Triple and Doubles Practice Test - Grade 2 Mathematics - Exercises with solutions

Master triple and doubles facts: doubles facts, near doubles, and triple addition facts 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 Near doubles
Exercise 2
What is 5 + 6?
Difficulty: Beginner Time: ~1 minute Skills: Near Doubles Strategy
Definition:

Near doubles: Addition problems where the numbers are consecutive (differ by 1)

Note: Near doubles can be solved using known doubles facts plus or minus 1.

Step-by-step near doubles method:
  1. Recognize that 5 and 6 are consecutive numbers
  2. Use the closest doubles fact: 5 + 5 = 10
  3. Add 1 more since 6 is 1 more than 5
Original Problem
5 + 6
Near Doubles Strategy
5 + 5 + 1
Solution
11
Step 1: Identify the pattern

5 and 6 are consecutive numbers (differ by 1)

Step 2: Use doubles fact

We know 5 + 5 = 10

Step 3: Add the difference

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:

• Near doubles: Consecutive numbers can use doubles strategy

• Strategy: Use closest doubles fact and adjust

• Memory tip: Near doubles are doubles ± 1

Related Examples:
  • 4 + 5: Use 4 + 4 = 8, then 8 + 1 = 9
  • 6 + 7: Use 6 + 6 = 12, then 12 + 1 = 13
  • 3 + 4: Use 3 + 3 = 6, then 6 + 1 = 7
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 near doubles?
A: Addition problems with consecutive numbers like 4+5 or 7+8.

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

3 Doubles plus one
Exercise 3
What is 4 + 5?
Difficulty: Beginner Time: ~1 minute Skills: Doubles Plus One Strategy
Definition:

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

Note: This is a specific type of near doubles where one number is exactly 1 more than the other.

Step-by-step doubles plus one method:
  1. Recognize that 5 is 1 more than 4
  2. Use the doubles fact: 4 + 4 = 8
  3. Add 1 more: 8 + 1 = 9
Original Problem
4 + 5
Doubles Plus One
4 + 4 + 1
Solution
9
Step 1: Identify the relationship

5 is exactly 1 more than 4

Step 2: Use doubles fact

We know 4 + 4 = 8

Step 3: Add the extra one

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

4 + 5 = 9
Final answer:

4 + 5 = 9

Applied rules:

• Doubles plus one: 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:
  • 3 + 4: Use 3 + 3 = 6, then 6 + 1 = 7
  • 6 + 7: Use 6 + 6 = 12, then 12 + 1 = 13
  • 2 + 3: Use 2 + 2 = 4, then 4 + 1 = 5
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 one?
A: Addition problems where one number is 1 more than the other, like 4+5 or 7+8.

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

Solutions: Exercises 4 to 5
4 Doubles plus two
Exercise 4
What is 4 + 6?
Definition:

Doubles plus two: Addition problems where one number is 2 more than the other

Note: This strategy uses the doubles fact and adds 2 more to the result.

Step-by-step doubles plus two method:
  1. Recognize that 6 is 2 more than 4
  2. Use the doubles fact: 4 + 4 = 8
  3. Add 2 more: 8 + 2 = 10
Original Problem
4 + 6
Doubles Plus Two
4 + 4 + 2
Solution
10
Step 1: Identify the relationship

6 is exactly 2 more than 4

Step 2: Use doubles fact

We know 4 + 4 = 8

Step 3: Add the extra two

Since 6 is 2 more than 4, add 2 to the doubles result: 8 + 2 = 10

4 + 6 = 10
Final answer:

4 + 6 = 10

Applied rules:

• Doubles plus two: One number is exactly 2 more than the other

• Strategy: Use doubles fact and add 2

• Memory tip: This builds on doubles knowledge

Related Examples:
  • 3 + 5: Use 3 + 3 = 6, then 6 + 2 = 8
  • 5 + 7: Use 5 + 5 = 10, then 10 + 2 = 12
  • 2 + 4: Use 2 + 2 = 4, then 4 + 2 = 6
Quick Tips:
  • Look for numbers that are 2 apart
  • Always use the smaller number for the doubles fact
  • Add 2 to the doubles result
Frequently Asked Questions:

Q: What is doubles plus two?
A: Addition problems where one number is 2 more than the other, like 4+6 or 5+7.

