Using Doubles and Near Doubles - Grade 2 Mathematics - Exercises with solutions

Master using doubles and near doubles: doubles facts, near doubles, and doubles plus/minus 1 strategy through these 10 detailed exercises with verified solutions.

Solutions: Exercises 1 to 10
1 Basic doubles
Exercise 1
What is 5 + 5?
Difficulty: Beginner Time: ~1 minute Skills: Basic Doubles Facts
Definition:

Doubles facts: Addition problems where the same number is added to itself

Note: Doubles facts are foundational for mental math and help with other addition strategies.

Step-by-step doubles method:
  1. Recognize that we're adding the same number twice
  2. Count the number of groups: 2 groups of 5
  3. Multiply: 2 × 5 = 10
Original Problem
5 + 5
Solution
10
Step 1: Recognize the pattern

We're adding 5 twice: 5 + 5

Step 2: Count the groups

2 groups of 5 objects: ⭐⭐⭐⭐⭐ and ⭐⭐⭐⭐⭐

Step 3: Add the groups

Total: 5 + 5 = 10 objects

5 + 5 = 10
Final answer:

5 + 5 = 10

Applied rules:

• Doubles: Same number added to itself

• Pattern: Doubles always result in even numbers

• Memory tip: Practice doubles facts until automatic

Related Examples:
  • 4 + 4 = 8 - Practice with smaller doubles
  • 6 + 6 = 12 - Practice with medium doubles
  • 3 + 3 = 6 - Practice with single digits
Quick Tips:
  • Doubles always result in even numbers
  • Memorize doubles facts for mental math speed
  • Use doubles to help with near doubles
Frequently Asked Questions:

Q: Why are doubles facts important?
A: They build fluency and help with other addition strategies like near doubles.

Q: What numbers can be doubled?
A: Any number can be doubled, but we focus on 1-10 for early grades.

2 Doubles plus 1
Exercise 2
What is 5 + 6?
Difficulty: Beginner Time: ~1 minute Skills: Doubles Plus 1 Strategy
Definition:

Doubles plus 1: Addition problems where one number is 1 more than the other

Note: This strategy uses the doubles fact and adds 1 more to the result.

Step-by-step doubles plus 1 method:
  1. Recognize that 6 is 1 more than 5
  2. Use the doubles fact: 5 + 5 = 10
  3. Add 1 more: 10 + 1 = 11
Original Problem
5 + 6
Doubles Plus 1
5 + 5 + 1
Solution
11
Step 1: Identify the relationship

6 is exactly 1 more than 5

Step 2: Use doubles fact

We know 5 + 5 = 10

Step 3: Add the extra one

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

5 + 6 = 11
Final answer:

5 + 6 = 11

Applied rules:

• Doubles plus 1: One number is exactly 1 more than the other

• Strategy: Use doubles fact and add 1

• Memory tip: This is the same as near doubles

Related Examples:
  • 4 + 5: Use 4 + 4 = 8, then 8 + 1 = 9
  • 7 + 8: Use 7 + 7 = 14, then 14 + 1 = 15
  • 3 + 4: Use 3 + 3 = 6, then 6 + 1 = 7
Quick Tips:
  • Look for numbers that are 1 apart
  • Always use the smaller number for the doubles fact
  • Add 1 to the doubles result
Frequently Asked Questions:

Q: What is doubles plus 1?
A: Addition problems where one number is 1 more than the other, like 5+6 or 7+8.

Q: How is this different from regular near doubles?
A: Doubles plus 1 is a specific case of near doubles where the difference is exactly 1.

3 Doubles minus 1
Exercise 3
What is 6 + 5?
Difficulty: Beginner Time: ~1 minute Skills: Doubles Minus 1 Strategy
Definition:

Doubles minus 1: Addition problems where one number is 1 less than the other

Note: This is another type of near doubles where we use the larger number's doubles fact and subtract 1.

