Adding Doubles and Near Doubles in Grade 2 - Mathematics - Exercises with solutions

Master addition using doubles and near doubles: mental math strategies, addition facts, and number sense through these 10 detailed exercises.

Solutions: Exercises 1 to 10
1 Basic doubles
Exercise 1
How do I solve 4 + 4 using the doubles strategy?
Difficulty: Beginner Time: ~1 minute Skills: Doubles Strategy
Definition:

Doubles: Adding the same number twice (like 4 + 4, 6 + 6, 8 + 8)

Note: Doubles are the foundation of mental math. When adding doubles, simply multiply the number by 2 or count by twos from the number.

Step-by-step addition method:
  1. Recognize that 4 + 4 is a doubles fact
  2. Use the rule: a + a = 2a (or a × 2)
  3. Therefore, 4 + 4 = 8
Original Problem
\(4 + 4\)
Doubles Rule
\(a + a = 2a\)
Solution
\(4 + 4 = 8\)
Step 1: Recognize the doubles pattern

4 + 4 is a doubles fact because both addends are the same

Step 2: Apply the doubles rule

When adding the same number twice, multiply by 2: 4 × 2 = 8

Step 3: Verify the answer

4 + 4 = 8, and 8 - 4 = 4 ✓

\(4 + 4 = 8\)
Final answer:

\(4 + 4 = 8\)

Applied rules:

• Doubles rule: a + a = 2a (multiply the number by 2)

• Number sense: Doubles create even numbers

• Mental math: Doubles facts are foundational for other strategies

• Practice Tip: Memorize doubles facts 1+1 through 10+10 for quick recall

Related Examples:
  • \(3 + 3 = 6\) - Practice with smaller doubles
  • \(5 + 5 = 10\) - Practice with odd starting number
  • \(7 + 7 = 14\) - Practice with larger doubles
Quick Tips:
  • Doubles always result in even numbers
  • Think "count by twos" to reinforce doubles facts
  • Memorize doubles facts for faster mental math
Frequently Asked Questions:

Q: What are doubles facts?
A: Addition problems where both numbers are the same, like 2+2, 5+5, or 8+8.

Q: Why are doubles important?
A: They form the foundation for near doubles and other mental math strategies.

2 Near doubles addition
Exercise 2
What is 4 + 5 using the near doubles strategy?
Difficulty: Beginner Time: ~2 minutes Skills: Near Doubles, Mental Math
Definition:

Near doubles: Adding numbers that are one apart (like 4 and 5, 7 and 8, 9 and 10)

Note: Use the known doubles fact and adjust by 1. Since 4 + 4 = 8, then 4 + 5 = 8 + 1 = 9.

Step-by-step addition method:
  1. Recognize that 4 and 5 are near doubles (one apart)
  2. Use the doubles fact: 4 + 4 = 8
  3. Add 1 more since 5 is 1 more than 4: 8 + 1 = 9
Original Problem
\(4 + 5\)
Related Doubles
\(4 + 4 = 8\)
Adjustment
\(8 + 1 = 9\)
Solution
\(4 + 5 = 9\)
Step 1: Recognize the near doubles relationship

4 and 5 are near doubles because they are one number apart

Step 2: Use the related doubles fact

4 + 4 = 8 (the known doubles fact)

Step 3: Adjust for the difference

Since 5 is 1 more than 4, add 1 to the doubles result: 8 + 1 = 9

Step 4: Verify the answer

4 + 5 = 9, and 9 - 4 = 5 ✓

\(4 + 5 = 9\)
Final answer:

\(4 + 5 = 9\)

Applied rules:

• Near doubles: Add the smaller number twice, then add 1

• Adjustment strategy: Use known facts to solve new problems

• Number sense: Recognize relationships between consecutive numbers

• Practice Tip: If numbers are consecutive, add the smaller twice and add 1

Related Examples:
  • \(6 + 7 = 13\) - 6 + 6 = 12, 12 + 1 = 13
  • \(8 + 9 = 17\) - 8 + 8 = 16, 16 + 1 = 17
  • \(3 + 4 = 7\) - 3 + 3 = 6, 6 + 1 = 7
Quick Tips:
  • Near doubles always equal the smaller number doubled plus 1
  • Think "smaller number doubled, then add 1" for consecutive numbers
  • This strategy builds on known doubles facts
Frequently Asked Questions:

Q: What are near doubles?
A: Addition problems where the numbers are one apart, like 4+5, 7+8, or 9+10.

