Math circle activities
About Math Circle
The questions, tasks and explorations in Maths Circles develop students’ mathematical reasoning and expand their mathematical curiosity, at the same time as refining their technical knowledge and skills.
In a Maths Circle, a small group of students come together regularly with an experienced, knowledgeable mentor to grapple with intriguing questions, to discover and explore exciting ideas, and to learn to think like advanced mathematicians.
Maths Circles are out-of-class maths clubs. Each Circle is small: ideally, at least one mentor for every six students.
In Maths Circles,
👉 students develop their knowledge of significant topics in mathematics;
👉 students engage with tasks that they find challenging but satisfying;
👉 students follow a coherent and carefully sequenced curriculum;
👉 students learn and develop mathematically by the conversations they have about the tasks they are engaging with: either individual conversations with their mentor, or conversations with their peers that are moderated and steered by the mentor;
👉 mentors guide students to understand what constitutes, verbally and on paper, “good mathematics”;
👉 sometimes students engage with tasks individually, sometimes they co-operate in pairs or groups.
Math circles are meeting between teacher and a group of students where they work on problem solving. These gatherings take place outside the regular school class and these meetings have a huge impact.
WHY IS THE MATH CIRCLE?
The Mathematics circle helps students think critically, solve problems and be creative while learning different Math ideas. By joining Math circle, students become more confident in their Math skills and understand Math better.
LIST OF THE STUDENTS IN MATHEMATICS CIRCLE
Report
As per guidelines from CBSE,
We Constructed Math Circle of students from class 6-12, to develop critical thinking, problem solving ability etc., among the students To achieve the target, we purchased 01 Math kit for Math Circle.
The kit Very useful for students and teachers to learn/teach many Mathematical Concepts.
Students will learn and understand mathematic Concepts mathematic of math kit with the help of Math Kit.
MATHS CIRCLE
INDEX
About Math circle
List of students
List of items
Use of items
Report
MATH CIRCLE
CIRCLE Number: 1
ACTIVITY – 1
VENUE: MATH LAB
DATE: 15.04.2024
NUMBER SYSTEM CHART
MATH CIRCLE NO 1 - ACTIVITY -1
NUMBER SYSTEM CHART
DATE: 15.04.2024
DAY-MONDAY
Aim:
To explain the different types of numbers.
Learning Outcomes:
Students are able to understand and explain about a number system.
Students are able to identify the numbers collectively as the groups.
Students are able to represents a valuable set of numbers that consists of Natural numbers, Whole numbers, Integers, Real numbers (Rational & Irrational) and so on.,
Students are able to explore the relationship between various type of numbers.
Teacher’s Feedback:
This Number system chart Math Kit helps the Student to develop a proper understanding of the number system.
It helps the students to understand the positioning of number bases in everyday life.
It helps the students to converting in one number System to another.
Student’s Feedback:
NUMBER SYSTEM-1
I learnt about collection of numbers Called number systems. These numbers are different types such as natural number, whole numbers, irrational and rational etc.
Also this help us in operation like addition. subtraction and division.
And I can recognise, read and position the whole numbers on a number line.
I am very Thankful to PM SHRI SCHEME
MATH CIRCLE - ACTIVITY 2
TYPES OF ANGLES CHART &
PAIR OF ANGLES CHART
DATE : 27.04.2024
DAY: SATURDAY
AIM:
To understand the different types and pair of angles formed by intersecting lines
LEARNING OUTCOMES:
Students are able to identify angles as right angle, acute angle, and obtuse angle.
Students will be able to build and draw angles.
Students are able to analyze and measure angles using a protractor.
Students are able to interpret angles with real life situations like position, direction, precision, and optimization.
Students are able to identify pairs of complementary, supplementary and adjacent angles.
It helps the students to understand the concept of parallel, perpendicular, Complementary and supplementary angles, vertically opposite angles and parallel lines cut by transversal.
Teacher’s Feedback:
Rounded Rectangle: This 3D Math kit helps Children identify and organize information visually recognize signs and symbols and develop an awareness of the relationship between people, objects and the space around them.
Student’s Feedback:
Rounded Rectangle: Three dimensional shapes often known as solid shapes have three different dimension i.e., length, width &height whereas 2 D shapes have only two dimensions i.e., length & width.
The 3D shapes have 2 types of surface are (i) Total surface area
(ii) Lateral surface areas
Very Thanks to PM SHRI Scheme.