Step-by-step doubles minus 1 method:
  1. Recognize that 5 is 1 less than 6
  2. Use the doubles fact: 6 + 6 = 12
  3. Subtract 1: 12 - 1 = 11
Original Problem
6 + 5
Doubles Minus 1
6 + 6 - 1
Solution
11
Step 1: Identify the relationship

5 is exactly 1 less than 6

Step 2: Use doubles fact

We know 6 + 6 = 12

Step 3: Subtract the difference

Since 5 is 1 less than 6, subtract 1 from the doubles result: 12 - 1 = 11

6 + 5 = 11
Final answer:

6 + 5 = 11

Applied rules:

• Doubles minus 1: One number is exactly 1 less than the other

• Strategy: Use the larger number's doubles fact and subtract 1

• Memory tip: This is the reverse of doubles plus 1

Related Examples:
  • 5 + 4: Use 5 + 5 = 10, then 10 - 1 = 9
  • 8 + 7: Use 8 + 8 = 16, then 16 - 1 = 15
  • 4 + 3: Use 4 + 4 = 8, then 8 - 1 = 7
Quick Tips:
  • Look for numbers that are 1 apart
  • Use the larger number for the doubles fact
  • Subtract 1 from the doubles result
Frequently Asked Questions:

Q: What is doubles minus 1?
A: Addition problems where one number is 1 less than the other, like 6+5 or 8+7.

Q: How do I solve doubles minus 1?
A: Use the doubles fact for the larger number and subtract 1.

Solutions: Exercises 4 to 5
4 Identifying near doubles
Exercise 4
Is 8 + 9 a near doubles fact? What is the answer?
Definition:

Identifying near doubles: Recognizing when an addition problem has consecutive numbers

Note: Being able to identify near doubles quickly helps with mental math strategies.

Step-by-step identification method:
  1. Look at both numbers in the addition problem
  2. Check if they are consecutive (differ by 1)
  3. If yes, it's a near doubles fact
  4. Calculate: 8 + 9 = 17
Original Problem
8 + 9
Is it near doubles?
Yes
Solution
17
Step 1: Examine the numbers

8 and 9 are consecutive numbers

Step 2: Identify the pattern

Since 8 and 9 differ by 1, this is a near doubles fact

Step 3: Calculate using doubles

8 + 8 = 16, then add 1: 16 + 1 = 17

8 + 9 = 17
Final answer:

Yes, 8 + 9 is a near doubles fact. The answer is 17.

Applied rules:

• Identification: Check if numbers differ by 1

• Pattern recognition: Near doubles use consecutive numbers

• Memory tip: Practice recognizing near doubles patterns

Related Examples:
  • 5 + 6: Yes, near doubles → 11
  • 7 + 8: Yes, near doubles → 15
  • 3 + 5: No, not near doubles (differ by 2)
Quick Tips:
  • Look for consecutive numbers in addition problems
  • Practice recognizing near doubles quickly
  • Use the smaller number's doubles fact for doubles plus 1
Frequently Asked Questions:

Q: How do I know if an addition problem is a near doubles fact?
A: Check if the two numbers differ by exactly 1.

Q: What if the numbers differ by more than 1?
A: Then it's not a near doubles fact.

5 Missing doubles
Exercise 5
What number added to itself equals 18?
Definition:

Missing doubles: Finding the number that, when doubled, equals a given sum

Note: This involves understanding the inverse of doubles facts.

Step-by-step missing doubles method:
  1. Think: ? + ? = 18, or ? × 2 = 18
  2. Find half of 18
  3. 18 ÷ 2 = 9
  4. Check: 9 + 9 = 18
Original Problem
? + ? = 18
Half of Total
18 ÷ 2 = 9
Solution
9
Step 1: Understand the problem

We need a number that when added to itself equals 18

Step 2: Use division

To find the number, divide 18 by 2: 18 ÷ 2 = 9

Step 3: Verify

Check: 9 + 9 = 18 ✓

9 + 9 = 18
Final answer:

The number is 9

Applied rules:

• Missing doubles: Find the number that when doubled equals the target

• Strategy: Divide the total by 2

• Verification: Always check by doubling the answer

Related Examples:
  • ? + ? = 12 → 12 ÷ 2 = 6 → 6 + 6 = 12
  • ? + ? = 16 → 16 ÷ 2 = 8 → 8 + 8 = 16
  • ? + ? = 14 → 14 ÷ 2 = 7 → 7 + 7 = 14
Quick Tips:
  • To find a missing double, divide the total by 2
  • Always verify by doubling your answer
  • This connects to division concepts
Frequently Asked Questions:

Q: How do I find missing doubles?
A: Divide the total by 2 to find the number that was doubled.