Q: Can I use this for numbers that are not consecutive?
A: Yes, but it's most efficient for consecutive numbers or numbers that are close together.

3 Mental math strategy
Exercise 3
How do I solve 6 + 7 using the near doubles strategy?
Difficulty: Beginner Time: ~2 minutes Skills: Near Doubles, Mental Math
Definition:

Mental math strategy: Using the doubles fact 6 + 6 = 12 to solve 6 + 7

Note: Since 7 is 1 more than 6, we can solve: 6 + 7 = 6 + 6 + 1 = 12 + 1 = 13.

Step-by-step mental math method:
  1. Recognize that 6 and 7 are near doubles (one apart)
  2. Use the doubles fact: 6 + 6 = 12
  3. Add 1 more since 7 is 1 more than 6: 12 + 1 = 13
Original Problem
\(6 + 7\)
Related Doubles
\(6 + 6 = 12\)
Adjustment
\(12 + 1 = 13\)
Solution
\(6 + 7 = 13\)
Step 1: Recognize the near doubles relationship

6 and 7 are near doubles because they are one number apart

Step 2: Use the related doubles fact

6 + 6 = 12 (the known doubles fact)

Step 3: Adjust for the difference

Since 7 is 1 more than 6, add 1 to the doubles result: 12 + 1 = 13

Step 4: Verify the answer

6 + 7 = 13, and 13 - 6 = 7 ✓

\(6 + 7 = 13\)
Final answer:

\(6 + 7 = 13\)

Applied rules:

• Near doubles: a + (a+1) = a + a + 1 = 2a + 1

• Mental math: Use known facts to build up to unknown facts

• Pattern recognition: Connect new problems to familiar ones

• Practice Tip: Think "double the smaller number plus 1" for consecutive numbers

Related Examples:
  • \(5 + 6 = 11\) - 5 + 5 = 10, 10 + 1 = 11
  • \(8 + 9 = 17\) - 8 + 8 = 16, 16 + 1 = 17
  • \(4 + 5 = 9\) - 4 + 4 = 8, 8 + 1 = 9
Quick Tips:
  • For consecutive numbers, double the smaller and add 1
  • Practice the pattern: n + (n+1) = 2n + 1
  • This strategy works for any pair of consecutive numbers
Frequently Asked Questions:

Q: Can I use the larger number for the doubles fact?
A: Yes! 6 + 7 = 7 + 7 - 1 = 14 - 1 = 13. Both approaches work.

Q: Is this faster than counting?
A: Yes, once you know doubles facts, near doubles are much faster than counting.

Solutions: Exercises 4 to 5
4 Number sense application
Exercise 4
How do I solve 8 + 8 using the doubles strategy?
Definition:

Number sense: Adding the same number twice follows the pattern a + a = 2a

Note: 8 + 8 is a doubles fact. Using the rule, 8 + 8 = 8 × 2 = 16.

