Using Near Doubles to Subtract in Grade 2 - Mathematics - Exercises with solutions

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

Solutions: Exercises 1 to 10
1 Basic near doubles
Exercise 1
How do I solve 8 - 7 using the near doubles strategy?
Difficulty: Beginner Time: ~2 minutes Skills: Near Doubles Strategy
Definition:

Near doubles: Pairs of numbers that are close to doubles (like 7 and 8, 5 and 6, 9 and 10)

Note: When subtracting near doubles, use the closest double as a reference point. Since 7 and 8 are near doubles (one apart), we can use the double of 7 to solve 8 - 7.

Step-by-step subtraction method:
  1. Identify the double: 7 + 7 = 14 (but we want 8, which is 7 + 1)
  2. Recognize that 8 is one more than 7
  3. So 8 - 7 = 1 (since 7 + 1 = 8, then 8 - 7 = 1)
Original Problem
\(8 - 7\)
Near Doubles Relationship
\(7 + 1 = 8\)
Solution
\(8 - 7 = 1\)
Step 1: Recognize the near doubles relationship

7 and 8 are near doubles because they are one apart (8 = 7 + 1)

Step 2: Use the relationship to solve

If 7 + 1 = 8, then 8 - 7 = 1

Step 3: Verify the answer

7 + 1 = 8, so 8 - 7 = 1 ✓

\(8 - 7 = 1\)
Final answer:

\(8 - 7 = 1\)

Applied rules:

• Near doubles: Numbers that are one apart (like 7 and 8)

• Subtraction relationship: If a + b = c, then c - a = b

• Number sense: Recognize that consecutive numbers differ by 1

• Practice Tip: Think "what number added to 7 makes 8?" to solve 8 - 7

Related Examples:
  • \(6 - 5 = 1\) - Practice with smaller near doubles
  • \(9 - 8 = 1\) - Practice with larger near doubles
  • \(4 - 3 = 1\) - Practice with single digits
Quick Tips:
  • Near doubles subtraction always equals 1 when subtracting the smaller from the larger
  • Think of near doubles as consecutive numbers (one apart)
  • Use your knowledge of doubles to help solve near doubles problems
Frequently Asked Questions:

Q: What are near doubles?
A: Numbers that are one apart, like 5 and 6, 7 and 8, or 9 and 10. They're close to doubles (which are the same number twice).

Q: Does 7 - 8 also equal 1?
A: No, 7 - 8 = -1. When subtracting the larger from the smaller, you get -1. The result is always ±1 depending on the order.

2 Near doubles subtraction
Exercise 2
What is 12 - 6 using the near doubles strategy?
Difficulty: Intermediate Time: ~3 minutes Skills: Near Doubles, Halving
Definition:

Near doubles: When one number is close to double the other (like 6 and 12, where 12 is double of 6)

Note: This is actually a doubles relationship since 6 + 6 = 12. However, it can be approached as a near doubles problem by recognizing that 12 is double of 6.

Step-by-step subtraction method:
  1. Recognize that 12 is double of 6 (6 + 6 = 12)
  2. Therefore, 12 - 6 = 6 (the other half of the double)
  3. Verify: 6 + 6 = 12, so 12 - 6 = 6
Original Problem
\(12 - 6\)
Doubles Relationship
\(6 + 6 = 12\)
Solution
\(12 - 6 = 6\)
Step 1: Recognize the doubles relationship

6 + 6 = 12, so 12 is double of 6

Step 2: Apply the inverse operation

If 6 + 6 = 12, then 12 - 6 = 6

Step 3: Verify the answer

6 + 6 = 12, so 12 - 6 = 6 ✓

\(12 - 6 = 6\)
Final answer:

\(12 - 6 = 6\)

Applied rules:

• Doubles relationship: When one number is double the other

• Subtraction relationship: If a + a = b, then b - a = a

• Halving: Subtracting a number from its double gives the original number

• Practice Tip: Remember that any number subtracted from its double equals itself

Related Examples:
  • \(10 - 5 = 5\) - Practice with 5 and 10
  • \(8 - 4 = 4\) - Practice with 4 and 8
  • \(14 - 7 = 7\) - Practice with 7 and 14
Quick Tips:
  • Any number subtracted from its double equals itself: n - n/2 = n/2
  • Recognize doubles relationships to solve subtraction problems quickly
  • This strategy works for any number and its double
Frequently Asked Questions:

Q: How do I know if numbers have a doubles relationship?
A: One number is exactly double the other. Examples: 6 and 12, 4 and 8, 7 and 14.

