Multi-Digit Addition & Subtraction

Florida B.E.S.T. Standard

MA.3.NSO.2.1

Add and subtract multi-digit whole numbers including using a standard algorithm with procedural fluency.

Clarifications:

A "standard algorithm" is any efficient and accurate procedure for computing. Students are not restricted to one specific method.
Students work with numbers aligned to MA.3.NSO.1.1 (numbers to 10,000).
Problems should be presented in both vertical and horizontal formats.
Students should justify their method and explain regrouping.
Connect to estimation (MA.3.NSO.1.4) to check reasonableness.

Key Understanding: Procedural Fluency

Procedural fluency means students can accurately, efficiently, and flexibly add and subtract multi-digit numbers.
This builds on Grade 2's work within 1,000 and extends to larger numbers (up to 10,000).
The "standard algorithm" does NOT mean only the traditional US method - any efficient procedure that students can explain counts.
Place value understanding must underpin all algorithm work - students should know WHY regrouping works.
Students should estimate before computing to predict reasonable answers.

Common Misconceptions & Fixes

Misconception: Regrouping errors ("carrying" or "borrowing" incorrectly)

Students add digits without regrouping when sum exceeds 9, or forget to add the regrouped amount.

Fix: Use base-ten blocks to physically show why 10 ones = 1 ten. Write the regrouped digit above the next column. Practice with place value disks.

Misconception: Subtracting smaller from larger regardless of position

In 43 - 28, student writes 25 (subtracting 3 from 8 in ones place instead of regrouping).

Fix: Ask "Can I take 8 from 3?" Teach that we must regroup from tens. Use "Can I?" check before each subtraction.

Misconception: Regrouping across zeros (e.g., 402 - 175)

Students get stuck when there's a zero in the tens place - can't "borrow" from nothing.

Fix: Show regrouping chain: 402 = 3 hundreds + 10 tens + 2 ones = 3 hundreds + 9 tens + 12 ones. Use base-ten blocks to demonstrate.

Misconception: Adding/subtracting different place values

Student misaligns digits when problems are written horizontally (e.g., 45 + 386).

Fix: Always rewrite horizontal problems vertically, aligning ones under ones, tens under tens, etc. Use graph paper.

Misconception: Not checking reasonableness

Student gets 156 + 238 = 1,394 and doesn't recognize the answer is unreasonable.

Fix: Require estimation before computing: "150 + 240 = about 390." Compare final answer to estimate.

Algorithm Options

Florida B.E.S.T. allows any standard algorithm that students can explain. Here are approved approaches:

Traditional Vertical Algorithm

¹
456
+278
────
734

The most common method. Record regrouped values above the next column.

Expanded Form Addition

456 + 278
= 400 + 50 + 6 + 200 + 70 + 8
= 600 + 120 + 14
= 600 + 134 = 734

Breaks numbers apart by place value. Great for building understanding.

Partial Sums

456
+278
────
600 (400 + 200)
120 (50 + 70)
14 (6 + 8)
────
734

Add each place value separately, then combine.

5-Day Lesson Sequence

Day 1: Review Place Value & Estimation

Review place value chart (ones through thousands)
Practice rounding to estimate sums and differences
Connect to MA.3.NSO.1.4 (rounding to nearest 10 and 100)
Introduce "estimate first, compute, then check" routine

Day 2: Addition with Regrouping

Use base-ten blocks to model 3-digit + 3-digit with regrouping
Connect physical model to written algorithm
Practice recording regrouped amounts
Emphasize: "10 ones = 1 ten, 10 tens = 1 hundred"

Day 3: Subtraction with Regrouping

Model subtraction with base-ten blocks
Teach "Can I?" check before each place value
Practice regrouping across one place
Emphasize checking by adding back

Day 4: Regrouping Across Zeros

Focus on numbers with zeros (e.g., 500, 402, 1,000)
Model regrouping chain with place value disks
Practice problems like 400 - 156, 1,002 - 547
Show multiple strategies for these challenging problems

Day 5: Mixed Practice & Word Problems

Mix addition and subtraction problems
Include word problems requiring students to choose operation
Practice FAST-format problems
Review estimation as reasonableness check

Differentiation Strategies

For Struggling Learners

Use base-ten blocks for every problem until regrouping clicks
Use graph paper to keep digits aligned
Focus on 2-digit numbers before moving to 3-digit
Color-code place values (ones = green, tens = blue, etc.)
Use the "Can I?" verbal check before each subtraction step

For Advanced Learners

Work with 4-digit numbers (up to 10,000)
Solve multi-step word problems
Find missing addends or missing digits
Create their own word problems for classmates
Explore mental math strategies for compatible numbers

Assessment Tip:

FAST tests procedural fluency - watch for students who can get correct answers but don't understand WHY. Ask students to explain their regrouping steps. If they can't explain, they may struggle when problem formats change on the test.

FAST Test Connection

Multi-digit addition and subtraction appears frequently on the FAST. Expect to see:

Computation problems in various formats (vertical, horizontal, fill-in-the-blank)
Word problems requiring students to set up and solve
Reasonableness questions asking "Which is the best estimate?"
Error analysis showing student work and asking to find the mistake
Comparison problems asking which expression has a greater/lesser value

Teacher Guide: Multi-Digit Addition & Subtraction