MATH CIRCLE CIRCLE NO: 4ACTIVITY – 4 VENUE: MATH LAB DATE: 20.07.2024 TRIANGLES PUZZLE
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Teacher’s feedback:
Students developed a strong understanding of shape properties by manipulating and arranging triangles.
Group discussions helped improve teamwork and problem-solving skills.
Some students needed extra time to complete the puzzles, so adjusting time limits might help.
STUDENT REVIEW
Activity Performed has allowed me to
visualize an concept. yet difficult formula and a difficult concept in the
easiest way as possible.
I Thank PM SHRI SCHEME for Giving me
this opportunity.
-By
MATH CIRCLE CIRCLE NO: 5
ACTIVITY – 5
VENUE: MATH LAB DATE: 24.08.2024
MAGIC SQUARES
• DATE : 24-08-2024
• DAY : Saturday
• Magic squares challenge students to find patterns and apply logical reasoning to arrange numbers correctly. It promotes critical thinking as they work to ensure that the sums in rows, columns, and diagonals are equal.
• Aim:
• Students will find a fun and engaging way to apply mathematical concepts, increasing their interest and motivation in the subject.
• Learning outcomes:
• Students will recognize patterns in numbers and understand the structure behind magic squares.
• Students will enhance their addition and subtraction skills by ensuring that the sums of rows, columns, and diagonals in the magic square are equal.
• Students will improve their memory and cognitive skills by remembering number placement and relations within the grid.
• Students will improve their ability to visualize and organize numbers spatially within a grid.
• Skill Developed: Pattern recognition, an essential skill in mathematics and problem-solving.
Teacher’s Feedback:
Students are showing interest of solving magic squares is to arrange numbers in a square grid so that the sum of the numbers in each row, column, and diagonal is equal.
This magic square activity can be a fun and challenging way to practice arithmetic and logical thinking skills.
This activity practice teamwork and communication when working together to solve magic squares.
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9 |
2 |
7 |
= 18 |
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4 |
6 |
8 |
= 18 |
|
5 |
10 |
3 |
= 18 |
|
= 18 |
= 18 |
= 18 |
= 18 |
Student’s Feedback:
At first, it was hard to figure out where each number should go, but after some practice, I got the hang of it.
I found solving magic squares really fun because it felt like a puzzle!
It helped me improve my addition skills, and I was surprised at how quickly I started calculating sums.
I liked how I had to think logically to place the numbers in the right spots. It made me feel like a problem-solver.
I Thank PM SHRI SCHEME for Giving me this opportunity.
-By
MATH CIRCLE CIRCLE NO: 6
ACTIVITY – 6 VENUE: MATH LAB DATE: 14.09.2024
suduko
MATH CIRCLE ACTIVITY 6 - SUDUKO
DATE: 14-09-2024 DAY: Saturday
• Solving Sudoku puzzles can have multiple positive outcomes for students, contributing to both their cognitive development and mathematical thinking.
Aim:
• The aim of teaching Sudoku is to enhance students' cognitive abilities and problem-solving skills by engaging them in a logical, structured, and enjoyable puzzle-solving activity.
Learning outcomes:
• Students will improve their ability to think logically, analyzing each number's placement based on given constraints.
• Students will enhance their ability to recognize patterns and sequences, which are crucial in solving Sudoku puzzles.
• Students will strengthen their working memory by recalling potential number placements while keeping track of constraints.
• Although Sudoku does not directly involve arithmetic, it reinforces mathematical concepts such as logic, sequencing, and grid-based problem solving.
Skill Developed:
Mathematical thinking skills, such as using logic and structure to solve problems, applicable in various areas of math.
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3 |
4 |
6 |
8 |
9 |
1 |
5 |
7 |
2 |
|
2 |
9 |
1 |
7 |
3 |
5 |
6 |
8 |
4 |
|
5 |
8 |
7 |
2 |
6 |
4 |
3 |
9 |
1 |
|
8 |
5 |
9 |
4 |
7 |
3 |
1 |
2 |
6 |
|
4 |
6 |
3 |
9 |
1 |
2 |
8 |
5 |
7 |
|
7 |
1 |
2 |
5 |
8 |
6 |
4 |
3 |
9 |
|
1 |
7 |
5 |
3 |
4 |
9 |
2 |
6 |
8 |
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9 |
3 |
4 |
6 |
2 |
8 |
7 |
1 |
5 |
|
6 |
2 |
8 |
1 |
5 |
7 |
9 |
4 |
3 |
Teacher’s Feedback:
Rounded Rectangle: I noticed improvements in students' attention to detail. They became more careful and precise when placing numbers in the puzzle. Sudoku significantly improved my students' logical reasoning and critical thinking skills.Overall, we found Sudoku to be a highly effective tool for enhancing critical thinking, focus, independence, perseverance, and collaborative skills, while also making learning enjoyable for students.
