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

Lesson 12: Missing Numbers in Subtraction

In Saxon Math Intermediate 4, Grade 4 students learn how to find missing numbers in subtraction equations using two strategies: "subtracting down" and "adding up." The lesson teaches students to apply the inverse relationship between addition and subtraction to solve for unknown values in problems where either the minuend or subtrahend is missing. Students practice checking their solutions by substituting the missing number back into the original equation.

Section 1

📘 Missing Numbers in Subtraction

New Concept

Remember that we "subtract down" to find the bottom number and "add up" to find the top number.

What’s next

Next, you'll use the 'add up' strategy to find missing numbers in subtraction problems and check your answers.

Section 2

Finding The Missing Piece

Property

To find a missing number in a subtraction problem, remember that you can either “subtract down” to find the bottom number or “add up” to find the top number. Subtraction and addition are inverse operations, which means they undo each other.

Examples

  • To solve for the top number in b8=5b - 8 = 5, just add up the bottom numbers: 5+8=135 + 8 = 13, so b=13b=13.
  • To solve for the middle number in 15n=915 - n = 9, think “add up”: 9+n=159 + n = 15. You know 9+6=159+6=15, so n=6n=6.

Explanation

Think of subtraction problems like a puzzle where you need to find the missing piece. You can either work backward from the start (subtract down) or build up from the answer (add up). The “add up” method is often a sneaky shortcut because our brains are awesome at adding!

Section 3

Subtract Down

Property

When you know the starting number (the top number) and the result, you can find the number being subtracted by “subtracting down.” For example, to solve 9n=39 - n = 3, you calculate 93=69 - 3 = 6.

Examples

  • To solve for nn in 14n=614 - n = 6, you can “subtract down”: 146=814 - 6 = 8. So, the missing number is 88.
  • If you have the problem 20x=1120 - x = 11, you can solve it by taking 2011=920 - 11 = 9. The missing piece, xx, is 99.

Explanation

This is the straightforward approach! It’s like knowing you had 14 cookies and now have 6 left. To find out how many you ate, you just subtract what’s left from what you started with. Simple as that! No tricks, just direct subtraction.

Section 4

Add Up

Property

To find a missing number in subtraction, you can rephrase it as addition by adding the bottom two numbers. For example, b5=7b - 5 = 7 is the same as asking 7+5=b7 + 5 = b.

Examples

  • To solve b5=7b - 5 = 7, you simply “add up” the parts you know: 7+5=127 + 5 = 12. The missing top number is 1212.
  • For a problem like n10=4n - 10 = 4, just add up to find the whole: 4+10=144 + 10 = 14. So, nn must be 1414.

Explanation

This is the super-sleuth detective method! Flip the problem around and use your addition skills to crack the code. It’s often much easier to find what you started with by adding up the pieces you can see. It feels like a magic trick, but it's pure logic!

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 2Current

    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 5

    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

📘 Missing Numbers in Subtraction

New Concept

Remember that we "subtract down" to find the bottom number and "add up" to find the top number.

What’s next

Next, you'll use the 'add up' strategy to find missing numbers in subtraction problems and check your answers.

Section 2

Finding The Missing Piece

Property

To find a missing number in a subtraction problem, remember that you can either “subtract down” to find the bottom number or “add up” to find the top number. Subtraction and addition are inverse operations, which means they undo each other.

Examples

  • To solve for the top number in b8=5b - 8 = 5, just add up the bottom numbers: 5+8=135 + 8 = 13, so b=13b=13.
  • To solve for the middle number in 15n=915 - n = 9, think “add up”: 9+n=159 + n = 15. You know 9+6=159+6=15, so n=6n=6.

Explanation

Think of subtraction problems like a puzzle where you need to find the missing piece. You can either work backward from the start (subtract down) or build up from the answer (add up). The “add up” method is often a sneaky shortcut because our brains are awesome at adding!

Section 3

Subtract Down

Property

When you know the starting number (the top number) and the result, you can find the number being subtracted by “subtracting down.” For example, to solve 9n=39 - n = 3, you calculate 93=69 - 3 = 6.

Examples

  • To solve for nn in 14n=614 - n = 6, you can “subtract down”: 146=814 - 6 = 8. So, the missing number is 88.
  • If you have the problem 20x=1120 - x = 11, you can solve it by taking 2011=920 - 11 = 9. The missing piece, xx, is 99.

Explanation

This is the straightforward approach! It’s like knowing you had 14 cookies and now have 6 left. To find out how many you ate, you just subtract what’s left from what you started with. Simple as that! No tricks, just direct subtraction.

Section 4

Add Up

Property

To find a missing number in subtraction, you can rephrase it as addition by adding the bottom two numbers. For example, b5=7b - 5 = 7 is the same as asking 7+5=b7 + 5 = b.

Examples

  • To solve b5=7b - 5 = 7, you simply “add up” the parts you know: 7+5=127 + 5 = 12. The missing top number is 1212.
  • For a problem like n10=4n - 10 = 4, just add up to find the whole: 4+10=144 + 10 = 14. So, nn must be 1414.

Explanation

This is the super-sleuth detective method! Flip the problem around and use your addition skills to crack the code. It’s often much easier to find what you started with by adding up the pieces you can see. It feels like a magic trick, but it's pure logic!

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 2Current

    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 5

    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