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.

 

 

 

 

 

 

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

  1. Cindy Wilson

    Thank you for sharing what you are doing with your district’s scope and sequence. I especially enjoy hearing your rationale behind making changes or not. Question, is there any particular you use math continuum resource you use for making instructional decisions, especially in regards to spiral review of previous grades (age) skills? Our district curriculum specialist has asked our group of math interventionists about a research-based math continuum, I assume to determine level of understanding for students who might need to be a part of a new walk to intervention program that we are implementing next year. I have only been able to find continuums from other countries, not from US. I thought you might be able to give me some information on where I might find something.While I understand that development of understanding isn’t specific to one country, I hoped that there had been some research in the US, not just in the rest of the world. Thanks for your input.

    Reply
    1. bstockus Post author

      Hi, Cindy! Thank you for your comment. To answer your question, there are a couple of resources I use to think about how we move students along within and across years. The first is Kathy Richardson’s How Children Learn Number Concepts book. This book details how students move through early number concepts in grades K-3. Some of our interventionists use this along with her Assessing Math Concepts series to diagnose where students are. Then they use activities from her Developing Number Concepts series to move students through the critical learning phases. They’ve had a lot of great success in filling gaps early in the school year so they can build those students up to grade level concepts as the year progresses.

      I also consult John Van de Walle’s Teaching Student-Centered Mathematics books when I want to think about the progression of ideas students need to go through when learning various topics. It definitely helped me as I planned geometry across the six grade levels.

      I haven’t done a lot of work with Cathy Fosnot’s Landscapes of Learning, but that might be a resource you want to check out along with her Young Mathematicians at Work series from Heinemann. And then of course I’d be remiss if I didn’t mention Douglas Clements’ work with learning trajectories. I’ll sheepishly admit I haven’t had the opportunity to dive deeply into his work, but from talks of his I’ve listened to, I know there’s some good stuff in there. You might want to check out this site for more info: https://www.learningtrajectories.org/ or get his book.

      I hope that gives you some ideas of resources to try out. Don’t hesitate to reach out with more questions. Good luck!

      Reply
      1. Cindy Wilson

        Thank you for all your suggestions. These are all resources I am familiar with, except for the learning trajectories work by Clements. The interventionists in our district use the assessments developed by Michael Battista to determine levels and develop intervention groups. I will definitely look into the Richardson assessments; I have all of her number concepts books, along with a planning guide. I will look more deeply into those resources as well. Thank you, again, for sharing your thinking (and resources) with me.

  2. Pingback: Moving On Before It’s Over (5th Grade) | Teaching to the Beat of a Different Drummer

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