# Better Questions: Math Rocks Meets Open Middle

This year I have been leading a cohort of elementary math educators in my district. We met for two full days in July – you can read about that here and here – and throughout this school year we’ve met every other Thursday after school.

In December, our meeting focused on the work of Robert Kaplinsky, specifically his IGNITE talk about productive struggle and his website openmiddle.com.

At the start of the session, everyone reflected on what “productive struggle” means to them. This is important because as certain phrases become popular in education, they quickly become jargon. I wanted to ensure everyone had a chance to think about how they interpret the phrase and share that with the group. Then we watched Robert’s IGNITE talk.

The image that stood out most to me from his talk was the one of the mom riding the bike for her child. It seems so silly, and yet there are many instances as teachers where we can find ourselves doing the thinking for our students instead of letting them try either on their own or with our support.

At the end of the video, Robert puts out a call to action for teachers to create opportunities for students to productively struggle. And why not start by having the Math Rocks participants do some productive struggling of their own? Regina and I posted 10 problems around the room. We let everyone loose to do some math for 15 minutes. They dove right in!

All 10 problems came from openmiddle.com. If you aren’t familiar with the open middle problem type, here’s a brief summary: (You can learn more here.)

• they have a “closed beginning” meaning they all start with the same initial problem
• they have a “closed end” meaning that they all end with the same answer
• they have an “open middle” meaning there are multiple ways to approach and ultimately solve the problem

After debriefing as a group and sharing information about open middle problems, we came back around to the idea of productive struggle with this video from Michael Pershan. The whole thing is interesting, but for the purposes of our discussion, we watched the first 30 seconds of the video, and then we watched from 1:45 to 5:45.

By this point, we had made our case and it was time for the participants to take a stab at designing their own open middle problems. They had a choice of writing one from scratch or taking an existing problem from our curriculum and redesigning it as an open middle problem. A nice surprise is that our adopted textbook, Stepping Stones, already uses open middle problems in many lessons and activities! They don’t name them as such, but that’s essentially what they are.

We shared out the open middle problems they wrote. Afterward we gathered them together in this document if you’d like to see our first attempts. We closed the session with their homework assignment – giving their students an open middle problem and reflecting on it in a blog post. If you’re interested in learning more about open middle problems – especially learning from teachers trying them out for the first time! – check out our open middle blog post collection.

The consensus from the group seems to be that they can initially throw kids off if they’re not used to being asked questions like this, especially for those kids who want to neatly and easily come to the correct answer, but the questions provide opportunities for the type of thinking and struggling we want our students to engage in and we need to be using them more often.

# My Favorite: Holidays at Target

Here we are in Week 2 of the ExploreMTBoS 2016 Blogging Initiative! This week’s challenge is to blog about one of my favorite things. During this school year, one of my favorite things has been visiting Target during the holidays. The holiday-themed merchandise is rich with mathematical possibilities! I already wrote three posts about a treasure trove of images from Halloween:

Valentine’s Day is around the corner, and I snapped some photos this evening to share with you. I’m going to cover a range of mathematical skills – mostly centered around estimation –  from Kinder through about Grade 6 to show you just how versatile this stuff is!

These first two images are good for estimating quantity. You can estimate the quantities individually. Don’t forget to ask students to estimate an answer that is TOO HIGH and one that is TOO LOW in addition to their actual estimate. Coming up with a reasonable range takes a lot of practice! You could also show students both images at the same time and ask, “Which package has more?”

I forgot to snap a picture of the answers, but I can tell you there are 15 bouncy balls and 24 eraser rings.

Here’s another one. How many Kisses are in the box?

I was kind of surprised that the answer wasn’t an even number like 10 or 12. This just seems oddly specific.

Students tend to estimate better when the quantities are smaller. Here’s a larger quantity package to up the challenge a bit. How many gumballs are in the bag?

I was kind of surprised to find out the answer myself.

This next one is tricky! How many truffles are in the box? Go ahead and make an estimate.

Now that you’ve made your estimate, I’d like to show you how deceptive product packaging can be. Would you like to revise your estimate?

And now for the reveal. How does your estimate compare to the actual amount?