Step-by-step number sense method:
  1. Recognize that 8 + 8 is a doubles fact
  2. Apply the doubles rule: a + a = 2a
  3. Calculate: 8 × 2 = 16
Original Problem
\(8 + 8\)
Doubles Rule
\(a + a = 2a\)
Solution
\(8 + 8 = 16\)
Step 1: Recognize the doubles pattern

8 + 8 is a doubles fact because both addends are the same

Step 2: Apply the doubles rule

When adding the same number twice, multiply by 2: 8 × 2 = 16

Step 3: Verify the answer

8 + 8 = 16, and 16 - 8 = 8 ✓

\(8 + 8 = 16\)
Final answer:

\(8 + 8 = 16\)

Applied rules:

• Doubles rule: a + a = 2a (multiply the number by 2)

• Number sense: Doubles always create even numbers

• Mental math: Doubles facts are foundational for other strategies

• Practice Tip: Memorize doubles facts 1+1 through 10+10 for quick recall

Related Examples:
  • \(7 + 7 = 14\) - 7 × 2 = 14
  • \(9 + 9 = 18\) - 9 × 2 = 18
  • \(10 + 10 = 20\) - 10 × 2 = 20
Quick Tips:
  • Doubles always result in even numbers
  • Think "count by twos" to reinforce doubles facts
  • Memorize doubles facts for faster mental math
Frequently Asked Questions:

Q: Do all doubles facts result in even numbers?
A: Yes! When you add the same number twice, you're essentially multiplying by 2, which always results in an even number.

Q: How can I practice doubles facts effectively?
A: Use flashcards, games, or songs to help memorize the patterns from 1+1 to 10+10.

5 Addition facts
Exercise 5
How do I solve 8 + 9 using the near doubles strategy?
Definition:

Addition facts: 8 and 9 are near doubles (one apart), so use 8 + 8 = 16

Note: Since 9 is 1 more than 8, we can solve: 8 + 9 = 8 + 8 + 1 = 16 + 1 = 17.

Step-by-step addition method:
  1. Recognize that 8 and 9 are near doubles (one apart)
  2. Use the doubles fact: 8 + 8 = 16
  3. Add 1 more since 9 is 1 more than 8: 16 + 1 = 17
Original Problem
\(8 + 9\)
Related Doubles
\(8 + 8 = 16\)
Adjustment
\(16 + 1 = 17\)
Solution
\(8 + 9 = 17\)
Step 1: Recognize the near doubles relationship

8 and 9 are near doubles because they are one number apart

Step 2: Use the related doubles fact

8 + 8 = 16 (the known doubles fact)

Step 3: Adjust for the difference

Since 9 is 1 more than 8, add 1 to the doubles result: 16 + 1 = 17

Step 4: Verify the answer

8 + 9 = 17, and 17 - 8 = 9 ✓

\(8 + 9 = 17\)
Final answer:

\(8 + 9 = 17\)

Applied rules:

• Near doubles: Add the smaller number twice, then add 1

• Adjustment strategy: Use known facts to solve new problems

• Number sense: Recognize relationships between consecutive numbers

• Practice Tip: If numbers are consecutive, add the smaller twice and add 1

Related Examples:
  • \(9 + 10 = 19\) - 9 + 9 = 18, 18 + 1 = 19
  • \(5 + 6 = 11\) - 5 + 5 = 10, 10 + 1 = 11
  • \(7 + 8 = 15\) - 7 + 7 = 14, 14 + 1 = 15
Quick Tips:
  • Near doubles always equal the smaller number doubled plus 1
  • Think "smaller number doubled, then add 1" for consecutive numbers
  • This strategy builds on known doubles facts
Frequently Asked Questions:

Q: What if I don't remember the doubles fact?
A: You can count by twos from the number or use other strategies like making ten.

Q: Can I use the larger number's doubles fact?
A: Yes! 8 + 9 = 9 + 9 - 1 = 18 - 1 = 17. Both approaches work.

Solutions: Exercises 6 to 10
6 Advanced near doubles
Exercise 6
How do I solve 9 + 10 using the near doubles strategy?
Definition:

Advanced near doubles: 9 and 10 are near doubles (one apart), so use 9 + 9 = 18

Note: Since 10 is 1 more than 9, we can solve: 9 + 10 = 9 + 9 + 1 = 18 + 1 = 19.

