Tag Archives: scope and sequence

Moving On Before It’s Over (5th Grade)

I’m finally reaching the end of my blog post series which has been a retrospective of my elementary curriculum work for the past three years. If you want to read the previous posts in this series, here they are:

Today I’ll be sharing our 5th grade scope and sequences. 5th grade is a strange beast, at least in Texas. It’s a Student Success Initiative grade which means students are required to pass the state reading and math tests (STAAR) in order to move on to 6th grade. If students fail the test, they are given two more chances to pass before a grade level placement meeting is held. In order to accommodate three testing dates, 5th graders have to take their test nearly a month and a half earlier than they did in 3rd and 4th grade.

The implication is that despite having a year’s worth of curriculum to teach like everyone else, 5th grade teachers have to teach all of their standards by late March rather than early May. This makes planning the scope and sequence a perpetual challenge because you’re always working with less time than other grade levels. And with all of the meaty rational number topics in 5th grade, teachers are definitely not clamoring for less time to teach.

With that in mind, here are the scope and sequences for the past three years. What do you notice? What do you wonder?

5th Grade – School Year 2015-16

5th15-16

5th Grade – School Year 2016-17

5th16-17

5th Grade – School Year 2017-18

5th17-18

Looking back, I’m noticing a trend across grade levels where I used to split topics up into chunks that ended up being too small for teachers. In 2015-16 I split the following topics into two units each:

  • Volume – The first unit focused on multiplication and the second on division
  • Addition and Subtraction, Data Analysis, and Perimeter – The first unit focused on fractions and the second on decimals
  • Multiplication and Division – The first unit focused on fractions and the second on decimals
  • Geometry – The first unit focused on coordinate geometry and the second on classifying 2-D shapes

That year we crammed in 11 units before the STAAR test (12 if you include a short review unit). Needless to say, 5th grade teachers let it be known that year that they felt like they were flying way too quickly through their units.

The next year I think I over-corrected. Instead of many short units, I offered fewer, longer units. We went from 11 units to 6 units before the STAAR test. I wanted teachers to feel like they could really dig into the topics for an extended period of time. I also tried to make moot a debate about whether fraction multiplication/division should come before or after decimal multiplication/division. Since they were combined into one unit, it meant teachers could choose their preferred teaching order.

Like I said, I think this was an over-correction. That year teachers let me know that the units were too long. Some of the feedback was that by the time they got to the end-of-unit assessment 25 days later, students had forgotten content from earlier in the unit. Other feedback was that teachers didn’t know how to utilize their time within the unit. They felt like there was too much to cover, even though they had a longer block of time in which to teach.

Last spring I sat down with my 5th Grade Curriculum Collaborative to (hopefully) find a sweet spot. First we talked about which units to keep combined and which to separate. They decided that the unit on volume, multiplication, and division could stay together. They also felt that the geometry unit didn’t need to be broken up.

What did need to be broken up were the units on rational number operations. They said these are the topics where students have the greatest struggles. Namely, students need dedicated time to work on addition and subtraction with fractions that have unlike denominators. They also wanted to introduce fraction multiplication and division earlier to give students even more time to encounter related word problems. One of the biggest struggles our students have is knowing when to multiply or divide fractions in a word problem, and if it’s a division problem, in what order to divide – unit fraction divided by whole number or whole number divided by unit fraction.

After deciding that we would have 8 units and the order in which they would be presented, I asked them to identify the unit that they felt was the most critical. They decided Unit 2 on adding and subtracting fractions is the most critical. I asked how many days they needed to ensure success with that unit. They decided on 20 days.

We repeated this process to identify their second priority unit, which was Unit 3 on multiplying and dividing fractions. Again, we talked about the amount of time needed to teach this topic well. Because we considered these two units to be our top two priority units, it was non-negotiable to steal days from these two units as we created the rest of the scope and sequence.

Have we found the sweet spot? I think so. I’ve received minimal feedback from teachers about the 5th grade scope and sequence this year. It helps that this year Texas shifted the date of the STAAR test a little later than it was in 2015-16 and 2016-17. Teachers ended up with two additional weeks of instruction than in years past which definitely gave them a bit of breathing room.

This impacted our post-STAAR units however. In 2015-16 and 2016-17, after the first STAAR administration, we had two mirror units (Units 13a and 13b in 2015-16 and Units 8a and 8b in 2016-17). The rationale was that based on all the data collected that year, teachers should have had a pretty good idea of which students would pass on the first administration and which students would not. When scores are returned 3 weeks after the test, campuses tend to scramble to create intervention groups and provide intense intervention. My philosophy is, why wait?

Once the first administration was done, we wanted teachers to start providing that intervention and support immediately so that they could intervene for a full 6 weeks instead of just 3. This might involve mixing students around across classes so that some students would learn from the Going Deeper Unit while others learned from the Enriching Connections unit. Both units had the same standards, we just provided different instructional resources.

Once the second STAAR administration was over in May, all of the 5th graders got to take part in the final unit of the year which focused on personal financial literacy. This is a unit students tend to enjoy so I wanted to make sure everyone got to take part. If we had offered this unit after the first administration, some students might have gotten yanked out of it when scores came back, which isn’t fair.

