Add Within 100 Using Strategies for 3rd Grade

Complete guide: mental math strategies, place value, regrouping, and efficient addition methods for sums up to 100.

Basic Addition Strategies
1 Adding Using Place Value
Example: 47 + 25
Break apart numbers by tens and ones, then add separately.
Key Concept:

Place value strategy: Separate tens and ones, add each place value separately

47
40 + 7
+
+
25
20 + 5
4 tens (40)
7 ones
2 tens (20)
5 ones
1
Break apart: 47 = 40 + 7 and 25 = 20 + 5
2
Add tens: 40 + 20 = 60
3
Add ones: 7 + 5 = 12
4
Combine: 60 + 12 = 72
47 + 25 = 72
Final answer:

47 + 25 = 72 using place value decomposition.

Place value rules:

• Separate by place: Tens and ones separately

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

• Combine results: Add partial sums together

2 Making Ten Strategy
Example: 38 + 6
Break apart the second number to make a ten with the first number.
Making Ten Strategy

Take 2 from 6 to make 38 into 40, then add the remaining 4.

30
8
6
38 + 6 = 38 + 2 + 4 = 40 + 4 = 44
Step 1: Identify what's needed to make 10

38 needs 2 more to make 40

Step 2: Break apart the second number

6 = 2 + 4

Step 3: Add to make the round number

38 + 2 = 40

Step 4: Add the remainder

40 + 4 = 44

38 + 6 = 44
Final answer:

38 + 6 = 44 using the making ten strategy.

Making ten rules:

• Round to nearest 10: Make one number a multiple of 10

• Adjust the other: Take what you gave from the second number

• Easy addition: Adding multiples of 10 is simpler

3 Counting On Strategy
Example: 45 + 3
Start with the larger number and count forward by the smaller number.
Counting On Strategy

Start at 45 and count 3 more: 46, 47, 48

40
5
3
45 + 3 = 48
Step 1: Start with the larger number

Begin at 45

Step 2: Count forward

Count 3 more: 46, 47, 48

Step 3: State the answer

45 + 3 = 48

45 + 3 = 48
Final answer:

45 + 3 = 48 using the counting on strategy.

Counting on rules:

• Start with larger: Begin with the larger number

• Count forward: Move ahead by the smaller number

• Works well: When adding small numbers (1-5)

Regrouping and Advanced Strategies
\(\text{Regrouping: } 10 \text{ ones} = 1 \text{ ten}\)
Regrouping Rule
Standard Algorithm with Regrouping

• Add ones column first

• If sum ≥ 10, write ones digit and carry tens

• Add tens column including carried tens

• Example: 58 + 27 = 85

Compensation Strategy

• Adjust one number to make addition easier

• Compensate by doing the opposite to the other number

• Example: 49 + 26 → 50 + 25 = 75

Doubles Plus/Minus Strategy

• Use known doubles facts

• Adjust for nearby numbers

• Example: 7 + 8 = 7 + 7 + 1 = 15

Key Terms:

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

Carrying: Moving excess from one place value to the next

Compensation: Adjusting numbers to make calculations easier

Place Value: Value of digits based on their position

Standard Algorithm: Traditional step-by-step method

Strategy Choice: Pick the method that works best for the numbers
Efficiency: Some strategies are faster for certain number combinations
Tip 1: Look for numbers that make 10 or multiples of 10.
Tip 2: Use compensation when one number is close to a round number.
Tip 3: Practice different strategies to find your favorites.
Advanced Examples and Problem-Solving
4 Compensation Strategy
Example: 59 + 28
Round 59 to 60, then subtract the extra 1 added.
Compensation Strategy

59 + 28 = (60 - 1) + 28 = 60 + 28 - 1 = 88 - 1 = 87

50
9
20
8
Step 1: Round one number up

59 → 60 (added 1)

Step 2: Add the rounded number

60 + 28 = 88

Step 3: Subtract the extra amount

88 - 1 = 87

59 + 28 = 87
Final answer:

59 + 28 = 87 using the compensation strategy.

Compensation rules:

• Round to make calculation easier: Usually to the nearest 10

• Balance the equation: Whatever you add to one number, subtract from the result

• Works well: When one number is close to a round number

5 Standard Algorithm with Regrouping
Example: 67 + 28
Use the standard algorithm, regrouping when the sum in any column is 10 or more.
67
60 + 7
+
+
28
20 + 8
67
+28
---
95
Step 1: Add the ones column

7 + 8 = 15 (write 5, carry 1 ten)

Step 2: Add the tens column

6 + 2 + 1 (carried) = 9

Step 3: Write the final answer

9 tens and 5 ones = 95

67 + 28 = 95
Final answer:

67 + 28 = 95 using the standard algorithm with regrouping.

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 Addition Within 100
\(\text{Addition} = \text{Addend} + \text{Addend} = \text{Sum}\)
Addition Components
Core Concepts:

Addition: Combining two or more numbers to find the total

Regrouping: Trading 10 ones for 1 ten when necessary

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

Mental Math: Calculating in your head without writing everything down

Strategic Thinking: Choosing the best method for each problem

Problem-Solving Strategy:
  1. Analyze: Look at the numbers and decide which strategy to use
  2. Choose: Select the most efficient method for the given numbers
  3. Execute: Apply the chosen strategy carefully
  4. Verify: Check your answer using a different method
Memorization Tip: "Make 10" - look for ways to combine numbers to reach 10 or multiples of 10.
Verification Method: Always check your answer by using a different strategy.
Strategy Selection: Choose the method that feels most comfortable and efficient.
Practice Pattern: Start with simple numbers, progress to more complex ones.
Common Pitfalls: Forgetting to regroup, misaligning columns, adding wrong place values.
Success Markers: Accurate calculations, strategic method selection, efficient problem-solving.
Master Rules:

• Regrouping rule: 10 ones = 1 ten

• Place value: Always align numbers by place value

• Check your work: Verify answers using different methods

• Strategy flexibility: Use different approaches for different problems

• Mental math: Build efficiency through strategic thinking

Quick Review Checklist
  • □ Can I break apart numbers by place value?
  • □ Do I know when to regroup?
  • □ Can I use multiple addition strategies?
  • □ Do I align numbers properly in standard algorithm?
  • □ Can I verify my answers?

Q&A: Add Within 100 Using Strategies

Question: Why do I need to learn different ways to add? Can't I just use the regular way?

Answer: Learning different strategies is like having different tools in your math toolbox!

  • Some problems are easier with specific strategies: 38 + 6 is easier with "making ten" than standard algorithm
  • Speed and efficiency: Mental math strategies are faster for certain numbers
  • Understanding: Different methods help you understand why addition works
  • Flexibility: You can choose the best method for each problem

Just like you might use different tools for different jobs, different addition strategies work better for different problems. Having multiple methods makes you a stronger mathematician!

The standard algorithm always works, but other strategies can be faster and more efficient for certain numbers.

Question: My child is struggling 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 blocks 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.

Practice with concrete materials first, then move to pictorial representations, and finally to abstract numbers.

Question: How do I know which strategy to use for a problem? There are so many!

Answer: Look for clues in the numbers to help you choose:

  • Near 10s: Use "making ten" (like 38 + 6 → 38 + 2 + 4)
  • Close to round numbers: Use compensation (like 49 + 26 → 50 + 25)
  • Small numbers: Use counting on (like 45 + 3)
  • No obvious patterns: Use standard algorithm

Start by looking at the numbers. If one number ends in 9, 8, or 7, think about making a ten. If numbers are close to multiples of 10, consider compensation.

As you practice more, choosing strategies will become natural. It's okay to experiment with different methods!