Add Within 20 Using Place Value Strategy for 3rd Grade

Complete guide: tens and ones decomposition, regrouping, and mental math strategies for addition within 20.

Basic Place Value Concepts
1 Understanding Tens and Ones
Example: Breaking Apart Numbers
Understand how numbers are composed of tens and ones.
Key Concept:

Place value: Each digit in a number has a value based on its position

TENS PLACE
1

= 10 ones

ONES PLACE
7

= 7 ones

1 ten (10)
7 ones
1
Identify the place value of each digit in the number
2
Separate tens and ones: 17 = 10 + 7
3
Understand that 1 ten = 10 ones
4
Combine: 10 + 7 = 17
17 = 1 ten + 7 ones
Key insight:

In 17, the 1 represents 1 ten (10) and the 7 represents 7 ones (7).

Place value rules:

• Position matters: Each position has a different value

• Tens place: Each digit represents groups of 10

• Ones place: Each digit represents individual units

2 Adding Using Place Value
Example: 14 + 5
Break apart 14 into tens and ones, then add the ones separately.
14 =
1

ten (10)

+
4

ones

1 ten (10)
4 ones
5 ones
Step 1: Break apart the first number

14 = 10 + 4

Step 2: Add the ones together

4 + 5 = 9

Step 3: Combine with tens

10 + 9 = 19

14 + 5 = 19
Final answer:

14 + 5 = 19 using place value decomposition.

Addition rules:

• Separate tens and ones: Break apart the first number

• Add like values: Add ones to ones

• Combine results: Add tens to the sum of ones

3 Visual Representation
Example: 12 + 8
Use base ten blocks to visualize adding with regrouping.
1 ten (10)
2 ones
8 ones
12 + 8 = (10 + 2) + 8 = 10 + (2 + 8) = 10 + 10 = 20
Step 1: Break apart 12

12 = 10 + 2

Step 2: Add the ones

2 + 8 = 10

Step 3: Combine with tens

10 + 10 = 20

12 + 8 = 20
Final answer:

12 + 8 = 20 using place value and regrouping.

Regrouping rules:

• When ones ≥ 10: Regroup as tens and ones

• 10 ones = 1 ten: Exchange when necessary

• Keep track: Maintain total value during exchanges

Place Value Addition Strategies
\(\text{10 + 10 = 20}\)
Key Benchmark
Decomposition Strategy

• Break apart numbers by place value

• Add tens with tens, ones with ones

• Combine partial sums

• Example: 16 + 3 = (10 + 6) + 3 = 10 + 9 = 19

Regrouping Strategy

• Add ones first

• If sum ≥ 10, regroup as tens and ones

• Add to tens place

• Example: 17 + 5 = 10 + (7 + 5) = 10 + 12 = 22

Making Ten Strategy

• Use the fact that 10 is easy to work with

• Break apart second number to make 10

• Add remaining amount

• Example: 8 + 7 = 8 + 2 + 5 = 10 + 5 = 15

Key Terms:

Place Value: Value of digits based on their position

Decomposition: Breaking apart numbers into smaller parts

Regrouping: Trading 10 ones for 1 ten

Tens: Groups of 10 (10, 20, 30...)

Ones: Individual units (1, 2, 3...)

Strategy Choice: Pick the method that works best for the numbers
Visualization: Use base ten blocks to understand concepts
Tip 1: Remember that 1 ten equals 10 ones.
Tip 2: When adding ones, if you get 10 or more, regroup.
Tip 3: Practice breaking apart numbers repeatedly.
Advanced Examples and Regrouping
4 Regrouping Example
Example: 15 + 7
Add ones that require regrouping into tens.
15 =
1

ten (10)

+
5

ones

1 ten (10)
5 ones
7 ones
5 ones + 7 ones = 12 ones = 1 ten + 2 ones
↓
Original 1 ten + New 1 ten + 2 ones = 2 tens + 2 ones = 22
Step 1: Break apart 15

15 = 10 + 5

Step 2: Add the ones

5 + 7 = 12 (which is 10 + 2)

Step 3: Regroup

12 ones = 1 ten + 2 ones

Step 4: Combine all tens and ones

1 original ten + 1 new ten + 2 ones = 22

15 + 7 = 22
Final answer:

15 + 7 = 22 using place value and regrouping.