Q: What if the total is odd?
A: Odd totals cannot be doubles of whole numbers (e.g., nothing doubled equals 7).

Solutions: Exercises 6 to 10
6 Fact families
Exercise 6
If 7 + 7 = 14, what is 14 - 7?
Definition:

Fact family with doubles: Using a doubles fact to solve related subtraction

Note: Doubles facts create special fact families with subtraction.

Step-by-step fact family method:
  1. Start with the doubles fact: 7 + 7 = 14
  2. Recognize the inverse relationship: 14 - 7 = 7
  3. Verify: 7 + 7 = 14 ✓ and 14 - 7 = 7 ✓
Given Fact
7 + 7 = 14
Related Subtraction
14 - 7 = ?
Solution
7
Step 1: Use the given doubles fact

We know 7 + 7 = 14

Step 2: Apply inverse operation

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

Step 3: Verify

7 + 7 = 14 ✓ and 14 - 7 = 7 ✓

14 - 7 = 7
Final answer:

14 - 7 = 7

Applied rules:

• Fact family: Doubles create special addition/subtraction relationships

• Inverse operations: Addition and subtraction undo each other

• Verification: Always check your answer

Related Examples:
  • If 6 + 6 = 12, then 12 - 6 = 6
  • If 8 + 8 = 16, then 16 - 8 = 8
  • If 5 + 5 = 10, then 10 - 5 = 5
Quick Tips:
  • Doubles facts create special fact families
  • The same number appears in both addition and subtraction
  • Use doubles to help with subtraction facts
Frequently Asked Questions:

Q: What is a fact family with doubles?
A: A group of related facts where the same number is added to itself.

Q: How do doubles help with subtraction?
A: Knowing 7 + 7 = 14 helps you know 14 - 7 = 7.

7 Word problem
Exercise 7
Tom has 8 red marbles. His sister gives him 9 blue marbles. How many marbles does Tom have now?
Definition:

Word problem with near doubles: A real-world problem that involves adding consecutive numbers

Note: This problem requires adding 8 + 9, which is a near doubles fact.

Step-by-step word problem method:
  1. Identify the numbers: 8 red marbles + 9 blue marbles
  2. Recognize this is a near doubles problem (8 and 9 are consecutive)
  3. Use doubles strategy: 8 + 8 = 16, then add 1 more
  4. 16 + 1 = 17
Red Marbles
8
Blue Marbles
9
Total Marbles
17
Step 1: Identify what we know

Tom has 8 red marbles and gets 9 blue marbles

Step 2: Set up the addition

8 + 9 = ?

Step 3: Use near doubles strategy

8 + 9 is the same as 8 + 8 + 1 = 16 + 1 = 17

Step 4: Answer the question

Tom has 17 marbles now

Tom has 17 marbles now
Final answer:

Tom has 17 marbles now

Applied rules:

• Problem solving: Identify key information

• Near doubles: 8 and 9 are consecutive numbers

• Strategy: Use 8 + 8 = 16, then add 1 more

• Contextual answer: Include units in your answer

Related Examples:
  • 5 + 6: Use 5 + 5 = 10, then 10 + 1 = 11
  • 9 + 8: Use 8 + 8 = 16, then 16 + 1 = 17
  • 4 + 5: Use 4 + 4 = 8, then 8 + 1 = 9
Quick Tips:
  • Look for consecutive numbers in word problems
  • Use doubles facts to solve near doubles quickly
  • Always answer with a complete sentence
Frequently Asked Questions:

Q: How do I know if a word problem uses near doubles?
A: Look for consecutive numbers like 8 and 9, or numbers that are close together.

Q: Should I always use the doubles strategy?
A: Use it when it makes the problem easier, especially with consecutive numbers.

8 Patterns
Exercise 8
What pattern do you notice in these problems: 3 + 4 = 7, 4 + 5 = 9, 5 + 6 = 11?
Definition:

Near doubles pattern: A consistent relationship in near doubles facts

Note: Near doubles always result in odd numbers and follow a predictable pattern.