As I mentioned previously, things changed this year when Texas moved the first administration two weeks later. They also moved the second administration a week later as well. That had a big impact on my 3rd, 4th, and 5th grade scope and sequences because now there isn’t enough time after STAAR in May to warrant a complete unit. That meant the personal financial literacy unit had to move immediately following the first administration of STAAR or else it wouldn’t get taught at all. It also meant the two mirror units are much shorter this year. Considering students got more time for first instruction this year, I’m not complaining.

5th Grade – School Year 2018-19

Based on the lack of feedback, I’m going to keep the scope and sequence the same for next year. Over the past two years, my 5th Grade Curriculum Collaborative has worked with me to develop suggested unit plans for 7 of the 8 units before STAAR. Teachers have been really happy with these model plans. Once we write the 8th plan, it will be nice to go back and start making revisions to the existing plans now that they’ve been in use for a couple of years.

I’m not sure whether I’ll make any adjustments to the computational fluency and spiral review topics this year either.

5thAAGFall

5thAAGSpring

You’ll notice that, like 4th grade, 5th grade also starts with a review of multiplication facts. I’ve done the math and across grades 3, 4, and 5, we’ve incorporated nearly 75 hours of instruction on multiplication and division facts across these three grade levels. Here’s the breakdown:

  • 3rd Grade – Nearly 50 hours focused on conceptual understanding and more than 10 hours of procedural fluency practice spread across the entire year
  • 4th Grade – Nearly 10 hours of procedural fluency practice spread across the first semester
  • 5th Grade – Five hours of procedural fluency practice in the first nine weeks

I have some work to do to help see this enacted in the way that I envision, but I feel good about the structure we’ve put in place to intentionally teach and reinforce this skill across the intermediate grades.

Looking at the spiral review topics, I’m pretty happy with their flow, especially at the beginning of the year. In Unit 1 we focus on 4th grade fraction topics. 5th grade is really a fraction- and decimal-heavy year. I totally get that students might have forgotten some of what they learned in 4th grade, but we just don’t have the luxury of time for excuses. The students need to hit the ground running if they’re going to have sufficient time to grapple and become proficient with the 5th grade material.

I like how the Unit 2 spiral review parallels the focus TEKS topics, but using whole numbers instead of fractions. We do the same thing in Unit 3. However in Unit 3 it’s doing double duty because in addition to being a parallel to the focus TEKS work, it’s also revisiting whole number multiplication and division which will be a focus in Unit 4. Then in Unit 4 the spiral review topic is decimals which is in preparation for Unit 5.

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. Otherwise, that just about wraps up this blog series.

Parting Thoughts

Over the course of this blog series, I’ve really appreciated the experience of reflecting on my past three year’s worth of curriculum work in each grade level. It’s been interesting to see how my thinking has changed over the past few years and how much of it has been influenced by the feedback from and collaboration with our teachers. I greatly appreciate that they’re willing to share what’s working and what’s not. I don’t teach in a classroom day in and day out, so I would be handicapped in my work without their expertise and insight.

Looking back over three years and six grade levels, I’m struck by how complex this work is. There are so many moving parts in terms of the numerous standards within a grade level, how they interconnect across grade levels, how to bundle standards meaningfully into units, and how to decide the appropriate amount of time for any given unit. If you ever find yourself in the position of doing this work, my advice is to invite a group of colleagues to work with you, do your best, and expect that you won’t get it “right” the first time.

That being said, what started as a blog series where I was planning to reflect on the changes I might make for next year has instead reaffirmed that the work I’ve done with my teachers over the past three years has resulted in six scope and sequences that make sense and don’t actually require much tweaking at all. I’m proud of what we’ve accomplished. Are they perfect? Probably not. But they appear to be working for our teachers and students, and at the end of the day that’s what matters.

Oh, and I have an exciting announcement for those who’ve read all the way to the end! My school district is currently in the process of making our entire curriculum for all subjects K-12 an open education resource for anyone to access. Copyrighted lessons will still be restricted to district employees, but all of our curriculum documents and a wide variety of non-copyrighted resources will be freely available. We’re currently in the process of transferring everything into our new curriculum site. I’ll be sure to share the link (and probably blog about it!) once the site goes live. I’ve always been a big fan of sharing because we’re better together, and I’m so thankful to work for a school district that shares this philosophy.

 

 

 

Moving On Before It’s Over (4th Grade)

After taking a break to prep my session for the 2018 NCTM Annual Conference, it’s time to get back to this blog series on my spring curriculum work as I prepare for the 2018-19 school year. If you’re just joining us, here are the previous posts in this series:

Today I’ll be talking about our 4th grade scope and sequence. Here they are for the past three years. What do you notice? What do you wonder?

4th Grade – School Year 2015-16

4th15-16

4th Grade – School Year 2016-17

4th16-17

4th Grade – School Year 2017-18

4th17-18

The first thing I notice are my efforts to figure out how I wanted to break up multiplication and division across two units. Here’s what we’ve tried over the past three years:

2015-16

  • Unit 3
    • Multiply 2-digit numbers by 2-digit numbers
    • Divide 2-digit numbers by 1-digit numbers
  • Unit 6
    • Multiply 3- and 4-digit numbers by 1-digit numbers
    • Divide 3- and 4-digit numbers by 1-digit numbers

What was our rationale?