The first few images dealt with disorganized quantities. Once we move into organization, the thinking can extend into multiplicative reasoning. The great thing is that it doesn’t have to! Students can find the total by counting by 1s, skip counting, and/or using multiplication.

There are several questions you can ask about these pictures. They’re of the same box. I just gave different perspective. I’d probably show the almost-front view first to see what kids think before showing the top-down view.

• How many boxes of chocolate were in the case when it was full?
• How many boxes of chocolate are left?
• How many boxes of chocolate are gone?

Here’s another package that could prove a bit tricky for some students. How many heart stickers are in this package?

Students might notice that the package says 2 sheets. If they don’t, you might show them the package from a different perspective.

And finally, you can reveal the total.

This next package can be shown one of two ways depending on how much challenge you want to provide the students. Even with some of the hearts covered, students can still reason about the total quantity.

This next one could simply be used to ask how many squares of chocolate are in the box, but what I’d really like to know is how many ounces/grams of chocolate are in the box.

After some estimating, you could show your students this and let them flex their decimal computation skills to find the total.

However, the reveal is likely to raise some eyebrows.

And finally, you can do some more decimal calculations with this final product. How much would it cost to buy all of the boxes shown?

And if you bought all 6 boxes, how many ounces of chocolate would you be getting?

Ten minutes in the holiday aisle and my iPhone are all it took to gather this wealth of math questions can now be shared with students. Even better, I didn’t have to purchase any of these products! Even better than that, I can go back for every major holiday to capture new images that will feel timely and relevant!

By the way, feel free to use any and all of these images with your own students. They’re fairly low quality so I don’t recommend printing them, but they should look just fine projected or shown on a screen.

Happy Valentine’s Day!

# A Day in the Life of a Curriculum Coordinator: Friday

Here are links to all the posts I wrote this week:

## Friday

If you’ve been following along this week, you’ll notice there’s no post for Thursday. That’s because I stayed home sick. I did check a few emails, but mostly I slept or lounged around the house feeling crummy. Not very exciting material to blog about. The highlight was going out in the backyard to refill the squirrel and bird feeders.

Granted, I took it slow today so I’m not sure how exciting today was either. I felt well enough to get up and go in to work, but after an hour or two, my energy level dipped and stayed low throughout most of the day. As I was getting ready to write this post I tried recalling my day and realized I did so many little things I couldn’t remember a lot of what I’d done! Thankfully much of it revolves around email, so a quick review of my Sent email folder did a pretty good job of refreshing my memory.

My first main task this morning was preparing our STAAR Ready assessment to be converted into Braille. The STAAR Ready is our spring district assessment for grades 3-5. Usually each subject area uses the previous year’s released state test. Unfortunately, Texas did not release the 2015 math tests so we had to put one together ourselves. Using the state test blueprints, we pulled one together for each grade level using sample items released by the state last summer and our own items we wrote for last year’s STAAR Ready. That was quite the ordeal right before and after winter break, and I’ll spare you the specifics. Needless to say, I’m looking forward to using the 2016 released tests next school year!

Anyway, back to today, I had to convert the PDF of the 5th grade assessment to a Word document because reproducing the test in Braille, especially the graphics, works much better in Word. Thankfully Adobe Pro makes converting a PDF to Word super easy, but that doesn’t mean the resulting document is flawless. I went through the Word document question by question to ensure text and/or graphics converted correctly. For the most part they did, but every now and then a table or fraction didn’t convert correctly so I had to fix it.

Once that was done, I stopped to review our department budget. This is one area of the job that was new for me when I started a year and a half ago. I haven’t really had to do a lot with budgeting in previous jobs. My department is only two people, me and Regina, but we have a department budget that we use to pay for:

• Substitutes so teachers can come work on curriculum
• Extra duty pay to teachers or coaches to do after hours curriculum work
• General supplies – office supplies, professional books, etc.
• Memberships to groups such as TASM and NCTM
• Registration to conferences
• Snacks for teachers who attend PD sessions
• Other miscellaneous expenses

Since our budget is limited, I have to monitor how we spend our money as well as plan ahead to ensure we can pay for the things we want. For example, bringing in K-5 teachers for a few days in the spring to do curriculum revisions with us is probably our largest expenditure each year, so I have to keep that money untouched for most of the school year.

