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.

1071 What I Bought at the School Book Fair

Our elementary school recently had a book fair. I purchased three books, and I’d like to tell you a little bit about each of them.

Optical Illusions by Gianni A. Sarcone and Marie-Jo Waeber will make a nice addition to my other books on optical illusions. This one is special not only because it has a moveable design on the front cover, but also because it includes instructions on how kids or adults can make their own optical illusions. Mathematics and art often both play a part when an optical illusion is created. There is so much information in this book that I haven’t read it completely yet, but I like what I’ve read so far.

When Sophie Thinks She Can’t by Molly Bang brings up several subjects including math anxiety, bullying, and growth mindset. It also introduces tangram puzzles and making rectangles from 12 squares. Anytime you feel inclined to say, “I can’t!” add the very important word, “yet.” I like this book a lot and read it to a class of 5th graders right before I introduced them to the Find the Factors puzzles. (As I handed out the puzzles, one student with a sense of humor called out, “I can’t do these puzzles.” I smiled and said, “That was a good one,” and then proceeded to make sure every kid in the class could at least do the first few levels of the puzzle.)

All Year Round by Susan B. Katz with cute pictures by Eiko Ojala. This book uses appealing rhymes to intertwine two important early mathematical concepts: the calendar and simple geometric shapes. Some of the shapes even introduce concepts in solid geometry.

At first, I didn’t buy this book because a few things disappointed me:

  1.  It seems to imply that flowers with four round petals are shaped like a square. (The flowers are in a square box, but the focus in on the flowers, not the box.)
  2. Baseball diamonds are actually squares. Turning it on its corner does not change it from a square to a diamond, or rhombus, as it is called in mathematics. (I decided to forgive this because every square is technically a rhombus even though not every rhombus is a square. And besides, a baseball playing field really is called a baseball diamond.)
  3. Unless you cut off the rounded top of a slice of pumpkin pie, you won’t really have a triangle shape; you will have a sector. Yes, sectors look a lot like triangles, but they are not triangles.

However, after going home and thinking about it, I decided that these complaints can be good conversation starters so I went back to the book fair and bought the book. Besides, commonly-used shape names do not necessarily match correct geometric terms. I have read this book to one of my granddaughters, and we enjoyed reading and seeing how the world changes over a calendar year and identifying the simple shapes in the illustrations.

Since this is my 1071st post, I’ll share some facts about the number 1071:

  • 1071 is a composite number.
  • Prime factorization: 1071 = 3 × 3 × 7 × 17, which can be written 1071 = 3² × 7 × 17
  • The exponents in the prime factorization are 2, 1, and 1. Adding one to each and multiplying we get (2 + 1)(1 + 1)(1 + 1) = 3 × 2 × 2 = 12. Therefore 1071 has exactly 12 factors.
  • Factors of 1071: 1, 3, 7, 9, 17, 21, 51, 63, 119, 153, 357, 1071
  • Factor pairs: 1071 = 1 × 1071, 3 × 357, 7 × 153, 9 × 119, 17 × 63, or 21 × 51,
  • Taking the factor pair with the largest square number factor, we get √1071 = (√9)(√119) = 3√119 ≈ 32.72614

1071 is the hypotenuse of a Pythagorean triple:
504-945-1071 which is (8-15-17) times 63

OEIS.org informs us that 6³ + 7³ + 8³ = 1071, making 1071 the sum of three consecutive cubes.

1071 is consecutive digits 567 in BASE 14 because 5(14²) + 6(14) + 7(1) = 1071

913 Haunted Ten Frame House for Ten Timid Ghosts

Last year right before Halloween, I read a wonderful book to a class of kindergartners. The book was Ten Timid Ghosts by Jennifer O’Connell. The students drew haunted houses and a few trees. As I read the story, they used ten bean counters to show where each ghost was during the story. At any given time each ghost was either in the house or in the woods. They could see lots of number sentences as the story progressed.

This year I liked the idea of making a haunted house with ten window frames and ten sections for the trees in the woods. That way each of the ten ghosts could have a specific place to be throughout the story. I made the ten frames vertical to make odd and even amounts easier to see. There seems to be some ghostly figures flying around the tree branches, too.

You are welcome to use this haunted house as you add and subtract ghosts from the house and the woods. You’ll need some ghosts, too. Dry great northern beans are white and make great ghosts. If you like, you can add eyes and a mouth to the ghostly beans with a marker.

For those who would rather use less printer ink, I’ve made a similar picture that can be colored after it is printed:

You may also want to look at another activity that uses this same book. Sara Gast’s power point was especially made for kids with autism, but other children would enjoy it as well. You can use her activity to reinforce the concept of ordinal numbers, too.

Young children everywhere are sure to enjoy this fun book as they learn to count and to add and subtract.

Now I’ll write a little bit about the number 913.

If you’ve read my last few posts, you may have noticed that 910, 911, and 912 can each be represented in BASE 26 using their base ten digits in a different order. That pattern continues for 913. In fact, it is true for 914 – 919, as well. However, 913 is even more special because not only is it 193 in BASE 26, it is also 391 in BASE 16. Thank you, OEIS.org for that fun fact.

9 – 1 + 3 = 11, so 913 is divisible by eleven.

  • 913 is a composite number.
  • Prime factorization: 913 = 11 × 83
  • The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1) = 2 × 2 = 4. Therefore 913 has exactly 4 factors.
  • Factors of 913: 1, 11, 83, 913
  • Factor pairs: 913 = 1 × 913 or 11 × 83
  • 913 has no square factors that allow its square root to be simplified. √913 ≈ 30.2158899