Q: How do I solve doubles plus two?
A: Use the doubles fact for the smaller number and add 2.

5 Triple addition
Exercise 5
What is 3 + 3 + 3?
Definition:

Triple addition: Adding the same number three times

Note: This builds on doubles knowledge and prepares for multiplication.

Step-by-step triple addition method:
  1. Recognize that we're adding 3 three times
  2. Group the addition: (3 + 3) + 3
  3. Solve the doubles first: 3 + 3 = 6
  4. Add the third number: 6 + 3 = 9
Original Problem
3 + 3 + 3
Grouping
(3 + 3) + 3
Solution
9
Step 1: Recognize the pattern

We're adding 3 three times

Step 2: Group for efficiency

First, add two of the threes: 3 + 3 = 6

Step 3: Add the third number

Add the result to the third 3: 6 + 3 = 9

Step 4: Alternative method

3 + 3 + 3 = 3 × 3 = 9

3 + 3 + 3 = 9
Final answer:

3 + 3 + 3 = 9

Applied rules:

• Triple addition: Adding the same number three times

• Strategy: Group into doubles first, then add the third

• Connection: This relates to multiplication (3 × 3 = 9)

• Memory tip: Practice triples as doubles plus the number again

Related Examples:
  • 2 + 2 + 2: Use 2 + 2 = 4, then 4 + 2 = 6
  • 4 + 4 + 4: Use 4 + 4 = 8, then 8 + 4 = 12
  • 5 + 5 + 5: Use 5 + 5 = 10, then 10 + 5 = 15
Quick Tips:
  • First add two of the numbers using doubles
  • Then add the third number to the doubles result
  • This connects to multiplication concepts
Frequently Asked Questions:

Q: What is triple addition?
A: Adding the same number three times, like 3+3+3 or 4+4+4.

Q: How do I solve triple addition?
A: Add two of the numbers first using doubles, then add the third.

Solutions: Exercises 6 to 10
6 Missing doubles
Exercise 6
What number added to itself equals 14?
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: ? + ? = 14, or ? × 2 = 14
  2. Find half of 14
  3. 14 ÷ 2 = 7
  4. Check: 7 + 7 = 14
Original Problem
? + ? = 14
Half of Total
14 ÷ 2 = 7
Solution
7
Step 1: Understand the problem

We need a number that when added to itself equals 14

Step 2: Use division

To find the number, divide 14 by 2: 14 ÷ 2 = 7

Step 3: Verify

Check: 7 + 7 = 14 ✓

7 + 7 = 14
Final answer:

The number is 7

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:
  • ? + ? = 10 → 10 ÷ 2 = 5 → 5 + 5 = 10
  • ? + ? = 16 → 16 ÷ 2 = 8 → 8 + 8 = 16
  • ? + ? = 12 → 12 ÷ 2 = 6 → 6 + 6 = 12
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).

7 Word problem
Exercise 7
Sarah has 6 red marbles. Her brother gives her 7 blue marbles. How many marbles does Sarah have now?
Definition:

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

Note: This problem requires adding 6 + 7, which is a near doubles fact.

Step-by-step word problem method:
  1. Identify the numbers: 6 red marbles + 7 blue marbles
  2. Recognize this is a near doubles problem (6 and 7 are consecutive)
  3. Use doubles strategy: 6 + 6 = 12, then add 1 more
  4. 12 + 1 = 13
Red Marbles
6
Blue Marbles
7
Total Marbles
13
Step 1: Identify what we know

Sarah has 6 red marbles and gets 7 blue marbles

Step 2: Set up the addition

6 + 7 = ?

