Lesson 2.2 Subtracting with Regrouping

Steps

1. Warm-up

   Do this: Ask these out loud. Your child answers out loud; no paper needed.

   • Ask: “700 + 400” Listen for: 1,100
   • Ask: “100 + 700” Listen for: 800
   • Ask: “200 + 400” Listen for: 600
   • Ask: “800 + 300” Listen for: 1,100
2. Teach the new idea

   Say this: “Start with the ones. Regroup from the next place whenever the top digit is too small.”

   Say this: “Across zeros, regroup from the first nonzero place: 3,000 becomes 2 thousands, 9 hundreds, 9 tens, 10 ones.”

   Say this: “Across zeros: regrouping through a 0.”

3. Show how

   Show: 2,205 − 634 = ___

   Say this: “Ones: 5 − 4 = 1”

   Say this: “Tens: 0 is less than 3, so regroup 1 hundred as 10 tens. The hundreds digit becomes 1.”

   Say this: “10 − 3 = 7”

   Say this: “Hundreds: 1 is less than 6, so regroup 1 thousand as 10 hundreds. The thousands digit becomes 1.”

   Say this: “11 − 6 = 5”

   Say this: “Thousands: 1 − 0 = 1”

   Say this: “Check: 1,571 + 634 = 2,205”

   Answer: 1,571

   Show: A wagon carried 4,196 sacks of flour. 2,354 sacks were left at the mill. How many sacks are still on the wagon?

   

   Say this: “Unknown: how many are left.”

   Say this: “Bar model: the whole is 4,196; one part is 2,354; the other part is unknown.”

   Say this: “Equation: 4,196 − 2,354 = ?”

   Say this: “4,196 − 2,354 = 1,842”

   Say this: “Answer: 1,842 sacks are still on the wagon.”

   Answer: 1,842 sacks. 1,842 sacks are still on the wagon.

4. Practice together

   Do this: Your child does these with you. Let them try first; help only after a real try.

   Ask: 774 − 588 = ___

   Listen for: 186

   If stuck: Ones: 4 is less than 8, so regroup 1 ten as 10 ones. The tens digit becomes 6.

   Ask: 998 − 479 = ___

   Listen for: 519

   If stuck: Ones: 8 is less than 9, so regroup 1 ten as 10 ones. The tens digit becomes 8.

   Ask: 747 − 661 = ___

   Listen for: 86

   If stuck: Ones: 7 − 1 = 6

   7 more practice items on the lesson page, and on Worksheet A and Worksheet B.

5. Watch for
   • Subtracting the smaller digit from the larger one in each column.
6. Game: Cross Check

   One player adds two 3-digit numbers on paper while the other estimates. Compare: is the exact answer close to the estimate? Swap roles.

7. Narration

   Say this: “Tell me what you learned today. Show me with your hands or the counters if you like.”

   Listen for: Subtract three- and four-digit numbers with the written method.

8. Daily habit

   Mental math warm-up: add or subtract 10, 100 or 1,000.

Spread over the week

5 sessions of 25–30 minutes. Stop while it is still going well.

1. Session 1. Warm-up, then teach the new idea (steps 1 and 2).
2. Session 2. Warm-up again, then show how with the examples.
3. Session 3. Practice together, then play the game.
4. Session 4. More practice on the worksheet, and the daily habit.
5. Session 5. Quick check: narration and a few practice items. Move on when it is mostly right.