In the spring prior to the 2015-16 school year, our adopted resource, Stepping Stones, underwent a revision to more closely align to the TEKS. In March 2015 we were sent preliminary scope and sequences of the revised courses. While doing our curriculum work that spring, we decided to try to follow certain topics in the order presented in the revised scope and sequence documents to ensure that students would see lessons in order. Our thinking was that presenting lessons out of order could lead to problems if later lessons assumed knowledge of earlier lessons.

In those preliminary documents, 2-digit by 2-digit multiplication was taught first followed by 3- and 4-digit by 1-digit multiplication. I was a little concerned about this, but we decided to stick to our plan. Lo and behold, when the revised Stepping Stones launched that summer, the order had been reversed. Our curriculum documents were already completed and posted for teachers to use by that point so we stuck it out for that year. However, as you can see below, we changed things up for the next school year.

2016-17

  • Unit 3
    • Multiply 3- and 4-digit numbers by 1-digit numbers
    • Divide 2-, 3-, and 4-digit numbers by 1-digit numbers
  • Unit 5
    • Multiply 2-digit numbers by 2-digit numbers

What was our rationale?

So we flip-flopped the multiplication topics, but we also merged all of the division into Unit 3. Our thinking was that students already did a lot of dividing with 2-digit numbers in 3rd grade, so really division with 3- and 4-digit numbers was just extending that. That allowed teachers to solely focus on 2-digit by 2-digit multiplication in Unit 5.

However, this came back to bite us in the butt because of a tricky little standard about interpreting remainders. Teachers emailed to let us know that they really wanted to revisit division in Unit 5 because their students were still having difficulty with interpreting remainders. This was great feedback, which leads us into the current school year.

2017-18

  • Unit 3
    • Multiply 3- and 4-digit numbers by 1-digit numbers
    • Divide 2-digit numbers by 1-digit numbers
  • Unit 5
    • Multiply 2-digit numbers by 2-digit numbers
    • Divide 3- and 4-digit numbers by 1-digit numbers

What was our rationale?

Multiplication remained untouched this year, but we did spread division out across Units 3 and 5. Our hope is that by only doing division of a 2-digit number by a 1-digit number in Unit 3, teachers can focus more of their energy on interpreting the remainder. Then in Unit 5 they can extend division to larger numbers while reinforcing what students learned about interpreting the remainder.

We’re in a good place now, and I don’t foresee changing this for next school year, but it gives me pause to think about the fact that this simple rearranging of a few topics was a 3-year process. It’s important to note: There are no absolute right answers in this work. I can consult teachers. I can read professional journals and books. I can read up about how other curriculums structure their scope and sequences. In the end, I have to use my best judgment…

…and then wait and see what happens when teachers and students interact with these units. I can (and do) iterate and revise, but by the nature of the work, it’s over a scale of years, not days or weeks. No pressure! It makes me think of how if I think back to my first year teaching, I feel bad for that group of students because I know so much more about teaching than I did back then. What I have to remind myself is that regardless of the specific decisions I’ve made each year, I’ve always been striving to do my best for the students (and now teachers) that I serve. And I’d rather know that I’m improving each year than continuing to make the same mistakes time and again.

Another noticing I have about the 4th grade scope and sequence is how I had too many units in the 2015-16 school year. Similar to 3rd grade, I tried breaking some topics up over multiple units to create opportunities for them to spiral back. Most notably I did this with fractions (Unit 4 and 7) and decimals (Unit 9 and 11). Teachers didn’t like this. They specifically requested one fraction unit and one decimal unit, which we created in 2016-17 and continued in 2017-18.

The last thing I’ll point out is how our angle measurement and 2D geometry unit shifted from the second semester in 2015-16 to the first semester in 2016-17 and 2017-18. This was influenced by the Level 1 Curriculum Audit training I attended in the fall of 2015. One of my big takeaways from that training was that topics that are absolutely brand new to students should be introduced as many months as possible prior to the first time students will be assessed on them. Angle measurement is completely new to students in 4th grade. Introducing it a couple of months before the state test doesn’t give students sufficient time to learn and reinforce it, so I moved it earlier in the school year. This gives plenty of time to revisit it between first instruction and the STAAR test.

4th Grade – School Year 2018-19

Here I am sharing the curriculum work I’m doing this spring, and it turns out I’m not really changing our courses that much. I don’t anticipate reordering any of the units in 4th grade. Our computational fluency and spiral review topics seem pretty solid as well.

4thAAGFall

4thAAGSpring

Looking at computational fluency and spiral review, the first four units basically serve as review of 3rd grade concepts. Notably, teachers have a whopping 59 days of computational fluency to work on multiplication and division fact fluency, which was a HUGE focus of the 3rd grade scope and sequence. This amounts to about 10-12 hours of practice at the start of 4th grade. We specifically organized this work around the thinking strategies taught in 3rd grade to create common language across grade levels.

