Did You Guess How Many?

Did you count, add, multiply, and subtract to find out?
Here's what I came up with. Do you agree? 

• How many quilts are in the book, including the cover?
• Did you know I cheated?  I only made one quilt for “Nose Knows” and “Mirage”.
• Can you see what I did to trick you into thinking it is two quilts?
• Mirage is upside-down.
• There are 20 quilts.
• How many different geometric shapes can you find in the book? 
• I found 6 that I can name. 
• Can you name them?
• Triangle, square, rectangle, trapezoid, parallelogram, and quadrangle. I also found 5, 6, 7 and 8 sided shapes. A shape with 5 sides and 5 angles is a pentagon, one with 6 sides and angles is a hexagon,  7 is a septagon, and 8 is an octagon.  We usually think of these shapes as having equal sides and angles, but the definitions don't say that.
• Here's where I found those shapes:
• 5 sided: butterfly, cows, "Magic Show"
• 6 sided: cherry leaf, "Magic Show"
• 7 sided: cherry
• 8 sided: snowman, cherry
• Do you know a name that would include all the other shapes?
• All of these shapes are polygons.
• How many of the quilts use geometric shapes? 
• 19
• How many don’t?
1

• How many quilts have at least one triangle?
• 11
• Which quilt has the most triangles?
• Pieces
• Can you figure out how many?
• 652 in the half-square triangle pattern, 14 in the snowman, 9 in the bird, 8 in the pumpkin, and 17 in the butterfly for a total of 700. Of these, about 56 got a corner cut off when I sewed on the border, so they don't show as complete triangles in the book. Without them the answer is 644. 
• Which of the quilts with at least one triangle has the fewest triangles?
• I think that would be "Do You Know Green", but it has a couple pieces which are very close to being triangles. If you count those, it ties with "Just When I Thought."
• How many does it have?
• I counted 4, but it could be 6.

• How many quilts in the book are made mostly with squares?
• 11
• How many quilts are made only with squares?
• 3
• How many quilts have squares as part of the design, including the borders?
• 14 (Pieces has squares that are made of triangles.)
• How many have squares ONLY in the borders?
• 2

• Not counting the cover, which quilt do you think has the most squares?
• Mirage and Nose Knows has 480. 
• If you counted the cover it has the most, 574, I think.
• Why do you think that?
• The fact that the squares go right to the edge is one good clue. To Each His Own would have the same number except some of them have been divided into triangles and quadrangles.  Come to think of it, those parts still make squares don't they, so maybe these two quilts tie.
• Are you counting the partial squares that you can see all around the edges of “To Each His Own”, “Nose Knows” and “Mirage”?
• If you don't count those I think that gives "Nose Knows" 418,  (396 on the "Mirage" page) and  "To Each..." 396 because of the way they are positioned on the page. 
• Isn't it interesting how even if you are dealing with number facts, you can think you are answering the same question but come up with different answers?
• I can think of two ways you could find out how many squares are in each quilt.
• How many ways can you think of?
• The ones I can think of are counting and multiplying (which involves some counting but not as much.)  I suppose another way would be to count the squares in one column and then add for each row. 
• What would be the easiest way for you?
• It's easy to get lost when you are counting such big numbers, but if you can't mulitply yet, it still could be easier.  Or maybe you just think it's more fun.
• How many squares are on the cover?
• Whoa! Was this one hard to count!  Those corners gave me a hard time. I decided to count the ones I could see easily and came up with 594 squares on the front cover. There are another 8 squares in the snowflake for a total of 604. If we're counting squares that show on the cover we'd need to double that, for a total of 1208 (unless you don't count the few squares hiding under the ISBN lable. The total number of squares I actually used in this quilt is 787. A lot of them don't show. The total number of pieces showing is 753. The total number I used is 938.
• How many squares in all do you think are in all twenty the quilts I made for this book?
• 46 in "Ballet", 480 in "Nose Knows", 357 each in "Encore" and "Misplaced", 228 in "Noontime", 204 in "Rock and Roll", 435 in "To Each His Own", 333 each in "Pageantry" and "Ode to a Rake", 252 each in "Silouhettes" and "Shadows", 68 in "Winter Sunshine", and 600 showing in the cover for a total of 3945 (4283 if you count the ones in the cover that don't show).  Of course, there are lots more if you count the squares that are made of triangles in "Pieces", "Rock and Roll", and "To Each His Own".
• How many squares are in “Encore”?
• 357
• If I added another row all the way around how many squares would that be?
• Another 80 for a total of 437
• If I added two rows all the way around how many would that be?
• Another 88, or 168 more, for 525
• Are there more squares or more rectangles in the book?
• Rectangles.
• Why?
• Every square is a rectangle, but every rectangle isn't a square. A rectangle has to have four sides and four square corners. A square has to have four square corners and four equal sides.
• Are there more quadrangles or more rectangles?
• Quadrangles.
• Why?
All rectangles are quadrangles, but not all quadrangles are rectangles. A quadrangle has to have four sides, but not necesssarily four square corners.

