From the BEATCALC mailing list: a weekly service from B. Lee Clay, archived here by the Math Forum. To subscribe to the BEATCALC mailing list, write to BEATCALC@aol.com.

Squaring Numbers Squaring a 2-digit number beginning with 1 Squaring a 2-digit number beginning with 5 Squaring a 2-digit number beginning with 9 Squaring a 2-digit number ending in 1 Squaring a 2-digit number ending in 2 Squaring a 2-digit number ending in 3 Squaring a 2-digit number ending in 4 Squaring a 2-digit number ending in 5 Squaring a 2-digit number ending in 6 Squaring a 2-digit number ending in 7 Squaring a 2-digit number ending in 8 Squaring a 2-digit number ending in 9 Squaring numbers made up of ones Squaring numbers made up of threes Squaring numbers made up of sixes Squaring numbers made up of nines Squaring numbers in the twenties Squaring numbers in the thirties Squaring numbers in the forties Squaring numbers in the fifties Squaring numbers in the sixties Squaring numbers in the seventies Squaring numbers in the eighties Squaring numbers in the hundreds Squaring numbers in the two hundreds Squaring numbers in the three hundreds Squaring numbers in the four hundreds Squaring numbers in the five hundreds Squaring numbers in the six hundreds Squaring numbers in the seven hundreds Squaring numbers between 800 and 810 Squaring numbers in the nine hundreds Squaring numbers between 1000 and 1100 Squaring numbers between 2000 and 2099 Squaring numbers between 3000 and 3099 Squaring numbers between 4000 and 4099 Squaring numbers between 5000 and 5099 Squaring numbers between 6000 and 6099 Squaring numbers between 7000 and 7099 Squaring special numbers (3's and final 1) Squaring special numbers (3's and final 2) Squaring special numbers (3's and final 4) Squaring special numbers (3's and final 5) Squaring special numbers (3's and final 6) Squaring special numbers (3's and final 7) Squaring special numbers (3's and final 8) Squaring special numbers (3's and final 9) Squaring special numbers (6's and final 1) Squaring special numbers (6's and final 2) Squaring special numbers (6's and final 3) Squaring special numbers (6's and final 4) Squaring special numbers (6's and final 5) Squaring special numbers (6's and final 7) Squaring special numbers (6's and final 8) Squaring special numbers (6's and final 9) Squaring special numbers (9's and final 1) Squaring special numbers (9's and final 2) Squaring special numbers (9's and final 3) Squaring special numbers (9's and final 4) Squaring special numbers (9's and final 5) Squaring special numbers (9's and final 6) Squaring special numbers (9's and final 7) Squaring special numbers (9's and final 8) Squaring special numbers (1 and repeating 3's) Squaring special numbers (1 and repeating 6's) Squaring special numbers (1 and repeating 9's) Squaring special numbers (2 and repeating 3's) Squaring special numbers (2 and repeating 6's) Squaring special numbers (2 and repeating 9's) Squaring special numbers (3 and repeating 6's) Squaring special numbers (3 and repeating 9's) Squaring special numbers (4 and repeating 3's) Squaring special numbers (4 and repeating 6's) Squaring special numbers (4 and repeating 9's) Squaring special numbers (5 and repeating 3's) Squaring special numbers (5 and repeating 6's) Squaring special numbers (5 and repeating 9's) Squaring special numbers (6 and repeating 3's) Squaring special numbers (6 and repeating 9's) Squaring special numbers (7 and repeating 3's) Squaring special numbers (7 and repeating 6's) Squaring special numbers (7 and repeating 9's) Squaring special numbers (8 and repeating 3's) Squaring special numbers (8 and repeating 9's) Squaring special numbers (9 and repeating 3's) Squaring special numbers (9 and repeating 6's) Squaring a repeating 6-digit number   Multiplying Numbers Multiplying two selected 2-digit numbers (same 1st digit) [1] Multiplying two selected 2-digit numbers (same 1st digit) [2] Multiplying two selected 2-digit numbers (same 2nd digit) Multiplying two selected 3-digit numbers (middle digit 0) Multiplying two selected 3-digit numbers (middle digit 1) Multiplying two selected 3-digit numbers (middle digit 2) Multiplying two selected 3-digit numbers (middle digit 3) Multiplying two selected 3-digit numbers (middle digit 4) Multiplying two selected 3-digit numbers (middle digit 5) Multiplying two 2-digit numbers with a difference of 1 Multiplying two 2-digit numbers with a difference of 2 Multiplying two 2-digit numbers with a difference of 3 Multiplying two 2-digit numbers with a difference of 4 Multiplying two 2-digit numbers with a difference of 6 Multiplying two 2-digit numbers with a difference of 8 Multiplying two 2-digit numbers with a difference of 10 Multiplying a 2-digit number by 1 1/9 Multiplying a 2-digit number by 1 1/8 Multiplying a 2-digit number by 1 1/6 Multiplying a 2-digit number by 1 1/5 Multiplying a 2-digit number by 1 1/4 Multiplying a 2-digit number by 1 1/3 Multiplying a 2-digit number by 1 1/2 Multiplying a 2- or 3-digit number by 1 2/3 Multiplying a 2-digit number by 1 3/4 Multiplying a 2-digit number by 1 5/6 Multiplying a 2-digit number by 2 1/5 Multiplying a 2-digit number by 2 1/4 Multiplying a 2-digit number by 2 2/9 Multiplying a 2-digit number by 2 1/3 Multiplying a 2- or 3-digit number by 2 1/2 Multiplying a 2-digit number by 2 2/3 Multiplying a 2-digit number by 2 3/4 Multiplying a 2-digit number by 3 1/3 Multiplying a 2-digit number by 3 1/2 Multiplying a 2-digit number by 3 3/4 Multiplying a 2-digit number by 4 1/2 Multiplying a 2-digit number by 5 5/7 Multiplying a 2-digit number by 5 5/9 Multiplying a 2-digit number by 6 1/4 Multiplying a 2-digit number by 6 2/3 Multiplying a 2-digit number by 7 1/2 Multiplying a 2-digit number by 8 1/3 Multiplying a 2-digit number by 8 8/9 Multiplying a 2-digit number by 12 1/2 Multiplying a 2-digit number by 15 Multiplying a 2- or 3-digit number by 16 2/3 Multiplying a 2-digit number by 18 Multiplying a 2-digit number by 22 Multiplying a 2- or 3-digit number by 25 Multiplying a 2-digit number by 27 Multiplying a 2-digit number by 33 Multiplying a 2-digit number by 33 1/3 Multiplying a 2-digit number by 35 Multiplying a 2-digit number by 36 Multiplying a 2-digit number by 37 1/2 Multiplying a 2-digit number by 44 Multiplying a 2-digit number by 45 Multiplying a 2-digit number by 55 (a) Multiplying a 2-digit number by 55 (b) Multiplying a 2-digit number by 63 Multiplying a 2-digit number by 66 Multiplying a 2-digit number by 72 Multiplying a 2- or 3-digit number by 75 Multiplying a 2-digit number by 77 Multiplying a 2-digit number by 81 Multiplying a 2-digit number by 88 Multiplying a 2-digit number by 99 Multiplying a 3-digit number by 99 Multiplying a 2- or 3-digit number by 101 Multiplying a 2-digit number by 125 Multiplying a 3-digit number by 143 Multiplying a 2-digit number by 198 Multiplying a 2-digit number by 250 Multiplying a 2-digit number by 297 Multiplying a 2-digit number by 375 Multiplying a 2-digit number by 396 Multiplying a 2-digit number by 495 Multiplying a 2-digit number by 594 Multiplying a 2-digit number by 625 Multiplying a 2-digit number by 693 Multiplying a 2-digit number by 792 Multiplying a 2-digit number by 875 Multiplying a 2-digit number by 891 