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
2nd Grade – School Year 2016-17
2nd Grade – School Year 2017-18
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.
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?
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.