• Of the quilts that are NOT made with squares, which one do you think has the most pieces?
• Be careful. Sometimes the quilting lines can make one piece look like more than one, and sometimes one fabric looks a lot like it's neighbor so it looks like one piece when it's two.
• This is VERY close. "Good Heavens" has 737 and "Pieces" has 734. Since the pieces are so hard to count, it may be close enough to call it a tie. 
• Why did you choose that quilt?
• You can probably tell just by looking. The pieces in "Good Heavens" are very hard to count because of the quilting and close color match. Since I knew how I made it, that was a big help.
• Do you think it has more or less pieces than the quilt with the least number of squares?
• More. This one's easy to see, right? You don't even have to count.
• Do you think it has more or less pieces than the quilt with the most squares?
• More again. In the case of "Pieces" it is a good clue that each two triangles makes one square that is the same size as the squares in the other quilts. 
• Which quilt do you think has the least number of pieces?
• Takeout has only 51 pieces.

• Can you estimate how many pieces of fabric are in all twenty quilts I made for this book?
• I’m going to include all the borders in my count.  Can you see how some of the borders are made with 4 pieces of fabric—2 across the top and bottom and 2 on the sides? Some have 8 pieces of fabric. 
• As nearly as I can count, going by what you can see in the book there are 7088 pieces.  Because some parts don't show, I believe I used 7273.  Some of these are VERY hard to count, so if you've come even close to this answer you've done a great job!

• Can you make up your own math problems about the quilts?
• PS: Maybe you could make some up problems and give them to your friends.
• PPS: Be sure you know the answers!

Pieces: Squares, triangles, quadrangles, trapezoids, and 5, 6, 7 and several 8 sided shapes, plus rectangles in the borders. I counted 26 pieces in the snowman, 24 in the butterfly, 17 in the pumpkin, and 14 in the bird, for a total of 81 pieces in the symbols. 48 of those are triangles. There are 652 pieces in the triangle pattern for a total of 733 pieces, 700 of them triangles. Add 4 for the border for 737.  This is a really hard one because some of the pieces barely show around the edges. If you used the patterns to count the pieces in the season symbol there are 24 in the snowman, 11 in the bird, 15 in the pumpkin and 19 in the butterfly, for a total of 69 pieces in the symbols. 35 of those are triangles. After I made my quilt I saw a better way to make these which is what I've put in the patterns.  This makes a total of 721, 687 of them triangles.

Ballet: Triangles and quadrangles in quilt, 162 pieces, 31 of them triangles. Border has 46 squares, 100 triangles and 8 rectangles for a total of 154 in the border and 316 all together.

In March: Trapezoid, parallelogram, quadrangle, triangle. 111 plus 8 borders, total 119. 

Just When I Thought: Trapezoid, parallelogram, quadrangle, triangle. 98 plus 8 borders, total 106.

Do You Know Green?: Trapezoid, parallelogram, quadrangle, triangle. 239 plus 4 borders, total 243. 

Good Heavens: Triangles, quadrangles. 691 plus 43 in the borders. This one is hard to count because sometimes the quilting makes it look like two pieces when it's one, and sometimes the fabrics are so alike it looks like it's one when it's two. Total 734.