The spiral review concepts in the first few units are critical, especially reviewing 3rd grade geometry concepts in Unit 3. As I was working with my 4th Grade Curriculum Collaborative this year to plan Unit 4, we talked about the 3rd grade geometry standards. The 4th grade teachers were surprised to hear that their students should come in already knowing a lot about a variety of quadrilaterals – parallelograms, trapezoids, squares, rhombuses, and rectangles.

I talked about how they have their own heavy work to do introducing angle measurement and parallel and perpendicular lines; they don’t have time to “teach” those quadrilaterals in their 4th grade unit. There was some resistance, but I pushed back that they have to utilize that spiral review time in Unit 3 to revisit all of those polygons and attributes that the students learned in 3rd grade. Otherwise they’re setting themselves up for some real (and potentially avoidable) challenges in Unit 4.

I am excited to check in with our 4th grade teachers next year because this school year our 3rd grade teachers were able to use a newly created suggested unit plan for their geometry unit that was chock full of amazing lessons. I’m hoping the 4th grade teachers will be pleasantly surprised by the level of thinking students bring next year. I made it a goal this year with all of my Curriculum Collaboratives to plan all of our geometry units K-5 to ensure students are always engaging with grade-appropriate standards and building the levels of geometric thinking they need across these six years.

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 wrap up this blog series with 5th grade’s scope and sequence in my next post.

 

 

 

 

 

 

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 2015-16

3rd15-16

3rd Grade – School Year 2016-17

3rd16-17

3rd Grade – School Year 2017-18

3rd17-18

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.

3rdAAGFall3rdAAGSpring

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.

 

 

 

 

 

Moving On Before It’s Over (2nd Grade)

In this series of blog posts, I’ve been taking a look at each grade level’s scope and sequence for mathematics as I consider changes to make (or not) for next school year. So far I’ve written about Kindergarten and 1st grade. Today I’d like to tackle 2nd grade.

Here are our scope and sequences for the past three school years. What do you notice? What do you wonder?

2nd Grade – School Year 2015-16

2nd15-16

2nd Grade – School Year 2016-17

2nd16-17

2nd Grade – School Year 2017-18

2nd17-18

One thing that jumps out at me while analyzing the past three years is how different topics have bounced around throughout the school year.

  • 3-digit place value has shifted from the 2nd nine weeks to the 1st nine weeks to the 3rd nine weeks
  • Measurement has shifted from the 1st nine weeks to the 3rd nine weeks and back to the 1st nine weeks
  • Fractions was in the 4th nine weeks for two years and then shifted to the 3rd nine weeks
  • Multiplication and division were in the 3rd nine weeks and then they moved to the 4th nine weeks for the past two years

I might have come to these decisions on my own anyway, but I do feel like an important influencer in my work has been the Level 1 Curriculum Audit training I took in the fall of 2016. It really helped me think about all the different components of our curriculum and their purpose in supporting teachers in planning high quality instruction. One thing it really got me thinking about is being even more intentional about where topics appear in the curriculum, not just within one school year, but also looking across school years.

In my previous post about 1st grade, I talked about how the fall semester is focused on working within 20 while the 2nd semester introduces place value and numbers to 120. The purpose of spending the spring semester in 1st grade on place value is to create more proximity to 2nd grade where students are expected to use what they’ve learned about place value to start adding and subtracting 2-digit numbers.

I’ve divided 2nd grade in half in a similar way to 1st grade. The focus in the fall semester is building conceptual understanding of adding and subtracting 2-digit numbers. There are 80 days in the fall semester and half of them are devoted to this topic. Mastery is not expected by winter break, however. Check out the computational fluency column in the at-a-glance below to see how we start working toward procedural fluency with 2-digit addition and subtraction in the spring semester.

2ndAAGSpring

After unit 4, 2-digit addition and subtraction moves into our 10- to 15-minute daily computational fluency block for the remaining 97 days of the school year. I hear consistently from 3rd grade teachers that their students aren’t coming to them proficient with adding and subtracting 2-digit numbers, much less 3-digit numbers, so it’s my goal to ensure that our students leaving 2nd grade are solid on this.

So if the first half of the year focuses on adding and subtracting 2-digit numbers, what is the second half of the year focusing on? 3-digit numbers, namely introducing 3-digit place value and adding and subtracting 3-digit numbers. To beat a dead horse, I’m continuing to strive for sufficient instructional time for each and every one of our students. There’s no need to rush into 3-digit numbers in the fall semester as students are still trying to grapple with 2-digit number concepts.

I’m also trying to create a flow of addition and subtraction across 2nd and 3rd grade. Take a look at these addition and subtraction standards for both grade levels:

  • Second grade
    • 2.4B Add up to four two-digit numbers and subtract two-digit numbers using mental strategies and algorithms based on knowledge of place value and properties of operations
    • 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

Notice how both grade levels are expected to add and subtract within 1,000. This is such important work that students are given two full years on it! I’ve noticed this is a theme across the primary grades of giving students ample time to engage with critical number concepts:

  • Kindergarten and 1st grade students spend two years getting to know the numbers to 20 really well through counting, representing, comparing, adding, and subtracting.
  • 1st grade and 2nd grade students spend two years getting to know 2-digit numbers really well through counting, representing, comparing, adding, and subtracting.
  • 2nd and 3rd grade students spend two years getting to know 3-digit numbers really well through counting, representing, comparing, adding, and subtracting.

