Regrouping Power Slides Value Vault Math Series
Grade 2–3 Addition Foundations
Place Value & Addition Discovery
The Power of Regrouping
Why trading 10 ones for 1 ten never changes your number's true value—and how to add like a math detective.
1
Explain the Value
2
Inquiry Habit Routine
3
Partner Strategies
The Mystery of the 14 Loose Coins
Inquiry Warm-Up
Scenario A
14 Single Dollar Bills
Imagine holding fourteen single $1 bills in your left hand.
Total: $14
Scenario B
One $10 Bill + Four $1 Bills
You trade 10 of those singles at the bank for one crisp ten-dollar bill.
Total: $14
Big Question: Did you get richer or poorer? Neither! The format changed, but the exact value remained 14.
Rule #1: Regrouping Never Changes Value
Core Concept
10
10 Ones
Ten individual unit cubes scattered in the ones place.
Value = 10
EXACT EQUIVALENT
Equal in value,
1
1 Ten
One solid ten-rod neatly locked together into a single rod.
Value = 10
10 ones = 1 ten. Regrouping is simply renaming our bundles so each column stays in single digits (0–9).
The Detective Habit: Ask Every Column
Inquiry Routine
The Golden Question
“Do I need to regroup? Why?”
Never just guess or automatically write a little 1 at the top. Test the column total every single time:
If column total is 0 to 9:
NO REGROUPING NEEDED
Because it fits in one single place value digit.
If column total is 10 or more:
YES! MUST REGROUP!
Because 10 of these units make 1 unit of the next column!
Say it loud with your team: “Ten or more? Move next door!”
How to Line Up & Record Clearly
Step-by-Step
Problem: 47 + 28
1
T O
4 7
7 5
1. Align columns strictly
Tens under tens, ones under ones. Clean columns prevent slip-ups.
2. Add the Ones column (7 + 8 = 15)
Inquiry check: 15 ≥ 10? Yes! Regroup 10 ones as 1 ten above the tens column. Leave 5 ones below.
3. Add all Tens (1 + 4 + 2 = 7 tens)
Do not forget the regrouped ten! Total tens = 7. Final sum = 75.
Notice: 47 + 28 = (40 + 7) + (20 + 8) = 60 + 15 = 60 + 10 + 5 = 75. Value is preserved!
Guided Practice: Think-Pair-Solve
Try Together
Target Problem
56
+ 39
? ? ?
Prompt 1: Ones Column
What is 6 + 9? Do we need to regroup? Why?
Prompt 2: Record & Add Tens
Where does the regrouped ten go? What is 1 + 5 + 3?
Prompt 3: Explain to Partner
How do you know 56 + 39 equals 95 and not 815?
Turn to your partner now. Take 60 seconds to solve and check each other's inquiry question!
Mission: Strategy Showdown
Partner Briefing
A
Partner A
Uses the Standard Column Algorithm. Lines up digits neatly and records the regrouped ten above the tens place.
B
Partner B
Uses the Expanded Value / Partial Sums method. Adds tens first, then ones, then bundles them together.
🤝
The Compare
Both partners ask: “Did we get the exact same sum? How does each method handle the 10 extra ones?”
Ready to unlock the vault? Grab your activity sheets and partner up!
Let's Solve
Value Vault Lesson Plan Lesson Plan Mathematics • Grades 2–3
Value Vault: Regrouping & Place Value Equivalence
Duration: 60 Minutes
Focus: CCSS 2.NBT.B.5, 3.NBT.A.2
Essential Question
“Why does trading ten ones for one ten change how a number looks without changing what the number is actually worth?”
Key Learning Goals
Explain that 10 ones = 1 ten (value is conserved).
Ask & answer: “Do I regroup? Why?”
Align digits neatly and compare partner strategies.
Lesson Pacing (60 Min)
10 min: Inquiry Hook
15 min: Interactive Modeling
15 min: Strategy Showdown
12 min: Independent Vault
8 min: Reflection & Exit Ticket
Materials Needed
• Regrouping Power Slide Deck
• Base-ten rods & unit cubes (or digital manipulatives)
• Value Vault Worksheet, Partner Activity, & Exit Tickets
1
Inquiry Hook: The 14 Loose Coins (10 Min)
Conceptual Anchor
Display Slide 2. Show 14 individual $1 bills (or unit cubes) alongside 1 ten-dollar bill and 4 singles. Ask students: “Which person can buy a $14 toy? Did trading 10 singles change what you can buy?”