Step-by-step pattern recognition method:
  1. Look at the first numbers: 3, 4, 5 (increasing by 1)
  2. Look at the answers: 7, 9, 11 (odd numbers increasing by 2)
  3. Notice: near doubles always result in odd numbers
  4. Pattern: consecutive numbers add to odd numbers
Pattern Sequence
3+4=7, 4+5=9, 5+6=11
Pattern Rule
Consecutive numbers add to odd numbers
Next in Pattern
6+7=13
Step 1: Analyze the inputs

The numbers being added: (3,4), (4,5), (5,6) - all consecutive pairs

Step 2: Analyze the outputs

The results: 7, 9, 11 (each increases by 2, all odd)

Step 3: Identify the pattern

Near doubles always result in odd numbers

Step 4: Predict next

Following the pattern: 6 + 7 = 13

Near doubles always result in odd numbers and increase by 2
Final answer:

When you add consecutive numbers, you get an odd number that increases by 2 from the previous result.

Applied rules:

• Pattern recognition: Near doubles always produce odd numbers

• Mathematical relationship: Consecutive numbers add to odd results

• Generalization: n + (n+1) = 2n+1 (always odd)

Related Examples:
  • 6 + 7 = 13, 7 + 8 = 15, 8 + 9 = 17 (pattern continues)
  • All results are odd numbers
  • Each result is 2 more than the previous result
Quick Tips:
  • Near doubles always result in odd numbers
  • Recognizing patterns helps with memorization
  • Consecutive numbers follow predictable addition patterns
Frequently Asked Questions:

Q: Why do near doubles always result in odd numbers?
A: Because you're adding an even number (doubles) and 1, which results in an odd number.

Q: What's the pattern in near doubles?
A: Consecutive numbers always add to odd numbers.

9 Mixed practice
Exercise 9
Solve: 4 + 4 + 1
Definition:

Mixed practice: Problems combining different addition strategies

Note: This problem combines doubles with adding one more.

Step-by-step mixed practice method:
  1. Recognize the doubles: 4 + 4 = 8
  2. Add the remaining number: 8 + 1 = 9
Original Problem
4 + 4 + 1
Doubles Part
4 + 4 = 8
Add Remaining
8 + 1 = 9
Final Answer
9
Step 1: Identify the doubles

First, add 4 + 4 = 8

Step 2: Add the remaining number

Now add the 1: 8 + 1 = 9

Step 3: Final answer

4 + 4 + 1 = 9

4 + 4 + 1 = 9
Final answer:

9

Applied rules:

• Sequential solving: Solve part of the problem first

• Doubles strategy: Use known doubles facts

• Flexibility: Combine multiple strategies as needed

Related Examples:
  • 5 + 5 + 2: First 5 + 5 = 10, then 10 + 2 = 12
  • 6 + 6 + 1: First 6 + 6 = 12, then 12 + 1 = 13
  • 3 + 3 + 3: First 3 + 3 = 6, then 6 + 3 = 9
Quick Tips:
  • Solve parts of the problem step by step
  • Use doubles facts when you see repeated numbers
  • Combine strategies as needed
Frequently Asked Questions:

Q: How do I solve problems with multiple additions?
A: Look for doubles or other patterns first, then add the remaining numbers.

Q: Should I add left to right?
A: You can, but look for doubles first to make it easier.

10 Advanced near doubles
Exercise 10
What is 9 + 8?
Definition:

Advanced near doubles: Larger consecutive numbers that require strong doubles knowledge

Note: This problem requires knowing the 8 + 8 or 9 + 9 doubles fact.

Step-by-step advanced near doubles method:
  1. Recognize that 9 and 8 are consecutive numbers
  2. Use the smaller number's doubles fact: 8 + 8 = 16
  3. Add 1 more since 9 is 1 more than 8: 16 + 1 = 17
Original Problem
9 + 8
Near Doubles Strategy
8 + 8 + 1
Solution
17
Step 1: Identify the pattern

9 and 8 are consecutive numbers (differ by 1)

Step 2: Use doubles fact

We know 8 + 8 = 16

Step 3: Add the difference

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

9 + 8 = 17
Final answer:

9 + 8 = 17

Applied rules:

• Near doubles: Consecutive numbers can use doubles strategy

• Strategy: Use closest doubles fact and adjust

• Memory tip: Near doubles are doubles ± 1

Related Examples:
  • 9 + 8: Use 8 + 8 = 16, then 16 + 1 = 17
  • 8 + 9: Use 8 + 8 = 16, then 16 + 1 = 17
  • 7 + 8: Use 7 + 7 = 14, then 14 + 1 = 15
Quick Tips:
  • Near doubles are one number apart
  • Use the smaller number for the doubles fact
  • Add 1 more than the doubles result
Frequently Asked Questions:

Q: What are advanced near doubles?
A: Addition problems with larger consecutive numbers like 9+8 or 7+6.

