at centres in select cities across India.
- Certification is based on evaluation of the same.
- Grade certificate will be issued by IIT Madras Pravartak only for students who take the exam and get grades.
Topics in Level 1 - Out Of The Box Thinking
Puzzles Math, Calendar Math, Odd and Even, Tuning Technique, Number Trip Game, Doing and Undoing, Visual Maths, Who am I?, Divisibility Blocks, Missing Digits, Follow the Sequence!, Mask Math, Cow Grass Theory.
Total number of Topics: 13. Net Lecture Duration: 20 hours.
About the Course by Prof. V. Kamakoti, Director, IIT Madras
Puzzles involve two aspects: definite and suspense. The challenge is to break the suspense using the definite paths. The order of using the definite paths, enhances logical thinking and concentration. The procedure for solving the puzzles is broken into small exercises which focus on the important steps in the solution. This helps in solving any complex puzzle of the same genre.
Outcomes: Concentration, Topic-specific knowledge, Problem Solving skills, Memory, Enhancement of self-esteem.
Everyone is familiar with the ordered arrangement of date numbers in rows and columns of a month in a calendar. The arrangement has many interesting properties based on the repetition of the week-days. Based on these many interesting problems and exercises are discussed.
Outcomes: Pattern-recognition, Periodicity, Identifying properties thereof.
As in computers where binary logic is used, in arithmetic we have “odd and even” as a powerful concept, effectively used to solve several mathematical problems. Here we focus on simple but powerful application of “odd and even” theory.
Outcomes: Proof technique in mathematics introduced!
To watch a sports event, we first switch on the TV, go to sports channels, pick the channel broadcasting the specific sports event and then finetune the brightness, volume to make it most enjoyable. Here we see that the required conditions conducive to our enjoyment are satisfied one by one. Similarly, certain class of mathematics problems can be solved, by satisfying the required conditions one by one in a chosen order. Such techniques can be termed as Tuning Techniques.
Outcomes: Stepwise logical procedure, Logical flow plan.
We have a word game wherein we travel from a source word to destination word of the same length, by changing one letter at a time with the intermediate steps being valid words. Here we have a number game where we travel from a source number to a destination number through intermediary numbers satisfying some conditions. The travel might involve factors or multiples or some other mathematical operations, where the intermediate numbers may be condition specific.
Outcomes: Decision making, Familiarity and speed of Math operations.
It is a simple ladder technique for solving certain algebraic equations, popularized by the legendary Math Educator (late) Sri P. K. Srinivasan. From unknown variable to the destination, the operations involved in the forward direction, have to be retraced in the reverse order, to reach the variable from the destination. Hence the name “doing and undoing”.
Outcomes: Avoidance of the use of variables for solving competition questions, Developing arithmetic manipulation skill over algebra.
Here we visualize a given problem situation and interpret in different ways to arrive at a solution. For example, think of proof without words, which effectively uses visual medium to prove identities or solve problems. We use combinatorial ideas of counting in different ways also.
Outcomes: Visual interpretation, Counting in different ways, Pattern recognition, Dimensional enhancement, and generalization.
An object, may be a number or geometrical figure, gives its characteristics and properties, and queries who am I? The process of assessing and analysing the properties to arrive at the answer, is what makes this an interesting technique.
Outcomes: Analysis of the properties, Use of characteristics to aid in solution procedure.
This involves problems typically with large number of digits like hundreds and thousands of digits. We solve for such numbers with certain required properties. This is typically solved, by using blocks of small number of digits and manipulating the blocks, to arrive at the properties required in the large number. The manipulations used, depend on the properties required.
Outcomes: Arithmetic properties, Divisibility rules, suitable blocking.
Numbers with some digits missing or hidden will be given. Need to solve so that the completed number satisfies the properties required. Known rules of arithmetic must be used to arrive at the solution.
Outcomes: Arithmetic properties, Divisibility rules.
A sequence of numbers is provided, which is generated following certain rules which are given. We emphasise the generating rule, as a given finite sequence can be extended in many different ways. This helps in learning many problem-solving techniques by using arithmetic translation, scaling etc. Further general properties of the terms can also be studied.
Outcomes: Pattern recognition leading to arithmetic translation and scaling, recognising inherent properties in the sequence.
This is also called alphamatics. Here alphabets take the place of digits, where different digits are represented by different alphabets. Here properties of addition, carryover, multiplication are used intelligently.
Outcomes: Arithmetic skills development, Quick Analysis.
