Mathematics Subject Enrichment Activity
Class: VI Chapter: 3 – Number Play (NCERT Ganita Prakash, Pages 67–68)
Activity Title: Playing with Number Patterns
Topic
Number Patterns and Quick Addition Techniques
Aim
To explore and identify mathematical patterns in given arrangements of numbers and to develop efficient strategies for addition using these patterns.
Materials Required
NCERT Ganita Prakash textbook (Page 67–68, Section 3.9)
Graph sheets or plain A4 sheets
Pencil, eraser, ruler, colour pens/markers
Procedure
Observe the number arrangements given in the textbook (e.g., repeated 40s, 50s, 32s, 64s, 125s, 25s, 15s, 35s etc.).
Write down the arrangement neatly on graph sheets.
Instead of adding one by one, look for repetition and use multiplication or grouping.
Example: If a row has 8 numbers of 32, then sum = 32 × 8.
Solve all the six given patterns (a–f) by grouping and applying multiplication.
Record your answers and compare methods used by classmates.
Observations (with Solutions)
a. Pattern of 40s and 50s
Count of 40s = 6 → Sum = 40 × 12 = 480
Count of 50s = 12 → Sum = 50 × 10 = 500
Total = 980
B. Mixed pattern of 1 dot and 5 dots
1 dot occurs 44 times → 44 × 1 = 44
5 dots occurs 20 times → 5 × 20 = 100
Total = 144
c. Square arrangement of 32s and 64s
32 occurs 32 times → 32 × 32 = 1024
64 occurs 16 times → 64 × 16 = 1024
Total = 2048
d. Pattern with 4 dots and 3 dots
4 dots occurs 18 times → 4 × 18 = 72
3 dots occurs 17 times → 3 × 17 = 51
Total = 123
e. (Hexagon with 15, 25, 35)
15 appears 22 times → 15 × 22 = 330
25 appears 22 times → 25 × 22 = 550
35 appears 22 times → 35 × 22 = 770
Total = 330 + 550 + 770 = 1650
f (Concentric circles with 125, 250, 500, 1000)
125 appears 18 times → 125 × 18 = 2250
250 appears 8 times → 250 × 8 = 2000
500 appears 4 times →500 × 4 = 2000
1000 appears 1 time →1000 × 1 = 1000
Total = 2250 + 2000 + 2000 + 1000 = 7250
Reflections
Adding repeated numbers individually is time-consuming.
Grouping numbers and using multiplication gives quicker and error-free results.
Number patterns help in mental math and save calculation time.
This develops logical reasoning and pattern recognition skills, which are useful in algebra and higher mathematics.
Higher Order Thinking Skills (HOTs)
Q1. Can you create your own number pattern where the total sum is exactly 1000?
✅ Answer:
Let’s choose the number 25 repeated 40 times.
Sum = 25 × 40 = 1000.
(Other possible answers: 100 × 10, 50 × 20, or mixed patterns like 400 + 600.)
Q2. If one number in the pattern is replaced with its double, how will the total change?
✅ Answer:
Suppose in the first pattern (40, 50), one 50 is replaced with 100.
Old contribution = 50
New contribution = 100
Increase = 100 – 50 = +50
Hence, the total sum increases by the same amount as the original number.
👉 In general, replacing a number x with 2x increases the total by x.
Q3. Extend this activity: Can you represent the sums of these patterns using algebraic expressions?
✅ Answer:
Yes, let’s generalize:
If a number a is repeated m times → contribution = a × m
If a number b is repeated n times → contribution = b × n
Total sum = a×m + b×n + c×p + …
Example (Pattern b with 32 and 64):
Total = (32 × 32) + (64 × 16)
= 32(32 + 2×16)
= 32 × 64 = 2048
This algebraic representation shows how grouping works and helps in finding quick shortcuts.
🌟 Creative HOTS Challenge
Q4. Design your own number pattern where the numbers are arranged in a square/rectangle grid, and then prove a shortcut formula for finding the total sum without adding individually.
✅ Answer (Example Solution):
Step 1 – Design a Pattern
Suppose we make a 5 × 5 square grid filled with the number 20.
So total numbers = 25.
Step 2 – Direct Sum
20 + 20 + 20 + … (25 times) = 20 × 25 = 500.
Step 3 – Generalize with Algebra
If a number n is written in an m × k grid (m rows, k columns),
then total numbers = m × k,
and sum = n × (m × k).
Example Extension Puzzle
Fill a 4 × 6 rectangle with the number 15.
Predict the sum using formula = 15 × (4 × 6).
Verify by manual addition.
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