Q: Can I use this for other numbers like 15 - 5?
A: No, 15 is not double of 5 (double of 5 is 10). 15 - 5 = 10, which is not related to the original number.

3 Mental math strategy
Exercise 3
How do I solve 9 - 4 using the near doubles strategy?
Difficulty: Intermediate Time: ~3 minutes Skills: Near Doubles, Mental Math
Definition:

Near doubles: Using doubles facts to solve subtraction problems. 4 and 5 are near doubles, and 9 is close to double of 4 (which is 8).

Note: We can think of 9 as 8 + 1, where 8 is double of 4. So 9 - 4 = (8 + 1) - 4 = 4 + 1 = 5.

Step-by-step mental math method:
  1. Recognize that 9 is 8 + 1, and 8 is double of 4
  2. So 9 - 4 = (8 + 1) - 4 = (8 - 4) + 1 = 4 + 1
  3. Therefore, 9 - 4 = 5
Original Problem
\(9 - 4\)
Break Down 9
\(9 = 8 + 1\)
Use Doubles Relationship
\(8 = 4 + 4\)
Solution
\(9 - 4 = 5\)
Step 1: Break down 9 using doubles

9 = 8 + 1, and 8 is double of 4 (4 + 4 = 8)

Step 2: Apply the breakdown to subtraction

9 - 4 = (8 + 1) - 4 = (4 + 4 + 1) - 4 = 4 + 1 = 5

Step 3: Verify the answer

4 + 5 = 9, so 9 - 4 = 5 ✓

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

\(9 - 4 = 5\)

Applied rules:

• Decomposition: Break numbers into doubles and remainders

• Subtraction with regrouping: Use known facts to solve new problems

• Mental math: Use doubles facts as building blocks

• Practice Tip: Think "what plus 4 equals 9?" to solve 9 - 4

Related Examples:
  • \(7 - 3 = 4\) - 7 = 6 + 1, 6 = 3 + 3, so 7 - 3 = (6 - 3) + 1 = 3 + 1 = 4
  • \(11 - 5 = 6\) - 11 = 10 + 1, 10 = 5 + 5, so 11 - 5 = (10 - 5) + 1 = 5 + 1 = 6
  • \(13 - 6 = 7\) - 13 = 12 + 1, 12 = 6 + 6, so 13 - 6 = (12 - 6) + 1 = 6 + 1 = 7
Quick Tips:
  • Think of the larger number as "double of smaller + remainder"
  • Use known doubles facts to build up to unknown facts
  • Practice decomposing numbers mentally to strengthen number sense
Frequently Asked Questions:

Q: Why break down 9 into 8 + 1 instead of other combinations?
A: Because 8 is double of 4, which connects to our known doubles fact. This makes the calculation easier.

Q: Can I use this for any subtraction problem?
A: It works best when one number is close to a doubles relationship with the other number.

Solutions: Exercises 4 to 5
4 Number sense application
Exercise 4
How do I solve 10 - 5 using the near doubles strategy?
Definition:

Near doubles: 10 is double of 5 (5 + 5 = 10), so this is actually a doubles relationship

Note: When one number is exactly double the other, the subtraction equals the original number. 10 - 5 = 5 because 5 + 5 = 10.