Step-by-step advanced method:
  1. Recognize that 9 and 10 are near doubles (one apart)
  2. Use the doubles fact: 9 + 9 = 18
  3. Add 1 more since 10 is 1 more than 9: 18 + 1 = 19
Original Problem
\(9 + 10\)
Related Doubles
\(9 + 9 = 18\)
Adjustment
\(18 + 1 = 19\)
Solution
\(9 + 10 = 19\)
Step 1: Recognize the near doubles relationship

9 and 10 are near doubles because they are one number apart

Step 2: Use the related doubles fact

9 + 9 = 18 (the known doubles fact)

Step 3: Adjust for the difference

Since 10 is 1 more than 9, add 1 to the doubles result: 18 + 1 = 19

Step 4: Verify the answer

9 + 10 = 19, and 19 - 9 = 10 ✓

\(9 + 10 = 19\)
Final answer:

\(9 + 10 = 19\)

Applied rules:

• Near doubles: a + (a+1) = a + a + 1 = 2a + 1

• Adjustment strategy: Use known facts to solve new problems

• Pattern recognition: Connect new problems to familiar ones

• Practice Tip: Think "double the smaller number plus 1" for consecutive numbers

Related Examples:
  • \(10 + 11 = 21\) - 10 + 10 = 20, 20 + 1 = 21
  • \(11 + 12 = 23\) - 11 + 11 = 22, 22 + 1 = 23
  • \(12 + 13 = 25\) - 12 + 12 = 24, 24 + 1 = 25
Quick Tips:
  • For consecutive numbers, double the smaller and add 1
  • Practice the pattern: n + (n+1) = 2n + 1
  • This strategy works for any pair of consecutive numbers
Frequently Asked Questions:

Q: What if the numbers are not consecutive?
A: You can still use the strategy, but it may involve more complex adjustments.

Q: Can I use this strategy for larger numbers?
A: Yes! The principle works for any numbers, though it's most helpful for numbers within 20.

7 Problem solving
Exercise 7
How do I solve 7 + 8 using the near doubles strategy?
Definition:

Problem solving: 7 and 8 are near doubles (one apart), so use 7 + 7 = 14

Note: Since 8 is 1 more than 7, we can solve: 7 + 8 = 7 + 7 + 1 = 14 + 1 = 15.

Step-by-step problem solving method:
  1. Recognize that 7 and 8 are near doubles (one apart)
  2. Use the doubles fact: 7 + 7 = 14
  3. Add 1 more since 8 is 1 more than 7: 14 + 1 = 15
Original Problem
\(7 + 8\)
Related Doubles
\(7 + 7 = 14\)
Adjustment
\(14 + 1 = 15\)
Solution
\(7 + 8 = 15\)
Step 1: Recognize the near doubles relationship

7 and 8 are near doubles because they are one number apart

Step 2: Use the related doubles fact

7 + 7 = 14 (the known doubles fact)

Step 3: Adjust for the difference

Since 8 is 1 more than 7, add 1 to the doubles result: 14 + 1 = 15

Step 4: Verify the answer

7 + 8 = 15, and 15 - 7 = 8 ✓

\(7 + 8 = 15\)
Final answer:

\(7 + 8 = 15\)

Applied rules:

• Near doubles: a + (a+1) = a + a + 1 = 2a + 1

• Problem solving: Use known facts to build solutions

• Pattern recognition: Connect new problems to familiar ones

• Practice Tip: Think "double the smaller number plus 1" for consecutive numbers

Related Examples:
  • \(6 + 7 = 13\) - 6 + 6 = 12, 12 + 1 = 13
  • \(5 + 6 = 11\) - 5 + 5 = 10, 10 + 1 = 11
  • \(4 + 5 = 9\) - 4 + 4 = 8, 8 + 1 = 9
Quick Tips:
  • For consecutive numbers, double the smaller and add 1
  • Practice the pattern: n + (n+1) = 2n + 1
  • This strategy builds strong number sense and mental math abilities
Frequently Asked Questions:

Q: How do I quickly identify near doubles?
A: Look for numbers that are next to each other on the number line (like 4 and 5, 7 and 8).

