1
3
6
8
2
5
7
SUM
6
2
5
• 8 + 7 = 15 ones → Regroup 1 ten, keep 5 ones.
• 1 + 6 + 5 = 12 tens → Regroup 1 hundred, keep 2 tens.
4 475 + 189 = 664
2 Pts
H
T
O
Regroup
1
1
4
7
5
1
8
9
SUM
6
6
4
• 5 + 9 = 14 ones → Regroup 1 ten, keep 4 ones.
• 1 + 7 + 8 = 16 tens → Regroup 1 hundred, keep 6 tens.
Level 3 Key • Detective Challenge Exemplar Critique & Accurate Calculation
3 Pts
5 Exemplar Student Analysis for Problem 5
Sam's Flawed Thinking:
Sam added each column separately but wrote only the ones digit without carrying over the 10s:
• 8 + 4 = 12 (wrote 2, lost the 10)
• 5 + 6 = 11 (wrote 1, lost the 100)
• 3 + 2 = 5 (forgot carried 100)
A. Model Explanation (Accept equivalent reasoning):
"Sam forgot to regroup! When he got 12 ones, he should have traded 10 ones for 1 ten and added it to the tens column. Then, when he got 12 tens (1 + 5 + 6), he should have traded 10 tens for 1 hundred."
B. Correct Sum: 358 + 264 = 622
(1 ten + 1 hundred regrouped)
Formative Assessment & Reteaching Guide:
If Student Writes Multi-Digits:
e.g., writing "12" in one box. Pull out physical base-ten unit cubes and show that only single digits (0-9) fit in each place-value room.
If Regrouped 1 is Forgotten:
Have students circle the regrouping box in orange before adding. Teach the rhythm: "Add the roof number first (1 + top + bottom)."
Extension for Mastery:
Ask students to create their own 3-digit problem where only the tens need regrouping, or challenge them to add three 3-digit numbers.
Place Value Power Teacher Key • Page 2 Answers Standards: 2.NBT.B.7, 3.NBT.A.2 • Mathematical Practices 1, 3, 4, 6, 7 Page 2 of 2
6
1
5
−
2
4
9
DIFF
• 5 − 9: Trade 1 ten → 15 − 9 =
• 0 − 4: Trade 1 hundred → 10 − 4 =
• Hundreds remaining: 5 − 2 =
Level 3: Math Detective Challenge Critique Reasoning & Spot the Bottom-Number Trap (MP3 & MP6)
5 Error Analysis: Why is Leo's answer wrong?
Leo's Solution: Incorrect!
4 5 3
− 1 8 6
3 3 3
Leo says: "6 minus 3 is 3, 8 minus 5 is 3, and 4 minus 1 is 3. That was so easy!"
A. What huge mistake did Leo make with subtraction?
B. Solve it correctly with place-value regrouping:
453 − 186 =
Self-Check: Can you remember to unbundle before subtracting?
Need More Practice Getting Good! Subtraction Master!
Place Value Power • Adaptive Subtraction Classwork Standards: 2.NBT.B.7, 3.NBT.A.2 • MP1, MP3, MP6, MP7 Page 2 of 2
H
T
O
Trade
4
12
14
5
3
4
−
2
7
8
DIFF
2
5
6
• 4 − 8: Trade 1 ten → 14 − 8 = 6
• 2 − 7: Trade 1 hundred → 12 − 7 = 5
• Hundreds remaining: 4 − 2 = 2
4 615 − 249 = 366
2 Pts
H
T
O
Trade
5
10
15
6
1
5
−
2
4
9
DIFF
3
6
6
• 5 − 9: Trade 1 ten → 15 − 9 = 6
• 0 − 4: Trade 1 hundred → 10 − 4 = 6
• Hundreds remaining: 5 − 2 = 3
Level 3 Key • Detective Challenge Exemplar Critique & Subtraction Properties
3 Pts
5 Exemplar Student Analysis for Leo's Digit-Flipping Trap
Leo's Flaw: Digit Flipping
Leo reversed the subtraction order whenever the bottom digit was bigger:
• He did 6 − 3 instead of 3 − 6
• He did 8 − 5 instead of 5 − 8
• Subtraction is NOT commutative!
A. Model Explanation (Accept equivalent reasoning):
"Leo flipped the numbers upside down! You cannot do 6 − 3 when 3 is on top. Since 3 is smaller than 6, he had to go next door and unbundle 1 ten to make 13 ones. Subtraction does not let you switch the numbers."
B. Correct Difference: 453 − 186 = 267
(Double unbundling required)
Targeted Subtraction Intervention Strategies:
Digit-Flipping Trap:
If a student writes "333" for 453-186, ask: "If you have 3 cookies, can I eat 6?" Connect this to why unbundling is non-negotiable.
Unbundling Across 1 (Problem 4):
When 1 ten donates to ones, it leaves 0 tens. Students frequently write 1 ten remaining. Emphasize crossing out before borrowing again.
Inverse Check Strategy:
Teach students to check their subtraction by adding: Difference + Subtrahend = Minuend ($267 + 186 = 453$). Builds MP6 precision.
Place Value Power Teacher Key • Subtraction Page 2 Standards: 2.NBT.B.7, 3.NBT.A.2 • Mathematical Practices 1, 3, 6, 7 Page 2 of 2