It’s one thing to say that these topics spread across years, it’s another to ensure there’s some connective tissue to make sure it happens. That’s why I greatly appreciate our computational fluency and spiral review components of the math block. Here’s a look at the first semester at-a-glance. Look at the computational fluency topics. Why do you think I included what I did in those first several units? Then look at the spiral review topics. How are those intentionally placed in the timeline?

2ndAAGFall

The computational fluency block kicks off the year reviewing all of the basic fact strategies that were taught in 1st grade. We devote 10-15 minutes per day for the first 73 days of school to reviewing those strategies in order to build fluency of the basic addition and subtraction facts, but also because we want our students to “more than know their facts” (a wonderful phrase I learned from Pam Harris).

What I love about the Stepping Stones curriculum is that in 2nd grade it explicitly extends those basic fact strategies to addition and subtraction with 2- and 3-digit numbers. Not only does the computational fluency work in those early units reinforce fluency of basic facts, but it’s priming the pump to build on those strategies as students start adding and subtracting bigger numbers. I love that we’re modeling for students how powerful strategic thinking can be. We can use what we know about working with smaller numbers to help us work with larger numbers.

Looking at spiral review, I followed a similar structure to the beginning of first grade’s scope and sequence. If you look at the topics in spiral review, they are usually a review of 1st grade topics in preparation for learning the related 2nd grade concepts.

  • Unit 1 reviews 1st grade addition and subtraction standards in preparation for learning 2nd grade addition and subtraction standards in Unit 2
  • Unit 2 reviews 1st grade measurement (length and time) standards in preparation for learning 2nd grade measurement standards in Unit 2
  • Unit 4 reviews 1st grade geometry standards in preparation for learning 2nd grade geometry standards in Unit 5

Back when I started in this job, the feedback I got most from 2nd grade teachers had to do with either telling time or counting change. Based on that feedback, you’d think those are the two most important topics in 2nd grade. They’re not. I’ve worked hard over the past few years to convey what are and are not focal points via the scope and sequence.

You might have noticed that telling time appears in spiral review a lot. Learning to tell time is not always easy for students, but that doesn’t mean it should eat up a lot of instructional time. After focusing on it in Unit 3, we moved telling time to spiral review throughout the rest of the year as a reminder to keep reinforcing the skill.

We did something similar with counting change. The first thing I wanted to do was ensure our 2nd grade teachers understand they’re only slightly extending the work students did in 1st grade. Here are the two standards about counting change:

  • 1st grade
    • 1.4C use relationships to count by twos, fives, and tens to determine the value of a collection of pennies, nickels, and/or dimes
  • 2nd grade
    • 2.5A determine the value of a collection of coins up to one dollar

Pretty much the only difference between the two grade levels is that 2nd grade includes quarters. Throughout most of our 2nd grade curriculum, we review counting change in computational fluency as students practice skip counting by twos, fives, and tens. We finally bring quarters into the mix in Unit 9 as students learn about multiplication and division concepts.

2nd Grade – School Year 2018-19

For the most part I’m happy with this scope and sequence. However, there’s one thing that I’m curious about. I do wonder whether we should introduce 3-digit place value earlier in the school year. You might remember this is a topic that has bounced around our scope and sequence during the past few years. I still want to hold off on adding and subtracting with 3-digit numbers until later in the year, but I do wonder whether students have sufficient time to get to know 3-digit numbers before they have to add and subtract with them.

When I moved 2-digit place value to the spring semester in 1st grade, I didn’t worry as much because that’s all students have to do in 1st grade, place value. They don’t start adding and subtracting 2-digit numbers until 2nd grade. In this case, however, I’m squeezing place value, adding, and subtracting together into the spring semester of 2nd grade. I asked my 2nd grade curriculum collaborative, and they’re okay leaving 3-digit place value where it is for next school year, but I’m leaving it as an open question and something I’ll be keeping my eye on.

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 3rd grade’s scope and sequence in my next post.

 

 

 

Moving On Before It’s Over (1st Grade)

In my previous post in this series, I shared how our Kindergarten scope and sequence for mathematics has evolved over the past three years. Today I’d like to share our 1st grade scope and sequence.

Here are our scope and sequences for the past three school years. What do you notice? What do you wonder?

1st Grade – School Year 2015-16

1st15-16

1st Grade – School Year 2016-17

1st16-17

1st Grade – School Year 2017-18

1st17-18

It’s interesting to notice that the three units in the first nine weeks have remained fairly consistent with only some slight variations in number of days. We always start each year with a unit that looks back as it looks forward. The purpose of Unit 1 is to revisit number concepts introduced in Kindergarten while simultaneously introducing 1st grade data analysis concepts. Considering all the counting and comparing you can do while making and discussing picture and bar-type graphs, it’s a great fit. Even better, teachers and students tend to like making graphs at the beginning of the year as a “getting to know you” activity for the class.

One thing that’s been consistent across the years is that addition and subtraction are sprinkled throughout the school year. And by sprinkled I mean 5 units spread across the school year. In Kindergarten, students got to know the numbers through 20 really well as they counted, represented, and compared. In 1st grade, students get to know these numbers even better as they deepen their understanding of addition and subtraction.