Step 3: Use near doubles strategy

6 + 7 is the same as 6 + 6 + 1 = 12 + 1 = 13

Step 4: Answer the question

Sarah has 13 marbles now

Sarah has 13 marbles now
Final answer:

Sarah has 13 marbles now

Applied rules:

• Problem solving: Identify key information

• Near doubles: 6 and 7 are consecutive numbers

• Strategy: Use 6 + 6 = 12, then add 1 more

• Contextual answer: Include units in your answer

Related Examples:
  • 4 + 5: Use 4 + 4 = 8, then 8 + 1 = 9
  • 8 + 9: Use 8 + 8 = 16, then 16 + 1 = 17
  • 3 + 4: Use 3 + 3 = 6, then 6 + 1 = 7
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 doubles?
A: Look for consecutive numbers like 6 and 7, 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 Fact families
Exercise 8
If 8 + 8 = 16, what is 16 - 8?
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: 8 + 8 = 16
  2. Recognize the inverse relationship: 16 - 8 = 8
  3. Verify: 8 + 8 = 16 ✓ and 16 - 8 = 8 ✓
Given Fact
8 + 8 = 16
Related Subtraction
16 - 8 = ?
Solution
8
Step 1: Use the given doubles fact

We know 8 + 8 = 16

Step 2: Apply inverse operation

If 8 + 8 = 16, then 16 - 8 = 8

Step 3: Verify

8 + 8 = 16 ✓ and 16 - 8 = 8 ✓

16 - 8 = 8
Final answer:

16 - 8 = 8

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 5 + 5 = 10, then 10 - 5 = 5
  • If 7 + 7 = 14, then 14 - 7 = 7
  • If 6 + 6 = 12, then 12 - 6 = 6
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 8 + 8 = 16 helps you know 16 - 8 = 8.

9 Patterns
Exercise 9
What pattern do you notice in these problems: 1 + 1 = 2, 2 + 2 = 4, 3 + 3 = 6?
Definition:

Doubles pattern: A consistent relationship in doubles facts

Note: Doubles always result in even numbers and follow a predictable pattern.

Step-by-step pattern recognition method:
  1. Look at the first numbers: 1, 2, 3 (increasing by 1)
  2. Look at the answers: 2, 4, 6 (even numbers increasing by 2)
  3. Notice: doubles always result in even numbers
  4. Pattern: number doubled = number × 2
Pattern Sequence
1+1=2, 2+2=4, 3+3=6
Pattern Rule
Doubles equal number × 2
Next in Pattern
4+4=8
Step 1: Analyze the inputs

The numbers being doubled: 1, 2, 3 (each increases by 1)

Step 2: Analyze the outputs

The results: 2, 4, 6 (each increases by 2, all even)

Step 3: Identify the pattern

Doubling any number equals that number times 2

Step 4: Predict next

Following the pattern: 4 + 4 = 8

Doubles always result in even numbers and equal the number × 2
Final answer:

When you double a number, you get an even number that equals the original number times 2.

Applied rules:

• Pattern recognition: Doubles always produce even numbers

• Mathematical relationship: Doubling equals multiplying by 2

• Generalization: n + n = 2n for any number n

Related Examples:
  • 4 + 4 = 8, 5 + 5 = 10, 6 + 6 = 12 (pattern continues)
  • All results are even numbers
  • Each result is double the input number
Quick Tips:
  • Doubles always result in even numbers
  • Doubling is the same as multiplying by 2
  • Recognizing patterns helps with memorization
Frequently Asked Questions:

Q: Why do doubles always result in even numbers?
A: Because you're adding the same number twice, which is the same as multiplying by 2.

Q: What's the pattern in doubles?
A: Any number doubled equals that number times 2.

10 Mixed practice
Exercise 10
Solve: 5 + 5 + 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: 5 + 5 = 10
  2. Add the remaining number: 10 + 1 = 11
Original Problem
5 + 5 + 1
Doubles Part
5 + 5 = 10
Add Remaining
10 + 1 = 11
Final Answer
11
Step 1: Identify the doubles

First, add 5 + 5 = 10

Step 2: Add the remaining number

Now add the 1: 10 + 1 = 11

Step 3: Final answer

5 + 5 + 1 = 11

5 + 5 + 1 = 11
Final answer:

11

Applied rules:

• Sequential solving: Solve part of the problem first

• Doubles strategy: Use known doubles facts

• Flexibility: Combine multiple strategies as needed

Related Examples:
  • 4 + 4 + 2: First 4 + 4 = 8, then 8 + 2 = 10
  • 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.

