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

### 1st Grade – School Year 2016-17

### 1st Grade – School Year 2017-18

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.

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.