Q: What if I'm not sure which number to double?
A: Double the smaller number and add 1, or double the larger and subtract 1. Both give the same result.

8 Word problems
Exercise 8
How do I solve 5 + 6 using the near doubles strategy?
Definition:

Word problems: 5 and 6 are near doubles (one apart), so use 5 + 5 = 10

Note: Since 6 is 1 more than 5, we can solve: 5 + 6 = 5 + 5 + 1 = 10 + 1 = 11.

Step-by-step word problem method:
  1. Recognize that 5 and 6 are near doubles (one apart)
  2. Use the doubles fact: 5 + 5 = 10
  3. Add 1 more since 6 is 1 more than 5: 10 + 1 = 11
Original Problem
\(5 + 6\)
Related Doubles
\(5 + 5 = 10\)
Adjustment
\(10 + 1 = 11\)
Solution
\(5 + 6 = 11\)
Step 1: Recognize the near doubles relationship

5 and 6 are near doubles because they are one number apart

Step 2: Use the related doubles fact

5 + 5 = 10 (the known doubles fact)

Step 3: Adjust for the difference

Since 6 is 1 more than 5, add 1 to the doubles result: 10 + 1 = 11

Step 4: Verify the answer

5 + 6 = 11, and 11 - 5 = 6 ✓

\(5 + 6 = 11\)
Final answer:

\(5 + 6 = 11\)

Applied rules:

• Near doubles: a + (a+1) = a + a + 1 = 2a + 1

• Adjustment strategy: Use known facts to solve new problems

• Problem solving: Break complex problems into simpler parts

• Practice Tip: Think "double the smaller number plus 1" for consecutive numbers

Related Examples:
  • \(3 + 4 = 7\) - 3 + 3 = 6, 6 + 1 = 7
  • \(4 + 5 = 9\) - 4 + 4 = 8, 8 + 1 = 9
  • \(6 + 7 = 13\) - 6 + 6 = 12, 12 + 1 = 13
Quick Tips:
  • For consecutive numbers, double the smaller and add 1
  • Practice recognizing the pattern: n + (n+1) = 2n + 1
  • This strategy builds strong number sense and mental math abilities
Frequently Asked Questions:

Q: What if the numbers are two apart instead of one?
A: Like 5 + 7? Then use 5 + 5 + 2 = 12, or 6 + 6 + 1 = 13 (center number doubled plus 1).

Q: Can I use this for word problems?
A: Yes! If a problem asks for 5 apples and 6 oranges, think 5 + 5 + 1 = 11 total fruits.

9 Mixed operations
Exercise 9
How do I solve 10 + 10 using the doubles strategy?
Definition:

Mixed operations: 10 + 10 is a doubles fact following the pattern a + a = 2a

Note: Using the rule, 10 + 10 = 10 × 2 = 20.

Step-by-step mixed operations method:
  1. Recognize that 10 + 10 is a doubles fact
  2. Apply the doubles rule: a + a = 2a
  3. Calculate: 10 × 2 = 20
Original Problem
\(10 + 10\)
Doubles Rule
\(a + a = 2a\)
Solution
\(10 + 10 = 20\)
Step 1: Recognize the doubles pattern

10 + 10 is a doubles fact because both addends are the same

Step 2: Apply the doubles rule

When adding the same number twice, multiply by 2: 10 × 2 = 20

Step 3: Verify the answer

10 + 10 = 20, and 20 - 10 = 10 ✓

\(10 + 10 = 20\)
Final answer:

\(10 + 10 = 20\)

Applied rules:

• Doubles rule: a + a = 2a (multiply the number by 2)

• Mixed operations: Use known facts as building blocks

• Number sense: Doubles always create even numbers

• Practice Tip: Memorize doubles facts 1+1 through 10+10 for quick recall

Related Examples:
  • \(9 + 9 = 18\) - 9 × 2 = 18
  • \(8 + 8 = 16\) - 8 × 2 = 16
  • \(11 + 11 = 22\) - 11 × 2 = 22
Quick Tips:
  • Doubles always result in even numbers
  • Think "count by twos" to reinforce doubles facts
  • Memorize doubles facts for faster mental math
Frequently Asked Questions:

Q: Why is 10 + 10 easy to calculate?
A: Because 10 is a benchmark number, and 10 × 2 = 20 is a familiar fact.

