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!
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! : )