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1st Grade Addition & Subtraction

Students need to understand addition and subtraction as joining and separating quantities — not just as procedures for combining digits — before they can reliably solve problems within 20 or apply the operations to word problems.

Where This Skill Fits

Addition and subtraction within 20 is the central focus of 1st grade math. It builds directly on counting and number sense, and it sets up the fact fluency and place-value reasoning that 2nd grade regrouping depends on.

Prerequisite Skills

Counting to 20 with one-to-one correspondence
Understanding that the last number counted tells "how many"
Recognizing and writing numbers to 20

Recommended Conceptual Progression

Join and separate small sets using counters (concrete)
Represent joining/separating on a ten frame
Count on and count back on a number line
Use "make ten" strategies for sums close to 10
Record equations that match the concrete action
Apply addition and subtraction to simple word problems

Common Student Misconceptions

Recounting a rearranged set — believing the total changed because the items look different, rather than trusting conservation of number.
Reading the equal sign as "the answer comes next" instead of as a balance between two equal amounts (e.g., struggling with 8 = 5 + 3).
Choosing an operation based on a keyword like "left" always meaning subtraction, rather than the actual action in the story.

Recommended Visual Models

Counters — for joining and separating small sets
Ten frames — for building numbers to 10 and seeing "how many more to make ten"
Number lines — for counting on and counting back

Small-Group Teaching Sequence

Model the day's strategy with counters or a ten frame, guide students through the same process with a new set of numbers, then have students apply the strategy independently on a similar problem while you observe.

I Do Example

"I have 6 counters. I'm going to add 3 more. I'll count on from 6: 7, 8, 9. So 6 + 3 = 9." (Teacher models counting on using a number line while narrating each step.)

We Do Example

"Let's try 8 + 4 together. Where do we start counting on the number line? Let's count on together: 9, 10, 11, 12." (Teacher and students count on together, with the teacher prompting rather than telling.)

You Do Example

Students solve 7 + 5 independently using a number line or ten frame, then explain their strategy to a partner or the teacher.

Quick Check

Three problems within 20, mixing addition and subtraction, with a visual model available. Watch whether the student chooses an efficient strategy (counting on from the larger number) rather than always counting from one.

If the Student Is Ready

Move to two-step word problems within 20, or begin building fact fluency within 10 through short daily practice.

If the Student Is Not Ready

Return to counters and ten frames for joining/separating small sets, and confirm the student can count a rearranged set without recounting from one.

Related Skills

Before: Counting and number sense to 20
Current: Addition and subtraction within 20
Next: Place value (tens and ones) and addition/subtraction within 100

Relevant SMS Resources

Browse more 1st grade addition and subtraction routines, task cards, and quick checks in the full catalog.

Related Guides

Teacher FAQ

My student can add within 10 but freezes on numbers to 20. What's happening?

This is common — bridging past 10 requires the "make ten" strategy, which is a new skill, not just bigger numbers. Spend extra time on ten frames before moving to abstract equations.

Should I teach addition and subtraction separately or together?

Teaching them as related (a fact family, like 8 + 4 = 12 and 12 − 4 = 8) tends to build stronger number sense than teaching them as unrelated procedures.