This can be effectively used in Geometric length inequalities, like polygonal inequalities. What is the shortest route for a cow to reach grass?
Outcomes: Geometric visualization, Estimating ability
Topics in Level 2 - Out Of The Box Thinking
Passenger and Compartment, Soccer Score Table, Frog Jumping Theory, Basic Counting, Story Math, Tabulation with Proper Header, Cows and Bulls, Dissection of Polygons, Sports Algebra, Post Box Algebra, Basic Geometry, Ruled Note-Book and Percentage, Area and Perimeter
Total number of Topics: 13. Net Lecture Duration: 20 hours.
OOBT Level 2
Puzzles involve two aspects: definite and suspense. The challenge is to break the suspense using the definite paths. The order of using the definite paths, enhances logical thinking and concentration. The procedure for solving the puzzles is broken into small exercises which focus on the important steps in the solution. This helps in solving any complex puzzle of the same genre.
Outcomes: Concentration, Topic-specific knowledge, Problem Solving skills, Memory, Enhancement of self-esteem.
Everyone is familiar with the ordered arrangement of date numbers in rows and columns of a month in a calendar. The arrangement has many interesting properties based on the repetition of the week-days. Based on these many interesting problems and exercises are discussed.
Outcomes: Pattern-recognition, Periodicity, Identifying properties thereof.
As in computers where binary logic is used, in arithmetic we have “odd and even” as a powerful concept, effectively used to solve several mathematical problems. Here we focus on simple but powerful application of “odd and even” theory.
Outcomes: Proof technique in mathematics introduced!
To watch a sports event, we first switch on the TV, go to sports channels, pick the channel broadcasting the specific sports event and then finetune the brightness, volume to make it most enjoyable. Here we see that the required conditions conducive to our enjoyment are satisfied one by one. Similarly, certain class of mathematics problems can be solved, by satisfying the required conditions one by one in a chosen order. Such techniques can be termed as Tuning Techniques.
Outcomes: Stepwise logical procedure, Logical flow plan.
We have a word game wherein we travel from a source word to destination word of the same length, by changing one letter at a time with the intermediate steps being valid words. Here we have a number game where we travel from a source number to a destination number through intermediary numbers satisfying some conditions. The travel might involve factors or multiples or some other mathematical operations, where the intermediate numbers may be condition specific.
Outcomes: Decision making, Familiarity and speed of Math operations.
It is a simple ladder technique for solving certain algebraic equations, popularized by the legendary Math Educator (late) Sri P. K. Srinivasan. From unknown variable to the destination, the operations involved in the forward direction, have to be retraced in the reverse order, to reach the variable from the destination. Hence the name “doing and undoing”.
Outcomes: Avoidance of the use of variables for solving competition questions, Developing arithmetic manipulation skill over algebra.
Here we visualize a given problem situation and interpret in different ways to arrive at a solution. For example, think of proof without words, which effectively uses visual medium to prove identities or solve problems. We use combinatorial ideas of counting in different ways also.
Outcomes: Visual interpretation, Counting in different ways, Pattern recognition, Dimensional enhancement, and generalization.
An object, may be a number or geometrical figure, gives its characteristics and properties, and queries who am I? The process of assessing and analysing the properties to arrive at the answer, is what makes this an interesting technique.
Outcomes: Analysis of the properties, Use of characteristics to aid in solution procedure.
This involves problems typically with large number of digits like hundreds and thousands of digits. We solve for such numbers with certain required properties. This is typically solved, by using blocks of small number of digits and manipulating the blocks, to arrive at the properties required in the large number. The manipulations used, depend on the properties required.
Outcomes: Arithmetic properties, Divisibility rules, suitable blocking.
Numbers with some digits missing or hidden will be given. Need to solve so that the completed number satisfies the properties required. Known rules of arithmetic must be used to arrive at the solution.
Outcomes: Arithmetic properties, Divisibility rules.
A sequence of numbers is provided, which is generated following certain rules which are given. We emphasise the generating rule, as a given finite sequence can be extended in many different ways. This helps in learning many problem-solving techniques by using arithmetic translation, scaling etc. Further general properties of the terms can also be studied.
Outcomes: Pattern recognition leading to arithmetic translation and scaling, recognising inherent properties in the sequence.
This is also called alphamatics. Here alphabets take the place of digits, where different digits are represented by different alphabets. Here properties of addition, carryover, multiplication are used intelligently.
Outcomes: Arithmetic skills development, Quick Analysis.
