2017-09-04 Numberless Word Problems

There are two things that I learned about toward the end of last school year that got me so excited I couldn’t wait to try them, Numberless Word Problems was one of them. One of my #eduheroes, Brian Bushart (@bstockus on Twitter), created this idea some time ago, and I was just learning about them. So, I wanted to get a couple reps in ASAP, and I was able to get a couple of reps in before the end of the year, and it confirmed my initial excitement.

With this school underway, I want to jump in early and often to get everyone on board with this idea, exposing all students to this opportunity and making it an ever growing area of powerful learning. On this journey last year, I was able to modify this into a sequence of learning events, where we start with a #NoticeWonder activity that builds the Numberless Word Problem the students create. Since students create the word problem, whether or not there are numbers is there choice, and it is so interesting what they come up with. The students smash their questions together to make a new question, and then they answer their question (or switch with another group and answer theirs) four ways.

Once the students have shared their answers and we’re all on board with the questions and answers, we compare our information to the state standards example(s). Students are always surprised that their questions are much harder than the state examples and think the state question is easy. Compared to previous times when given the state question, they typically shut down because it’s “too hard,” I’d say this is an amazing outcome.

Anyway, it’s still a work in progress and I’m super excited about it. Thanks Brian for sharing and making us all a little better.

Cheers to Better Deals – The Inequality Story

downloadAlthough I have attempted to teach this topic in many ways at a variety of levels, I always find it interesting to see how learners attempt to grapple with the concept and understanding. Learners who struggle with understanding linear graphs typically have an even more difficult, and when you add-on this is the first time the learners have literally ever met the material I am at the source of the stream that I  see in higher education. The topic is linear inequalities, the grade level is sixth grade, and I am attempting to teach these young minds this topic in 50 minutes, or less, and it is their first time (Does anyone else hear the Mission Impossible theme song here?) Well, I accepted the mission, I would attempt this process, twice actually, as I would teach this lesson back-to-back in two different group of 6th grade learners. As you are aware, I am a huge fan of 3 Act math lessons, with one of my favorite resources coming from La Cucina Matematica, where they shared Estimation 180 and found this amazing 3 Act lesson. As with any lesson, I have to adapt it a little to make it match my teaching style, and went in feeling ready to give it a tackle. In my career, this is the first time I have attempted to teach this lesson with a 3 Act component, and it is the first time I felt compelled to not give any instruction, but let the students conversation and discovery lead the way. One of the big pieces I was looking forward to was having students see their responses projected in front of them with Desmos, using their group responses to guide the inquiry. One note on this topic, I would prefer to have assigned each student their own opportunity to play on Desmos and then share out whole class, but I would need some additional front loading days to teach students how to interact and use Desmos, which I am unfortunate in that I didn’t have that opportunity, so we did that part whole class. My lesson followed this the PPT I made here or you can see below, which went off overall pretty well.

Immediately, I must say that the kids in the first class thought that Woody had cussed in the first act, so the second time I gave the lesson I had to front load that the bleep was covering up the answer to a question we were looking to answer. Another thing I picked up on right away, is that students struggled with figuring out what the humor was, they needed the mathematical background to understand what the reason for the humor was, which is an avenue to pursue with them later. The way that the various groups interacted, the way in which the conversations went within each group depended a lot on what they noticed from the clip. I was surprised by the number of kids who actually knew the show, a big thanks to reruns and older parents, as those students were more interested in the problem since they had more background knowledge of the show. The beautiful thing about this lesson, is that the discussion and interactions gave the students the opportunity to discuss and find the break even point, with about half the students understanding why the deal was better or worse. Quantitatively speaking more than 90% of the learners were able to understand that $25 per week was the break even point, and they were able to understand that certain values like $30 a week was greater than while $20 a week was less than the value of the original deal. We started to talk about how $24.99 per week was still less than the original $100 a month raise, while $25.01 per week was greater than the original $100 a month raise; however, there were only about six kids per class that were able to articulate this point and why in their exit slips. The next steps in this lesson would be to flush out the idea mentioned above, that any value greater that then $25 per week is a better deal (more money) for Woody, while any deal of $24.99 per week or less is a worse deal (less money) for Woody. The discreteness of money helps make this more concrete which was one reason I thought it might be very valuable for these learners, not to mention money is something they are familiar with. Overall, I would say the lesson went well and promoted a lot of great discussions among the students, it removed any prior need for mathematical knowledge so all kids had an entry-level assessment into the game, and the students discussing the break even point was a huge win. The use of Desmos really helped visualize it for students, and will give them some place to start building on. I feel confident this was by far the best attempt at securing an understanding of this difficult concept and I imagine that with follow-up and repeated visits this topic will be mastered by most of these young learners.

