# Consecutive Sums – 5th Grade

We did Fawn’s Visual Pattern #8 today! http://www.visualpatterns.org/

After completing steps 1-4 the class quickly saw that each time, the step added with the previous step’s unit count to get the new unit amount. From there, they struggled to get to the nth expression. They tried a bunch of different things, as you can see on this paper and saw various ways it was growing, but could not come to an agreement on this one!

On their calculator they could get the 43rd step, but if I asked about the 100th, they would just continue adding on the calculator. In their explanations, they kept saying that they would visually “set that one penguin on the bottom row aside and then it would be 3+2+1 or 4+3+2+1…etc” And then one student came up with this at the bottom of their paper..

This group also had some very nice work toward the nth expression…

They wanted me to tell them what it was, but of course I would not:) I will let them sit with that overnight and do a Notice/Wonder about consecutive numbers tomorrow to start our day together. I am thinking after some noticing, they will be able to apply it to this work!

-Kristin

# Visual Patterns Fun!

Each day, I start class with a math routine. Whether it is a Number Talk string, If I Know Then I Know, Closest Estimate or Quick Image, those first 10-15 minutes are always my favorite math conversations of the day! Today I added Fawn’s (@fawnnguyen) Visual Patterns into the mix.  I spend a lot of class time having students look for patterns and regularity in their math work, but this visual brought a wonderfully different “feel” to their work. As Fawn had previously blogged, the Visual Patterns have an entry level for everyone and every student in my classroom engaged immediately with the images.

I chose this one to kick off our work today:

I asked the students to work as a group to find the number of unit for Steps 1 – 6, 13, 43, and then n. Being their first time, we had to deal with what the “n” meant and after the initial “Is this algebra?” followed by numerous stories of siblings who are doing this math with letters, they were on their way. It was interesting to see some students go straight to drawing each image, others started looking for what was changing as the steps progressed, and then there were the students who love going straight for an expression for finding 13 and 43. After they all had the table completed, we came together to fill it in. I was so impressed with their work and their ability to find the expression for the nth shape, however the BEST part of the conversation was taking that expression and connecting it back to the images. Why was n doubling? Why is that 1 being subtracted?

I love how this student used a specific example to connect his expression (or almost an expression, we’ll get there:)

This student found the equation and decided to use “a” to stand for “answer.” I loved how she then tested it with other numbers.

These two students then put a different spin our our work. Every group in the room came to the expression n x 2 -1, and as one student was explaining how the 1 needed to be subtracted because it was being double counted, another student exclaimed that his group figured out that if you just split that block in half and made each said a mixed number you just had to multiply that by 2. For example on step 4, if you made each side 3 1/2 x 2, you would arrive at the same answer. How awesome!

I am excited to make this a part of my daily math routines, thanks Fawn for sharing, awesome stuff! I had students asking for another one before they left class that day, they loved it!

-Kristin