Learn on PengiSaxon Math, Intermediate 4Chapter 2: Lessons 11–20, Investigation 2

Lesson 15: Subtracting Two-Digit Numbers with Regrouping, Activity Subtracting Money

In this Grade 4 Saxon Math lesson, students learn how to subtract two-digit numbers using regrouping, also called borrowing or exchanging, by trading 1 ten for 10 ones when the ones digit is too small to subtract from. The lesson uses money manipulatives and real-world dollar amounts to build understanding of the regrouping process. Students practice applying this skill to subtract two-digit monetary values and standard numbers with pencil and paper.

Section 1

📘 Subtracting Two-Digit Numbers with Regrouping

New Concept

Trading 1 ten for 10 ones is an example of regrouping, or exchanging.

What’s next

Next, you'll use money manipulatives and drawings to practice regrouping, then solve subtraction problems using pencil and paper.

Section 2

Guess and Check

Property

A problem-solving strategy where you make a reasonable guess, check if it fits the problem's conditions, and revise your guess if it is wrong. Repeat the process until you find the correct answer.

Examples

  • Problem: Two numbers add to 20 and their difference is 6. Guess: 10 and 10. Check: 1010=010-10=0. Revise: 13 and 7. Check: 13+7=2013+7=20 and 137=613-7=6. Correct!
  • Problem: A toy costs 45 cents. You pay with 10 coins (nickels and dimes). Guess: 5 nickels, 5 dimes = 75 cents. Revise: 7 nickels, 3 dimes = 65 cents. Revise again: 9 nickels, 1 dime = 55 cents.

Explanation

Think of yourself as a super sleuth! Make a smart guess to crack the case, check your clues, and if you're wrong, just try another angle. Every guess gets you closer to the solution, detective!

Section 3

Regrouping

Property

When subtracting, if a digit in the top number is smaller than the digit below it, you must regroup. This means trading 1 from the next higher place value for 10 of the current place value.

Examples

  • To solve 532953 - 29: Regroup 5 tens and 3 ones into 4 tens and 13 ones. Now you can subtract: 139=413-9=4 in the ones place and 42=24-2=2 in the tens place. The answer is 24.
  • For 633663 - 36, you show regrouping like this:
65313306207\begin{array}{r} \cancel{6}^5\cancel{3}^{13} \\ - 3\phantom{0}6 \\ \hline 2\phantom{0}7 \\ \end{array}

Explanation

You can't subtract 9 from 3! Regrouping is like trading a ten-dollar bill for ten one-dollar bills. You still have the same total value, but now you have enough ones to subtract from.

Section 4

Renaming Numbers For Subtraction

Property

A number's total value remains the same even when its place values are regrouped. For instance, 5 tens and 3 ones is equal to 4 tens and 13 ones.

53=50+3=40+1353 = 50 + 3 = 40 + 13

Examples

  • The number 72 can be represented as 7 tens and 2 ones, or it can be renamed as 6 tens and 12 ones. The total value is still seventy-two.
  • Before solving 451745 - 17, you can rename 45 (4 tens, 5 ones) as 3 tens and 15 ones to make the subtraction possible.

Explanation

Think about money! Having 5 ten-dollar bills and 3 one-dollar bills is the same as having 4 ten-dollar bills and 13 one-dollar bills. The total is still 53 dollars, but the bills are just arranged differently.

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 2: Lessons 11–20, Investigation 2

  1. Lesson 1

    Lesson 11: Addition Word Problems with Missing Addends

  2. Lesson 2

    Lesson 12: Missing Numbers in Subtraction

  3. Lesson 3

    Lesson 13: Adding Three-Digit Numbers, Activity Adding Money

  4. Lesson 4

    Lesson 14: Subtracting Two-Digit and Three-Digit Numbers, Missing Two-Digit Addends

  5. Lesson 5Current

    Lesson 15: Subtracting Two-Digit Numbers with Regrouping, Activity Subtracting Money

  6. Lesson 6

    Lesson 16: Expanded Form, More on Missing Numbers in Subtraction

  7. Lesson 7

    Lesson 17: Adding Columns of Numbers with Regrouping

  8. Lesson 8

    Lesson 18: Temperature, Activity Measuring Temperature

  9. Lesson 9

    Lesson 19: Elapsed Time Problems, Activity Finding Elapsed Time

  10. Lesson 10

    Lesson 20: Rounding

  11. Lesson 11

    Investigation 2: Units of Length and Perimeter, Activity Estimating the Perimeter

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

📘 Subtracting Two-Digit Numbers with Regrouping

New Concept

Trading 1 ten for 10 ones is an example of regrouping, or exchanging.