It might seem like overkill to spend so much time on such a small span of numbers, but this work is rigorous for young children and there is a lot of ground to cover. No, really, here are all the critical learning phases students need abundant time to work through in Kindergarten and 1st grade (keeping in mind that they might need to pass through these phases more than once as the magnitude of numbers increases):

Understanding Counting

  • Counting Objects
    • Counts one item for each number
    • Keeps track of an unorganized pile
    • Notices when recounting a group results in a different number
    • Is bothered when counting a group results in a different number
    • Spontaneously checks by recounting to see if the result is the same
    • Knows “how many” after counting
    • Counts out a particular quantity
    • Reacts to estimate while counting
    • Spontaneously adjusts estimate while counting and makes a closer estimate
  • Knowing One More/One Less
    • Knows one more in sequences without counting
    • Knows one less in sequences without counting
    • Notices if counting pattern doesn’t make sense
    • Knows one more without counting when numbers are presented out of sequence
    • Knows one less without counting when numbers are presented out of sequence
  • Counting Objects by Groups
    • Counts by groups by moving the appropriate group of counters
    • Knows quantity stays the same when counted by different-sized groups
  • Using Symbols
    • Uses numerals to describe quantities

Understanding Number Relationships

  • Changing One Number to Another
    • Changes a number to a larger number by counting on or adding on a group
    • Changes a number to a smaller number by counting back or removing a group
  • Describing the Relationship Between Numbers
    • After changing one number to another, is aware of how many were added or taken aaway
    • Knows how many to add or take away from a number to make another number
  • Comparing Two Groups: Lined Up
    • Compares two groups that are lined up and determines which is more and which is less
    • When the groups are lined up, tells how many more or less, when the difference is 1 or 2
    • When the groups are lined up, tells how many more or less, when the difference is more than 2
  • Comparing Two Groups: Not Lined Up
    • Compares two groups that are not lined up and tells which is more and which is less
    • When the groups are not lined up, tells how many more or less, when the difference is 1 or 2
    • When the groups are not lined up, tells how many more or less, when the difference is more than 2
  • Using Symbols
    • Uses the greater than (>) and less than (<) symbols as a shortcut for the commonly used words (is more than, is less than) when comparing objects

Understanding Addition and Subtraction: Parts of Numbers

  • Identifying Parts of Numbers
    • Recognizes groups of numbers to 5 in a variety of configurations
    • Recognizes and describes parts contained in larger numbers
  • Combining Parts of Numbers
    • Recognizes and describes parts of numbers; counts to determine total
    • Knows the amount is not changed when a number is broken apart and recombined in various ways
    • Combines parts by using related combinations
  • Decomposing Numbers
    • Identifies missing parts by using related combinations
    • Knows missing parts of numbers to 10
  • Using Symbols
    • Uses equations to record combining and taking away parts
    • Interprets equations in terms of combining and taking away parts

Whew! Being a Kindergartner or 1st Grader is hard work!

You might be wondering how we spread out addition and subtraction across 5 units. I know some of our teachers have asked that same question! While we don’t follow a textbook verbatim, I do value the scope and sequence provided by our adopted resource, Stepping Stones by ORIGO Education. Here’s what we correlated from Stepping Stones with each of our addition and subtraction units:

Unit 2 – Introducing Count-On Addition Fact Strategies and Addition Properties

  • Stepping Stones, Module 2
    • Lesson 1: Identifying One More and One Less
    • Lesson 2: Counting in Steps of Two
    • Lesson 3: Counting On From Five
    • Lesson 4: Using a Number Track to Count On (to 15)
    • Lesson 5: Using the Count-On Strategy with Coins
    • Lesson 6: Using the Count-On Strategy
    • Lesson 7: Using the Commutative Property of Addition with Count-On Facts
    • Lesson 8: Using a Number Track to Count-On (to 20)

Unit 4 – Revisiting Subtraction Concepts and Introducing the Use Doubles Addition Fact Strategy

  • Stepping Stones, Module 4
    • Lesson 1: Reviewing Subtraction Language
    • Lesson 2: Using Subtraction Language
    • Lesson 3: Working with the Subtraction Symbol
    • Lesson 4: Writing Related Subtraction Sentences
    • Lesson 5: Working with Related Subtraction Sentences
    • Lesson 6: Solving Word Problems Involving Addition and Subtraction
    • Lesson 7: Writing Addition and Subtraction Number Sentence

Unit 7 – Introducing the Make Ten Addition Fact Strategy and Revisiting Equality

  • Stepping Stones, Module 7
    • Lesson 1: Exploring Combinations of Ten
    • Lesson 2: Using the Associative Property of Addition with Three Whole Numbers
    • Lesson 3: Introducing the Make-Ten Strategy for Addition
    • Lesson 4: Using the Make-Ten Strategy for Addition
    • Lesson 5: Using the Commutative Property of Addition with Make-Ten Facts
    • Lesson 6: Consolidating the Addition Strategies
    • Lesson 7: Applying Addition Strategies
    • Lesson 8: Adding Equal Groups
    • Lesson 9: Solving Addition Word Problems
  • Stepping Stones, Module 9
    • Lesson 1: Balancing Number Sentences (Two Addends)
    • Lesson 2: Balancing Number Sentences (More Than Two Addends)
    • Lesson 3: Working with Equality
    • Lesson 4: Representing Word Problems