Step-by-step number sense method:
  1. Recognize that 10 is double of 5
  2. Therefore, 10 - 5 = 5 (the other half of the double)
  3. Verify: 5 + 5 = 10, so 10 - 5 = 5
Original Problem
\(10 - 5\)
Doubles Relationship
\(5 + 5 = 10\)
Solution
\(10 - 5 = 5\)
Step 1: Recognize the doubles relationship

5 + 5 = 10, so 10 is double of 5

Step 2: Apply the inverse operation

If 5 + 5 = 10, then 10 - 5 = 5

Step 3: Verify the answer

5 + 5 = 10, so 10 - 5 = 5 ✓

\(10 - 5 = 5\)
Final answer:

\(10 - 5 = 5\)

Applied rules:

• Doubles relationship: When one number is double the other

• Subtraction relationship: If a + a = b, then b - a = a

• Number sense: Recognize that a number subtracted from its double equals itself

• Practice Tip: Any number subtracted from its double equals the original number

Related Examples:
  • \(6 - 3 = 3\) - 6 is double of 3
  • \(12 - 6 = 6\) - 12 is double of 6
  • \(14 - 7 = 7\) - 14 is double of 7
Quick Tips:
  • When the first number is exactly double the second, the answer is the second number
  • Recognize these relationships quickly for faster mental math
  • This pattern holds true for any number and its double
Frequently Asked Questions:

Q: Is 10 - 5 really a near doubles problem?
A: Technically it's a doubles relationship since 10 is exactly double of 5, but it's included here because it uses the same principle.

Q: What if I don't recognize the doubles relationship?
A: Count backwards from 10: 10, 9, 8, 7, 6, 5. That's 5 steps, so 10 - 5 = 5.

5 Subtraction facts
Exercise 5
How do I solve 11 - 6 using the near doubles strategy?
Definition:

Near doubles: 6 and 5 are near doubles (one apart), and 11 is close to double of 6 (which is 12)

Note: We can think of 11 as 12 - 1, where 12 is double of 6. So 11 - 6 = (12 - 1) - 6 = (12 - 6) - 1 = 6 - 1 = 5.

Step-by-step subtraction method:
  1. Recognize that 11 is 12 - 1, and 12 is double of 6
  2. So 11 - 6 = (12 - 1) - 6 = (12 - 6) - 1 = 6 - 1
  3. Therefore, 11 - 6 = 5
Original Problem
\(11 - 6\)
Break Down 11
\(11 = 12 - 1\)
Use Doubles Relationship
\(12 = 6 + 6\)
Solution
\(11 - 6 = 5\)
Step 1: Recognize the relationship to doubles

11 is 1 less than 12, and 12 is double of 6 (6 + 6 = 12)

Step 2: Apply the relationship to subtraction

11 - 6 = (12 - 1) - 6 = (12 - 6) - 1 = 6 - 1 = 5

Step 3: Verify the answer

6 + 5 = 11, so 11 - 6 = 5 ✓

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

\(11 - 6 = 5\)

Applied rules:

• Adjustment strategy: Adjust to a known doubles fact and compensate

• Subtraction with compensation: Use nearby known facts

• Number sense: Recognize relationships between numbers

• Practice Tip: Think "what plus 6 equals 11?" to solve 11 - 6

Related Examples:
  • \(9 - 4 = 5\) - 9 is 1 less than 10 (double of 5), but 4 is 1 less than 5
  • \(13 - 7 = 6\) - 13 is 1 less than 14 (double of 7), so 13 - 7 = 7 - 1 = 6
  • \(15 - 8 = 7\) - 15 is 1 less than 16 (double of 8), so 15 - 8 = 8 - 1 = 7
Quick Tips:
  • Think of numbers close to doubles facts and adjust accordingly
  • Use the relationship: if n is 1 more than double of m, then n - m = m + 1
  • Practice adjusting to and from doubles facts to strengthen mental math
Frequently Asked Questions:

Q: How do I know whether to add or subtract the adjustment?
A: If the first number is larger than the double, subtract the adjustment. If it's smaller, add the adjustment.

Q: Is this method faster than counting backwards?
A: Yes, once you master the doubles relationships, this method is much faster than counting.