Student’s
Feedback:
Rounded Rectangle: At first, it was difficult, but I kept trying, and I felt great when I completed it.It made me realize that math is not just about numbers but also about thinking and strategy.I think I’m better at solving problems now because I had to figure out where each number fit.I Thank PM SHRI SCHEME for Giving me this opportunity. -By
MATH CIRCLE
CIRCLE NO: 7
ACTIVITY – 7
VENUE: MATH LAB
DATE: 26.10.2024
Find Dice or Cube (Sum of
Opposite Faces = 7)
Exploring Dice and Their Hidden Math
DAY:
Saturday
Aim:
•
Students
will explore the properties of a standard six-sided die, focusing on how the
sum of opposite faces always equals 7.
They will use logical reasoning, arithmetic, and spatial awareness to
understand cube properties and probability concepts.
Learning
outcomes:
Students will be able to
• Identify a standard six-sided die and explain its number arrangement.
• Recall that the sum of opposite faces on a standard die is always 7.
• Apply logical reasoning to determine whether a given cube follows the dice pattern.
• Analyze different cube representations (physical, drawn, or digital) to verify number placements.
• Relate the concept to board games and probability in real-world scenarios.
Skill Developed: Mathematical thinking skills, such as using logic and structure to solve problems, applicable in various areas of math.
Teacher’s
Feedback:
Concept Understanding: The activity helped reinforce the concept of opposite faces on a cube summing to 7, improving spatial reasoning.
Some students struggled initially but improved after discussions and hands-on practice.
Group discussions were productive, and students helped each other understand the pattern
Student’s
Feedback:
Rounded Rectangle: Myself and my friends enjoyed the hands-on nature of the activity.
Some found it tricky at first but appreciated the logic behind the sum of 7.
I Understand how numbers are arranged on a dice made the concept of cubes and opposite faces clearer.
Some of my friends suggested additional activities with different types of dice or variations in rules.
I Thank PM SHRI SCHEME for Giving me this opportunity.
-By
MATH CIRCLE CIRCLE NO: 8
ACTIVITY – 8 VENUE: MATH LAB
DATE: 29.11.2024 Calendar magic
• DATE: 29-11-2024 • DAY: Friday
Students will explore numerical patterns using the Calendar Magic 153 activity, enhancing their understanding of arithmetic sequences, number properties, and algebraic reasoning.
Aim:
• The aim of teaching Sudoku is to enhance students' cognitive abilities and problem-solving skills by engaging them in a logical, structured, and enjoyable puzzle-solving activity.
Learning outcomes:
Students will be able to
• Recognize patterns in arithmetic sequences.
• Develop algebraic reasoning by deriving formulas.
• Improve mental math skills with multiplication and addition.
• Understand how numbers relate to their positions in structured grids.
Skill Developed: Mathematical thinking skills, such as using logic and structure to solve problems, applicable in various areas of math.
1. Choose any 3×3 grid from a monthly calendar (e.g., a section where 3 rows and 3 columns of dates form a square).
2. Write down all the numbers in your 3×3 section.
3. Add up all the numbers in the grid.
4. Identify the middle number of the grid.
5. Multiply the middle number by 9.
6. Compare your total sum with 9 times the middle number. Do you notice a pattern?
Teacher’s Feedback:
Rounded Rectangle: This activity effectively engages students in recognizing numerical patterns and strengthens their arithmetic and algebraic reasoning skills.
Students enjoyed verifying their results and predicting future sums, which helped build confidence in mathematical problem-solving.
To enhance the activity, I would suggest incorporating technology, such as spreadsheets, to allow students to automate and analyze multiple grids quickly.
student’s Feedback:
Rounded Rectangle: This activity was fun and surprising! I never knew that selecting a simple 3×3 calendar grid could lead to such a cool mathematical pattern.