Unit 8 – Relating Addition and Subtraction

  • Stepping Stones, Module 8
    • Lesson 1: Identifying Parts and Total
    • Lesson 2: Writing Related Addition and Subtraction Facts
    • Lesson 3: Writing Fact Families
    • Lesson 4: Introducing Unknown-Addend Subtraction
    • Lesson 5: Using Addition to Solve Subtraction Problems
    • Lesson 6: Working with Addition and Subtraction
    • Lesson 7: Counting On and Back to Subtract
    • Lesson 8: Decomposing a Number to Solve Subtraction Problems

Unit 10 – Applying Inequality and Comparison Subtraction to Measurement and Data

  • Stepping Stones, Module 8
    • Lesson 9: Solving Subtraction Word Problems
  • Stepping Stones, Module 9
    • Lesson 5: Working with Inequality
    • Lesson 6: Introducing Comparison Symbols
    • Lesson 7: Recording Results of Comparisons (with Symbols)
    • Lesson 8: Comparing Two-Digit Numbers (with Symbols)

Whether a teacher chooses to use any or all of these lessons in a given unit (along with other resources we provide) the chunking of topics is beneficial to help teachers plan out 5 unique, yet related, units of instruction rather than rehashing the exact same thing over and over again.

One major change that happened this school year was moving place value completely to the second semester. In the past we started teaching place value in the second nine weeks, but I feel like that sent a bit of a mixed message. Here I am saying that really getting to know numbers to 20 is critically important, but I was telling teachers to start teaching numbers to 99 after only a few months of school. What’s the rush? Learning unitizing and place value is important, but our standards don’t expect students to do anything with 2-digit numbers until 2nd grade.

So in effect, I split the 2017-18 school year in half. The first half of the year students get to focus on numbers to 20. As I said in my previous post in this series:

“One of my primary goals across each grade in grades K-5 is to ensure sufficient instructional time on core concepts for that grade level. I want students who need intervention later on to end up there because they truly aren’t understanding concepts, not because they weren’t given sufficient time to learn during first instruction.”

I can’t tell you how many times I’ve heard teachers tell me, “They’re in 5th grade, but they don’t even know combinations to 10!” This isn’t to say that teachers can’t differentiate throughout the school year by providing students opportunities to add or subtract beyond 20, but from an equity standpoint, we owe it to each and every one of our children to provide sufficient opportunity to grapple with and master grade level expectations.

The second half of the year allows students to continue learning about addition and subtraction within 20, but we introduce an additional focus of unitizing and place value in 4 different units across the second semester. Unitizing can be a challenging concept for young students, but it’s so important to so many concepts down the road. My hope is that holding off until after winter break allows those young minds a little longer to develop and be ready to tackle this important concept. I also hope that making it a focal point of the second half of 1st grade will create more continuity when students start 2nd grade in the fall where they start using place value concepts to add and subtract 2-digit numbers.

1st Grade – School Year 2018-19

Like Kindergarten, I’m pretty happy with our scope and sequence for 1st grade. I did ask my 1st grade curriculum collaborative if they were comfortable leaving place value only in the spring, and they had no complaints.

I’m still trying to decide what to do about spiral review for next year. I don’t want to dictate, but I know it can be helpful to have guidance about which topics to review throughout the school year.

1stAAGFall

1stAAGSpring

One thing you’ll see in 1st grade spiral review is something I’m also doing in grades 2-5, which is reviewing a concept from the previous grade level right before that concept comes up in the current grade level. For example:

  • Unit 1 spiral review is Kindergarten addition and subtraction concepts right before Unit 2 introduces 1st grade addition and subtraction concepts
  • Unit 4 spiral review is Kindergarten geometry concepts right before Unit 5 introduces 1st grade geometry concepts

I did this intentionally because a common complaint I hear from teachers is that students aren’t ready for instruction in the current grade level standards for whatever unit they happen to be in. The (non)-issue is that kids forget things. It’s natural. When learning ends, forgetting begins.

What we need to do is re-frame this experience. It’s not a fault of the children or of a teacher. Rather, it’s a normal human phenomenon. With the spiral review planned the way it is, teachers now have time to jog memories and re-solidify understandings of last year’s content before students are expected to tackle this year’s content.

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 2nd grade’s scope and sequence in my next post.

 

 

Moving On Before It’s Over (Kindergarten)

This school year isn’t even over yet, but in my role as a Curriculum Coordinator, I’m already starting to look ahead to next school year. I feel like I’m cheating on the current school year, but if I don’t start now, there’s no way I’ll have everything ready when the teachers come back in August.

One of my responsibilities every spring is to analyze our instructional units to determine whether any changes need to be made for the upcoming school year. Over the past several years, I’ve made some pretty drastic changes to our scope and sequence, but each year I feel like it’s been less and less and that we’re settling on a coherent plan that works for our teachers and students.

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 – I thought I’d share our scope and sequences to give you a sense of what kinds of changes we’ve made over time and what we’re planning for next year. I have no idea whether this will be useful to anyone, but if I don’t share then I’ll never know.