This can be effectively used in Geometric length inequalities, like polygonal inequalities. What is the shortest route for a cow to reach grass?
Outcomes: Geometric visualization, Estimating ability
Topics in Level 3 - Out Of The Box Thinking
Total number of Topics: 20. Net Lecture Duration: 30 hours.
OOBT Level 3
Puzzles involve two aspects: definite and suspense. The challenge is to break the suspense using the definite paths. The order of using the definite paths, enhances logical thinking and concentration. The procedure for solving the puzzles is broken into small exercises which focus on the important steps in the solution. This helps in solving any complex puzzle of the same genre.
Outcomes: Concentration, Topic-specific knowledge, Problem Solving skills, Memory, Enhancement of self-esteem.
Everyone is familiar with the ordered arrangement of date numbers in rows and columns of a month in a calendar. The arrangement has many interesting properties based on the repetition of the week-days. Based on these many interesting problems and exercises are discussed.
Outcomes: Pattern-recognition, Periodicity, Identifying properties thereof.
As in computers where binary logic is used, in arithmetic we have “odd and even” as a powerful concept, effectively used to solve several mathematical problems. Here we focus on simple but powerful application of “odd and even” theory.
Outcomes: Proof technique in mathematics introduced!
To watch a sports event, we first switch on the TV, go to sports channels, pick the channel broadcasting the specific sports event and then finetune the brightness, volume to make it most enjoyable. Here we see that the required conditions conducive to our enjoyment are satisfied one by one. Similarly, certain class of mathematics problems can be solved, by satisfying the required conditions one by one in a chosen order. Such techniques can be termed as Tuning Techniques.
Outcomes: Stepwise logical procedure, Logical flow plan.
We have a word game wherein we travel from a source word to destination word of the same length, by changing one letter at a time with the intermediate steps being valid words. Here we have a number game where we travel from a source number to a destination number through intermediary numbers satisfying some conditions. The travel might involve factors or multiples or some other mathematical operations, where the intermediate numbers may be condition specific.
Outcomes: Decision making, Familiarity and speed of Math operations.
It is a simple ladder technique for solving certain algebraic equations, popularized by the legendary Math Educator (late) Sri P. K. Srinivasan. From unknown variable to the destination, the operations involved in the forward direction, have to be retraced in the reverse order, to reach the variable from the destination. Hence the name “doing and undoing”.
Outcomes: Avoidance of the use of variables for solving competition questions, Developing arithmetic manipulation skill over algebra.
Here we visualize a given problem situation and interpret in different ways to arrive at a solution. For example, think of proof without words, which effectively uses visual medium to prove identities or solve problems. We use combinatorial ideas of counting in different ways also.
Outcomes: Visual interpretation, Counting in different ways, Pattern recognition, Dimensional enhancement, and generalization.
An object, may be a number or geometrical figure, gives its characteristics and properties, and queries who am I? The process of assessing and analysing the properties to arrive at the answer, is what makes this an interesting technique.
Outcomes: Analysis of the properties, Use of characteristics to aid in solution procedure.
This involves problems typically with large number of digits like hundreds and thousands of digits. We solve for such numbers with certain required properties. This is typically solved, by using blocks of small number of digits and manipulating the blocks, to arrive at the properties required in the large number. The manipulations used, depend on the properties required.
Outcomes: Arithmetic properties, Divisibility rules, suitable blocking.
Numbers with some digits missing or hidden will be given. Need to solve so that the completed number satisfies the properties required. Known rules of arithmetic must be used to arrive at the solution.
Outcomes: Arithmetic properties, Divisibility rules.
A sequence of numbers is provided, which is generated following certain rules which are given. We emphasise the generating rule, as a given finite sequence can be extended in many different ways. This helps in learning many problem-solving techniques by using arithmetic translation, scaling etc. Further general properties of the terms can also be studied.
Outcomes: Pattern recognition leading to arithmetic translation and scaling, recognising inherent properties in the sequence.
This is also called alphamatics. Here alphabets take the place of digits, where different digits are represented by different alphabets. Here properties of addition, carryover, multiplication are used intelligently.
Outcomes: Arithmetic skills development, Quick Analysis.
This can be effectively used in Geometric length inequalities, like polygonal inequalities. What is the shortest route for a cow to reach grass?
