Saturday, September 29, 2012

Fabric Pumpkins

I love the fall! It's a perfect time of year for making soups with lots of veggies! Lately I've had this obsession with squash soup. Have you ever tried it? It's pretty tasty! So, speaking of squash-like things...this year I've started up a new tradition...sewing up fabric pumpkins!
This idea was inspired by my friend, Gina's kindness. She generously gave me a box of all different types of fabrics. Of course, I needed to make her something to say thank you! Since fall is here, I thought that a little pumpkin patch would look just perfect in her house! And then I totally needed my own set!

Do you want your own set of pumpkins? Let me know and I will sew you up a trio!

Wednesday, September 12, 2012

Distributive Duo Quilt (Part 2 of 2)

After I had such a good time making the first distributive property quilt, I just knew that my work was not complete! I had to make another quilt to show a different way to look at the same problem-29 x 39. So basically, here is a new quilt illustrating a new strategy using the same problem!
This strategy is basically single number partitioning by a decade number. For example, I did not partition or break up the factor 29. The only factor partitioned was the 39 using the decade number 10, so I ended up with 10 + 10 + 10 + 9 = 39.
This strategy is easier for me to do mentally because I only have to keep track of the partitioning of one factor in my mind.  Also, when students think of this problem in context of a real-life situation, many times they will use this strategy because it doesn't always make sense to break up the amount in the group. Let's look at an example: Bettina has 39 photo albums. There are 29 pictures in each album. How many total pictures does she have? Based on the context of the problem, a child would likely partition the photo albums (groups) and keep the number in each group together.

The quilt also helps visualize how you could use compensation to solve the problem.  For example, since 29 is so close to 30, I can actually solve the problem by using (30 x 10) + (30 x 10) + (30 x 10) + (30 x 9). The tricky part in finding the exact answer comes from making sure to deal with the extra at the end because I added a row of 39 by rounding to 30. So, now I have to subtract a row of 39. Can you follow my thinking?

Back to the pictures...
The Distributive Duo! 29 x 39 = 1,131 (in square inches)
Two different quilt backs. The left one has beautiful elephants and the right one has feathers!

Thanks for reading about my quilts and the mathematics involved! Can you think of another way to look at this same problem? My friend Diana did! I think I might have to make a 3rd quilt. 
Could this be the beginning of the distributive trio?

Monday, September 3, 2012

Distributive Duo Quilt (Part 1 of 2)

Heads Up: This is a math concept quilt so be prepared to read about math! I will be creating a series of math projects. If you are interested in reading about these, you will find them linked on this page.

I knew I needed a lap quilt for the office, but I went back and forth about the type of pattern I was going to create. Should I do another log cabin, something three-dimensional looking, just improvise something?....I really couldn't decide. Then it hit me like a ton of bricks! I proudly present to you the Distributive Duo Quilt (Part 1 of 2)!
A little background story...
Have you ever felt like you KNOW you learned something in school several times but you never UNDERSTOOD what you learned until one day you suddenly UNDERSTAND what you thought you KNEW? Yep. Something like that.

That question sort of describes my journey with elementary mathematics and is a big part of who I am today. I used to have math anxiety and now my full time job has privileged me the opportunity to relearn elementary mathematics. It's one of the most interesting jobs I've had to date. Approximately one-third of my work day is spent studying patterns, making conjectures and learning the best way for children to have this same opportunity.

For the 'Distributive Duo Quilts', I wanted a lap quilt for the office paired with the area model using square inches to show the distributive property of multiplication or commonly called, the distributive property of multiplication over addition. This quilt is basically the multiplication problem, 29 x 39--in square inches. If you are a 3rd, 4th or 5th grade teacher this might look familiar because it is an important mathematical model! : )
A big understanding in elementary math is that numbers can be composed and decomposed. So, I purposefully sewed the rows of squares into groups of 5-an important benchmark number.
Here are all of the pieces before they came together.
'Mac the Ripper' was in the mix as I sewed the rows and columns of squares together.
I love how the back looked with all of the sewing. I wore it around like a cape for a few days. : )
Then, I draped it in the window for birthday week! The way the light illuminated the sewing patterns in the quilt was gorgeous. I didn't really want to quilt it at first! 
Quilt Sandwich!
Annie and the halfway done yellow binding! She is the real owner of all my quilts.
Skyping with Grandma!
It feels so satisfying to put a label on my projects! The backing fabric was full of those pretty feathers. I love feathery things!
Here is a close up so you can see the square inches. Now, I know that you could get your calculator out and figure out exactly how many square inches are in this quilt, but how could you estimate the product using the distributive property? (HINT: there are several ways to do it.)