This morning I went through my budget, determined where money needed to be moved around to, and then sent off a request to make that happen. That’s one of the lessons I’ve learned in this role: We are highly accountable for our money and how it’s used! There are very strict policies and procedures surrounding it. For example, I can’t just spend willy-nilly. If I want to buy snacks but all of my money is in extra duty pay, then I have to submit a budget amendment for approval before I can spend the money. Most likely it’s going to be approved, but that goes to show how firm they are about the process. Considering our district is funded by tax payer money, they want to ensure we are using our money responsibly, ethically, and legally. And we must be doing something right, because we’re the only district in the state of Texas to earn a AAA bond rating from Fitch and Moody’s. (I had no idea what that meant at first, but apparently it speaks to how fiscally responsible we are.)

Speaking of money, once I sent off that email, I hopped in the car and drove over to our Purchasing department to pick up my new Purchasing credit card. This is what I use to pay for small expenses such as  food if I’m traveling out of town or if I’m at a conference and want to pay for some books. I was supposed to pick up the card back in December, but I’d been so busy I never felt like I could get away to go pick it up. Thankfully I can check that off my to-do list finally!

Now that I think a bout it, today was a very financial day for me. Once I got back to the office, I had to do some work with two orders that I recently submitted for the books Beyond Pizzas and Pies and Beyond Invert and Multiply and sets of Cuisenaire rods. All of the materials are going to our campus libraries, so I needed to communicate with them to let them know that the orders are going to be coming in soon. First I had to talk to our Library Coordinator to give her the information so she could create records of the items in our library system. Then I shared a spreadsheet with the campuses where they can log when the orders are received so we can then pay the vendor for the materials. The teachers who attended our fraction PD sessions on Wednesday are chomping at the bit for these materials, so I’m excited that they should be arriving any day now!

Before lunch I met with our Director of Response to Intervention to talk about training and support for math intervention. I shared ideas for diagnostic assessments and PD opportunities, including Math Recovery and Kathy Richardson’s Assessing Math Concepts series. It makes me happy that our district has been providing a lot of support to our interventionists last year and this year. I’ve been hearing some great success stories from some of our campuses which makes me even happier!

After lunch the entire Teaching & Learning Department (elementary and secondary) met in curriculum work committees. Back in September we took Level I Curriculum Auditing training, and now we’re doing work in committees to take what we learned and do what we can to improve our curriculum processes and materials. My committee is looking at the curriculum writing and review process. We’re looking at it from the perspective of any given year – what does the revision process look like in terms of timeline and tasks. But we are also looking at the cycle over multiple years – what work is done in year 1 of a curriculum, year 2, year 3+?

This has been interesting for me because last year was year 1 for the elementary math curriculum. The 2014-15 school year was the first year that teachers taught the new math TEKS, and boy was it a bumpy ride! We learned a lot, and as a result we made pretty significant changes for the 2015-16 school year. Now I have my eye on the revisions for the 2016-17 school year, and it’s interesting to see how I’m able to focus on different things now than I was able to in years 1 and 2. Those first two years were just about getting a handle on it. Now I feel like we’re in a place to refine and improve. It’s a lot of work, but I’m excited to see the curriculum evolving as we go.

After our committee meetings, we met as a whole group to share out, provide feedback, and ask questions. There’s a lot of work left to do, but it’s exciting that we’re able to shape our district’s curriculum together as a team.

And that wraps up my week! That’s just a taste of what I do day in and day out, but hopefully it provides some insights. If you have any questions, hit me up in the comments. Otherwise, I’m off to enjoy the weekend with my family!

# A Day in the Life of a Curriculum Coordinator: Wednesday

Here are links to all the posts I wrote this week:

## Wednesday

I am without a doubt sick. Yet I was so excited about our fraction PD sessions today that I made myself get out bed and go to work this morning. I’m so glad I did! Both sessions went so well, and I had such a great time working with the grade 3 and 4 teachers today.