This activity made me feel more confident in solving number problems. I also learned how to use multiplication and addition in a new way.
PM SHRI’s focus on experiential learning really helped us explore math in an engaging way. It’s much more exciting than just reading from a textbook!
I now see that math isn’t just about formulas—it’s about discovering patterns everywhere, even in a calendar!
I Thank PM SHRI SCHEME for Giving me this opportunity.
MATH CIRCLE
CIRCLE NO: 10
ACTIVITY – 10
VENUE: MATH LAB
DATE: 30.01.2025
Building Patterns:
Exploring
Cube Arrangements
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DATE:
30-01-2025
DAY:
Thursday
•
Exploring
the pattern formed can have multiple positive outcomes for students,
contributing to both their cognitive development and mathematical thinking.
Aim:
•
Students
will explore the pattern formed by arranging small cubes in stages and derive a
mathematical formula for the sequence. This activity will enhance their pattern
recognition, algebraic thinking, and problem-solving skills.
Learning
outcomes:
•
Students will be able to
•
Observe
and describe the numerical sequence formed by arranging cubes.
•
Identify
the pattern of increasing differences between consecutive stages.
•
Relate
the cube arrangement pattern to the sum of natural numbers.
•
Derive
a mathematical formula to represent the cube arrangement pattern.
•
Extend
the pattern to discover new relationships and generalizations.
Skill
Developed: Pattern
Recognition Skills, Algebraic Thinking, Logical and Analytical Thinking,
Spatial and Geometric Reasoning, Problem-Solving Skills, Numeracy and
Arithmetic Fluency, Critical Thinking.
|
|
Stage 1 |
Stage 2 |
Stage 3 |
Stage 4 |
|
C(n)= |
|
add to previous
(1+3 = 4) |
add to previous
(4+6 = 10) |
add to previous
(10+10 = 20) |
So, the total cubes at stage n follow the formula:
Teacher’s Feedback: Rounded Rectangle: This activity was a great way to explore patterns and sequences in a hands-on manner. It helped the students to understand how numbers grow in a structured way
The step-by-step approach helped students gradually build their understanding of triangular numbers and their connection to cube arrangements
The real-life applications of this pattern in architecture and engineering added depth to the lesson, making students see the relevance of math beyond the classroom.
I liked how this activity connected math to real-life applications like architecture and engineering. It made me see how important patterns are in everyday life
The hands-on experience of building with cubes made it easier to understand than just reading about patterns in a textbook
I Thank PM SHRI SCHEME for Giving me this opportunity.
-By
MATH CIRCLE
CIRCLE NO: 11
ACTIVITY – 11
VENUE: MATH LAB
DATE: 18.02.2025
Create a Mobius Strip
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•
DATE: 14-10.2024
•
DAY: Saturday
•
To
help students understand non-orientable surfaces, develop spatial reasoning,
and recognize mathematical properties through hands-on exploration.
Aim:
•
To
explore the concept of topology by constructing and analyzing the properties of
a Mobius strip.
Learning outcomes:
Students
will be able to
•
Understand
the fundamental concept of non-orientable surfaces in topology.
•
Develop
spatial reasoning skills through hands-on exploration.
•
Recognize
the Mobius strip’s unique properties and mathematical significance.
•
Apply
topology concepts to real-world applications, such as conveyor belts,
electrical circuits, and 3D design.
Skill
Developed: Mathematical
thinking skills, such as using logic and structure to solve problems,
applicable in various areas of math.
Teacher’s Feedback:Rounded Rectangle: The Mobius strip activity was an engaging and thought-provoking experience for students.
It allowed them to explore the concept of topology hands-on, fostering curiosity and deeper understanding.
Students were particularly fascinated by the one-sided nature of the strip and enjoyed the challenge of predicting what would happen when it was cut in different ways.
The activity successfully encouraged mathematical discussions and creativity, making abstract concepts more accessible and enjoyable.
Rounded Rectangle: Creating a Mobius strip was so much fun! At first, I thought it was just a regular paper loop, but after drawing and cutting along it, I was amazed at how it changed.
I loved discovering that it only has one surface and one edge!
This activity helped me understand a completely new mathematical idea in a hands-on way. It made me curious about topology and how shapes can behave in unexpected ways!
I Thank PM SHRI SCHEME for Giving me this opportunity.
-By
Student’s Feedback:
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