Nose Knows and Mirage: All squares. 20 x 24 = 480.

Takeout: No geometric shapes. 47 pieces and 4 border pieces for a total of 51.

Encore: Squares, 21 x 17 = 357, plus 18 flowers and hummingbirds sewn on top for a total 375, plus 4 border pieces for 379.

Misplaced: Squares, 21 x 17= 357, plus 21 flowers sewn on top, for 378, plus 4 borders is 382.

Noontime: Squares,  triangles, quadrangles,  2 five-sided and 1 six-sided shape, plus rectangles in the border.  Also rectangles in the border. 228 squares, 10 triangles, 257 pieces, plus 8 in the borders, total 265.

Rock and Roll: Squares and triangles, rectangles in the border. 204 squares, 88 triangles, 301 pieces, plus 8 in the border, total 309.

To Each His Own: Squares, triangles and rectangles. Full squares showing are 22 x 18 for a total of 396 minus 45 squares that were replaced with 80 triangles and 15 quadrangles, or 351. Actual squares used (we can barely see the edge of the ones along the bottom, are 20 x 24, or 480,  So 435 squares, 80 triangles, 15 rectangles and 5 stems equals a total of 580.

Pageantry: All squares with rectangles in the border. 283 squares plus 50 that show only a corner equals 333 plus 8 pieces in the border for 341.

Ode to a Rake: Same as Pageantry, 341.

Silhouettes: Squares, rectangles in the border. 252 squares (14 x 18), 68 pieces in the tree trunks (as near as I can tell!), for a total of 320, plus 4 in the border, for 324.

Shadows: Squares, rectangles in the border. 252 squares , 70 pieces in the tree trunks for a total of 322, plus 4 in the border, for 326.

Winter Sunshine: Triangle and quadrangles in quilt, squares and rectangles in border. Of 66 pieces in quilt, 47 of them are triangles. 68 squares in the border, plus 2 little rectangles because squares didn't fit, plus 4 rectangles in the outer border for a total of 140.

Magic Show: Rectangles, triangles, quadrangles, and a few 5 and 6 sided shapes. 164 pieces, 42 of them triangles, plus 4 border pieces equals 168. 

Total 6335 pieces in the interior quilts.

Cover: Squares, triangles, quadrangles, rectangles, plus 5, 6 7 and 8 sided pieces. This is another really hard one.  Those diagonals are tricky, especially, when they get a little skewed. I counted 594 squares on the front cover, including corners that were big enough to see easily.  I actually used 779 squares, but the edges don't all show. I counted the following pieces; bird 11, snowflake 33, leaf 19, flower 29, pumpkin 16, butterfly 19 and snowman 24, plus 8 rectangles to space the pumpkin, flower, leaf, and bird which makes a total of 753 pieces showing, 938 in the actual quilt. (Later I put on a border of 8 pieces.)  In the snowflake 8 of the pieces are squares so if we are counting the total number of squares I used it's 787, showing are 600.

Total for all the quilts, going by what you can see is 7088; actual quilts, 7273.  Some of these are VERY hard to count so if you came anywhere close to this number you've done a great job. In fact, I'm not so sure I'm exactly right.
 
The following table shows the numbers of pieces, squares and triangles in each quilt as accurately as I was able to count.

Name of Quilt	Number of pieces	Squares	Triangles
Cover	753	600	80
Pieces	737		700
Good Heavens	734		70
To Each His Own	580	435	80
Nose Knows and Mirage	480	480
Misplaced	382	357
Encore	379	357
Pageantry	341	333
Ode to a Rake	341	333
Shadows	326	252
Silouhettes	324	252
Ballet	316	46	131
Rock & Roll	309	204	88
Noontime	265	228	10
Do you Know Green?	243		4 or 6
Magic Show	168		42
Winter Sunshine	140	68	47
In March	119		10
Just When I Thought	106		6
Take Out	51

Do more math to Pieces...

• The amazing shrinking squares!
• Designing with Half-square Triangles