Regrouping rules:

• When ones ≥ 10: Regroup as tens and ones

• 10 ones = 1 ten: This is the key conversion

• Add to tens place: Don't forget to include new tens

5 Standard Algorithm
Example: 18 + 4
Use the standard algorithm with place value understanding.
Tens
1
Ones
8
1 ten (10)
8 ones
4 ones
18
+4
--
22
Step 1: Add ones column

8 + 4 = 12 (write 2, carry 1 ten)

Step 2: Add tens column

1 + 1 (carried) = 2

Step 3: Write the answer

2 tens and 2 ones = 22

18 + 4 = 22
Final answer:

18 + 4 = 22 using the standard algorithm with place value.

Standard algorithm rules:

• Add ones first: Start from the rightmost column

• Regroup when needed: If sum ≥ 10, carry to next column

• Carry systematically: Add carried numbers to next column

Complete Study Guide: Mastering Place Value Addition Within 20
\(\text{Number} = \text{Tens} + \text{Ones}\)
Place Value Decomposition
Core Concepts:

Place Value: Understanding that digits have different values based on position

Decomposition: Breaking apart numbers into tens and ones

Regrouping: Trading 10 ones for 1 ten when necessary

Tens Place: Represents groups of 10

Ones Place: Represents individual units

Problem-Solving Strategy:
  1. Analyze: Look at the numbers and identify place values
  2. Decompose: Break apart numbers into tens and ones
  3. Add like values: Add tens with tens, ones with ones
  4. Regroup if needed: Convert 10+ ones to tens and ones
  5. Combine: Add all parts together
Memorization Tip: "10 ones make 1 ten" - this is the key regrouping rule.
Verification Method: Always check your answer by using a different strategy.
Visualization Aid: Use base ten blocks to see the concept concretely.
Practice Pattern: Start with no regrouping, then advance to regrouping.
Common Pitfalls: Forgetting to regroup, misaligning place values, adding wrong place values together.
Success Markers: Accurate decomposition, proper regrouping, correct final answers.
Master Rules:

• Regrouping rule: 10 ones = 1 ten

• Place value: Always align numbers by place value

• Add like values: Tens with tens, ones with ones

• Check your work: Verify answers using different methods

• Visualization: Use models to understand the concept

Quick Review Checklist
  • □ Can I break apart numbers into tens and ones?
  • □ Do I know when to regroup?
  • □ Can I add numbers using place value?
  • □ Do I understand that 10 ones = 1 ten?
  • □ Can I verify my answers?

Q&A: Add Within 20 Using Place Value Strategy

Question: Why do I need to break apart numbers? Can't I just add them the normal way?

Answer: Breaking apart numbers helps you understand WHY addition works!

  • Understanding: You'll know why 14 + 5 = 19, not just memorize it
  • Regrouping: It helps you see when 10 ones become 1 ten
  • Mental math: Breaking apart makes mental calculations easier
  • Foundation: It prepares you for larger numbers later

The "normal way" (standard algorithm) uses place value too - breaking apart just makes it more visible. As you practice, you'll be able to do it mentally!

Think of it like taking apart a toy to see how it works - then you can put it back together.

Question: My child is having trouble with regrouping. How can I help them understand this concept?

Answer: Use hands-on materials to make regrouping concrete:

  • Base ten blocks: Use 10 individual cubes to trade for 1 ten rod
  • Money: Trade 10 pennies for 1 dime
  • Grouping objects: Bundle 10 straws into 1 group
  • Visual demonstrations: Show the exchange process clearly

The key is understanding that regrouping is just trading - 10 ones for 1 ten is like trading 10 pennies for 1 dime. Both have the same value, but one is more convenient.

Start with concrete materials, then move to drawings, and finally to abstract numbers. This progression helps build a solid understanding.

Question: How do I know when I need to regroup? It's confusing!

Answer: It's simple! You only need to regroup when adding the ONES:

  • Count the ones: When adding ones, count the total
  • Check if ≥ 10: If you have 10 or more ones, you need to regroup
  • Trade: 10 ones = 1 ten
  • Example: 8 + 5 = 13 ones → regroup as 1 ten + 3 ones

Remember: You only regroup when adding ONES and getting 10 or more. Just ask yourself: "Do I have 10 or more ones?" If yes, trade 10 for 1 ten.

Practice with small numbers first until you feel confident!