Solved Exercises on Doubles and Near Doubles in Grade 1

Master doubles and near doubles math: definitions, methods, and practical applications through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Basic Doubles
Exercise 1
Find the sum: 4 + 4
Definition:

Doubles: Adding the same number twice (e.g., 2+2, 3+3, 4+4)

Method:
  1. Identify if both numbers are the same (doubles pattern)
  2. Count up by the number being doubled
  3. Or multiply the number by 2
4
+
4
Expression
4 + 4
Doubles Pattern
2 × 4
Result
8
Step 1: Recognize the doubles pattern

Both numbers are the same: 4 and 4, so this is a doubles fact

Step 2: Apply the doubles rule

Doubles of 4 means 4 + 4, which equals 2 groups of 4

Step 3: Count or calculate

4 + 4 = 8, or 2 × 4 = 8

Doubles Fact Family:
4 + 4 = 8
8 - 4 = 4
Memory Trick:

Think of "double trouble" - you're adding the same number twice!

4 + 4 = 8
Final answer:

4 + 4 = 8

Applied rules:

• Doubles Rule: Same number added to itself

• Pattern Recognition: Look for identical addends

• Multiplication Connection: Doubles equal 2 times the number

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1
2
3
4
5
6
7
8
2 Near Doubles
Exercise 2
Find the sum: 5 + 6
Definition:

Near Doubles: Adding consecutive numbers (e.g., 4+5, 5+6, 7+8)

5
+
6
Expression
5 + 6
Near Doubles
5 + (5+1)
Result
11
Step 1: Recognize the near doubles pattern

Numbers are consecutive: 5 and 6 differ by 1

Step 2: Use the doubles fact

Think of the doubles fact: 5 + 5 = 10

Step 3: Add one more

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

Near Doubles Strategy:
5 + 6 = 5 + 5 + 1 = 10 + 1 = 11
6 + 5 = 6 + 6 - 1 = 12 - 1 = 11
Memory Trick:

"One apart" - find the doubles and adjust by 1!

5 + 6 = 11
Final answer:

5 + 6 = 11

Applied rules:

• Near Doubles Rule: Use known doubles and adjust by 1

• Consecutive Numbers: Differ by 1

• Strategy: Double the smaller number and add 1

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1
2
3
4
5
6
7
8
9
10
11
3 Mixed Doubles Practice
Exercise 3
Find the sum: 7 + 7
Definition:

Doubles Facts: Essential addition facts to memorize (0+0 to 10+10)

7
+
7
Expression
7 + 7
Doubles Pattern
2 × 7
Result
14
Step 1: Identify the doubles pattern

Both addends are 7, so this is a doubles fact

Step 2: Apply the doubles strategy

Count up by 7: 7, then 7 more gives 14

Step 3: Verify with multiplication

7 + 7 = 2 × 7 = 14

Step 4: Check with counting

Start at 7 and count 7 more: 8, 9, 10, 11, 12, 13, 14

Doubles Fact Family:
7 + 7 = 14
14 - 7 = 7
14 ÷ 2 = 7
Memory Trick:

Think of "lucky seven" doubled - 7 days in a week × 2 = 14 days!

7 + 7 = 14
Final answer:

7 + 7 = 14

Applied rules:

• Doubles Rule: Same number added to itself

• Memorization: Essential facts for quick recall

• Multiplication Connection: Doubles equal 2 times the number

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2
3
4
5
6
7
8
9
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12
13
14
Doubles and Near Doubles Rules and Methods
n + n = 2n
Doubles Formula
Basic Doubles
n + n
Same number twice
Near Doubles
n + (n+1)
Consecutive numbers
Strategy
(n+n)+1
Add 1 to doubles
Key Definitions:

Doubles: Addition facts where both addends are the same number (e.g., 3+3, 8+8)

Near Doubles: Addition facts where addends differ by 1 (e.g., 4+5, 7+8)

Consecutive Numbers: Numbers that follow each other in order (e.g., 5 and 6)

Complete Methodology:
  1. Recognize the pattern: Identify if it's a doubles or near doubles fact
  2. Apply the strategy: Use doubles facts as a foundation
  3. Calculate the result: Use known facts or counting strategies
  4. Verify the answer: Check by counting or using another strategy
Doubles
1+1=2
2+2=4
3+3=6
4+4=8
Near Doubles
1+2=3
2+3=5
3+4=7
4+5=9
More Examples
5+5=10
6+6=12
7+7=14
8+8=16
Tip 1: Memorize doubles facts (0+0 to 10+10) for quick recall.
Tip 2: For near doubles, find the doubles fact and add or subtract 1.
Tip 3: Use fingers, counters, or drawings to visualize the numbers.
Tip 4: Practice with number lines to see the relationships between numbers.
Common Errors: Forgetting that doubles mean the same number twice, confusing near doubles with other addition facts.
Memory Strategies: Use songs, rhymes, or games to remember doubles facts.
Key Formulas to Remember:

• Doubles: n + n = 2n

• Near Doubles: n + (n+1) = (n+n) + 1

• Near Doubles Alternative: (n-1) + n = (n+n) - 1

Solution: Exercises 4 to 5
4 Advanced Near Doubles
Exercise 4
Find the sum: 8 + 9
Definition:

Near Doubles Strategy: Use doubles facts to solve problems with consecutive numbers

8
+
9
Expression
8 + 9
Near Doubles
8 + (8+1)
Result
17
Step 1: Recognize the near doubles pattern

8 and 9 are consecutive numbers (differ by 1)

Step 2: Use the larger doubles fact

Think of 9 + 9 = 18

Step 3: Subtract one since 8 is one less than 9

18 - 1 = 17

Alternative: Use the smaller doubles fact

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

Near Doubles Strategies:
Method 1: 8 + 9 = 8 + 8 + 1 = 16 + 1 = 17
Method 2: 8 + 9 = 9 + 9 - 1 = 18 - 1 = 17
Memory Trick:

"Eight and nine, just add one more to eight-eight!"

