Expanded Addition Slides Math Workshop
Grade 4 • Place Value & Operations
Mental Strategy & Concrete Concept
Adding with
Expanded Form
Unlock large number addition by breaking numbers down into their true place values—from ones up to ten thousands!
1 5-Min Warm-Up
2 3-Digit Modeling
3 4-Digit Numbers
4 Ten Thousands
Warm-Up • 5 Minutes
What is Place Value?
Quick Recall
Ten Thousands
10,000
10 groups of 1,000
Thousands
1,000
10 groups of 100
Hundreds
100
10 groups of 10
Tens
10
10 ones
Ones
1
Single units
?
Think-Pair-Share: What is the value of 7 in 74,329?
Explain how you know using its place on the place value chart.
Value = 70,000
Strategy
The Expanded Addition Method
3-Step Process
1
EXPAND
Write both numbers in expanded form by stretching each digit into its true place value.
524 = 500 + 20 + 4
2
COMBINE
Add like place values vertically: ones with ones, tens with tens, hundreds with hundreds.
Add column by column
3
REUNITE
Add all place value sums together to find the final total sum in standard form.
700 + 50 + 7 = 757
Why this works: You never lose track of what numbers actually represent! 4 isn't just a 4—it might mean 4, 40, 400, 4,000, or 40,000.
Level 1: 3-Digit
Example 1: No Regrouping
342 + 253
Standard Form
342
+ 253
595
Expanded Place Value Addition
First: 300 + 40 + 2
Second: + 200 + 50 + 3
Sums: 500 + 90 + 5
Combine Place Sums: 500 + 90 + 5 = 595
Notice: Each column adds easily with basic facts: 3+2=5 (hundreds), 4+5=9 (tens), 2+3=5 (ones)!
Level 1: 3-Digit
Example 2: With Regrouping
468 + 275
Standard Form
¹ ¹
468
+ 275
743
Expanded Regrouping Step-by-Step
468: 400 + 60 + 8
275: + 200 + 70 + 5
Sums: 600 + 130 + 13
Break down the tens & ones:
600 + (100 + 30) + (10 + 3) = 743
Regrouping insight: 13 ones = 10 + 3. 130 tens = 100 + 30. Expanded form reveals why you "carry the 1"!
Level 2: 4-Digit
Example 1: No Regrouping
3,245 + 1,632
Place Thousands Hundreds Tens Ones
3,245 3,000 + 200 + 40 + 5
+ 1,632 + 1,000 + 600 + 30 + 2
Totals: 4,000 + 800 + 70 + 7
Combine partial sums: 4,000 + 800 + 70 + 7 = 4,877
Pattern Check: Adding 4-digit numbers works exactly like 3-digit numbers—we just added one more place value column: Thousands!
Level 2: 4-Digit
Example 2: With Regrouping
5,864 + 2,479
Standard Form
¹ ¹ ¹
5,864
+ 2,479
8,343
Column-by-Column Value Breakdown
Thousands: 5,000 + 2,000 = 7,000
Hundreds: 800 + 400 = 1,200
Tens: 60 + 70 = 130
Ones: 4 + 9 = 13
Assemble all partial sums:
7,000 + 1,200 + 130 + 13 = 8,343
Pro-Tip: Notice how 1,200 feeds 1,000 to the thousands place, and 130 feeds 100 to the hundreds place!
Level 3: Ten Thousands
Example 1: No Regrouping
24,316 + 13,542
Number Ten Th. Thousands Hundreds Tens Ones
24,316 20,000 + 4,000 + 300 + 10 + 6
+ 13,542 + 10,000 + 3,000 + 500 + 40 + 2
Totals: 30,000 + 7,000 + 800 + 50 + 8
Final Standard Form: 37,858
Ten Thousands Mastery: Even huge numbers are painless when broken down into place values!
Level 3: Ten Thousands
Example 2: Multi-Place Regrouping
47,865 + 38,596
Standard Form
¹ ¹ ¹ ¹
47,865
+ 38,596
86,461
Expanded Value Addition
Ten Thousands: 40,000 + 30,000 = 70,000
Thousands: 7,000 + 8,000 = 15,000
Hundreds: 800 + 500 = 1,300
Tens: 60 + 90 = 150
Ones: 5 + 6 = 11
Sum of all parts: 70,000 + 15,000 + 1,300 + 150 + 11 = 86,461
Total Clarity: 70,000 + 15,000 = 85,000, plus 1,300 = 86,300, plus 150 = 86,450, plus 11 = 86,461!
Wrap-Up
Keys to Success
Ready for Action!
Line Up Places
Always match ones with ones, tens with tens, and thousands with thousands. Don't mix up columns!
Watch Regrouping
When a place sum exceeds 9 units (like 12 tens = 120), break it into its component values cleanly.
Recombine & Check
Add your expanded values back together to verify your answer matches standard addition!
Now It's Your Turn!
Complete your guided notes worksheet, then tackle today's exit ticket.
Worksheet Time →
Expanded Addition Worksheet Math Workshop Multi-Digit Addition
Place Value Power: Expanded Addition
Name:
Date: Class:
! Alignment Rule: Line up each expanded number vertically in its matching column. Add columns, then recombine!
