# Moving On Before It’s Over (3rd Grade)

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 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.

• 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
• 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.

# Play With Me

On Wednesday I had the chance to visit my first classroom this school year. Sadly, in my role as curriculum coordinator, I don’t get to do this nearly enough. So I relish opportunities like this. Even better than visiting, the teacher allowed me to play a math game with her class.

I wanted something simple and quick to get the kids engaged before moving on to another activity. I also wanted it to involve adding 3-digit numbers because her class is in the middle of a unit on that very topic. I also wanted to bring in some place value understanding and reasoning, which are very much related to adding multi-digit numbers.

Basically I brought two decks of cards – one had Care Bears on the back and the other had Spider-Man on the back. I wanted different backs to the cards so it would be easier to tell which cards were mine and which were my opponent’s in case we needed to reference them during or after the game. I also pulled out all of the 10s and face cards, with the exception of the aces. I kept those and we decided to use them as zeroes. I tell you this because if you ever want to play a game that involves digit cards, here is a great way to get some without having to painstakingly cut out cards to make your own sets. Decks of cards are cheap enough. Just use those.

The game was me vs. the class. The goal is to make two 3-digit numbers. Whoever has the greater sum wins. On my turn, I drew a card, and I had a choice of putting it blank spots that I used to create two 3-digit numbers. Once a digit was placed it couldn’t be moved. On the class’ turn, I drew the card for them, but I let them tell me where to place the digit.

My favorite part of the game was at the end when the kids started shouting out that they’d won without even finding the sum. Take a look and see why they got excited: (Just pretend I hadn’t written the sums yet. I took the picture after the game was over.)

“You have a 9 and a 4 in the hundreds place. We have a 5 and a 9.”

“Interesting, and how does that tell you you’ve won?”

“Because the 9s are the same. And we have a 5 which is greater than 4. You should have put your 5 in the hundreds place.”

“I was hedging my bets and I lost.”

Such wonderful thinking from a 3rd grader! How often do students rush to calculate and find an answer to a problem? How amazing that these students were paying attention to the place value that matters most in these numbers – the hundreds – and then comparing the digits to determine who had a greater sum?

Since I was just the lead-in to the day’s activities we only got to play once, but I would have loved to play again. I would have liked to change it up a bit. I would still construct my number on the board, but then I would have allowed everyone to create their own number at their desk using the cards that I drew on their turn. At the end we would discuss who thinks they have the greatest sum and talk about their placement of digits.

Even though I didn’t get to play again, I’ll take the time I did have. It was the highlight of my week!

# Weighty Matters

This year I won a grant from our district’s Partners In Education Foundation. (Yay!) With the money, I was able to purchase quite a few platform scales for every third grade team in our district. Today I got to visit a class using the scales, and I got to see the amazing Julie Hooper teach a lesson I developed with my partner Regina. It was so much fun!

The class started with a computation warm-up which made my math heart happy. It was so amazing to listen to Julie’s students solve the problem in so many different ways. They were so comfortable doing it, too. You can tell they have internalized the idea that they are able to solve problems in ways that make sense to them.

After the warm-up, the class dove into the day’s lesson. Julie started by asking the students to name things that are heavy and things that are light.

She asked some thought provoking questions after they had compiled their list.

• Is 100 pounds heavy to you?
• Do you think it’s heavy to a weight lifter?
• Are big things always heavy?

I love how the conversation got the students thinking about their current conceptions of weight.

Next, the students had the opportunity to explore two different scales. Julie asked them to notice and wonder as they tried out the scales. I noticed that 3rd grade students *love* to put as many items as they can on the scale all at once. They couldn’t believe how much it took on the larger scale to make the dial move.

After having some time to explore, Julie asked the class to think about which scale they would use to measure different objects in the room. The reason for this is because one scale can measure weight up to 11 pounds while the other can only measure up to 2 pounds. She was curious to see if students had already started noticing that the bigger scale would measure heavier things while the smaller scale would max out unless the objects were lighter.

After all of this exploring, Julie brought the class together to focus on the scale and to make connections between the scale and the number line. The class talked about whole number connections first, but then she drilled down to fractions and mixed numbers.

Finally, Julie asked the students what unit of weight they thought the fractional parts might represent. Someone volunteered ounces. Then she asked a wonderful question: “How many ounces do you think are in a pound?” Many students thought there must be 8 ounces in a pound, which makes sense given the number of parts between 4 and 5, but then she transitioned to the other scale to see what students would notice.

She wants the students to figure out that there are 16 ounces in a pound, but unfortunately she ran out of time for the day. I did like that the final comment from a student was, “That scale goes up to 4 pounds.” Just wait until they continue their work tomorrow!

Thank you to Julie for letting me spend an hour learning with her students!