Q: How do doubles help with other math?
A: They form the foundation for multiplication, division, and other mental math strategies.

10 Comprehensive review
Exercise 10
How do I solve 11 + 12 using the near doubles strategy?
Definition:

Comprehensive review: 11 and 12 are near doubles (one apart), so use 11 + 11 = 22

Note: Since 12 is 1 more than 11, we can solve: 11 + 12 = 11 + 11 + 1 = 22 + 1 = 23.

Step-by-step comprehensive method:
  1. Recognize that 11 and 12 are near doubles (one apart)
  2. Use the doubles fact: 11 + 11 = 22
  3. Add 1 more since 12 is 1 more than 11: 22 + 1 = 23
Original Problem
\(11 + 12\)
Related Doubles
\(11 + 11 = 22\)
Adjustment
\(22 + 1 = 23\)
Solution
\(11 + 12 = 23\)
Step 1: Recognize the near doubles relationship

11 and 12 are near doubles because they are one number apart

Step 2: Use the related doubles fact

11 + 11 = 22 (the known doubles fact)

Step 3: Adjust for the difference

Since 12 is 1 more than 11, add 1 to the doubles result: 22 + 1 = 23

Step 4: Verify the answer

11 + 12 = 23, and 23 - 11 = 12 ✓

\(11 + 12 = 23\)
Final answer:

\(11 + 12 = 23\)

Applied rules:

• Near doubles: a + (a+1) = a + a + 1 = 2a + 1

• Adjustment strategy: Use known facts to solve new problems

• Review: Apply learned strategies to more challenging problems

• Practice Tip: Master these patterns for quick mental math: consecutive numbers

Related Examples:
  • \(13 + 14 = 27\) - 13 + 13 = 26, 26 + 1 = 27
  • \(15 + 16 = 31\) - 15 + 15 = 30, 30 + 1 = 31
  • \(17 + 18 = 35\) - 17 + 17 = 34, 34 + 1 = 35
Quick Tips:
  • For consecutive numbers, double the smaller and add 1
  • Practice all variations to build fluency
  • These strategies form the foundation for more advanced mental math
Frequently Asked Questions:

Q: How do I apply this to subtraction?
A: The same principle works: 12 - 11 = 1 because they're consecutive numbers.

Q: Should I memorize all these patterns?
A: With practice, these relationships become automatic. Focus on understanding the concept first.

Detailed Summary: Adding Doubles and Near Doubles
Key Concepts and Definitions:

Doubles: Addition problems where both numbers are the same (like 3+3, 6+6, 8+8). The result is always an even number.

Near Doubles: Addition problems where the numbers are one apart (like 4+5, 7+8, 9+10). These are also called "consecutive number pairs."

Mental Math: Performing calculations in your head using strategies and known facts rather than counting or writing steps.

Core Rules and Principles:
  1. Doubles Rule: a + a = 2a (add the same number twice equals that number times 2)
  2. Near Doubles Rule: a + (a+1) = 2a + 1 (add consecutive numbers equals double the smaller plus 1)
  3. Adjustment Strategy: Use known facts to solve new problems by adding or subtracting small amounts
  4. Even Number Result: All doubles facts result in even numbers
Step-by-Step Procedures

For Doubles (a + a):

  1. Recognize that both numbers are identical
  2. Apply the doubles rule: multiply the number by 2
  3. Example: 6 + 6 = 6 × 2 = 12

For Near Doubles (a + (a+1)):

  1. Recognize that the numbers are consecutive (one apart)
  2. Use the smaller number's doubles fact
  3. Add 1 to the doubles result
  4. Example: 6 + 7 = (6 + 6) + 1 = 12 + 1 = 13
Concrete Examples (Simple → Advanced)

