# HUES 6th Grade Math Choice - Sample Problems

Hollis Upper Elementary School, Hollis, New Hampshire

1. What's My Rule?
1A. IN   1  2  3  4  5  6  7  8  9  (Hint: Spell out the numbers)
OUT  3  3  5  4  4  3  5  5  4
1B. IN   1  2  3  4  5  6  7  8  9
OUT  O  T  T  F  F  S  S  E  N
1C. IN   1  2  3  4  5  6  7  8  9 10 11 12
OUT 31 29 31 30 31 30 31 31 30 31 30 31

2. Which number comes next in the sequence?
2A. 3, 5, 7, 9, 11, 13, 15, 17, 19, ?
2B. 3, 5, 7, 11, 13, 17, 19, ?
2C. 2, 5, 10, 17, 26, 37, 50, 65, 82, ?  (Hint: Think instead about 1, 4, 9, 16, 25, ...)
2D. 1, 2, 4, 8, 16, 32, 64, 128, ?

3. Alphametics (Substitute a unique digit for each letter - these are hard without hints for several letters)
3A: WYOMING x 8 = ILLINOIS
3B: FLORIDA    x 5 = OKLAHOMA (Hint: There are just 2 possible digits for A)
3C: AB x C = DE and FG - DE = HI  (Don't use 0 in the solution)

4. Digits in dates - Assume dates are written mm/dd/yyyy with no leading zeros and the date is 3/7/2000
4A. What was the last date which had all odd digits?
4B. What is the next date which will have all odd digits?
4C. What was the last date which had all even digits?
4D. What is the next date which will have all even digits?
4E. What is the next date which will alternate odd and even digits starting with an odd digit?

5. Counting and spelling  - Spell out the numbers starting with 1 (Example: 41 = forty one)
5A. What is the first number whose spelling includes the letter "a"?
5B. What is the first number whose spelling includes the letter "n" 7 times?

6. Probability - Assume you have a multiple choice test with 40 problems and 4 choices per problem.
6A. How many problems would you expect to get correct on average if you guessed on each problem?

7. Change for a dollar - "I need to make a phone call, and all I have is a dollar bill," said George.  "Can you make change for a dollar?"  "Sure," replied Susan, rummaging through her purse.  "Hmm. I have more than a dollar, but I can't give you exact change."
7A. How much money could Susan have in pennies, nickels, dimes, and quarters and still not be able to make exact change for a dollar?
Source: Discover (magazine) Oct-1999, page 119 (Scott Kim's Bogglers column)

8. Math League contests (5th through 8th grade)
Source: The Math League contest problem books - http://www.mathleague.com

9. Problems of the week (elementary school and middle school)
Source: The Math Forum - http://forum.swarthmore.edu

Don Braffitt

1A. OUT is the number of letters in the spelling of IN
1B. OUT is the first letter of the spelling of IN
1C. OUT is the number of days in each month for a leap year

2A. 3, 5, 7, 9, 11, 13, 15, 17, 19, 21      (odd numbers)
2B. 3, 5, 7, 11, 13, 17, 19, 23               (odd prime numbers)
2C. 2, 5, 10, 17, 26, 37, 50, 65, 82, 101 (squares+1 - 1+1, 4+1, 9+1, 16+1, 25+1, ...)
2D. 1, 2, 4, 8, 16, 32, 64, 128, 256        (double previous number; powers of 2)

3A. WYOMING x 8 = ILLINOIS         7920658 x 8 = 63365264
3B. FLORIDA    x 5 = OKLAHOMA    8741290 x 5 = 43706450
3C. AB x C = DE and FG - DE = HI     17 x 4  = 68  and 93 - 68  = 25

4A. What was the last date which had all odd digits?         11/19/1999
4B. What is the next date which will have all odd digits?   1/1/3111
4C. What was the last date which had all even digits?        2/28/2000
4D. What is the next date which will have all even digits?  4/2/2000
4E. What is the next date which will alternate odd and even digits starting with an odd digit? 1/2/3010

5A. What is the first number whose spelling includes the letter "a"?             one thousand
5B. What is the first number whose spelling includes the letter "n" 7 times?  nine hundred ninety nine

6A. 10 problems out of 40 (25% or 1 problem out of 4)

7A. 3 quarters, 4 dimes, and 4 pennies = \$1.19

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