Doubles and Near Doubles Addition Concepts for Grade 1

Master doubles and near doubles: learn the foundational addition strategies, visual representations, and memory techniques through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Basic Doubles
Exercise 1
Solve: 4 + 4 = ?
Visual: 🟢🟢🟢🟢 + 🟢🟢🟢🟢
Definition:

Doubles: Addition facts where both numbers are the same (e.g., 3+3, 5+5, 8+8)

Doubles Method:
  1. Identify that both addends are the same number
  2. Count the total by doubling the number
  3. Remember doubles facts as they are building blocks for near doubles
Problem
4 + 4
Doubles Rule
4 × 2 = 8
Step 1: Recognize the doubles pattern

Both numbers are 4, so this is a doubles fact: 4 + 4

Step 2: Apply the doubles rule

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

Step 3: Count to verify

Count: 4, 5, 6, 7, 8 (adding 4 more starting from 4)

4 + 4 = 8
Final answer:

4 + 4 = 8

Applied rules:

• Doubles Rule: n + n = 2n (multiply by 2)

• Pattern Recognition: Identifying when both addends are equal

• Memorization: Doubles facts are foundational for near doubles

2 Near Doubles Strategy
Exercise 2
Solve: 5 + 6 = ?
Visual: 🔵🔵🔵🔵🔵 + 🔵🔵🔵🔵🔵🔵
Definition:

Near Doubles: Addition facts where one number is one more than the other (e.g., 4+5, 7+8, 9+10)

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

5 and 6 are consecutive numbers (one apart), so this is a near doubles fact

Step 2: Use the doubles relationship

Think of 5 + 5 = 10, then add 1 more: 10 + 1 = 11

Step 3: Alternative counting method

Start at 5 and count 6 more: 5, 6, 7, 8, 9, 10, 11

5 + 6 = 11
Final answer:

5 + 6 = 11

Applied rules:

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

• Pattern Recognition: Numbers differ by 1

• Building on Known Facts: Leverage memorized doubles

3 Mixed Doubles Practice
Exercise 3
Solve: 7 + 7 = ?
Visual: 🔴🔴🔴🔴🔴🔴🔴 + 🔴🔴🔴🔴🔴🔴🔴
Definition:

Doubles Facts: Essential addition facts: 1+1=2, 2+2=4, 3+3=6, 4+4=8, 5+5=10, 6+6=12, 7+7=14, 8+8=16, 9+9=18, 10+10=20

Problem
7 + 7
Doubles Rule
7 × 2 = 14
Result
14
Step 1: Identify the doubles pattern

Both numbers are 7, so this is a doubles fact: 7 + 7

Step 2: Apply the multiplication shortcut

Adding the same number twice equals that number times 2: 7 × 2 = 14

Step 3: Count to verify

Count: 7, 8, 9, 10, 11, 12, 13, 14 (adding 7 more starting from 7)

Step 4: Connect to visual representation

Seven dots plus seven more dots equals fourteen dots total

7 + 7 = 14
Final answer:

7 + 7 = 14

Applied rules:

• Doubles Multiplication: n + n = 2n

• Visual Counting: Representing abstract numbers concretely

• Memorization Strategy: Remembering key doubles facts

Doubles and Near Doubles: Core Concepts
n + n = 2n
Doubles Formula
Basic Doubles
n + n
n + n = 2n
Near Doubles
n + (n+1)
n + (n+1) = 2n + 1
Near Doubles
(n+1) + n
(n+1) + n = 2n + 1
Key definitions:

Doubles: Addition of identical numbers (e.g., 3+3, 8+8)

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

Strategy: Use known doubles to solve near doubles efficiently

Complete methodology:
  1. Identify the pattern: Recognize doubles vs near doubles
  2. Apply the strategy: Use doubles facts for near doubles
  3. Calculate: Execute the addition
  4. Verify: Check your answer through counting or reverse operation
Tip 1: Memorize doubles facts 1+1 through 10+10 as building blocks.
Tip 2: For near doubles, find the smaller number and double it, then add 1.
Tip 3: Use fingers or counters to visualize the doubles and near doubles.
Tip 4: Practice skip counting by 2s to reinforce doubles concept.
Common errors: Confusing near doubles with regular addition, forgetting doubles facts, miscounting.
Memory aids: Songs, rhymes, visual patterns, and repeated practice.
Essential facts to memorize:

• 1+1=2, 2+2=4, 3+3=6, 4+4=8, 5+5=10

• 6+6=12, 7+7=14, 8+8=16, 9+9=18, 10+10=20

• Near doubles: 1+2=3, 2+3=5, 3+4=7, 4+5=9, 5+6=11

• 6+7=13, 7+8=15, 8+9=17, 9+10=19

Doubles & Near Doubles Infographic
📊
Doubles Patterns

All doubles results are even numbers

Results increase by 2 each time

Pattern: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20

Near Doubles Patterns

All near doubles results are odd numbers

Results increase by 2 each time

Pattern: 3, 5, 7, 9, 11, 13, 15, 17, 19

Doubles & Near Doubles Strategy Flow
1
Identify
2
Match
3
Calculate
4
Verify
Visual Pattern Recognition

Doubles: Equal groups side by side

Near Doubles: One group has one more item

Practice Makes Perfect! Master these patterns!
Solution: Exercises 4 to 5
4 Advanced Near Doubles
Exercise 4
Solve: 8 + 9 = ?
Visual: ⚪⚪⚪⚪⚪⚪⚪⚪ + ⚪⚪⚪⚪⚪⚪⚪⚪⚪
Definition:

Advanced Near Doubles: Using doubles facts for larger numbers (8+9 uses 8+8 as foundation)

Problem
8 + 9
Doubles Base
8 + 8 = 16
Add One More
16 + 1 = 17
Step 1: Recognize the near doubles pattern

8 and 9 are consecutive numbers (one apart), so this is a near doubles fact

Step 2: Recall the related doubles fact

8 + 8 = 16 (memorized doubles fact)

Step 3: Add the extra amount

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

Step 4: Verify through alternative method

Count 9 more starting from 8: 8, 9, 10, 11, 12, 13, 14, 15, 16, 17

8 + 9 = 17
Final answer:

8 + 9 = 17

Applied rules:

• Near Doubles Strategy: Use related doubles fact and adjust

• Building on Known Facts: Leverage memorized doubles for efficiency

• Addition Properties: Commutative and associative properties

5 Word Problem Application
Exercise 5
Sarah has 6 apples. Her brother gives her 7 more apples. How many apples does she have now?
Visual: 🍎🍎🍎🍎🍎🍎 + 🍎🍎🍎🍎🍎🍎🍎
Definition:

Word Problem Application: Real-world context for near doubles (6 and 7 are consecutive numbers)

Problem
6 + 7
Doubles Base
6 + 6 = 12
Add One More
12 + 1 = 13
Step 1: Translate the word problem

"Sarah has 6 apples and gets 7 more" means 6 + 7 = ?

Step 2: Recognize the near doubles pattern

6 and 7 are consecutive numbers (one apart), so this is a near doubles fact

Step 3: Apply the near doubles strategy

Use the doubles fact: 6 + 6 = 12, then add 1 more: 12 + 1 = 13

Step 4: Interpret the result in context

Sarah has 13 apples in total

Step 5: Verify the answer

Count: 6, 7, 8, 9, 10, 11, 12, 13 (adding 7 more starting from 6)

6 + 7 = 13 apples
Final answer:

Sarah has 13 apples in total.