Core Takeaway: Regrouping is not doing math to change an amount—it is renaming an amount into groups of tens and ones so it fits into our base-ten number system.
2
Modeling the Inquiry Habit: “Do I Need to Regroup? Why?” (15 Min)
Direct Instruction
Present problem 47 + 28 (Slide 5). Emphasize vertical place-value alignment. Walk through the 3-step script:
Step 1: Align & Add Ones: 7 ones + 8 ones = 15 ones.
Step 2: Ask the Golden Question: “Do I need to regroup? Why?” Answer: Yes, because 15 is 10 or greater! 15 ones is 1 ten and 5 ones.
Step 3: Record Cleanly: Write 5 in the ones column; write the 1 regrouped ten in the tens box above the 4. Then add tens: 1 + 4 + 2 = 7 tens. Sum = 75.
Value Vault Teacher Guide • Lesson 1 Page 1 of 2
Value Vault: Guided Practice & Teacher Strategies
Part II: Implementation & Support
3
Strategy Showdown: Collaborative Practice (15 Min)
Peer Collaboration
Distribute the Strategy Showdown Partner Activity. Students pair up to solve problems using dual lenses: Partner A executes the standard column algorithm while Partner B uses expanded form / partial sums.
Accountable Talk Prompt: “Partner A, show Partner B where your regrouped ten came from. Partner B, show Partner A where that same ten appears in your partial sums!”
Value Vault Worksheet Math Mission Place Value & Addition
Value Vault: Regrouping Mission
Name:
Date:
1
Warm-Up: The Law of Value Equivalence
Trading units never changes what you have. Complete the equivalence statements:
15 Ones =
Ten + Ones
Total Value: 15
23 Ones =
Tens + Ones
Total Value: 23
1 Ten + 8 Ones =
Total Ones
Total Value: 18
2
Column Addition: The Inquiry Routine
Ask: “Do I need to regroup? Why?”
Add the ones first. Answer the inquiry prompt, record any regrouped ten in the box, then add the tens.
T O
3 8
Inquiry Check (Ones)
8 + 5 =
Do I need to regroup?
Yes No
Why?
T O
5 4
Inquiry Check (Ones)
4 + 9 =
Do I need to regroup?
Yes No
Why?
T O
4 6
Inquiry Check (Ones)
6 + 7 =
Do I need to regroup?
Yes No
Why?
T O
6 3
Inquiry Check (Ones)
3 + 8 =
Do I need to regroup?
Yes No
Why?
Value Vault Student Mission • Regrouping Routine Page 1 of 2
Value Vault Mission: Application & Reasoning
Part III: Reading & Writing
3
Word Problem Detectives
Read carefully. Identify the numbers, name the operation, align by place value, and solve.
Case 1: The Library Book Fair
On Monday, the school library sold 48 adventure books. On Tuesday, they sold 36 science books. How many total books did they sell?
Numbers: ______ & ______
Operation: ___________
4 8
+ 3 6
Answer Statement:
The library sold books in all.
Case 2: The Vault Gold Tokens
Team Amber collected 57 tokens in the vault challenge. Team Emerald collected 29 tokens. How many tokens did both teams collect together?
Numbers: ______ & ______
Strategy Showdown Activity Partner Lab Dual Strategy Investigation
Strategy Showdown: Compare & Connect
Partner A:
Partner B:
Partner Protocol: How to Play
1. Solve Independently Each partner uses their assigned strategy in their own column.
2. Compare Solutions Check if your sums match. If not, trace each step together!
3. Explain the Ten Point to where the regrouped ten lives in both strategies.
1
ROUND 1: Target Problem → 36 + 47
Showdown Time
Partner A: Standard Column Vertical Grid
Line up by place value. Record regrouping in the box.
T O
3 6
Partner B: Partial Sums Expanded Form
Break into tens and ones. Add each, then combine.
36 = 30 + 6
47 = 40 + 7
Add Tens: 30 + 40 =
Add Ones: 6 + 7 =
Total:
Partner Compare & Explain:
1. Did both strategies result in the exact same answer? [ ] YES [ ] NO Our Sum = ________
2. Explain the Ten: In Partner A's work, the regrouped 1 represents ones. In Partner B's work, that same ten appears in the number .