1
Warm-Up: Place Value Value Check (5 Min)
State the value of the underlined digit
In 3,842:
Digit: 8 Value:
In 61,409:
Digit: 6 Value:
In 47,315:
Digit: 7 Value:
2
Level 1: 3-Digit Expanded Addition
Columns: Hundreds + Tens + Ones
Problem 1: 425 + 352 No Regrouping
Hundreds Tens Ones
400 + 20 + 5
+ 300 + 50 + 2
Recombine partial values:
Sum =
Problem 2: 578 + 264 With Regrouping
Hundreds Tens Ones
Recombine partial values:
Sum =
3
Level 2: 4-Digit Expanded Addition
Columns: Thousands + Hundreds + Tens + Ones
Problem 3: 4,361 + 2,518 Thousands
Thousands Hundreds Tens Ones
Recombine partial values:
Sum =
Problem 4: 6,487 + 1,745 Multi-Regrouping
Thousands Hundreds Tens Ones
Recombine partial values:
Sum =
Place Value Power • Expanded Addition Practice Page 1 of 2 • Turn over for Level 3 Ten Thousands →
Level 3: Ten Thousands Alignment
5-Digit Expanded Form Addition Practice
Student Name:
4
Level 3: 5-Digit Addition (Part 1)
Columns: 10,000s + 1,000s + 100s + 10s + 1s
Problem 5: 32,415 + 16,352 No Regrouping
10,000s1,000s100s10s1s
Recombine partial values:
Expanded Addition Exit Ticket Formative Check Multi-Digit Addition
Expanded Addition Exit Ticket
Name:
Date: Score: / 3
1 Level 1 (3-Digit): 356 + 218
Hundreds + Tens + Ones
Hundreds Place Tens Place Ones Place
Recombine partial sums into standard form:
Final Sum =
2 Level 2 (4-Digit): 4,372 + 2,819
Thousands to Ones
Thousands Hundreds Tens Ones
Recombine partial sums into standard form:
Final Sum =
3 Level 3 (5-Digit): 25,480 + 13,264
Ten Thousands Mastery
Ten Th. Thousands Hundreds Tens Ones
Recombine partial sums into standard form:
Final Sum =
Student Confidence: 1 - Still Learning 2 - Almost There 3 - Got It!
Teacher Checked:
Expanded Addition Homework Homework Daily Math Practice
Expanded Addition Practice
Name:
Date: Due:
Family Tip: Line up numbers vertically by place value in the large boxes below. Add each place column, then recombine the partial sums!
A
Place Value Warm-Up: Write in Expanded Form
1. 648 =
2. 4,815 =
3. 18,304 =
4. 50,792 =
B
Level 1: 3-Digit Expanded Addition
Hundreds + Tens + Ones
5. 523 + 346 No Regroup
HundredsTensOnes
Recombine:
Sum =
6. 478 + 385 Regroup
HundredsTensOnes
Recombine:
Sum =
C
Level 2: 4-Digit Expanded Addition
Thousands + Hundreds + Tens + Ones
7. 3,425 + 4,263
Thousands Place
ThousandsHundredsTensOnes
Recombine:
Sum =
8. 5,784 + 2,648
With Regrouping
ThousandsHundredsTensOnes
Recombine:
Sum =
Place Value Power Homework • Page 1 of 2 Turn over for 5-Digit Ten Thousands Practice →
Level 3: Ten Thousands Alignment
5-Digit Addition Practice
Student Name:
D
Level 3: 5-Digit Expanded Addition
Ten Thousands to Ones
9. 24,135 + 51,742 No Regrouping
Ten Th.ThousandsHundredsTensOnes
Recombine:
Final Sum =
10. 46,895 + 37,458 Multi-Regrouping
Ten Th.ThousandsHundredsTensOnes
Expanded Addition Teacher Guide Teacher Facilitation Guide Grade 4 • Operations & Base Ten
Place Value Power: Expanded Addition
Total Time: 45–50 Mins
Standards: CCSS.4.NBT.B.4
Learning Target
Students will accurately add multi-digit whole numbers up to the ten thousands place by decomposing numbers into expanded place value form, aligning like place values in vertical columns, adding each column, and recombining partial sums.
Materials Needed
Instructional Slides Deck
Student Worksheet (2 pp.)
Full-Page Exit Ticket
Homework Practice Sheet
Warm-Up Protocol
5-Minute Place Value Activation
Slides 2 & Worksheet Part 1
Teacher Script / Prompts: "Before we can add huge numbers, we must remember what numbers are really built from. Look at the number 74,329 on Slide 2. When you look at the 7, what is it worth? Turn to your partner and explain why it's not just 7."
Look-For: Students identify that 7 is in the 10,000s column, giving it a value of 70,000 .
Question to Ask: "How many thousands make ten thousand? How does our base-10 system multiply by 10?"
Quick Check: Have students complete the 3 warm-up problems in Part 1 of the worksheet (2 minutes).
Instructional Pacing & Alignment Guidance
00–05 Min
Place Value Warm-Up: Review place values (ones to ten thousands). Emphasize vertical alignment of like columns.
05–20 Min
Direct Instruction & Paired Modeling (Slides 3–9):
• Level 1 (3-Digit): Model 342+253 (no regroup) then 468+275 (show 13 ones = 10+3; 130 tens = 100+30).
• Level 2 (4-Digit): Model 3,245+1,632 then 5,864+2,479 (demonstrate spacious thousands column alignment).
• Level 3 (5-Digit): Model 24,316+13,542 then 47,865+38,596 (regrouping into ten thousands: 70,000+15,000).
20–38 Min
Guided & Independent Practice: Students solve Worksheet Problems 1–9 using the large color-coded alignment grids.
38–48 Min
Debrief & Exit Ticket: Administer the 3-question full-page Exit Ticket with spacious number boxes. Collect for grading.
Common Misconceptions
Dropping Zeroes: Omitting the zero place value in 75,308 instead of writing \(0 \times 10 = 0\) in the tens column.