Solutions: Exercises 6 to 10
6 Advanced near doubles
Exercise 6
How do I solve 13 - 6 using the near doubles strategy?
Definition:

Advanced near doubles: 13 is close to double of 6 (which is 12). Specifically, 13 = 12 + 1

Note: Since 13 is 1 more than double of 6, we can use: 13 - 6 = (12 + 1) - 6 = (12 - 6) + 1 = 6 + 1 = 7

Step-by-step advanced method:
  1. Recognize that 13 is 1 more than double of 6 (12)
  2. So 13 - 6 = (12 + 1) - 6 = (12 - 6) + 1
  3. Since 12 - 6 = 6, then 13 - 6 = 6 + 1 = 7
Original Problem
\(13 - 6\)
Break Down 13
\(13 = 12 + 1\)
Use Doubles Relationship
\(12 = 6 + 6\)
Solution
\(13 - 6 = 7\)
Step 1: Recognize the relationship to doubles

13 is 1 more than 12, and 12 is double of 6 (6 + 6 = 12)

Step 2: Apply the relationship to subtraction

13 - 6 = (12 + 1) - 6 = (12 - 6) + 1 = 6 + 1 = 7

Step 3: Verify the answer

6 + 7 = 13, so 13 - 6 = 7 ✓

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

\(13 - 6 = 7\)

Applied rules:

• Adjustment strategy: Adjust to a known doubles fact and add the adjustment

• Compensation: When the first number is larger than double, add the difference

• Pattern recognition: Use known facts to solve new problems

• Practice Tip: If the first number is 1 more than double the second, the answer is the second number plus 1

Related Examples:
  • \(11 - 5 = 6\) - 11 is 1 more than 10 (double of 5), so 5 + 1 = 6
  • \(15 - 7 = 8\) - 15 is 1 more than 14 (double of 7), so 7 + 1 = 8
  • \(9 - 4 = 5\) - 9 is 1 more than 8 (double of 4), so 4 + 1 = 5
Quick Tips:
  • When the first number is 1 more than double the second, the answer is the second number + 1
  • When the first number is 1 less than double the second, the answer is the second number - 1
  • Practice recognizing these patterns quickly for mental math fluency
Frequently Asked Questions:

Q: What if the first number is 2 more than double the second?
A: Then the answer would be the second number + 2. For example, 14 - 6 = 8 (since 14 = 12 + 2, and 12 is double of 6).

Q: Can I use this for larger numbers too?
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 14 - 7 using the near doubles strategy?
Definition:

Problem solving: 14 is exactly double of 7 (7 + 7 = 14), so this is a direct doubles relationship

Note: When one number is exactly double the other, the subtraction equals the original number. 14 - 7 = 7.

Step-by-step problem solving method:
  1. Recognize that 14 is double of 7
  2. Therefore, 14 - 7 = 7 (the other half of the double)
  3. Verify: 7 + 7 = 14, so 14 - 7 = 7
Original Problem
\(14 - 7\)
Doubles Relationship
\(7 + 7 = 14\)
Solution
\(14 - 7 = 7\)
Step 1: Recognize the doubles relationship

7 + 7 = 14, so 14 is double of 7

Step 2: Apply the inverse operation

If 7 + 7 = 14, then 14 - 7 = 7

Step 3: Verify the answer

7 + 7 = 14, so 14 - 7 = 7 ✓

\(14 - 7 = 7\)
Final answer:

\(14 - 7 = 7\)

Applied rules:

• Doubles relationship: When one number is double the other

• Subtraction relationship: If a + a = b, then b - a = a

• Problem solving: Recognize and apply mathematical relationships

• Practice Tip: Remember that any number subtracted from its double equals itself

Related Examples:
  • \(8 - 4 = 4\) - 8 is double of 4
  • \(16 - 8 = 8\) - 16 is double of 8
  • \(18 - 9 = 9\) - 18 is double of 9
Quick Tips:
  • When you see a number and its double, the subtraction always equals the original number
  • Practice recognizing doubles quickly: 1&2, 2&4, 3&6, 4&8, 5&10, etc.
  • This relationship is fundamental to many mental math strategies
Frequently Asked Questions:

Q: How do I quickly identify doubles relationships?
A: Practice with the doubles facts: 1+1=2, 2+2=4, 3+3=6, 4+4=8, 5+5=10, etc.

Q: What if I'm not sure if one number is double another?
A: Try adding the smaller number to itself. If it equals the larger number, it's a doubles relationship.

