Solved Exercises on Doubles and Near Doubles in Grade 1

Master doubles and near doubles: basic facts, visual representation, and word problems through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Basic Doubles
Exercise 1
Solve: 6 + 6 = ?
Definition:

Doubles: Addition problems where both numbers are the same

Examples: 2 + 2, 3 + 3, 4 + 4, etc.

Pattern: Doubles always equal an even number

Doubles Method:
  1. Identify that both numbers are the same
  2. Remember the doubles fact or count both groups
  3. Double the number (multiply by 2)
  4. Write the complete equation
First 6
+
Second 6
=
Total
Step 1: Identify the double

This is 6 + 6, which is a doubles fact

Step 2: Count the first group

First group has 6 dots

Step 3: Count the second group

Second group also has 6 dots

Step 4: Add both groups together

6 + 6 = 12

6 + 6 = 12
Final answer:

6 + 6 = 12

Applied rules:

• Doubles pattern: Same number + same number = double the number

• Even result: Doubles always equal even numbers

• Multiplication connection: 6 + 6 = 6 × 2 = 12

2 More Doubles
Exercise 2
Solve: 8 + 8 = ?
Definition:

Doubles: Addition problems where both numbers are identical

Memory building: Learning doubles helps with other addition facts

First 8
+
Second 8
=
Total
Step 1: Identify the double

This is 8 + 8, which is a doubles fact

Step 2: Remember the pattern

8 + 8 means we have 8 and another 8

Step 3: Count both groups

First group: 8, Second group: 8, Total: 16

Step 4: State the answer

8 + 8 = 16

8 + 8 = 16
Final answer:

8 + 8 = 16

Applied rules:

• Doubles recognition: Both numbers are the same

• Quick recall: Memorizing doubles makes other problems easier

• Even results: Doubles always produce even sums

3 Near Doubles
Exercise 3
Solve: 7 + 8 = ? using doubles strategy
Definition:

Near Doubles: Addition problems where numbers are consecutive (like 7 + 8)

Doubles Strategy: Using known doubles facts to solve nearby problems

First 7
+
Second 8
=
Total
Step 1: Identify the near double

7 + 8 is a near double (consecutive numbers)

Step 2: Think of the related double

7 + 7 = 14 (known doubles fact)

Step 3: Adjust for the extra

Since 8 is 1 more than 7, add 1 more to the double

14 + 1 = 15

Step 4: State the answer

7 + 8 = 15

7 + 8 = 15
Final answer:

7 + 8 = 15

Applied rules:

• Near doubles strategy: Use known doubles and adjust by 1

• Consecutive numbers: One number is 1 more than the other

• Memory building: Doubles knowledge helps solve near doubles

Rules and methods, laws,...
\(6 + 6 = 12\)
Doubles Facts
Doubles
Formula
n + n = 2n
Near Doubles
Strategy
n + (n+1) = 2n + 1
Even Result
Rule
Doubles = Even
Key definitions:

Doubles: Addition problems where both addends are the same number

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

Doubles Strategy: Using known doubles facts to solve related problems

Complete methodology:
  1. Identify pattern: Recognize doubles or near doubles
  2. Recall doubles: Remember the related doubles fact
  3. Adjust for near: Add or subtract 1 for near doubles
  4. Verify answer: Check through counting or alternative method
  5. Record result: Write the complete equation
Tip 1: Memorize doubles facts: 1+1, 2+2, 3+3, ..., 10+10.
Tip 2: Use doubles to solve near doubles (7+8 = 7+7+1 = 15).
Tip 3: Doubles always equal even numbers.
Tip 4: Practice with visual aids like dot patterns.
Common errors: Confusing doubles with near doubles, misremembering facts.
Key concepts: Understanding number patterns, building automaticity.
Rules to remember:

• Doubles rule: n + n = 2n (always even)

• Near doubles: n + (n+1) = 2n + 1 (always odd)

• Strategy: Use doubles to solve near doubles

• Memorization: Practice doubles for automatic recall

Doubles 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
Near Doubles Examples
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
Solution: Exercises 4 to 5
4 Word Problems
Exercise 4
Tom has 5 marbles. His brother has 6 marbles. How many marbles do they have altogether? (This is a near double problem!)
Definition:

Word Problem: A math question written in story form

Near Double: 5 and 6 are consecutive numbers (differ by 1)

Step 1: Identify the numbers

Tom has 5 marbles, his brother has 6 marbles

Step 2: Recognize the pattern

5 + 6 is a near double (consecutive numbers)

Step 3: Use doubles strategy

5 + 5 = 10 (known doubles fact)

Since 6 is 1 more than 5, add 1 more: 10 + 1 = 11

Step 4: State the answer

They have 11 marbles altogether

5 + 6 = 11
Final answer:

They have 11 marbles altogether

Applied rules:

• Story understanding: Find the important numbers

• Pattern recognition: Identify near doubles

• Strategy application: Use known doubles to solve

5 Mixed Problems
Exercise 5
Solve: 9 + 9 = ? and 9 + 10 = ?
Definition:

Doubles vs Near Doubles: Comparing similar but different problem types

Pattern building: Understanding the relationship between doubles and near doubles