Q: How do I solve advanced near doubles?
A: Use the doubles fact for the smaller number and add 1.

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

Doubles Facts: Addition problems where the same number is added to itself (e.g., 5 + 5 = 10). These are foundational for mental math and help with other addition strategies.

Near Doubles: Addition problems where the numbers are consecutive (differ by 1) (e.g., 5 + 6 = 11). This includes both doubles plus 1 and doubles minus 1.

Doubles Plus 1: Addition problems where one number is exactly 1 more than the other (e.g., 5 + 6 = 11). This is solved by using the smaller number's doubles fact and adding 1.

Doubles Minus 1: Addition problems where one number is exactly 1 less than the other (e.g., 6 + 5 = 11). This is solved by using the larger number's doubles fact and subtracting 1.

Fact Families: Groups of related addition and subtraction facts that use the same numbers, including doubles relationships.

Core Rules and Principles:
  1. Doubles Rule: When you double a number, the result is always even and equals the number × 2.
  2. Doubles Plus 1 Rule: Use the smaller number's doubles fact and add 1 more to the result.
  3. Doubles Minus 1 Rule: Use the larger number's doubles fact and subtract 1 from the result.
  4. Sequential Addition: When adding three or more numbers, look for doubles first to simplify the problem.
  5. Pattern Recognition: Doubles and near doubles follow predictable patterns that aid in memorization.
Effective Strategies:
  • Doubles Strategy: Memorize doubles facts for quick recall
  • Doubles Plus 1: Use smaller number's doubles fact and add 1
  • Doubles Minus 1: Use larger number's doubles fact and subtract 1
  • Pattern Recognition: Look for consecutive or repeated numbers
Common Mistakes to Avoid:
  • Confusing doubles with other addition facts
  • Forgetting that doubles always result in even numbers
  • Not recognizing near doubles opportunities
  • Mixing up when to add versus subtract
  • Choosing the wrong number for the doubles fact
Memory Techniques:
  • Practice doubles facts daily until automatic
  • Use visual aids like dot patterns or counters
  • Create rhymes or songs for difficult facts
  • Connect doubles to real-world situations
Checking Your Work:
  • Verify doubles by counting or using objects
  • Use inverse operations to check answers
  • Estimate to ensure answers are reasonable
  • Look for patterns to confirm accuracy
Progressive Examples:
  • Basic Doubles: 2 + 2 = 4, 3 + 3 = 6, 4 + 4 = 8
  • Doubles Plus 1: 3 + 4 = 7, 5 + 6 = 11, 7 + 8 = 15
  • Doubles Minus 1: 4 + 3 = 7, 6 + 5 = 11, 8 + 7 = 15
  • Near Doubles: 4 + 5 = 9, 7 + 6 = 13, 9 + 8 = 17

Key Takeaways for Memorization

  • Doubles facts are foundational for all addition strategies
  • Doubles always result in even numbers
  • Doubles Plus 1 uses the smaller number's doubles fact plus 1
  • Doubles Minus 1 uses the larger number's doubles fact minus 1
  • Near doubles always result in odd numbers
  • Recognizing patterns speeds up computation
  • Practice leads to automaticity with doubles facts
  • Understanding relationships helps with problem-solving
Key Laws, Methods, Rules, and Definitions
n + n = 2n (doubles), n + (n+1) = 2n+1 (near doubles)
Doubles and Near Doubles Structure
Key definitions:

Doubles: Addition of the same number to itself (n + n)

Near Doubles: Addition of consecutive numbers where the second is 1 more (n + (n+1))

Doubles Minus 1: Addition of consecutive numbers where the first is 1 more ((n+1) + n)