Simple Doubles:

  • 1 + 1 = 2
  • 2 + 2 = 4
  • 3 + 3 = 6

Simple Near Doubles:

  • 1 + 2 = 3 (1 + 1 + 1 = 3)
  • 2 + 3 = 5 (2 + 2 + 1 = 5)
  • 3 + 4 = 7 (3 + 3 + 1 = 7)

Advanced Doubles:

  • 8 + 8 = 16
  • 9 + 9 = 18
  • 10 + 10 = 20

Advanced Near Doubles:

  • 8 + 9 = 17 (8 + 8 + 1 = 17)
  • 9 + 10 = 19 (9 + 9 + 1 = 19)
  • 11 + 12 = 23 (11 + 11 + 1 = 23)
Tips, Tricks, and Common Pitfalls

Tips:

  • Memorize doubles facts from 1+1 to 10+10 for quick recall
  • Think "count by twos" to reinforce doubles facts
  • For near doubles, always think of the smaller number doubled plus 1
  • Practice with visual models like counters or drawings

Tricks:

  • Near doubles pattern: n + (n+1) = 2n + 1
  • All doubles are even numbers
  • Consecutive number sums are always odd numbers

Common Pitfalls:

  • Confusing near doubles with regular addition facts
  • Forgetting to add the adjustment (+1) for near doubles
  • Not recognizing when numbers are consecutive
  • Mixing up which number to double
Key Notes and Memorization Aids

Memory Aids:

  • "Doubles are twins" - they look the same (5 + 5)
  • "Near doubles are neighbors" - they sit next to each other (5 + 6)
  • "Double the smaller, add one more" for consecutive numbers
  • Practice with rhymes: "5 and 6 make 11, because 5 and 5 make 10!"

To Remember:

  • Doubles facts are foundational - master them first
  • Near doubles build on doubles facts
  • These strategies make mental math faster and more accurate
  • Pattern recognition is key to mathematical fluency
Common Errors to Avoid

Error 1: Not recognizing when to use the doubles strategy

Error 2: Adding instead of doubling for doubles facts

Error 3: Forgetting the adjustment (+1) for near doubles

Error 4: Confusing which number to double in near doubles

Error 5: Not verifying answers by checking with a different method

Key Laws, Methods, Rules, and Definitions
\(a + a = 2a \text{ (doubles)}\)
Doubles Strategy
Key definitions:

Doubles: Adding the same number twice (like 4 + 4, 6 + 6, 8 + 8)

Near doubles: Adding numbers that are one apart (like 4 + 5, 7 + 8, 9 + 10)

Mental math: Performing calculations in your head using strategies and known facts

Complete methodology:
  1. Recognize the pattern: Identify if it's a doubles or near doubles problem
  2. Use known facts: Apply doubles facts as building blocks
  3. Adjust if needed: Add or subtract for differences from exact doubles
  4. Verify the result: Check by using a different method or counting
Tip 1: Master doubles facts first (1+1, 2+2, 3+3, ..., 10+10) as they form the foundation.
Tip 2: For near doubles, double the smaller number and add 1.
Tip 3: Doubles always result in even numbers; near doubles result in odd numbers.
Tip 4: Always verify your answer by using a different method or counting.
Common errors: Misidentifying doubles relationships, forgetting adjustments, not verifying answers.
Exam preparation: Practice all doubles facts, focus on speed and accuracy, verify answers.
Formulas to remember:

• Doubles: a + a = 2a (multiply the number by 2)

• Near doubles: a + (a+1) = 2a + 1 (double the smaller, add 1)

• All doubles facts result in even numbers

• All near doubles facts result in odd numbers

Rules and Methods for Adding Doubles and Near Doubles

Doubles and Near Doubles Strategy

Using Known Facts to Solve New Problems

Core Concept

The doubles and near doubles strategy uses known addition facts to solve new problems. Instead of counting, students recognize patterns and relationships between numbers.