Step 1: Solve the double

9 + 9 = 18 (doubles fact)

Step 2: Solve the near double

9 + 10 is a near double (consecutive numbers)

Use 9 + 9 = 18, then add 1 more: 18 + 1 = 19

Step 3: Compare the results

9 + 9 = 18 (doubles = even)

9 + 10 = 19 (near doubles = odd)

Step 4: Notice the pattern

Near doubles are always 1 more than the related double

9 + 9 = 18
9 + 10 = 19
Final answer:

9 + 9 = 18 and 9 + 10 = 19

Applied rules:

• Doubles recognition: Same numbers added together

• Near doubles strategy: Use doubles and adjust by 1

• Pattern recognition: Consecutive numbers differ by 1

Doubles and Near Doubles - Complete Guide
\(7 + 8 = 15\)
Using Doubles Strategy
Key definitions:

Doubles: Addition problems where both addends are identical (n + n)

Near Doubles: Addition problems where addends are consecutive integers (n + (n+1))

Doubles Strategy: Using known doubles facts to solve related addition problems

Complete methodology:
  1. Pattern Recognition: Identify whether problem is doubles or near doubles
  2. Fact Recall: Remember the relevant doubles fact
  3. Strategic Adjustment: Add or subtract 1 for near doubles
  4. Verification: Check answer through alternative method
  5. Equation Recording: Write the complete mathematical sentence
Tip 1: Practice doubles until they become automatic (memorize 1+1 through 10+10).
Tip 2: Use doubles to solve near doubles (7+8 = 7+7+1 = 15).
Tip 3: Doubles always result in even numbers.
Tip 4: Near doubles always result in odd numbers.
Visual benefits: Dot patterns and visual aids make number relationships clear.
Memory aids: Learning doubles creates a foundation for other addition facts.
Essential formulas:

• Doubles: n + n = 2n (always even)

• Near doubles: n + (n+1) = 2n + 1 (always odd)

• Strategy: (n + n) + 1 = n + (n+1)

• Pattern: Consecutive numbers differ by 1

Doubles and Near Doubles Workflow

📊
Step-by-Step Process
1
Identify Pattern
2
Recall Doubles
3
Adjust if Needed
4
Calculate
5
Verify
Doubles Patterns

1 + 1 = 2

2 + 2 = 4

3 + 3 = 6

4 + 4 = 8

5 + 5 = 10

Practice Makes Perfect!

Questions & Answers

Question: Why do we need to learn doubles? They seem so easy!

Answer: Great question! Doubles are actually super important building blocks. Here's why:

  • Foundation: Doubles facts help solve harder problems quickly
  • Near doubles: Once you know 7 + 7 = 14, you can easily figure out 7 + 8 = 15
  • Future math: Multiplication builds on doubles (8 + 8 = 8 × 2)
  • Speed: Automatic recall lets you focus on harder concepts

Think of doubles like learning your ABCs - they're the building blocks for everything that comes next!

Example: Knowing 6 + 6 = 12 helps you solve 6 + 7 = 13 instantly.

Question: My child sometimes confuses 7 + 7 with 7 + 8. How can I help them understand the difference?

Answer: This is very common! Here's how to help:

  • Visual comparison: Show 7 + 7 = 14 dots, then add 1 more dot to make 7 + 8 = 15
  • Language connection: "7 + 7 is double 7, but 7 + 8 is one more than double 7"
  • Pattern recognition: 7 + 7 = 14, so 7 + 8 = 15 (just one more)
  • Practice with manipulatives: Use counters to physically show the difference

Create a "doubles family" for each number: 6 + 6 = 12, 6 + 7 = 13, 6 + 8 = 14.

The key is showing that near doubles are just one more than the related double!

Question: Why do doubles always make even numbers?

Answer: Excellent observation! Here's why doubles are always even:

  • Pairing concept: When you add the same number twice, you're pairing everything up
  • Even definition: Even numbers can be divided into pairs with nothing left over
  • Mathematical reason: n + n = 2n, and any number multiplied by 2 is even
  • Visual proof: Try drawing dots - you'll always be able to pair them up

Example: 5 + 5 = 10. You can make 5 pairs: ●● ●● ●● ●● ●●

This is true for any number: 1 + 1 = 2, 2 + 2 = 4, 3 + 3 = 6, and so on!

Question: What are some fun ways to practice doubles and near doubles?

Answer: Fun practice makes learning stick! Here are engaging activities:

  • Dice games: Roll one die, double the number, then try the near double
  • Dominoes: Use dominoes to see doubles and near doubles visually
  • Dot cards: Flash cards with dot patterns for quick recognition
  • Number line hops: Hop twice the same distance for doubles

Engaging activities:

  • Create doubles songs or chants
  • Play "Doubles War" with playing cards
  • Use fingers to show doubles (both hands same number)
  • Build with blocks to visualize the patterns

The key is making practice feel like play, not work!