Applied rules:

• Problem Translation: Convert words to mathematical expressions

• Near Doubles Strategy: Use related doubles fact and adjust

• Contextual Understanding: Relate math back to real-world scenario

Comprehensive Guide: Doubles and Near Doubles Mastery
n + n = 2n
Doubles Formula
Key definitions:

Doubles: Addition of identical numbers (e.g., 3+3, 8+8)

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

Strategy: Use known doubles to solve near doubles efficiently

Complete methodology:
  1. Identify the pattern: Recognize doubles vs near doubles
  2. Apply the strategy: Use doubles facts for near doubles
  3. Calculate: Execute the addition
  4. Verify: Check your answer through counting or reverse operation
Tip 1: Memorize doubles facts 1+1 through 10+10 as building blocks.
Tip 2: For near doubles, find the smaller number and double it, then add 1.
Tip 3: Use fingers or counters to visualize the doubles and near doubles.
Tip 4: Practice skip counting by 2s to reinforce doubles concept.
Common errors: Confusing near doubles with regular addition, forgetting doubles facts, miscounting.
Memory aids: Songs, rhymes, visual patterns, and repeated practice.
Essential facts to memorize:

• 1+1=2, 2+2=4, 3+3=6, 4+4=8, 5+5=10

• 6+6=12, 7+7=14, 8+8=16, 9+9=18, 10+10=20

• Near doubles: 1+2=3, 2+3=5, 3+4=7, 4+5=9, 5+6=11

• 6+7=13, 7+8=15, 8+9=17, 9+10=19

Doubles & Near Doubles Strategies
🎯
Doubles Patterns

All doubles results are even numbers

Results increase by 2 each time

Pattern: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20

Near Doubles Patterns

All near doubles results are odd numbers

Results increase by 2 each time

Pattern: 3, 5, 7, 9, 11, 13, 15, 17, 19

Doubles & Near Doubles Strategy Flow
1
Identify
2
Match
3
Calculate
4
Verify
Visual Pattern Recognition

Doubles: Equal groups side by side

Near Doubles: One group has one more item

Practice Makes Perfect! Master these patterns!

Questions & Answers

Question: My child is struggling with near doubles. Why is it important to learn doubles first before near doubles?

Answer: Learning doubles first is crucial because they serve as the foundation for near doubles! Think of doubles as "anchor facts" that make near doubles much easier:

  • When children know 5+5=10 automatically, they can quickly figure out 5+6 by thinking "5+5=10, and one more is 11"
  • Doubles facts are symmetrical and easier to remember, building confidence
  • The near doubles strategy relies on knowing doubles facts fluently

Without mastering doubles first, children often resort to counting each number individually, which is slower and more error-prone. The doubles-to-near-doubles connection helps develop efficient mental math strategies.

Practice doubles consistently until they're automatic, then introduce near doubles using the doubles connection!

Question: How can I help students visualize the difference between doubles and near doubles?

Answer: Visual representations are extremely effective for teaching doubles vs. near doubles! Here are some techniques:

  • Dot patterns: Show 4 dots + 4 dots for doubles, then 4 dots + 5 dots for near doubles
  • Finger counting: Hold up the same number of fingers on each hand for doubles, then add one more finger for near doubles
  • Objects: Use counters, blocks, or manipulatives arranged in matching pairs for doubles, then add one extra for near doubles
  • Number lines: Show jumps of equal size for doubles, then one extra jump for near doubles

The key is showing the "equal groups" for doubles versus "one group plus one more" for near doubles. This visual difference helps students internalize the conceptual difference.

Color-coding also works well: use the same color for both groups in doubles, and a different color for the extra item in near doubles.

Question: Are there any fun games or activities to reinforce doubles and near doubles?

Answer: Absolutely! Games make learning doubles and near doubles engaging and memorable:

  • Doubles dice game: Roll one die, double the number, then try near doubles by adding/subtracting 1
  • Doubles dominoes: Match dominoes with doubles facts (3|3, 4|4, etc.)
  • Memory match: Cards with doubles facts and their answers
  • Jump rope counting: Skip count by 2s while chanting doubles facts
  • Interactive songs: Create rhythmic chants for doubles facts

Digital tools like online math games can also provide immediate feedback and make practice more engaging. The key is repetition in varied, enjoyable formats.

Group activities work well too: students can partner up and quiz each other, or play competitive games where they race to solve doubles and near doubles problems.