For example: To solve 6 + 7, think "6 + 6 = 12, and 7 is 1 more than 6, so 6 + 7 = 12 + 1 = 13."

Basic Doubles
4 + 4 = 8

Think: 4 × 2 = 8

Near Doubles
4 + 5 = 9

Think: 4 + 4 + 1 = 9

Advanced Near Doubles
7 + 8 = 15

Think: 7 + 7 + 1 = 15

Key Strategies

Strategy 1: For doubles (a + a), multiply the number by 2

Strategy 2: For near doubles (a + (a+1)), double the smaller and add 1

Strategy 3: For near doubles, you can also double the larger and subtract 1

Strategy 4: Practice with visual models like counters or drawings

Strategy 5: Use rhymes and memory aids to remember patterns

Memory Tips

Tip 1: Master doubles facts first (1+1, 2+2, 3+3, ..., 10+10)

Tip 2: Think "double the smaller number plus 1" for consecutive numbers

Tip 3: Use visual models: 6 red dots + 6 blue dots = 12 total dots

Tip 4: Practice with concrete objects before moving to abstract numbers

Common Errors

Error 1: Not recognizing when numbers are doubles or near doubles

Error 2: Forgetting to add the adjustment for near doubles

Error 3: Not verifying the answer

Error 4: Mixing up which number to double

Key Takeaways

  • Doubles strategy builds on known facts for new problems
  • Always verify by using a different method
  • Practice recognizing doubles relationships quickly
  • Near doubles = smaller number doubled + 1
  • This strategy develops strong number sense and mental math

Questions & Answers

Question: How do I teach students to recognize when to use the doubles strategy versus other addition methods?

Answer: The key is helping students recognize the patterns! Teach them to ask: "Are the numbers the same?" or "Are the numbers one apart?"

  • For doubles: Look for identical numbers (like 5+5, 8+8)
  • For near doubles: Look for consecutive numbers (like 5+6, 8+9)
  • For making ten: Look for numbers that combine to make 10 (like 7+3, 6+4)

Start with obvious doubles facts and gradually introduce near doubles. Students will develop pattern recognition over time.

Example: For 6+7, students should think "6+6=12, and 7 is 1 more than 6, so 6+7=13"

Question: When I need to solve 7+8, how do I know it's a near doubles problem and not just count on?

Answer: Great question! Both methods work, but near doubles is usually faster:

  • Counting on: Start at 7, count 8 more: 8, 9, 10, 11, 12, 13, 14, 15 (8 steps) → 7+8=15
  • Near doubles: 7+7=14, and 8 is 1 more than 7, so 14+1=15

With near doubles, you use what you already know (7+7=14) and make a small adjustment. As you practice, this becomes much faster than counting!

Tip: If both numbers are 5 or more, near doubles is often quicker than counting on.

Question: I have trouble remembering which number to double when using near doubles. Any tips?

Answer: Here's a simple memory trick:

  • Always double the smaller number and add 1 for consecutive numbers
  • Example: For 6+7, double 6 (6+6=12) and add 1: 12+1=13
  • You can also double the larger number and subtract 1: 7+7=14, 14-1=13

The "double smaller, add 1" approach is usually easiest to remember. Practice with visual aids like counters or drawings until the pattern becomes automatic!

Also remember: near doubles always result in odd numbers!

Math Glossary

Doubles
Addition facts where the same number is added to itself (like 3+3, 6+6, 8+8). These always result in even numbers.
Near Doubles
Addition facts where the numbers are one apart (like 4+5, 7+8, 9+10). These always result in odd numbers.
Consecutive Numbers
Numbers that follow each other in order (like 5 and 6, 11 and 12). These form near doubles when added together.
Mental Math
Performing mathematical calculations in your head using strategies and known facts rather than counting or writing down steps.
Adjustment Strategy
A mental math approach that adjusts a known fact to solve a related problem by adding or subtracting the difference.

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