Bridge Programme Content: Detailed Activity
Activities for Week1
Activity W1.1: Recreational Puzzle
A calendar of any month, coloured sketch pens and sheet of paper
May 2025
A calendar may be given to students in pairs.
They have to observe the calendar keenly and write their observations in the notebook.
Let the students do on their own.
Teacher can suggest question but should not reveal the conclusions before taking responses of students’ observations.
Teacher may ask students to do the following:
Draw boxes around square numbers (number obtained when a number is multiplied to itself two times. 9 = 3 × 3 is a square number) and colour them with a single colour.
Draw circles around cube numbers (number obtained when a number is multiplied to itself three times. 8 = 2 × 2 × 2 is a cube number.) and colour them with a new colour.
Draw triangle around prime numbers. O Students may be asked to choose any 2 by 2 number square grid from the calendar they have.
Instructions for Students
1. Observing the Calendar:
Students are given a calendar (in pairs). For example, May 2025 starts on Thursday and has 31 days.
They are asked to observe patterns in the calendar and note down their own observations.
Examples of what students might observe:
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The month starts on a Thursday.
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All weeks have 7 days.
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The 1st, 8th, 15th, 22nd, and 29th are all Thursdays.
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The numbers in the same column increase by 7.
2. Marking Specific Numbers:
Using coloured pens, students mark special types of numbers:
Square Numbers (draw boxes around and colour with one colour):
→ 1, 4, 9, 16, 25
Cube Numbers (draw circles around and colour with a second colour):
→ 1, 8, 27
Prime Numbers (draw triangles around):
→ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31
3. Choose any 2x2 number square from the calendar
(For example: Choose the block with 8, 9, 15, 16)
They should try to answer the following questions:
What is the sum of the numbers in the diagonals of the grid?
What is the sum of numbers in the diagonals?
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Diagonal 1 (8 + 16) = 24
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Diagonal 2 (9 + 15) = 24
What magic do you observe?
Observation / Magic:
The sum of both diagonals is the same in a 2x2 grid.
Based on the above activity, some reflective questions may be discussed, such as:
Reflective Questions & Sample Student Responses
Q1: How do you differentiate between square and cube numbers?
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A square number is a number multiplied by itself once (e.g., 4 = 2 × 2).
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A cube number is a number multiplied by itself twice more (e.g., 8 = 2 × 2 × 2).
Q2: How do you identify prime numbers?
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Prime numbers have exactly two factors: 1 and itself.
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They are not divisible by any other number.
Q3: Why is the sum of diagonals always same in a 2x2 grid?
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Because the opposite corners in a 2x2 square are symmetrical and balance each other.
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The sums (top-left + bottom-right) and (top-right + bottom-left) are always equal due to arithmetic symmetry.
Extension of the Activity
Teacher can extend this activity by suggesting students to take a 3 by 3 grid.
Extension Activity (3x3 Grid)
Take a 3x3 grid (e.g., from 8 to 16):
Why is the sum of diagonals always same for any 2 by 2 grid?
They may find—
1. The sum of diagonal numbers.
Sum of diagonals:
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Diagonal 1 (8 + 16 + 24) = 48
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Diagonal 2 (10 + 16 + 22) = 48
2. The mean of all numbers.
Mean of all numbers in the grid:
Sum of all numbers: 8+9+10+15+16+17+22+23+24 = 144
Mean = 144 ÷ 9 = 16
Special Observations:
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The center number (16) is the mean.
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Diagonals again have equal sums.
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There is a symmetry in the calendar numbers.
They may be asked to see what special thing they observed.
Teacher may encourage students to explore more such patterns in the calendar
Encouragement for Exploration
Students can be encouraged to:
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Try different-sized grids (like 4x4).
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Observe symmetry across weeks.
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Explore patterns in odd/even numbers.
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Make their own puzzles from the calendar.
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