Being sick, I’m not going to write a lengthy post today because I really just want to curl up on the couch and watch TV. (I already came home and crashed in bed for a few hours.) I took pictures throughout the day so I’ll let those do the talking for me today.

The grade 3 session focused on several activities: measuring with Cuisenaire rods to develop understanding of equivalent fractions, making and using fraction kits to draw attention to the importance of the unit fraction when composing and decomposing fractions, and using pattern blocks as a model for changing units and renaming what fraction each pattern block represents. Unfortunately I only snapped pictures during the Cuisenaire activities:

How many brown rods long is the marker?

If it is 1 brown and 2 reds long, how do we say that as one number in terms of brown rods?

Using Cuisenaire rods to measure on the number line to identify equivalent fractions between 0 and 1.

The fourth grade section had a different focus. We focused on relating fraction and decimal notation to build strong connections between the notation systems and what they represent, using multiple representations to build a more robust understanding of fractions and a more versatile repertoire of modeling strategies, and encouraging multiple strategies for comparing fractions to build students’ fraction sense and support later work in fraction computation.

We built our PD sessions around the book Beyond Pizzas and Pies. I was really happy with most of the book, with the exception of the chapter on relating fractions and decimals. All of the activities shared in the chapter are focused on the symbolic representations of fractions and decimals, but the understanding of the symbolic forms and how they’re related comes from making connections to concrete and pictorial models. So I made sure to talk about that some before sharing the activities from the book:

I also modified one of the activities from the book. It had the students make a human number line of fraction and decimal values. I didn’t like this idea because if students are *in* the number line, that makes it extremely challenging to simultaneously observe the number line as a whole and to see how different values relate to one another. Instead, I did a clothesline number line that allowed teachers to position and reposition numbers as needed. From the session feedback, the teachers loved it!

You can’t read the numbers in this picture, but it gives a sense of how much room in which we had to play.

We talked about ways to modify this activity. For example, just making a number line of tenths in fraction and decimal form. The idea being that you can make a number line any time and in any way you want. What’s important is the thinking and talking as you go and after you’re done.

Another favorite activity was Fraction and Decimal Flip. This is great for building some estimation and reasonableness skills. The teacher calls out a fraction or decimal. Students clip their clothespin on the blank number line where they think that number is located. On the count of 3, everyone flips their number line to check their accuracy. In a few minutes of practice over several days, students can become more and more accurate in identifying the correct locations of the numbers.

I just realized I never snapped any more pictures of the other major sections of the session. Oops! My partner Regina did snap one of me introducing the section on multiple representations. I even managed to have my eyes closed.

In the final portion of the 4th grade session, we talked about strategies for comparing fractions. I shared two resources that are not from Beyond Pizzas and Pies. I did share the activities from the book, but I wanted to share the extra stuff here since you can’t find it in the book. The first is an activity called Fix It that came from a recent blog post by Marilyn Burns. The other resource is three “books” I wrote and shared in a blog post last year. The thought was that teachers could project and use them to help students reason about three comparing fraction strategies: common denominators, common numerators, and comparing to 1/2. I’ve found the books work best when opened in Adobe Acrobat because then you can jump from page to page rather than scrolling from page to page.

And that’s a wrap! Copies of the book Beyond Pizzas and Pies should be on campuses in a few short weeks along with class sets of Cuisenaire rods. From the comments and questions we got during our sessions, teachers are excited and ready for them to arrive. I couldn’t ask for better than that!

# A Day in the Life of a Curriculum Coordinator: Tuesday

Here are links to all of the posts I wrote this week:

## Tuesday

So in stark contrast to yesterday, today was quite the whirlwind! I started the morning at our office where I checked email, drank a cup of coffee, and chatted with Regina about our fraction PD sessions tomorrow.

Before I knew it, it was time to head out to the principals meeting to present about the upcoming STAAR math test. The principals meeting was being hosted at Dell this month instead of at our Admin office. When I arrived, a panel of Dell excecs was imparting leadership wisdom and answering the principals’ questions.

