Write down two consecutive numbers.
Square each of them and find the difference.
Do the same for other pairs of numbers. What do you notice?
Answers
The first thing you may notice is that all of your answers are odd numbers.
Did you also notice that your answers are always the sum of the two consecutive numbers?
22 - 12 = 3 32 - 22 = 5 42 - 32 = 7 52 - 42 = 9 62 - 52 = 11 72 - 62 = 13 82 - 72 = 15 92 - 82 = 17 102 - 92 = 19 112 - 102 = 21 122 - 112 = 23 132 - 122 = 25 142 - 132 = 27 152 - 142 = 29 162 - 152 = 31 172 - 162 = 33 182 - 172 = 35 192 - 182 = 37 202 - 192 = 39 212 - 202 = 41 222 - 212 = 43 232 - 222 = 45 242 - 232 = 47 252 - 242 = 49 262 - 252 = 51 272 - 262 = 53 282 - 272 = 55 292 - 282 = 57 302 - 292 = 59 312 - 302 = 61 322 - 312 = 63 332 - 322 = 65 342 - 332 = 67 352 - 342 = 69 362 - 352 = 71 372 - 362 = 73 382 - 372 = 75 392 - 382 = 77 402 - 392 = 79 412 - 402 = 81 422 - 412 = 83 432 - 422 = 85 442 - 432 = 87 452 - 442 = 89 462 - 452 = 91 472 - 462 = 93 482 - 472 = 95 492 - 482 = 97 502 - 492 = 99 512 - 502 = 101 522 - 512 = 103
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"The difference of the squares of two consequetive numbers will always equal the sum of those two numbers. Mr Frost, John Summers High School
"or Mr Frost, John Summers High School, Flintshire
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| Number Patterns
sum of the numbers:
a + (a-1) = 2a - 1
Difference of the square of the numbers
a2 - (a-1)2 = a2 - (a2 - 2a + 1)
= 2a - 1"
Tuesday, October 03, 2006
Difference in squares
a2 - (a + 1)2 = a2 - (a2 + 2a + 1)
= 2a + 1
Sum of the numbers
a + (a + 1) = 2a + 1"
Wednesday, October 04, 2006
Good, achieved the results I required
Satisfactory
Didn't really capture the interest of the students
Not for me! I wouldn't use this type of activity.
This starter has scored a mean of 3.8 out of 5 based on 22 votes.
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