If you’re just joining us, I’ve been writing a series of posts as I embark on my spring curriculum work to prepare for the 2018-19 school year. I’m sharing how our scope and sequence has evolved over time, rationales for why things are the way they are, and thoughts on what changes I might make for next school year. If you’d like to back up and read about an earlier grade level, here are the previous posts in this series:

Today I’ll be talking about our 3rd grade scope and sequence. Here they are for the past three school years. What do you notice? What do you wonder?

### 3rd Grade – School Year 2015-16

### 3rd Grade – School Year 2016-17

### 3rd Grade – School Year 2017-18

Remember back in my first post in this series when I said, “*Now that I’ve been doing this for a few years – and I’m starting to feel like I actually know what I’m doing…*“? Yeah, 3rd grade is a prime example of how I have learned a lot over the past few years. I’m a little (maybe a lot) embarrassed to show you what it used to look like back in 2015. I had good reasons for what I attempted to do, but this was just a tough nut to crack.

So what was going on several years ago when I put our 3rd grade teachers through the wringer with 18 units in one school year? If you look at the 2015-16 scope and sequence closely, you’ll notice that one topic appears waaaaay more frequently than the others – multiplication and division. There were a total of 7 units just on multiplying and dividing.

This was very intentional. Just like I have specific numeracy goals in the previous grade levels, my goal in 3rd grade is to ensure students leave the school year as strong as possible in their understanding of multiplication and division. Specifically, I want to ensure students have the chance to develop mental strategies for multiplication and division.

Before I became the Curriculum Coordinator in my district, a team of folks analyzed fluency programs and ultimately decided that ORIGO’s Book of Facts is the one we would purchase for our entire district. After that decision, but still before I started working in this role, our district went through the adoption process for a new math instructional resource. Teachers selected ORIGO’s Stepping Stones program.

This turned out to be a wonderful fit because the mental strategies from the Book of Facts are baked into the lessons in Stepping Stones. (If you want to learn more about these mental strategies, check out these awesome 1-minute videos from ORIGO.) I didn’t want to rush students through the strategies, so I followed the Stepping Stones sequence of multiplication and division lessons. This gave each strategy its due, but it also resulted in 7 units on just this one topic.

Unfortunately, this meant squeezing in *everything else* in between all of those multiplication and division units. To my credit, I did share this scope and sequence with a team of six or eight 3rd grade teachers to get their feedback before putting it in place. I must be a good salesman because they thought it made sense and wanted to give it a try.

I’m sure you can imagine, it was *tough* that year. Just as teachers started a unit, it felt like it was ending. This happened to also be the year that our district started requiring teachers to give a district common assessment at the end of every unit. That decision was made *after* I’d already made all of my scope and sequences, otherwise I might have thought twice….maybe. The teachers felt like they were rushing through unit after unit and assessing their kids constantly. It was too much.

The next year we tightened things up quite a bit. We were able reconfigure concepts to end up with five fewer units than the year before. Without sacrificing my ultimate goal, I do feel like we ended up with a scope and sequence that has a reasonable amount of breathing room.

A major change that happened between last year and this year is that we removed the 10-day STAAR Review unit. We took 5 of those days and gave them to teachers at the beginning of the year to kick off with a Week of Inspirational Math from YouCubed. We took the other 5 days and gave them to units that needed more time. My rationale is that teachers often tell me they don’t have enough time to teach topics the first go round. If that’s the case, then I can’t justify spending 10 days at the end of the year for review. Those days should be made available earlier in the year to ensure there’s enough time for first instruction. If you’re interested, I shared additional reasons for this change along with an alternative to the traditional test prep review unit in this post on my district blog.

As embarrassed as I am to share the scope and sequence I inflicted on our 3rd grade teachers for an entire school year, looking at it now, I am proud of what we attempted and proud of the revisions we’ve been able to make over time. It’s finally a wieldy scope and sequence!

My reason for sharing this is to let people to know this work isn’t easy, especially people who are in the same boat as me or considering moving into this kind of role. There are a lot of moving parts within and across years, and you’re bound to make some mistakes. The important thing is to always have an eye for continuous improvement, because there is *always* something that could use improving. And if you can enlist the help of great teachers to provide their expertise and feedback, even better. This is not work that should be undertaken solo.

### 3rd Grade – School Year 2018-19

So what’s the plan for next school year? One area that’s been nagging me is addition and subtraction. If you read the 2nd and 3rd grade standards on this topic, you’ll notice the first half of each standard is identical except for one word: fluency.

**Second grade****2.4C***Solve one-step and multi-step word problems involving addition and subtraction within 1,000*using a variety of strategies based on place value, including algorithms

**Third grade****3.4A***Solve with***fluency***one-step and two-step problems involving addition and subtraction within 1,000*using strategies based on place value, properties of operations, and the relationship between addition and subtraction

One of the 8 effective teaching practices from NCTM’s *Principles to Actions* is that we should build procedural fluency from conceptual understanding. I see this happening in in our 2nd grade curriculum:

- We build conceptual understanding of multi-digit addition and subtraction across 60 days in 3 units
- And this helps us build fluency of 2-digit addition and subtraction in our computational fluency component across up to 97 days in 6 units

What about in 3rd grade? We kick off the year reconnecting with 2-digit addition and subtraction in our computational fluency component for 30 days in Units 1 and 2. This overlaps with our efforts to reconnect with the conceptual understanding of adding and subtracting 3-digit numbers in Unit 2.

Starting in Unit 3, our goal becomes moving students toward fluency. We strive to achieve this by having it as a computational fluency topic for up to 64 days in 4 units. Problem solving with addition and subtraction, and later with all four operations, also appears throughout the year in 41 days of spiral review in 3 units.

When I write it all out like that, I feel pretty good about it, but I do wonder if it’s enough. I hear from 3rd grade teachers, especially in the fall, that their students are having a really difficult time with addition and subtraction, a much harder time than they are with multiplication and division.

I’m not sure I want to make a change to 3rd grade’s scope and sequence though. They have enough on their plate. I want their kids to begin building multiplicative thinking, build a strong understanding of how multiplication and division are related, and, oh yeah, build fluency with all of their multiplication and division facts. That’s a lot to accomplish!

What I really want to do is look at *how* our 2nd and 3rd grade teachers are teaching addition and subtraction. My gut tells me the problems I’m hearing about have something to do with the standard US algorithms for addition and subtraction.

In case you’re wondering, the phrase “standard algorithm” does not appear in our addition and subtraction TEKS until 4th grade. And that makes sense. When you’re adding or subtracting 2- and 3-digit numbers, that can be done fluently in your head, given practice. However, once you hit 4th grade, and you start adding 6-, 7-, and 8- digit numbers, you’re going to want to pull out a calculat…er…I mean algorithm.

Despite my best efforts, I know there are some 2nd and 3rd grade students being taught the standard US algorithms which might be causing some of the issues I’m hearing about. As I like to say in this sentence I just made up, “When standard algorithms are in play, number sense goes away.” If teachers are still teaching standard algorithms despite everything in our curriculum pointing to the contrary, then I’ve got some work to do to shift some practices, including providing professional development. Thankfully I’ve already got some lined up this summer! I also need to work more with our instructional coaches on this topic so they’re better equipped to support the teachers on their campuses.

Got a question about our scope and sequence? Wondering what in the world I’m thinking about planning things this way? Ask in the comments. I’ll continue with 4th grade’s scope and sequence in my next post.