Outcomes: Geometric visualization, Estimating ability
Topics in Level 4 - Out Of The Box Thinking
Chasing the Ratios, What’s your Chance? Transformation Geometry, The Graphman (Function), Coloring Math, Friendly Trigonometry, Dr Calculus, Playing the Series, Gate way to Conic Caves, Vector – The powerful arrow, Travel with Coordinates! Is it Possible? Imagine the Complex! Induction – The Relayman, The Art of Counting-1!, The Art of Counting-2!, Driving Algebra, Recursion, Collecting Special Numbers, Mixed Bag.
Total number of Topics: 20. Net Lecture Duration: 30 hours.
OOBT Level 4
Puzzles involve two aspects: definite and suspense. The challenge is to break the suspense using the definite paths. The order of using the definite paths, enhances logical thinking and concentration. The procedure for solving the puzzles is broken into small exercises which focus on the important steps in the solution. This helps in solving any complex puzzle of the same genre.
Outcomes: Concentration, Topic-specific knowledge, Problem Solving skills, Memory, Enhancement of self-esteem.
Everyone is familiar with the ordered arrangement of date numbers in rows and columns of a month in a calendar. The arrangement has many interesting properties based on the repetition of the week-days. Based on these many interesting problems and exercises are discussed.
Outcomes: Pattern-recognition, Periodicity, Identifying properties thereof.
As in computers where binary logic is used, in arithmetic we have “odd and even” as a powerful concept, effectively used to solve several mathematical problems. Here we focus on simple but powerful application of “odd and even” theory.
Outcomes: Proof technique in mathematics introduced!
To watch a sports event, we first switch on the TV, go to sports channels, pick the channel broadcasting the specific sports event and then finetune the brightness, volume to make it most enjoyable. Here we see that the required conditions conducive to our enjoyment are satisfied one by one. Similarly, certain class of mathematics problems can be solved, by satisfying the required conditions one by one in a chosen order. Such techniques can be termed as Tuning Techniques.
Outcomes: Stepwise logical procedure, Logical flow plan.
We have a word game wherein we travel from a source word to destination word of the same length, by changing one letter at a time with the intermediate steps being valid words. Here we have a number game where we travel from a source number to a destination number through intermediary numbers satisfying some conditions. The travel might involve factors or multiples or some other mathematical operations, where the intermediate numbers may be condition specific.
Outcomes: Decision making, Familiarity and speed of Math operations.
It is a simple ladder technique for solving certain algebraic equations, popularized by the legendary Math Educator (late) Sri P. K. Srinivasan. From unknown variable to the destination, the operations involved in the forward direction, have to be retraced in the reverse order, to reach the variable from the destination. Hence the name “doing and undoing”.
Outcomes: Avoidance of the use of variables for solving competition questions, Developing arithmetic manipulation skill over algebra.
Here we visualize a given problem situation and interpret in different ways to arrive at a solution. For example, think of proof without words, which effectively uses visual medium to prove identities or solve problems. We use combinatorial ideas of counting in different ways also.
Outcomes: Visual interpretation, Counting in different ways, Pattern recognition, Dimensional enhancement, and generalization.
An object, may be a number or geometrical figure, gives its characteristics and properties, and queries who am I? The process of assessing and analysing the properties to arrive at the answer, is what makes this an interesting technique.
Outcomes: Analysis of the properties, Use of characteristics to aid in solution procedure.
This involves problems typically with large number of digits like hundreds and thousands of digits. We solve for such numbers with certain required properties. This is typically solved, by using blocks of small number of digits and manipulating the blocks, to arrive at the properties required in the large number. The manipulations used, depend on the properties required.
Outcomes: Arithmetic properties, Divisibility rules, suitable blocking.
Numbers with some digits missing or hidden will be given. Need to solve so that the completed number satisfies the properties required. Known rules of arithmetic must be used to arrive at the solution.
Outcomes: Arithmetic properties, Divisibility rules.
A sequence of numbers is provided, which is generated following certain rules which are given. We emphasise the generating rule, as a given finite sequence can be extended in many different ways. This helps in learning many problem-solving techniques by using arithmetic translation, scaling etc. Further general properties of the terms can also be studied.
Outcomes: Pattern recognition leading to arithmetic translation and scaling, recognising inherent properties in the sequence.
This is also called alphamatics. Here alphabets take the place of digits, where different digits are represented by different alphabets. Here properties of addition, carryover, multiplication are used intelligently.
Outcomes: Arithmetic skills development, Quick Analysis.
This can be effectively used in Geometric length inequalities, like polygonal inequalities. What is the shortest route for a cow to reach grass?
Outcomes: Geometric visualization, Estimating ability