Task #1

Take any 2 consecutive whole numbers, square both of them and find the difference.

Actual Student Response:

34, 35

34² = 1156
35² = 1225

 1225 -
 1156
 -----
 69

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Task #2

Write down any pattern you observe.

Actual Student Response:

I observed that when you subtract the squared numbers of two consecutive numbers, they give you the sum of the two consecutive numbers.

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Task #3

Creat a table to visualize patterns and sub-problems.

Actual Student Response:

n	n²	(n + 1)²	Difference ((n + 1)² − n²)
1	1	4	3
2	4	9	5
3	9	16	7
4	16	25	9
5	25	36	11
6	36	49	13
7	49	64	15
8	64	81	17
9	81	100	19
10	100	121	21

Pattern in the differences:

3 = 1 + 2
5 = 2 + 3
7 = 3 + 4
9 = 4 + 5
11 = 5 + 6
13 = 6 + 7
15 = 7 + 8
17 = 8 + 9
19 = 9 + 10
21 = 10 + 11

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Task #4

Write a formula using n which produces the difference of 2 consecutive squares.

Actual Student Response:

Formula:$$(n+1)^2 – n^2 = 2n + 1$$(n+1)2−n2=2n+1

Therefore, the difference between two consecutive squares is:$$\boxed{2n + 1}$$

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Task #5 (Challenge H.W.)

Why does this work?

See Class Demonstration Below: https://islandclass.org/2026/06/05/c45-difference-of-2-squares-exercise-3na-2026-06-05_10-09-39/

Excel File from video: https://docs.google.com/spreadsheets/d/180mwZ2zbkKp81QkcMFD8vnRJA6IummOF/edit?usp=sharing&ouid=114406882972532424108&rtpof=true&sd=true

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