After the panel discussion ended, our elementary science coordinator spoke about the successes of implementing the Writing in Science program in our district over the past 4 years. It was really impressive to see photos and videos of the program in action, and it reaffirmed that the next chance I get, I need to attend one of her trainings to learn more about it! We have a couple of instructional coaches who are already looking at how to adapt and extend the components of Writing in Science to math, and they’re planning to share this during a summer PD session in July. I can’t wait!

After that inspiring presentation, I had my turn at the podium. The session went well and I got some good questions from the principals. One of them was if I’ll be repeating this session for the teachers. It got me thinking that I could probably do it as a webinar that teachers can attend live, but those who can’t attend could watch a recording of it after the fact. Now I just need to figure out the logistics and schedule a date!

On my way back to the office, I decided to stop for lunch at a local restaurant. It’s close enough to the office that I was able to call Regina to invite her to join me, and she convinced our elementary social studies coordinator to come along. That was my calm moment for the day. I enjoyed getting to eat and talk without worrying where I was off to next.

After lunch, I headed back to the office to answer emails before heading out to a meeting at one of our elementary campuses. While I was back in the office, I realized that we have more interest in our upcoming Developing Number Concepts session than I can accommodate in one day. Rather than turn people away, I’ve decided to add a second session a week later. This way we’ll be able to host almost 100 teachers, up from the original 60. I’m really excited that so many people want to attend this training!

Unfortunately I didn’t have enough time to email principals about the new session before I hopped back in the car and headed over to one of our elementary campuses. Since October, principals have been meeting in groups once a month to take various Heinemann online courses together. The elementary curriculum coordinators were each invited to join one of the groups.

My group is made up of about 6 principals, and we’re taking Steve Leinwand’s Making Math Far More Accessible to Our Students. It’s been a lot of fun! The material is great, and the discussion it prompts among us is so valuable. Today’s session was about the importance of using multiple representations and supporting students’ language development in mathematics. We had a great discussion at one point about strip diagrams, and I was clapping on the inside when one of the principals referenced the notice and wonder strategy as a way to make sense of them.

It was during this meeting that I realized I’m getting sick. Boo!

I have a full day of PD planned for tomorrow. I can’t be sick! Well, I can. If necessary, Regina can lead the sessions on her own. I just don’t want to do that to her. I’m crossing my fingers that I’ll feel better after a good night’s sleep, but I still went over the 4th grade presentation with her when I got back to the office just in case!

At 3:30, an instructional coach followed shortly by a team of 2nd grade teachers showed up to our K-2 open planning session. The 2nd grade team are our regulars. They come each time and plan the assessment for their upcoming unit. It’s awesome! Today I worked with them to create assessment items for a geometry unit. We also had a 1st grade teacher show up. She worked with the instructional coach to plan activities for an upcoming addition unit. So, not a huge turnout, but incredibly productive for those who were there!

At 5 o’clock, I helped Regina load up her car with the materials we need to take with us to the PD session tomorrow, and then I headed home. At this point it’s becoming clearer and clearer I’m under the weather, but I’m still holding out hope I’ll feel better in the morning.

# A Day in the Life of a Curriculum Coordinator: Monday

I’m always a sucker for a good blogging initiative. As luck would have it, my online PLC, #MTBoS is kicking off just such an initiative this week! If you’re interested in joining or if you just want to find out what the MathTwitterBlogosphere is all about, head on over to the ExploreMTBoS site.

We were given two options for blog post topics this week. The first is to write a post about one good thing. The other is to write about a day in the life. The assumption is that you’re a teacher and you’ll write about a day in the life of a teacher. However, I’m not a teacher currently. I’m the elementary math curriculum coordinator for my district. I don’t imagine many people know what I actually do – Dan Meyer had lunch with my secondary counterparts last week and was surprised to hear our jobs weren’t terminated once the scope and sequence was in place – so I thought this is a timely opportunity to share a sliver of what my job entails.

We’ll start with Monday. If all goes well, I’ll write a short post each day. If all does not go well, then you might just get Monday. At least I can guarantee one day in the life!

[UPDATE] – I did manage to write a post each day:

## Monday

In many ways today was not a typical day which is why I’m hoping to write a few posts this week. On the other hand, I’m not sure there is such a thing as a typical day in my job, so today’s post might be just as representative as any other day I could have chosen to write about.