What’s next

Next, you'll use money manipulatives and drawings to practice regrouping, then solve subtraction problems using pencil and paper.

Section 2

Guess and Check

Property

A problem-solving strategy where you make a reasonable guess, check if it fits the problem's conditions, and revise your guess if it is wrong. Repeat the process until you find the correct answer.

Examples

  • Problem: Two numbers add to 20 and their difference is 6. Guess: 10 and 10. Check: 1010=010-10=0. Revise: 13 and 7. Check: 13+7=2013+7=20 and 137=613-7=6. Correct!
  • Problem: A toy costs 45 cents. You pay with 10 coins (nickels and dimes). Guess: 5 nickels, 5 dimes = 75 cents. Revise: 7 nickels, 3 dimes = 65 cents. Revise again: 9 nickels, 1 dime = 55 cents.

Explanation

Think of yourself as a super sleuth! Make a smart guess to crack the case, check your clues, and if you're wrong, just try another angle. Every guess gets you closer to the solution, detective!

Section 3

Regrouping

Property

When subtracting, if a digit in the top number is smaller than the digit below it, you must regroup. This means trading 1 from the next higher place value for 10 of the current place value.

Examples

  • To solve 532953 - 29: Regroup 5 tens and 3 ones into 4 tens and 13 ones. Now you can subtract: 139=413-9=4 in the ones place and 42=24-2=2 in the tens place. The answer is 24.
  • For 633663 - 36, you show regrouping like this:
65313306207\begin{array}{r} \cancel{6}^5\cancel{3}^{13} \\ - 3\phantom{0}6 \\ \hline 2\phantom{0}7 \\ \end{array}

Explanation

You can't subtract 9 from 3! Regrouping is like trading a ten-dollar bill for ten one-dollar bills. You still have the same total value, but now you have enough ones to subtract from.

Section 4

Renaming Numbers For Subtraction

Property

A number's total value remains the same even when its place values are regrouped. For instance, 5 tens and 3 ones is equal to 4 tens and 13 ones.

53=50+3=40+1353 = 50 + 3 = 40 + 13

Examples

  • The number 72 can be represented as 7 tens and 2 ones, or it can be renamed as 6 tens and 12 ones. The total value is still seventy-two.
  • Before solving 451745 - 17, you can rename 45 (4 tens, 5 ones) as 3 tens and 15 ones to make the subtraction possible.

Explanation

Think about money! Having 5 ten-dollar bills and 3 one-dollar bills is the same as having 4 ten-dollar bills and 13 one-dollar bills. The total is still 53 dollars, but the bills are just arranged differently.

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 2: Lessons 11–20, Investigation 2

  1. Lesson 1

    Lesson 11: Addition Word Problems with Missing Addends

  2. Lesson 2

    Lesson 12: Missing Numbers in Subtraction

  3. Lesson 3

    Lesson 13: Adding Three-Digit Numbers, Activity Adding Money

  4. Lesson 4

    Lesson 14: Subtracting Two-Digit and Three-Digit Numbers, Missing Two-Digit Addends

  5. Lesson 5Current

    Lesson 15: Subtracting Two-Digit Numbers with Regrouping, Activity Subtracting Money

  6. Lesson 6

    Lesson 16: Expanded Form, More on Missing Numbers in Subtraction

  7. Lesson 7

    Lesson 17: Adding Columns of Numbers with Regrouping

  8. Lesson 8

    Lesson 18: Temperature, Activity Measuring Temperature

  9. Lesson 9

    Lesson 19: Elapsed Time Problems, Activity Finding Elapsed Time

  10. Lesson 10

    Lesson 20: Rounding

  11. Lesson 11

    Investigation 2: Units of Length and Perimeter, Activity Estimating the Perimeter