Complete methodology:
  1. Identify the pattern: Recognize doubles, doubles plus 1, or doubles minus 1
  2. Select the strategy: Use appropriate doubles-based method
  3. Apply the method: Execute the chosen strategy systematically
  4. Verify the result: Check by counting or using inverse operations
Tip 1: Memorize doubles facts (1+1 through 10+10) for quick recall.
Tip 2: Use doubles facts to solve near doubles quickly.
Tip 3: Doubles always result in even numbers.
Tip 4: Use the smaller number for doubles plus 1, larger number for doubles minus 1.
Common errors: Confusing doubles with other facts, mixing up plus/minus strategies.
Fluency building: Daily practice, flashcards, math games.
Rules to remember:

• Doubles facts are foundational for mental math fluency

• Doubles Plus 1 uses smaller number's doubles fact plus 1

• Doubles Minus 1 uses larger number's doubles fact minus 1

• Doubles always result in even numbers

• Near doubles always result in odd numbers

• Pattern recognition improves computational speed

• Verification ensures accuracy

Rules and Methods for Doubles and Near Doubles
n + n = 2n, n + (n+1) = 2n+1, (n+1) + n = 2n+1
Core Formulas
Formula 1
Doubles
n + n = 2n
Formula 2
Doubles Plus 1
n + (n+1) = 2n+1
Formula 3
Doubles Minus 1
(n+1) + n = 2n+1

Key Takeaways

  • Doubles facts form the foundation for other addition strategies
  • Doubles Plus 1 uses the smaller number's doubles fact plus 1
  • Doubles Minus 1 uses the larger number's doubles fact minus 1
  • Near doubles always result in odd numbers
  • Recognizing patterns accelerates problem-solving
  • Practice leads to automaticity with basic facts

Questions & Answers

Question: Why are doubles and near doubles facts so important in math?

Answer: Doubles and near doubles facts are extremely important because they:

  • Build a strong foundation for mental math
  • Help with solving other addition problems efficiently
  • Lead to faster computation and greater accuracy
  • Develop number sense and pattern recognition
  • Prepare students for multiplication concepts

Once you know your doubles facts automatically, you can use them to solve many other addition problems quickly. For example, if you know 7 + 7 = 14, you can easily figure out 7 + 8 = 15.

Question: My child struggles with near doubles. How can I help them master these facts?

Answer: Here are effective strategies to help with near doubles:

  • Build on doubles: Make sure your child knows doubles facts well first
  • Use visual aids: Show with objects that 7 + 8 is the same as 7 + 7 + 1
  • Practice sequentially: Start with smaller numbers (3+4) before larger ones (8+9)
  • Make connections: Explain that near doubles are just doubles plus or minus 1
  • Play games: Use dice or cards to generate near doubles problems

Regular practice with concrete examples will help your child see the relationship and develop fluency with near doubles facts.

Question: How can I remember all these doubles and near doubles facts?

Answer: Here are memory techniques for doubles and near doubles:

  • Practice regularly: Do a few minutes each day
  • Use rhythm and rhyme: "6 + 6 is 12, that's a fact divine!"
  • Visualize: Picture two equal groups
  • Connect to real life: Eggs come in doubles (6+6=12), wheels on cars (2+2=4)
  • Use flashcards: Practice until automatic

Remember, doubles always result in even numbers, and near doubles always result in odd numbers. The more you practice, the easier they become!

Math Glossary

Doubles Facts
Addition problems where the same number is added to itself (e.g., 5 + 5 = 10).
Doubles Plus 1
Addition problems where one number is exactly 1 more than the other (e.g., 5 + 6).
Doubles Minus 1
Addition problems where one number is exactly 1 less than the other (e.g., 6 + 5).
Near Doubles
Addition problems with consecutive numbers (e.g., 5 + 6).
Fact Family
A group of related addition and subtraction facts using the same numbers.
Pattern Recognition
Identifying consistent relationships between numbers in mathematical operations.

Elementary Math Educational Team

Certified Elementary Teachers & Curriculum Specialists

Our team of experienced elementary math teachers and curriculum developers creates research-based, student-friendly doubles and near doubles resources. All content is aligned with Common Core State Standards for Mathematics and reviewed by mathematics education experts to ensure accuracy and pedagogical effectiveness for Grade 2 learners.