Let’s start with Kindergarten!

Here are our scope and sequences of units for the past three school years. What do you notice? What do you wonder?

Kindergarten – School Year 2015-16

K15-16

Kindergarten – School Year 2016-17

K16-17

Kindergarten – School Year 2017-18

K17-18

Let me explain some of the big changes that have happened over the past few years as well as the rationale behind our scope and sequence.

Kindergarten starts with introducing students to the numbers through 5 and then the numbers through 10. This has been fairly stable over the past few years. At this early part of the year, the focus is on counting, counting, counting and representing, representing, representing. Students come to us with a wide range of abilities. We can’t presume their understanding so we want to ensure everyone has a solid foundation in the first month or so of the school year.

You’ll notice over the past few years that unit 3 on sorting and classifying jumped up from 11 days to 15 days to 25 days. Sorting and classifying are huge verbs in mathematics, and we wanted students to start engaging with them right away via our data and geometry standards. The jump in days came because the unit used to only include 3D figures. We used to introduce 2D figures later in the school year. Now this unit includes both 3D and 2D figures.

We circle back around to numbers to 10 in unit 4. Students continue to count, count, count and represent, represent, represent, but they also start comparing in this unit. This is followed by our measurement unit which extends the concept of comparison as students talk about things being longer or shorter, heavier or lighter, and more full or less full.

During the 2017-18 school year we made it so our addition and subtraction units are back to back, followed by our unit on numbers to 20. This is because the old scope and sequence confused teachers. For the first half of the year students engage with numbers to 10. After winter break, students used to work in a unit where they engaged with numbers to 20, only to encounter a subtraction unit afterward that suddenly said to only focus on numbers to 10 again. Teachers were baffled by this. If students were learning about numbers to 20, then why weren’t they subtracting with numbers to 20 in the next unit? The answer is because our standards explicitly state to add and subtract within 10.

We opted to remove the confusion by putting both the addition and subtraction units before the unit on numbers to 20. That way it maintains a flow of working within 10: They learn to count and represent numbers to 10, compare numbers to 10, and then add/subtract numbers to 10 (in contexts). Finally we extend to numbers to 20. Our unit on numbers to 20 is a long one because it takes the concepts of counting, representing, and comparing and puts them together all in one unit.

The year closes out with two units. The first is our personal financial literacy unit, which introduces skills such as identifying coins by name, identifying ways to earn income, differentiating money received as income vs gifts, listing simple skills required for jobs, and distinguishing between wants and needs.

The second unit to close out the year is our addition and subtraction unit that brings the operations together to give students an opportunity to start having to identify which operation is needed in a given situation. The earlier units focused on working through the language stages of addition and subtraction separately to help students connect those operations to the actions of joining and separating (as per our standards), but at the end of the year we want students to have the opportunity to problem solve and make decisions about whether a given situation involves joining or separating.

These last two units used to be in reverse order, but after some feedback from teachers I changed it for the 2017-18 school year. Basically we ran into an issue where teachers couldn’t give grades on the report card regarding the financial literacy standards because grades were due before they completed that unit. Since addition and subtraction were already introduced earlier in the school year, I moved that to become the final unit so that teachers could teach the entire financial literacy unit before they have to submit report cards.

Kindergarten – School Year 2018-19

I’m pretty happy with the Kindergarten scope and sequence from this school year. I’m going to meet with my Kindergarten curriculum collaborative in a month or so to see if they agree, but I’m not anticipating making any changes for next school year.

You’ll notice that our scope and sequence spends a TON of time on numbers to 10 because that is the focus of our Kindergarten standards. Students do extend these understandings as they work with numbers to 20, but numbers to 20 is actually the focus of the 1st grade standards. You’ll see what I mean in my next post on 1st grade.

One of my primary goals across each grade in grades K-5 is to ensure sufficient instructional time on core concepts for that grade level. I want students who need intervention later on to end up there because they truly aren’t understanding concepts, not because they weren’t given sufficient time to learn during first instruction.

One thing I am trying to decide about for next year is whether I’ll specify spiral review topics throughout the year. Here’s our at-a-glance so you can see how each unit is broken down into three instructional goals – focus TEKS (standards), computational fluency, and spiral review.

KAAGFall

KAAGSpring

In Kindergarten we don’t have spiral review in the fall semester because the math block is only 60 minutes – 50 minutes for core lesson and 10 minutes for computational fluency. In the spring semester we add in 20 minutes of daily spiral review to bring up our math block to 80 minutes daily.

I suggest topics to review during spiral review to help teachers out, but I am afraid that this creates a confusing message. I wholeheartedly want teachers to review the concepts their students need to review. For example, if a teacher knows some students are struggling comparing numbers to 10 in unit 8, then by all means, review that concept rather than sorting and classifying with 2-D and 3-D figures.

The only reason I list topics is to give some guidance to help teachers ensure that topics are coming up again throughout the year. I know from firsthand experience as a classroom teacher that I was often working at the day-to-day or, if I was extremely lucky, the week-to-week level. Now that I’m in a position that allows me to look at the level of the entire year, I try to provide as much guidance as possible for teachers to help them navigate the school year.

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 1st grade’s scope and sequence in my next post.