Multiplying a 2-digit number by 999 Multiplying a 2- or 3-digit number by 1001 and adding 21 (or 201) Multiplying a 2-, 3-, or 4-digit number by 10001 and adding 21, 201, or 2001 Multiplying a 2-, 3-, 4-, or 5-digit number by 100001 Multiplying a repeating 3-digit number by 2, then dividing it by 37 Multiplying a repeating 3-digit number by 5, then dividing it by 37 Multiplying a repeating 9-digit number by 3, then dividing it by 12345679 Multiplying a multi-digit number by 8 and adding the last digit Multiplying a number sequence by 8, adding a number, and subtracting 20 Multiplying the sum and the difference of a 2-digit and a 1-digit number Multiplying two mixed numbers Multiplying a 4-digit number by 99 Multiplying a 4-digit number by 137 and 73; subtracting 1200 Multiplying a 5-digit number by 9091 and 11; subtracting 1200   Dividing Numbers Dividing a 2-digit number by 1 1/5 Dividing a 2-digit number by 1 1/4 Dividing a 2-digit number by 1 1/3 Dividing a 2-digit number by 1 3/7 Dividing a 2-digit number by 1 1/2 Dividing a 2-digit number by 1 2/3 Dividing a 2-digit number by 1 3/4 Dividing a 2-digit number by 2 1/3 Dividing a 2- or 3-digit number by 2 1/2 Dividing a 2-digit number by 2 2/3 Dividing a 2- or 3-digit number by 3 1/3 Dividing a 2-digit number by 3 1/2 Dividing a 2-digit number by 4 1/2 Dividing a 2-digit number by 7 1/2 Dividing a 2-digit number by 12 1/2 Dividing a 2-digit number by 15 Dividing a 2- or 3-digit number by 16 2/3 Dividing a 2- or 3-digit number by 25 Dividing a 2- or 3-digit number by 33 1/3 Dividing a 2- or 3-digit number by 35 Dividing a 2-digit number by 37 1/2 Dividing a 2-digit number by 45 Dividing a 2- or 3-digit number by 75 Dividing a 2-digit number by 125 Dividing a 2-digit number by 375 Dividing a 2-digit number by 625 Dividing a repeating 3-digit number by 37 and adding 41 Dividing a repeating 6-digit number by 15873 Dividing a repeating 6-digit number by 7, then by 13 Dividing a repeating 6-digit number by 13, then by 11 Dividing a repeating 6-digit number by 7, 11, and 13, then subtracting 101 Dividing a repeating 6-digit number by 37037, then multiplying by 5 Dividing mixed numbers by 2 Finding the difference of the squares of two consecutive 2-digit numbers Finding the difference of the squares of two different 2-digit numbers Finding the square root of squares of 2-digit numbers ending in 1 Finding the square root of a perfect square ending in 5   Adding Numbers Finding the sum of all even numbers from 2 through a selected 2-digit even number Adding a sequence of consecutive odd numbers Adding consecutive numbers between two numbers Adding a sequence of numbers from one to a selected 2-digit number Adding a sequence of numbers from one to a selected 1-digit number and back Adding sequences of numbers in the 10's Adding sequences of numbers in the 20's Adding sequences of numbers in the 30's Adding sequences of numbers in the 40's Adding sequences of numbers in the 50's Adding sequences of numbers in the 60's Adding sequences of numbers in the 70's Adding sequences of numbers in the 80's Adding a series of doubles Adding a series of quadruples Adding a series of ten numbers   Subtracting Numbers Subtracting from a repeating 1's number, dividing by 9, subtracting 21 Subtracting from a repeating 8's number, dividing by 9, subtracting 10 Subtracting the squares of two numbers Reversing/adding/subtracting 3-digit numbers   Finding Percents Finding 2.5 percent of a number Finding 5 percent of a number Finding 15 percent of a number Finding 45 percent of a number Finding 55 percent of a number Calculation Practice Exercises