Add and Subtract Within 100 Using Place Value Strategies: Complete Guide for Grade 3

Learn how to add and subtract within 100 using place value strategies with visual models, step-by-step instructions, and practice problems for 3rd grade students.

Addition Using Place Value Strategies
1 Adding Without Regrouping
Concept:

Addition without regrouping: Adding tens and ones separately when no regrouping is needed

Example: 34 + 25
+
=
Step 1: Break apart by place value

34 = 30 + 4, 25 = 20 + 5

Step 2: Add tens and ones separately

30 + 20 = 50, 4 + 5 = 9

Step 3: Combine the sums

50 + 9 = 59

34 + 25 = 59
2 Adding With Regrouping
Concept:

Addition with regrouping: When ones add up to 10 or more, we carry to the tens place

Example: 47 + 36
Regrouping occurs when: Ones digits sum to 10 or more
+
=
Step 1: Break apart by place value

47 = 40 + 7, 36 = 30 + 6

Step 2: Add ones first

7 + 6 = 13 (more than 10, so regroup)

Step 3: Regroup 13 ones as 1 ten and 3 ones

Take 10 ones and trade for 1 ten

Step 4: Add tens

40 + 30 + 10 (regrouped) = 80

Step 5: Combine tens and remaining ones

80 + 3 = 83

47 + 36 = 83
3 Subtraction Without Regrouping
Concept:

Subtraction without regrouping: Subtracting tens and ones separately when no borrowing is needed

Example: 58 - 23
-
=
Step 1: Break apart by place value

58 = 50 + 8, 23 = 20 + 3

Step 2: Subtract ones first

8 - 3 = 5

Step 3: Subtract tens

50 - 20 = 30

Step 4: Combine the differences

30 + 5 = 35

58 - 23 = 35
Complete Summary: Place Value Strategies
Number = Tens + Ones
Place Value Formula
Key Definitions:

Place value: The value of a digit based on its position in a number

Tens place: The second digit from the right, representing groups of 10

Ones place: The rightmost digit, representing single units

Regrouping: Trading 10 ones for 1 ten (or vice versa) when adding or subtracting

Breaking apart: Separating a number into its tens and ones components

Place Value Addition Method:
  1. Break apart numbers: Separate tens and ones
  2. Add tens together: Calculate the sum of tens
  3. Add ones together: Calculate the sum of ones
  4. Check for regrouping: If ones sum to 10 or more, regroup
  5. Combine final amounts: Add tens and ones together
Tens
Groups of 10
Ones
Single units
Regroup
Trade when needed
Addition
T + T, O + O
Separate and add
Subtraction
T - T, O - O
Separate and subtract
Regrouping
10 ones = 1 ten
Trade for simplicity
Tip 1: Always start with the ones place when adding or subtracting.
Tip 2: Check if you need to regroup before combining the final answer.
Tip 3: Use visual models to understand the regrouping process.
Tip 4: Practice with smaller numbers before moving to larger ones.
Common patterns: Adding tens, adding ones, regrouping when necessary, combining results.
Key insight: Place value allows us to work with numbers systematically and efficiently.
Essential Place Value Rules:

• Separate first: Always break numbers into tens and ones before operating

• Work systematically: Handle tens and ones separately

• Regroup when needed: Trade 10 ones for 1 ten (or vice versa)

• Combine at end: Add final tens and ones together for answer

Subtraction With Regrouping
4 Subtraction With Regrouping
Concept:

Subtraction with regrouping: When ones in the minuend are fewer than ones in the subtrahend, borrow from tens

Example: 62 - 37
Regrouping occurs when: Minuend ones are less than subtrahend ones
-
=
Step 1: Break apart by place value

62 = 60 + 2, 37 = 30 + 7

Step 2: Check if regrouping is needed

2 < 7, so we need to regroup

Step 3: Regroup by trading 1 ten for 10 ones

62 = 50 + 12 (take 1 ten from 60, add 10 to 2)

Step 4: Subtract ones

12 - 7 = 5

Step 5: Subtract tens

50 - 30 = 20

Step 6: Combine the differences

20 + 5 = 25

62 - 37 = 25
5 Verification Strategy
Verification:

Check your work: Use inverse operations to verify your answer

Verification Method: Add your answer to the subtrahend to get the minuend
Step 1: Take your answer

From 62 - 37 = 25, take 25

Step 2: Add to the number you subtracted

25 + 37

Step 3: Calculate

25 + 37 = 62

Step 4: Compare to original number

62 = 62 ✓ (Your answer is correct!)