8 Word problems
Exercise 8
How do I solve 12 - 5 using the near doubles strategy?
Definition:

Word problems: 12 is close to double of 5 (which is 10). Specifically, 12 = 10 + 2

Note: Since 12 is 2 more than double of 5, we can use: 12 - 5 = (10 + 2) - 5 = (10 - 5) + 2 = 5 + 2 = 7

Step-by-step word problem method:
  1. Recognize that 12 is 2 more than double of 5 (10)
  2. So 12 - 5 = (10 + 2) - 5 = (10 - 5) + 2
  3. Since 10 - 5 = 5, then 12 - 5 = 5 + 2 = 7
Original Problem
\(12 - 5\)
Break Down 12
\(12 = 10 + 2\)
Use Doubles Relationship
\(10 = 5 + 5\)
Solution
\(12 - 5 = 7\)
Step 1: Recognize the relationship to doubles

12 is 2 more than 10, and 10 is double of 5 (5 + 5 = 10)

Step 2: Apply the relationship to subtraction

12 - 5 = (10 + 2) - 5 = (10 - 5) + 2 = 5 + 2 = 7

Step 3: Verify the answer

5 + 7 = 12, so 12 - 5 = 7 ✓

\(12 - 5 = 7\)
Final answer:

\(12 - 5 = 7\)

Applied rules:

• Adjustment strategy: Adjust to a known doubles fact and add the adjustment

• Compensation: When the first number is larger than double, add the difference

• Problem solving: Break complex problems into simpler parts

• Practice Tip: If the first number is 2 more than double the second, the answer is the second number + 2

Related Examples:
  • \(11 - 4 = 7\) - 11 is 3 more than 8 (double of 4), so 4 + 3 = 7
  • \(13 - 5 = 8\) - 13 is 3 more than 10 (double of 5), so 5 + 3 = 8
  • \(16 - 7 = 9\) - 16 is 2 more than 14 (double of 7), so 7 + 2 = 9
Quick Tips:
  • When the first number is more than double the second, add the difference to the second number
  • Practice the pattern: if first = (double of second) + n, then answer = second + n
  • This strategy builds strong number sense and mental math abilities
Frequently Asked Questions:

Q: What if the first number is less than double the second?
A: Then you subtract the difference. For example, 8 - 5: 8 is 2 less than 10 (double of 5), so 5 - 2 = 3.

Q: How do I decide which number to double?
A: Always double the smaller number in the subtraction problem.

9 Mixed operations
Exercise 9
How do I solve 15 - 8 using the near doubles strategy?
Definition:

Mixed operations: 15 is close to double of 8 (which is 16). Specifically, 15 = 16 - 1

Note: Since 15 is 1 less than double of 8, we can use: 15 - 8 = (16 - 1) - 8 = (16 - 8) - 1 = 8 - 1 = 7

Step-by-step mixed operations method:
  1. Recognize that 15 is 1 less than double of 8 (16)
  2. So 15 - 8 = (16 - 1) - 8 = (16 - 8) - 1
  3. Since 16 - 8 = 8, then 15 - 8 = 8 - 1 = 7
Original Problem
\(15 - 8\)
Break Down 15
\(15 = 16 - 1\)
Use Doubles Relationship
\(16 = 8 + 8\)
Solution
\(15 - 8 = 7\)
Step 1: Recognize the relationship to doubles

15 is 1 less than 16, and 16 is double of 8 (8 + 8 = 16)

Step 2: Apply the relationship to subtraction

15 - 8 = (16 - 1) - 8 = (16 - 8) - 1 = 8 - 1 = 7

Step 3: Verify the answer

8 + 7 = 15, so 15 - 8 = 7 ✓

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

\(15 - 8 = 7\)

Applied rules:

• Adjustment strategy: Adjust to a known doubles fact and subtract the adjustment

• Compensation: When the first number is smaller than double, subtract the difference

• Mixed operations: Use multiple strategies in sequence

• Practice Tip: If the first number is 1 less than double the second, the answer is the second number - 1

Related Examples:
  • \(13 - 7 = 6\) - 13 is 1 less than 14 (double of 7), so 7 - 1 = 6
  • \(11 - 6 = 5\) - 11 is 1 less than 12 (double of 6), so 6 - 1 = 5
  • \(9 - 5 = 4\) - 9 is 1 less than 10 (double of 5), so 5 - 1 = 4
Quick Tips:
  • When the first number is less than double the second, subtract the difference from the second number
  • Remember: if first = (double of second) - n, then answer = second - n
  • Combine multiple strategies for complex problems
Frequently Asked Questions:

Q: What if I make a mistake identifying the relationship?
A: Always verify your answer by adding the result to the subtracted number to see if you get the original number.