The first hour of my day I spent reviewing, editing, and finalizing a presentation I’m giving to all of our elementary principals tomorrow. I have about 50 minutes to do an overview session about the state math test (STAAR) and give some tips and advice for how teachers and students should spend time between now and then.

SPOIILER ALERT! I’m going to tell them their teachers should stay the course. The year is only half over and there are still a lot of concepts to introduce. If anything, now is a great time to revisit how things are going and work together with grade level teams to ensure they are providing the best lessons and experiences they can during the upcoming units. Teachers can and should review concepts along the way, but massive test prep is not called for at this time.

While putting together the presentation, I got to try out Snap & Read, some new software our Special Education Department purchased, though it’s going to be available as a general instructional tool for all students. It’s a Chrome extension that allows users to highlight text and have it read out loud. I didn’t get to do a whole lot with it, but it was nice to discover how quick and easy it is to use. Students should be able to pick it up immediately!

The rest of the day I prepared for a PD session I’m leading on Wednesday. This year I received funding from our superintendent – a huge thanks to Dr. Flores! – to purchase multiple copies of the books Beyond Pizzas and Pies and Beyond Invert and Multiply for our intermediate elementary teachers. In addition, I also received funding to provide a full day of PD to one grade 3 teacher from every campus and one grade 4 teacher from every campus.

There’s a lot of information in the books, so my partner Regina and I opted to do two half-day sessions for each grade level. Back in December we facilitated part 1 for each grade and this Wednesday we’re facilitating part 2. We didn’t have enough money to bring grade 5 into the fold so we’re offering them a 2-hour session on an early release day in February.

Normally I have a lot of different tasks to jump between each day, but somehow I only managed to schedule PD prep today, and I sure needed the time! Regina is handling the grade 3 session which left me with the grade 4 session. I had to figure out what I was going to cover from the 3 chapters I chose for this session, make slides, plan out activities – specifically modifications I wanted to make to the activities shared in the book – and get copies made of all the materials teachers will use.

All in all I’m happy with how the session has shaped up, and I look forward to working with the teachers on Wednesday. Now I just have to hope we can get through everything I planned! That’s one area I’m still learning with regard to PD planning. I feel pretty good about the amount of content in my sessions, but I find that I always tend to put just one too many things in every session. Or two or three, but usually it feels like it’s just a bit too much.

I also did some odds and ends throughout the day whenever I needed a short break from PD planning:

• I shared a reminder about this week’s open planning sessions on our grade-level Google communities. Once a month, Regina and I host two open planning sessions after school – one for K-2 teachers and one for 3-5 teachers. All teachers from the district are invited to come and collaborate together on upcoming math units. Regina and I are there to help answer questions and take part in the process. This year is the first time we’ve offered this. The sessions aren’t attended by a ton of folks, but the teachers who do come let us know how valuable they think the time is. I actually just got an email this afternoon from an AP who shared some feedback a teacher gave her during a pre-observation conference: “Going to open planning was the best decision we’ve ever made. It helps us understand the TEKS and pace our unit.” Hooray! I think this also counts as my one good thing. 🙂
• I emailed a vendor to get a quote for some books I’m going to purchase for our K-2 teachers. For each campus we’re purchasing multiple copies of books 1-3 in the Developing Number Concepts series by Kathy Richardson. (Another thanks to our superintendent, Dr. Flores!) Regina and I will be leading a full day PD session on those for K-2 teachers in February.
• Speaking of, I emailed back and forth with a couple principals who are hoping to get a few more teachers signed up for the February PD session I just mentioned. Win!
• And finally, I watched an Ignite talk that one of our instructional coaches shared with me. Gradual release of responsibility has come up somewhat frequently recently and we’re still trying to wrap our heads around what it should/could mean in math. My fear is similar to what’s shown in the video, that it becomes all about what the teacher is thinking and getting students to merely reflect/parrot that.

There you have it. A day in the life of an elementary math curriculum coordinator. This was a fairly calm day, and I am so appreciative of that. Tomorrow is looking to be a bit more hectic. Hopefully I’ll have a chance to blog about that when it’s over.