Detailed Summary: Triple and Doubles Practice Test
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 or differ by 1 (e.g., 5 + 6 = 11). These can be solved using doubles facts plus or minus 1.

Doubles Plus One: A specific type of near doubles where one number is exactly 1 more than the other (e.g., 4 + 5 = 9).

Doubles Plus Two: Addition problems where one number is exactly 2 more than the other (e.g., 4 + 6 = 10).

Triple Addition: Adding the same number three times (e.g., 3 + 3 + 3 = 9). This builds on doubles knowledge and prepares for multiplication.

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. Near Doubles Rule: Use the closest doubles fact and adjust by adding or subtracting the difference.
  3. Sequential Addition: When adding three or more numbers, look for doubles first to simplify the problem.
  4. Commutative Property: Order doesn't matter in addition (4 + 5 = 5 + 4).
  5. Pattern Recognition: Doubles follow predictable patterns that aid in memorization.
Effective Strategies:
  • Doubles Strategy: Memorize doubles facts for quick recall
  • Near Doubles: Use doubles facts and adjust by the difference
  • Grouping: When adding multiple numbers, group into doubles first
  • Visualization: Use objects or drawings to represent doubles
Common Mistakes to Avoid:
  • Confusing doubles with other addition facts
  • Forgetting that doubles always result in even numbers
  • Not recognizing near doubles opportunities
  • Miscalculating when adding three or more numbers
  • Mixing up the order of operations in multi-step problems
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
  • Near Doubles: 3 + 4 = 7, 5 + 6 = 11, 7 + 8 = 15
  • Doubles Plus Two: 3 + 5 = 8, 4 + 6 = 10, 5 + 7 = 12
  • Triple Addition: 2 + 2 + 2 = 6, 3 + 3 + 3 = 9, 4 + 4 + 4 = 12

Key Takeaways for Memorization

  • Doubles facts are foundational for all addition strategies
  • Doubles always result in even numbers
  • Near doubles can be solved using doubles plus or minus the difference
  • Triple addition builds on doubles knowledge
  • 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 (n + (n+1))

Triples: Addition of the same number three times (n + n + n)

Complete methodology:
  1. Identify the pattern: Recognize doubles, near doubles, or triples
  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: Group numbers strategically when adding multiple values.
Common errors: Confusing doubles with other facts, miscalculating differences.
Fluency building: Daily practice, flashcards, math games.
Rules to remember:

• Doubles facts are foundational for mental math fluency

• Near doubles can be solved using doubles plus/minus the difference

• Doubles always result in even numbers

• Triple addition builds on doubles knowledge

• Pattern recognition improves computational speed

• Verification ensures accuracy

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

Key Takeaways

  • Doubles facts form the foundation for other addition strategies
  • Near doubles use doubles facts with small adjustments
  • Recognizing patterns accelerates problem-solving
  • Triple addition connects to multiplication concepts
  • Practice leads to automaticity with basic facts

Questions & Answers

Question: Why are doubles facts so important in math?

Answer: Doubles facts are extremely important because they:

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

Once you know your doubles facts automatically, you can use them to solve many other addition problems quickly. For example, if you know 6 + 6 = 12, you can easily figure out 6 + 7 = 13.

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 5 + 6 is the same as 5 + 5 + 1
  • Practice sequentially: Start with smaller numbers (4+5) before larger ones (8+9)
  • Make connections: Explain that near doubles are just doubles plus 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.

Question: How can I remember all these doubles facts?

Answer: Here are memory techniques for doubles facts:

  • 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, which is a helpful clue. 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).
Near Doubles
Addition problems with consecutive numbers (e.g., 5 + 6 = 11).
Doubles Plus One
A near double where one number is exactly 1 more than the other (e.g., 4 + 5).
Doubles Plus Two
Addition where one number is exactly 2 more than the other (e.g., 4 + 6).
Triple Addition
Adding the same number three times (e.g., 3 + 3 + 3 = 9).
Fact Family
A group of related addition and subtraction facts using the same numbers.

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.