Q: Can I use this method for addition too?
A: Yes! You can use doubles relationships for addition as well: 7 + 8 = 7 + 7 + 1 = 14 + 1 = 15.

10 Comprehensive review
Exercise 10
How do I solve 17 - 9 using the near doubles strategy?
Definition:

Comprehensive review: 17 is close to double of 9 (which is 18). Specifically, 17 = 18 - 1

Note: Since 17 is 1 less than double of 9, we can use: 17 - 9 = (18 - 1) - 9 = (18 - 9) - 1 = 9 - 1 = 8

Step-by-step comprehensive method:
  1. Recognize that 17 is 1 less than double of 9 (18)
  2. So 17 - 9 = (18 - 1) - 9 = (18 - 9) - 1
  3. Since 18 - 9 = 9, then 17 - 9 = 9 - 1 = 8
Original Problem
\(17 - 9\)
Break Down 17
\(17 = 18 - 1\)
Use Doubles Relationship
\(18 = 9 + 9\)
Solution
\(17 - 9 = 8\)
Step 1: Recognize the relationship to doubles

17 is 1 less than 18, and 18 is double of 9 (9 + 9 = 18)

Step 2: Apply the relationship to subtraction

17 - 9 = (18 - 1) - 9 = (18 - 9) - 1 = 9 - 1 = 8

Step 3: Verify the answer

9 + 8 = 17, so 17 - 9 = 8 ✓

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

\(17 - 9 = 8\)

Applied rules:

• Adjustment strategy: Adjust to a known doubles fact and subtract the adjustment

• Compensation: When the first number is smaller than double, subtract the difference

• Review: Apply learned strategies to more challenging problems

• Practice Tip: Master these patterns for quick mental math: ±1, ±2 from doubles

Related Examples:
  • \(15 - 8 = 7\) - 15 is 1 less than 16 (double of 8), so 8 - 1 = 7
  • \(14 - 8 = 6\) - 14 is 2 less than 16 (double of 8), so 8 - 2 = 6
  • \(16 - 7 = 9\) - 16 is 2 more than 14 (double of 7), so 7 + 2 = 9
Quick Tips:
  • Practice all variations: +1, +2, -1, -2 from doubles relationships
  • Build fluency by practicing with all combinations
  • These strategies form the foundation for more advanced mental math
Frequently Asked Questions:

Q: How do I know which strategy to use for each problem?
A: Look for doubles relationships first, then decide if the first number is more or less than the double.

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

Key Laws, Methods, Rules, and Definitions
\(a - b = ? \text{ (use near doubles)}\)
Near Doubles Strategy
Key definitions:

Near doubles: Pairs of numbers that are close to doubles (like 6 and 7, 8 and 9, or 5 and 6)

Doubles: Two identical numbers added together (like 5 + 5 = 10)

Number sense: Understanding the relationships between numbers and their values

Complete methodology:
  1. Recognize the relationship: Identify if one number is close to double the other
  2. Use doubles facts: Apply known doubles relationships to solve the problem
  3. Adjust if needed: Add or subtract the difference from the doubles result
  4. Verify the result: Check by adding the answer to the subtracted number
Tip 1: When the first number is 1 more than double the second, add 1 to the second number.
Tip 2: When the first number is 1 less than double the second, subtract 1 from the second number.
Tip 3: Master doubles facts first (1+1, 2+2, 3+3, etc.) as they form the foundation.
Tip 4: Always verify your answer by adding it back to check if you get the original number.
Common errors: Misidentifying doubles relationships, incorrect adjustments, forgetting verification.
Exam preparation: Practice all variations of near doubles, focus on speed and accuracy, verify answers.
Formulas to remember:

• If first number = (double of second) + n, then answer = second + n

• If first number = (double of second) - n, then answer = second - n

• When first number is exactly double the second, answer = second

• Always verify: (second number) + (answer) = (first number)

Rules and Methods for Using Near Doubles to Subtract

Near Doubles Strategy

Using Known Facts to Solve New Problems

Core Concept

The near doubles strategy uses known doubles facts to solve subtraction problems. Instead of counting backward, students recognize relationships between numbers.