A Hard Act to Follow

After attending one of the most powerful mathematics professional developments with Matt Vaudrey and John Stevens as the chefs in La Cucina Matematica they shared a wonderful site that fits right up my teaching alley, Estimation 180. The site offers a day-to-day estimation scheme, which helps students increase their mathematical thinking and sharpens their estimating skills. I love the idea getting students to use their instinct and to reason through their thinking on figuring out these problems. I always find it amazing how even the most reluctant learner will throw their hat in the ring with a compelling prompt, taking a risk when there is no wrong or right answer. The learners are always so passionate about their reasoning and it sparks some great on topic discussions.

That aside, Estimation 180 offers another nugget of gold, which are pre-made lessons, based on the 3 Act strategy implemented by Dan Meyer (to the best of my knowledge he is the first person I know to coin this term). On the teaching front, I often adopt this model, I find it is a natural way to increase students buy in and a fun way to facilitate learning. My background is based heavily in secondary and college curriculum, so I have spent this year getting my feet wet with the elementary grades. Of the number of lessons I have done this year in lower grades, I was extremely excited to see an awesome lesson prepared at Estimation 180, ready to go, which I saw as the second graders I was planning the lesson for are just entering addends with three digit numbers. The lesson, Bester Egg Tower, was a perfect starting point, I built a presentation around it, and went to try out the lesson. A preview of the materials I downloaded and my presentation are here.

The lesson went off very well, the kids were so excited, we had them sharing in groups of three, building the trays of eggs with ice cube trays, and Styrofoam colored eggs (colored for each group). The pace was pretty quick, as I tend to be very high energy in the classroom (a behavior management and buy in tactic as much as my personality), and I like to keep things moving according to my quick formative assessments, I adjust as necessary.

Although I felt great about the lesson, there were many things I learned that I will be more aware of with more practice. First of all, when students wrote what they noticed and what they wondered, I was surprised that about half the class didn’t know what to write. As a teacher, I am concerned because the 6 year-olds in my life are suffering from the same condition, they are not as excited about school, and don’t ask nearly as many questions as I would imagine they should be at this age. If kids don’t wonder about anything, then learning doesn’t follow as readily. So front loading what it is to wonder, and having question stems (and sentence frames) will be great additions to this lesson.

That being said, the next thing I was surprised to have students share out as their questions (which are recorded in the notepad document here) were either about why the chickens moved so fast or why the teacher was stacking the eggs. I was anticipating the latter, but reflecting on the lesson the former makes a lot of sense, as kids wouldn’t be used to seeing chickens moving in high speeds….leave it to kids to point out the obvious and make the teacher wonder.

The biggest moment for me came, when I asked the kids about the ten frame the carton of eggs, I asked the kids to compare and contrast the two. One student shared he contrasted that one was even and one was odd.

Ten Frame vs Egg Carton

As you can imagine, my teacher brain was thinking but they are both even, and I was thinking I needed to ask for clarification. My normal inclination may have been to ‘jump in’ to ‘save this poor kid’, but I didn’t and I asked for clarification. The student said that the ten frame as five in a column and the egg carton had six, so one is odd and one is even (granted those weren’t his exact words, but that’s what he meant). Do I really need to say more here? Wow, I know.

One adjustment I would make for next time is to have a picture of just one row of the stack of eggs, I think having the kids get to the point where they are understanding just one row (3 dozen eggs, so 36 eggs in a row) is a great starting point to move forward. We finished on getting kids to the “doubles” plus 1 number of 12, and we talked about the strategies the kids used to get their result.

All in all, it was a tremendous amount of fun, and I can’t wait to do this lesson, in another second grade class. I can also tell the students loved the time we spent, because it took literally 3 full class hugs and several high fives for me to be able to get out the door. Two weeks later, I see a group of those kids on campus, they run over to me, hug me with unison cries of “When are you coming back….” Needless to say, second graders may be my new favorite grade level, at least until I teach Kindergarten again.

Here are some students’ work from the day, I tried to capture the range of responses that the kids produced, the gradient of abilities.

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A huge thanks to the chefs at  La Cucina Matematica and for the folks at  Estimation 180 for making these great resources available and for inspiring some alternative fun. I have loved the 3 Acts theme for a while, but seeing that it works with second grade was amazing. The last thing I forgot to mention is that the kids had a very hard time estimating how many eggs they thought would be in the tower, this shows that the kids may not have a strong sense of the size and quantity of these numbers. As they are just now learning about 3 digit addends, I think this reflects in their difficulties with estimation, which is another reason why the estimation practice may be helpful – especially in terms of thinking about the reasonableness of their answers in their own work (some SMPs) in the mix as well.