8 + 9 = 17
Final answer:

8 + 9 = 17

Applied rules:

• Near Doubles Rule: Use known doubles and adjust by 1

• Flexibility: Choose the easier doubles fact to work with

• Verification: Both methods should yield the same result

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7
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17
5 Problem Solving with Doubles
Exercise 5
Sarah has 6 apples and her brother gives her 7 more. How many apples does Sarah have now?
Definition:

Word Problems: Real-life scenarios requiring mathematical operations

Sarah's apples: 6
+
Brother's apples: 7
Problem
6 + 7
Near Doubles
6 + (6+1)
Result
13
Step 1: Identify the operation

Sarah starts with 6 apples and gets 7 more, so we add: 6 + 7

Step 2: Recognize the near doubles pattern

6 and 7 are consecutive numbers (differ by 1)

Step 3: Apply the near doubles strategy

Think of 6 + 6 = 12, then add 1 more: 12 + 1 = 13

Step 4: Verify the answer

Alternative method: 7 + 7 = 14, then subtract 1: 14 - 1 = 13 ✓

Problem Context:
Initial amount: 6 apples
Added amount: 7 apples
Total: 13 apples
Memory Trick:

"Six and seven went up to heaven, 13 angels is what they gave!"

6 + 7 = 13 apples
Final answer:

Sarah has 13 apples altogether.

Applied rules:

• Problem Solving: Translate words into mathematical expressions

• Near Doubles Strategy: Use doubles facts to solve consecutive number addition

• Verification: Check answer using alternative methods

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7
8
9
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12
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Complete Guide: Doubles and Near Doubles Fundamentals
n + n = 2n
Doubles Formula
Key definitions:

Doubles: Addition facts where both addends are identical (e.g., 2+2, 5+5, 9+9)

Near Doubles: Addition facts where addends are consecutive numbers (e.g., 3+4, 6+7, 8+9)

Consecutive Numbers: Numbers that follow each other in sequence (differ by 1)

Complete methodology:
  1. Pattern Recognition: Identify if the problem involves doubles or near doubles
  2. Strategy Selection: Choose the most efficient method (doubles + 1, or doubles - 1)
  3. Calculation: Apply the chosen strategy using known doubles facts
  4. Verification: Check the answer using counting or alternative methods
Basic Doubles
0+0=0
1+1=2
2+2=4
3+3=6
4+4=8
5+5=10
Higher Doubles
6+6=12
7+7=14
8+8=16
9+9=18
10+10=20
Near Doubles
0+1=1
1+2=3
2+3=5
3+4=7
4+5=9
5+6=11
Tip 1: Memorize all doubles facts from 0+0 to 10+10 for quick recall.
Tip 2: For near doubles, find the middle number and double it, then adjust.
Tip 3: Use visual aids like counters, dots, or fingers to see the patterns.
Tip 4: Practice skip counting by 2s to reinforce doubles patterns.
Common errors: Mixing up doubles and near doubles, forgetting to adjust by 1 in near doubles.
Success strategies: Regular practice, using visual representations, connecting to real-world examples.
Essential formulas and patterns:

• Doubles pattern: n + n = 2n

• Near doubles (larger number): n + (n+1) = (n+n) + 1

• Near doubles (smaller number): (n-1) + n = (n+n) - 1

• Commutative property: Order doesn't matter (3+4 = 4+3)

Memory Tricks for Success:
  • Doubles Rhyme: "Double the number, double the fun!"
  • Near Doubles: "One apart, start with doubles and add or subtract!"
  • Visual Pattern: Draw dots in pairs to see doubles naturally

Questions & Answers

Question: My child is struggling with near doubles. They understand 5+5=10, but get confused when it comes to 5+6. How can I help them see the connection?

Answer: Great question! The key is to make the connection visible:

  • Use manipulatives: Have your child place 5 blocks in one group and 5 in another (showing 5+5=10). Then add 1 more block to one group to show 5+6, counting the total to see it's 11.
  • Verbalize the strategy: "We know 5+5=10, so 5+6 is just one more, which makes 11."
  • Number line approach: Start at 5, jump 5 more to reach 10, then jump 1 more to reach 11.

Practice with concrete objects first, then gradually move to mental math. The connection between doubles and near doubles builds strong foundational skills!

Question: I want to learn all the doubles facts quickly. Are there any tricks to remember them?

Answer: Yes! Here are some helpful tricks for memorizing doubles:

  • Rhyming: "2+2=4, let's do some more!" "6+6=12, that's divine!"
  • Visual patterns: Think of eyes (2+2), hands (5+5), spider legs (4+4), etc.
  • Body connections: 2 eyes + 2 ears = 4 senses, 5 fingers on left + 5 fingers on right = 10 fingers total
  • Practice in order: Start with smaller numbers and build up: 0+0, 1+1, 2+2, etc.

Songs and games also make memorization fun! Once you know the doubles, near doubles become much easier too!

Question: Should I teach doubles and near doubles together or separately? What's the best sequence for introducing these concepts?

Answer: The sequence matters for building conceptual understanding:

  1. Start with doubles: Focus on recognizing and practicing doubles facts (0+0 to 10+10) until students are comfortable
  2. Introduce the connection: Show how near doubles relate to doubles facts
  3. Teach near doubles: Use doubles as a foundation, emphasizing the "+1" or "-1" adjustment
  4. Combine practice: Mix both types to strengthen the relationship between them

This sequence builds confidence with doubles first, then uses that knowledge as a bridge to tackle near doubles. Students see doubles as a helpful tool rather than a separate concept.