Verification works for addition too: Subtract your answer from the sum to get the original number.
Verification Rule:

• Subtraction: Answer + Subtrahend = Minuend

• Addition: Sum - One Addend = Other Addend

Practice Problems & Strategies
Practice + Understanding = Mastery!
Repetition & Application
Practice Problems:

Problem 1: 45 + 28

Solution: 45 = 40 + 5, 28 = 20 + 8; 5 + 8 = 13 (regroup: 1 ten + 3 ones); 40 + 20 + 10 = 70; 70 + 3 = 73

Answer: 73

Problem 2: 63 - 29

Solution: 63 = 60 + 3, 29 = 20 + 9; Need to regroup: 63 = 50 + 13; 13 - 9 = 4; 50 - 20 = 30; 30 + 4 = 34

Answer: 34

Problem 3: 37 + 46

Solution: 37 = 30 + 7, 46 = 40 + 6; 7 + 6 = 13 (regroup: 1 ten + 3 ones); 30 + 40 + 10 = 80; 80 + 3 = 83

Answer: 83

Problem 4: 81 - 45

Solution: 81 = 80 + 1, 45 = 40 + 5; Need to regroup: 81 = 70 + 11; 11 - 5 = 6; 70 - 40 = 30; 30 + 6 = 36

Answer: 36
Tip 1: Always check if you need to regroup before starting the operation.
Tip 2: Use scratch paper to keep track of your regrouping.
Tip 3: Verify your answers using inverse operations.
Success indicators: Accurate regrouping, correct final answers, understanding of place value relationships.
Next steps: Apply these strategies to larger numbers within 1,000.
Mastery Checklist:

• ✓ I can break apart numbers into tens and ones

• ✓ I can add tens and ones separately

• ✓ I can regroup when necessary

• ✓ I can subtract using place value strategies

• ✓ I can verify my answers are correct

Place Value Strategy Steps

📊
Step 1

Break apart numbers

Step 2

Work with tens

Step 3

Work with ones

Step 4

Regroup if needed

Step 5

Combine results

Questions & Answers

Question: I don't understand when I need to regroup. How do I know when to do it?

Answer: Here's how to know when to regroup:

  • For addition: When the ones digits add up to 10 or more
  • For subtraction: When the ones digit in the top number is smaller than the ones digit in the bottom number

Examples:

  • Addition: 27 + 15 → 7 + 5 = 12 (need to regroup)
  • Subtraction: 42 - 18 → 2 < 8 (need to regroup)
  • No regrouping: 34 + 23 → 4 + 3 = 7 (no regrouping needed)

Think of regrouping as trading: 10 ones can be traded for 1 ten, and 1 ten can be traded for 10 ones.

Practice with visual models to see how the blocks move between places!

Question: My child is struggling with place value. How can I help them understand tens and ones?

Answer: Here are strategies to help with place value:

  • Use manipulatives: Base-ten blocks, beans, or coins to represent tens and ones
  • Visual models: Draw tens sticks and ones dots
  • Real objects: Group items into tens and count leftovers
  • Verbal practice: Say "3 tens and 7 ones" for 37
  • Games: Play place value games with dice or cards

For example, with 45: use 4 bundles of 10 straws and 5 individual straws. This shows 4 tens and 5 ones.

Practice breaking apart numbers: 63 = 60 + 3, 28 = 20 + 8.

The more concrete experiences they have, the better they'll understand abstract concepts!

Question: Sometimes I get confused and add the tens and ones together wrong. How can I make sure I do it right?

Answer: Here are ways to stay organized:

  • Line up numbers: Write problems vertically with tens under tens, ones under ones
  • Work in steps: Add tens first, then ones, then combine
  • Check yourself: Ask if your answer makes sense
  • Verify: Use the opposite operation to check your work

Example: 47 + 26

  • Step 1: Tens → 40 + 20 = 60
  • Step 2: Ones → 7 + 6 = 13
  • Step 3: Combine → 60 + 13 = 73
  • Check: 73 - 26 = 47 ✓

If your answer seems too big or too small, double-check your work.

Remember: tens and ones are different types of units, just like apples and oranges!