1643 Thrift Store Find

Today’s Puzzle:

Yesterday I walked to a thrift store located about a mile and a half from my house. I looked through their picture books and was delighted to find all of these:

I love reading math picture books to my grandchildren. My eighteenth (nine girls and nine boys) grandchild was born earlier this month, so each book will be treasured.

The display of books made me think of some math questions:

How many books do you see? How did you count them?

How many of the books have you read? How many haven’t you read?

If you’ve read X number of the books, but haven’t read Y of them, write an expression for the total number of books.

The thrift store price of each book was $1.29. How much did I expect to pay for all these books?

I wasn’t aware of the store’s “buy four get one free” policy before I checked out. How many free books did I get? Could I have done better than that?

I was charged 7.25% sales tax. What was the total tax I paid? What was the total amount I paid for the books?

I didn’t have time to look through every shelf of books yesterday, so today I went back and found a few more treasures. (I also bought four non-mathy books that are not pictured.) Ten Apples Up On Top was a book I read to my children when they were young. We loved it so much that eventually, it fell apart. Some of my grandchildren haveTen Tiny Tickles in their home libraries, but now they can enjoy it at my house as well.

What kind of math can be found in the books I bought?

  1. One Hundred Days (Plus One) – What number comes after 100?
  2. The Stephen Cartwright 123 – Count to 21.
  3. Boom Chicka Rock – Hour hand clock math.
  4. Numbears – Count to 12.
  5. Ten Happy Whales – Adding one more; Introduction to addition.
  6. 10 Black Dots – Count to 10.
  7. One Hundred Hungry Ants – Dividing 100 by 2, 4, 5, and 10.
  8. A Remainder of One – Dividing 25 by 2, 3, or 4 leaves a remainder of one, but dividing by 5 does not.
  9. Sixteen Runaway Pumpkins – Powers of 2.
  10. 10 for dinner – Ways to add four or five numbers to make 10.
  11. Great Estimations – Estimating tens, hundreds, or thousands of objects.
  12. Baby Counts – Count to 4.
  13. Counting Farm – Count to 10.
  14. 123 First Board Book – Count to 10, 20, 50, 100.
  15. Ten Apples Up On Top – Count to 10 (Count by 10’s also).
  16. Cookie’s Week – Calendar math – Days of the week.
  17. Millions of Snowflakes – Count to 5.
  18. A House for Hermit Crab – Calendar Math – Months of the Year.
  19. Ten Tiny Tickles – Count to 10.
  20. Each Orange Had 8 Slices – Word problems, multiplying three numbers together.
  21. One Less Fish – Counting down from 12 to 0.
  22. Lunch Money and Other Poems about School has three poems about math: Eight-Oh-Three (clock math), Lunch Money (types of coins), Math My Way (should 2 + 2 be 22 instead of 4? What about 3 + 3 and 4 + 4?)
  23. Nine O’Clock Lullaby – Clock math, time zones around the world.
  24. One Monday Morning – Calendar Math, Days of the week.
  25. A Quarter from the Tooth Fairy – Different ways to make 25¢.

All of these books have charming pictures, and I was confident I would enjoy reading them aloud. So many books, so little time to spend with grandkids! We didn’t read even half of them today, but we enjoyed the ones we did read very much. I will mention only three of them here:

  1. Baby Counts has only ten words in it, but the pictures made my 2-year-old grandson laugh so much that we reread it as soon as we finished it several times. He already knew how to count to four and delighted in counting along with me.
  2. Ten Apples Up On Top is as captivating now as it was when my children were young.
  3. I was surprised how much kids who have never heard of the tooth fairy enjoyed A Quarter from the Tooth Fairy.

I look forward to enjoying all of the books with my grandkids when they visit me in the future.

I looked but didn’t find any math-related games at this thrift store this time. One of the people I follow on Twitter reminds us that some great games can often be found there.

Factors of 1643:

  • 1643 is a composite number.
  • Prime factorization: 1643 = 31 × 53.
  • 1643 has no exponents greater than 1 in its prime factorization, so √1643 cannot be simplified.
  • The exponents in the prime factorization are 1 and 1. Adding one to each exponent and multiplying we get (1 + 1)(1 + 1) = 2 × 2 = 4. Therefore 1643 has exactly 4 factors.
  • The factors of 1643 are outlined with their factor pair partners in the graphic below.

More about the number 1643:

1643 is the hypotenuse of a Pythagorean triple:
868-1395-1643, which is 31 times (28-45-53).

From OEIS.org, we learn that not only is
1643 = 31 × 53, but also
1643₁₀ = 3153₈.

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