Value Vault Partner Lab • Strategy Showdown Page 1 of 2
Strategy Showdown: Roles Switched & Final Challenge
Part II: Deepening the Connection
2
ROUND 2: SWITCH ROLES! Target Problem → 58 + 27
Role Swap
Partner A: Partial Sums Expanded Form
58 = 50 + 8
27 = 20 + 7
Tens: 50 + 20 =
Ones: 8 + 7 =
Sum:
Partner B: Standard Column Vertical Grid
T O
5 8
Partner Check: 58 + 27 = ________ • Did our trading match? [ ] Match confirmed!
3
ROUND 3: Team Vault Challenge → 65 + 78
Solve together using whichever strategy your team prefers, then write your shared discovery.
Shared Workspace:
Final Sum =
Team Conclusion:
Complete this sentence together:
“Both strategies always give the same answer because regrouping is just...”
We coached each other and verified all math:
Sign A:
Sign B:
Value Vault Partner Lab • Strategy Showdown Page 2 of 2
Regroup Check Exit Ticket Exit Ticket
Value Vault: Quick Regroup Check
Name:
Date:
1. Add with Place Value
T O
4 8
2. The Detective Question
After adding the ones column (8 + 5 = 13):
Do I need to regroup?
Yes No
Why?
3. Concept Check: Value Equivalence
In 1–2 complete sentences, explain why regrouping 10 ones into 1 ten does not change the value of your number:
Self-Rating: [ ] I got this! [ ] Need a little practice [ ] Need help Value Vault Exit Ticket
CUT HERE FOR TWO HALF-SHEETS
Exit Ticket
Value Vault: Quick Regroup Check
Name:
Date:
1. Add with Place Value
T O
4 8
2. The Detective Question
After adding the ones column (8 + 5 = 13):
Do I need to regroup?
Yes No
Why?
3. Concept Check: Value Equivalence
In 1–2 complete sentences, explain why regrouping 10 ones into 1 ten does not change the value of your number:
Self-Rating: [ ] I got this! [ ] Need a little practice [ ] Need help Value Vault Exit Ticket
Value Vault Answer Key Answer Key & Guide Teacher Master Reference
Value Vault: Master Solutions
Classroom Edition
All Student Materials Included
1
Worksheet Part 1: Warm-Up Solutions
15 Ones = 1 Ten + 5 Ones
23 Ones = 2 Tens + 3 Ones
1 Ten + 8 Ones = 18 Total Ones
2
Worksheet Part 2: Column Addition & Inquiry Check
[1]
3 8
+ 2 5
6 3
8 + 5 = 13
[1]
5 4
+ 1 9
7 3
4 + 9 = 13
[1]
4 6
+ 3 7
8 3
6 + 7 = 13
[1]
6 3
+ 2 8
9 1
3 + 8 = 11
3
Worksheet Part 3: Word Problems
Case 1: Book Fair
Numbers: 48 and 36 • Op: Addition (+)
48 + 36 = 84
Statement: The library sold 84 books in all.
Case 2: Vault Gold Tokens
Numbers: 57 and 29 • Op: Addition (+)
57 + 29 = 86
Statement: Both teams collected 86 tokens.
Worksheet Part 4: Writing Exemplar Response
Exemplar (Full Credit)
“Regrouping does not change the value of a number because 10 ones is exactly equal in value to 1 ten rod. When we add 47 + 28, the 15 ones are simply traded into 1 ten and 5 ones. We are not adding or taking away any amounts; we are only bundling ten loose ones into a single ten rod so it can live in the tens place. The total sum is still exactly 75.”
• Key Idea 1: States 10 ones = 1 ten (equivalence).
• Key Idea 2: Explains no amount was added or lost.
• Key Idea 3: Connects trading to place value rules.
Value Vault Teacher Reference • Solutions Master Page 1 of 2
Value Vault: Strategy Showdown & Exit Ticket Solutions
Part II: Collaborative & Formative Assessments
1
Strategy Showdown Solutions
Round 1: 36 + 47 = 83 Both methods must match
Partner A (Column): 6 + 7 = 13 (write 3, regroup 1); 1 + 3 + 4 = 8 tens → 83
Partner B (Partial Sums): Tens: 30 + 40 = 70; Ones: 6 + 7 = 13; 70 + 13 = 83
