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

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

In this Grade 4 Saxon Math lesson, students practice subtracting two-digit and three-digit numbers by working through ones and tens columns in order, and learn to find missing two-digit addends by solving for each digit one place value at a time. The lesson uses real-world contexts like money and variables such as w and m to build understanding of how addition and subtraction are related. It is part of Chapter 2 in Saxon Math Intermediate 4.

Section 1

📘 Subtracting Two-Digit and Three-Digit Numbers, Missing Two-Digit Addends

New Concept

Find the missing addend: 36+w=8736 + w = 87. The letter ww stands for a number.

Why it matters

This type of problem introduces you to the core idea of algebra: using logic to find unknown values in a relationship. Mastering this skill now builds the foundation for solving complex equations that can describe everything from rocket trajectories to financial markets.

What’s next

Next, you’ll practice finding missing two-digit addends by solving for one digit at a time, starting with the ones place.

Section 2

Subtracting Two-Digit and Three-Digit Numbers

Property

To subtract, align the numbers and subtract one column at a time, starting from the ones place on the right. For example:

85−3253\begin{array}{r} 85 \\ - 32 \\ \hline 53 \\ \end{array}

Examples

To subtract 123 from 365, we write the problem as 365−123=242365 - 123 = 242.
Subtracting fifty-three from ninety-seven is calculated as 97−53=4497 - 53 = 44.

Explanation

Think of it like spending money! You have a certain amount, and you give some away. To find what's left, you start with the small change (ones) and then count the larger bills (tens). This keeps the math organized and simple.

Section 3

Missing Two-Digit Addends

Property

To find a missing addend in an equation like 36+w=8736 + w = 87, you can find the missing number one digit at a time, starting with the ones place.

Examples

In m+31=67m + 31 = 67, we find m=36m=36 because 6+1=76+1=7 (ones) and 3+3=63+3=6 (tens).
For 24+e=6524 + e = 65, the missing addend is e=41e=41 since 4+1=54+1=5 and 2+4=62+4=6.
In y+45=99y + 45 = 99, the missing number is y=54y=54 because 4+5=94+5=9 and 5+4=95+4=9.

Explanation

Become a math detective! You have one clue and the final result, so you must find the missing piece. Solve the mystery by figuring out which digit fits in the ones column, then move on to the tens column to crack the case.

Section 4

Writing Fact Families

Property

Any set of three related numbers can form a "fact family" with two addition facts and two subtraction facts. For the numbers 9, 7, and 2, we have 7+2=97+2=9 and 9−2=79-2=7.

Examples

Using 8, 5, and 3, we can write the addition facts 5+3=85 + 3 = 8 and 3+5=83 + 5 = 8.
Using the same numbers 8, 5, and 3, we can write the subtraction facts 8−5=38 - 5 = 3 and 8−3=58 - 3 = 5.

Explanation

Think of three numbers like members of a family—they are connected! You can arrange them in different ways to tell two true addition stories and two true subtraction stories. The largest number is always the result for addition and the starting number for subtraction.

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

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  2. Lesson 2

    Lesson 12: Missing Numbers in Subtraction

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  3. Lesson 3

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

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  4. Lesson 4Current

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

    LearnPractice
  5. Lesson 5

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

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  6. Lesson 6

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

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  7. Lesson 7

    Lesson 17: Adding Columns of Numbers with Regrouping

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  8. Lesson 8

    Lesson 18: Temperature, Activity Measuring Temperature

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  9. Lesson 9

    Lesson 19: Elapsed Time Problems, Activity Finding Elapsed Time

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  10. Lesson 10

    Lesson 20: Rounding

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  11. Lesson 11

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

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Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

📘 Subtracting Two-Digit and Three-Digit Numbers, Missing Two-Digit Addends

New Concept

Find the missing addend: 36+w=8736 + w = 87. The letter ww stands for a number.

Why it matters

This type of problem introduces you to the core idea of algebra: using logic to find unknown values in a relationship. Mastering this skill now builds the foundation for solving complex equations that can describe everything from rocket trajectories to financial markets.

What’s next

Next, you’ll practice finding missing two-digit addends by solving for one digit at a time, starting with the ones place.

Section 2

Subtracting Two-Digit and Three-Digit Numbers

Property

To subtract, align the numbers and subtract one column at a time, starting from the ones place on the right. For example:

85−3253\begin{array}{r} 85 \\ - 32 \\ \hline 53 \\ \end{array}

Examples

To subtract 123 from 365, we write the problem as 365−123=242365 - 123 = 242.
Subtracting fifty-three from ninety-seven is calculated as 97−53=4497 - 53 = 44.

Explanation

Think of it like spending money! You have a certain amount, and you give some away. To find what's left, you start with the small change (ones) and then count the larger bills (tens). This keeps the math organized and simple.

Section 3

Missing Two-Digit Addends

Property

To find a missing addend in an equation like 36+w=8736 + w = 87, you can find the missing number one digit at a time, starting with the ones place.

Examples

In m+31=67m + 31 = 67, we find m=36m=36 because 6+1=76+1=7 (ones) and 3+3=63+3=6 (tens).
For 24+e=6524 + e = 65, the missing addend is e=41e=41 since 4+1=54+1=5 and 2+4=62+4=6.
In y+45=99y + 45 = 99, the missing number is y=54y=54 because 4+5=94+5=9 and 5+4=95+4=9.

Explanation

Become a math detective! You have one clue and the final result, so you must find the missing piece. Solve the mystery by figuring out which digit fits in the ones column, then move on to the tens column to crack the case.

Section 4

Writing Fact Families

Property

Any set of three related numbers can form a "fact family" with two addition facts and two subtraction facts. For the numbers 9, 7, and 2, we have 7+2=97+2=9 and 9−2=79-2=7.

Examples

Using 8, 5, and 3, we can write the addition facts 5+3=85 + 3 = 8 and 3+5=83 + 5 = 8.
Using the same numbers 8, 5, and 3, we can write the subtraction facts 8−5=38 - 5 = 3 and 8−3=58 - 3 = 5.

Explanation

Think of three numbers like members of a family—they are connected! You can arrange them in different ways to tell two true addition stories and two true subtraction stories. The largest number is always the result for addition and the starting number for subtraction.

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

    LearnPractice
  2. Lesson 2

    Lesson 12: Missing Numbers in Subtraction

    LearnPractice
  3. Lesson 3

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

    LearnPractice
  4. Lesson 4Current

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

    LearnPractice
  5. Lesson 5

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

    LearnPractice
  6. Lesson 6

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

    LearnPractice
  7. Lesson 7

    Lesson 17: Adding Columns of Numbers with Regrouping

    LearnPractice
  8. Lesson 8

    Lesson 18: Temperature, Activity Measuring Temperature

    LearnPractice
  9. Lesson 9

    Lesson 19: Elapsed Time Problems, Activity Finding Elapsed Time

    LearnPractice
  10. Lesson 10

    Lesson 20: Rounding

    LearnPractice
  11. Lesson 11

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

    LearnPractice