Name:
Page: 3 of 3
5 Solve: 38,647 + 25,876
5-digit multi-column regrouping
1. Standard Algorithm TTh | Th | H | T | O
TTh
Th
H
T
O
2. Place Value (Expanded) Decompose & Sum
3. Open Number Line Long Workspace • Record jumps above, landmarks below
Start → +Ten-Th → +Th → +H → +T → +O
4. Place Value Disks / Chips Draw disks & show trades across columns
Disks: [10k] • [1k] • [100] • [10] • [1]
6 Solve: 54,789 + 36,548
5-digit multi-column regrouping
1. Standard Algorithm TTh | Th | H | T | O
TTh
Th
H
T
O
2. Place Value (Expanded) Decompose & Sum
3. Open Number Line Long Workspace • Record jumps above, landmarks below
Start → +Ten-Th → +Th → +H → +T → +O
4. Place Value Disks / Chips Draw disks & show trades across columns
Disks: [10k] • [1k] • [100] • [10] • [1]
Pedagogical scaffolds for guiding students through the 6 practice problems
Page 2 of 2
10 Min: Warmup & Model
Walk through 4,678 + 3,854 using Slide Deck / Anchor Chart.
15 Min: Guided Practice
Solve Q1 & Q2 (3-digit) together or with partner checks.
25 Min: Independent/Pairs
Students complete Q3–Q6 (4-digit & 5-digit) on worksheet.
10 Min: Exit Ticket
Individual exit ticket check to assess strategy flexibility.
Modeling the Regrouping Moment:
“Look at my ones column: 8 plus 4 gives me 12 ones. Can 12 fit in the single-digit ones column? No! Only values 0 through 9 can live there. So I break 12 into 1 ten and 2 ones. I record 2 in the ones spot, and I carry the 1 ten up to the tens family.”
Connecting Place Value to Standard Algorithm:
“Notice how in Strategy 2, our hundreds gave us 1,400. In Strategy 1, we wrote down a 5 and carried a 1. Where did that 1 go? It went to the thousands place—representing exactly 1,000, just like the 1,400 in expanded form!”
1. Forgetting the Carried Unit
Adds addends but forgets the ‘1’ on top of the next column.
“Circle carried digits in red or add them first before the addends.”
2. Misaligned Columns (5-Digit)
Aligning from the left instead of right, causing tens to add with hundreds.
“Use the vertical grid lines to verify ones align with ones.”
3. Number Line Jump Arithmetic
Miscalculating landmark landing spots when jumping across thousands.
“Check that each jump only changes the specific place value digit.”
Support (Struggling Learners)
Extension (Advanced Learners)
Strategy Vault Instructional Guide • Alignment: CCSS.MATH.CONTENT.4.NBT.B.4
3. Number Line
Start: 5,489
+3,000 → 8,489
+700 → 9,189 | +60 → 9,249
+4 → 9,253
4. Base Blocks
8 cubes, 11 flats, 14 rods, 13 units
Bundle to: 9 cubes, 2 flats, 5 rods, 3 units
= 9,253
Strategy Vault Answer Key • Questions 1 through 4
Answer Key
Teacher Reference • Page 2 of 2
Q5 (5-Digit): 38,647 + 25,876 = 64,523 4-Column Regrouping
1. Standard
¹ ¹ ¹ ¹
3 8 , 6 4 7
+2 5 , 8 7 6
-----------
6 4 , 5 2 3
2. Place Value
30k+20k = 50,000
8k+5k = 13,000
600+800 = 1,400
40+70 = 110 | 7+6 = 13
Sum = 64,523
3. Number Line
Start: 38,647
+20k → 58,647
+5k → 63,647
+800 → 64,447
+70 → 64,517 | +6 → 64,523
4. Place Value Disks
Bundles 13 ones → 1 ten
Bundles 12 tens → 1 hundred
Bundles 15 hundreds → 1 thousand
Bundles 14 thousands → 1 ten-th.
= 64,523
Q6 (5-Digit): 54,789 + 36,548 = 91,337 4-Column Regrouping
1. Standard
¹ ¹ ¹ ¹
5 4 , 7 8 9
+3 6 , 5 4 8
-----------
9 1 , 3 3 7
2. Place Value
50k+30k = 80,000
4k+6k = 10,000
700+500 = 1,200
80+40 = 120 | 9+8 = 17
Sum = 91,337
3. Number Line
Start: 54,789
+30k → 84,789
+6k → 90,789
+500 → 91,289
+40 → 91,329 | +8 → 91,337
4. Place Value Disks
Bundles 17 ones → 1 ten
Bundles 13 tens → 1 hundred
Bundles 13 hundreds → 1 thousand
Bundles 11 thousands → 1 ten-th.
= 91,337
Exit Ticket Challenge: 4,586 + 2,749 = 7,335 Scoring: 4 Points (1 pt per strategy)
1. Standard
¹ ¹ ¹
4 , 5 8 6
+2 , 7 4 9
---------
7 , 3 3 5
2. Place Value
4,000+2,000 = 6,000
500+700 = 1,200
80+40 = 120 | 6+9 = 15
Sum = 7,335
3. Number Line
Start: 4,586
+2,000 → 6,586
+700 → 7,286
+40 → 7,326 | +9 → 7,335
4. Base Blocks / Disks
6 cubes, 12 flats, 12 rods, 15 units
Bundles to:
7 cubes, 3 flats, 3 rods, 5 units
= 7,335
Exit Ticket Scoring Rubric:
4 Points: All 4 strategies correctly modeled with accurate regrouping and correct sum (7,335).
3 Points: 3 strategies modeled accurately; minor regrouping calculation error in one.
2 Points: 2 strategies completed accurately; struggles with visual representations (blocks/line).
1 Point: Only 1 strategy attempted or significant regrouping misconceptions across representations.
Strategy Vault Master Answer Key • Complete Lesson Solutions