For example: To solve 9 - 4, think "4 + 4 = 8, and 9 is 1 more than 8, so 9 - 4 = 5."

Basic Near Doubles
8 - 7 = 1

Think: 7 + 1 = 8

Doubles Relationship
12 - 6 = 6

Think: 6 + 6 = 12

Advanced Near Doubles
13 - 6 = 7

Think: 12 - 6 = 6, and 13 is 1 more than 12

Key Strategies

Strategy 1: When the first number is exactly double the second: answer = second number

Strategy 2: When the first number is 1 more than double: answer = second + 1

Strategy 3: When the first number is 1 less than double: answer = second - 1

Strategy 4: When the first number is 2 more than double: answer = second + 2

Strategy 5: When the first number is 2 less than double: answer = second - 2

Memory Tips

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

Tip 2: Think "What number added to the second gives the first?"

Tip 3: Use visual models: 8 dots minus 7 dots leaves 1 dot

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

Common Errors

Error 1: Not recognizing when numbers are near doubles (missing the relationship)

Error 2: Adding instead of subtracting the adjustment

Error 3: Forgetting to verify the answer

Error 4: Confusing which number is the double

Key Takeaways

  • Near doubles strategy builds on known doubles facts
  • Always verify by adding the answer to the subtracted number
  • Practice recognizing doubles relationships quickly
  • Adjust the doubles result based on the difference
  • This strategy develops strong number sense and mental math

Questions & Answers

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

Answer: The key is helping students recognize the pattern! Teach them to ask: "Is one number close to double the other?"

  • For near doubles: Look for numbers that are one apart or close to doubles (like 8-7, 13-6, 11-5)
  • For counting back: Use when the second number is small (like 10-2, 15-3)
  • For making ten: Use when the numbers work well with 10 (like 14-6, 12-5)

Start with obvious doubles relationships (12-6, 10-5) and gradually introduce near doubles (13-6, 11-5). Students will develop pattern recognition over time.

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

Question: When I need to solve 14-8, how do I know it's a near doubles problem and not just count backwards?

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

  • Counting back: 14, 13, 12, 11, 10, 9, 8, 7, 6 (8 steps) → 14-8=6
  • Near doubles: 8+8=16, 14 is 2 less than 16, so 14-8=8-2=6

With near doubles, you use what you already know (8+8=16) and make a small adjustment. As you practice, this becomes much faster than counting!

Tip: If the second number is 5 or more, near doubles is often quicker than counting back.

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

Answer: Here's a simple memory trick:

  • When the first number is LARGER than double the second: ADD the difference to the second number
  • When the first number is SMALLER than double the second: SUBTRACT the difference from the second number

Examples:

  • 13-6: 6+6=12, 13 is 1 MORE than 12, so answer = 6+1 = 7
  • 11-6: 6+6=12, 11 is 1 LESS than 12, so answer = 6-1 = 5

Practice with visual aids like counters or drawings until the pattern becomes automatic!

Math Glossary

Near Doubles
Pairs of numbers that are close to doubles (like 7 and 8, 5 and 6, 9 and 10). Used to solve subtraction problems by leveraging known doubles facts.
Doubles Facts
Addition facts where the same number is added to itself (like 3+3, 6+6, 8+8). These form the foundation for near doubles strategies.
Number Sense
Understanding the relationships between numbers, their relative magnitudes, and how they can be manipulated through mathematical operations.
Compensation Strategy
A mental math approach that adjusts a known fact to solve a related problem by adding or subtracting the difference.
Mental Math
Performing mathematical calculations in your head using strategies and known facts rather than counting or writing down steps.

Math Mastery Educational Team

Certified Elementary Mathematics Educators & Curriculum Specialists

Our team of experienced elementary math teachers and curriculum developers creates research-based, student-friendly math resources. All content is aligned with Common Core State Standards and reviewed by mathematics education experts to ensure accuracy and pedagogical effectiveness.