This quilt shows a certain type of strategy called double number partitioning by decade numbers. Many people refer to this as partial products. In this case, I partitioned both factors by decade numbers, for example, 30 is partitioned into 30 and 9 and 29 is partitioned into 20 and 9. In the picture below, the factors are labeled in black. The products are labeled in white. There are basically 4 number sentences when partitioned in this manner:
20 x 30 = 600 (teal)
20 x 9 = 180 (mint)
9 x 39 = 270 (light blue)
9 x 9 = 81 (tangerine)

This strategy is the one that resembles the standard U.S. algorithm for multiplication. However, when children don't understand the meaning of the algorithm, mental computation is often difficult. One common error would be that students would only multiply 20 x 30 and 9 x 9,  forgetting the other two number sentences. Worse yet, some students never actually build an area model to help understand the meaning of multiplication.

The distributive property is really fascinating, so here is another way that you can look at this quilt. When I quilted the vertical and horizontal lines, I thought it would be useful to do the sewing in groups of 25 or every 5 rows and 5 columns. Twenty-five is a benchmark number that students enjoy using when counting. So, even if you didn't understand the multiplication in the quilt, you could have another way to count up all the squares.

Whoa! Haha! Now, this might not be the most efficient way to tackle the problem, but I did it to illustrate that there are many ways to manipulate numbers when learning and understanding concepts.

For example, let's look at this part of the quilt. If you remember, it represents 9 x 9. If you didn't know this multiplication fact (yes, I know the 9s trick, but let me ask you...why does that work?) how could you solve the problem using smaller facts that you do know? When I made this section of the quilt I noticed that 9x9, which is a square number, has two other square numbers inside of it! (5x5=25 and 4x4=16) And that got me thinking, is that true for all square numbers? It's these types of questions that elementary students should ask and answer every day in their math class! 

If you are confused about the distributive property, here is a video from KHAN Academy that might help. If you are a teacher considering what you could do with students, I would take a problem-solving approach vs. watching a KHAN Academy video where he explains it. Let the students discover and explain instead! Simply ask, "What is the area of a 29 inch by 39 inch rectangle?" Give them base-ten blocks and/or inch grid paper and have some fun! :)

Thank you for reading (part 1 of 2)--especially if you have math anxiety! : ) 

I made another quilt showing a different way to consider the distributive property. It's my favorite! Stay tuned for Part 2! : )

Sunday, September 2, 2012

Lavender Thank You Hearts

Recently, I celebrated my birthday! I have officially been around the sun 29 times!

Each year, I am truly blessed to have family and friends who always reach out to me. In fact, my Mama, Aunt Pam in Colorado, and both of my Grandmothers have never missed one! My boyfriend and his father have been celebrating all month long with me (I love 'BirthDayMonth'!) and my work friends made my day special as well. So, for all of these amazing people in my life, I created some thank you gifts as an expression of my gratitude!
 Heart-shaped lavender sachets!
Look what came in the mail! My labels!!! This project was a perfect way to get familiar with sewing them in the seam.
The same day I decided to make the hearts, I remembered that the farmer's market has TEXAS lavender! I purchased this quart sized bundle. My house smells goooooood.
Each heart has my label on the side.
I enjoy picking out fabric for my loved ones. When I Skyped with my Grandmother last week she loved the yellow fabric and my Mom was drawn to the purple. I love video chat!
The numbered ones were for my math expert friends.
Once I made one, I couldn't STOP!
Birthday rose blessings before the packages went into the mail. There will be some fragrant mail boxes this week!
THANK YOU to everyone for remembering me on my birthday!