Doubles and Near Doubles Second Grade: Advanced Practice for 1st Graders

Advanced practice with doubles and near doubles: visual explanations, challenging exercises, and step-by-step solutions.

Advanced Doubles and Near Doubles Exercises & Solutions
1 Advanced Doubles
Exercise 1
Solve: 7 + 7 using the doubles strategy
Advanced Doubles Definition:

Advanced Doubles: Addition facts with larger numbers (6+6 to 9+9)

Advanced Doubles Strategy:
  1. Recognize that both addends are identical
  2. Double the number (multiply by 2)
  3. Use known facts to derive new ones
1
2
3
4
5
6
7
+
8
9
10
11
12
13
14
=
14
Step 1: Identify the double

Both numbers are 7

Step 2: Count both groups

7 + 7 = 14

Step 3: State the answer

7 + 7 = 14

7 + 7 = 14
Final answer:

7 + 7 = 14

Applied rules:

• Advanced Doubles Pattern: When both addends are the same, multiply by 2

• Memorization: Advanced doubles facts build on basic ones

• Visual Recognition: Seeing equal groups helps with understanding

2 Advanced Near Doubles
Exercise 2
Solve: 7 + 8 using the near doubles strategy
Advanced Near Doubles Definition:

Advanced Near Doubles: Addition facts with larger consecutive numbers (6+7 to 8+9)

Advanced Near Doubles Strategy:

Use the closest advanced doubles fact and add or subtract 1

For 7 + 8: Think of 7 + 7 = 14, then add 1 more = 15

1
2
3
4
5
6
7
+
8
9
10
11
12
13
14
15
=
15
Step 1: Identify the near double

7 and 8 are consecutive numbers

Step 2: Think of the doubles fact

7 + 7 = 14

Step 3: Add the extra amount

Since 8 is 1 more than 7, add 1 more to 14 = 15

7 + 8 = 15
Final answer:

7 + 8 = 15

Applied rules:

• Advanced Near Doubles Pattern: Use advanced doubles facts to solve nearby problems

• Adjustment: Add or subtract the difference from the doubles fact

• Number Relationships: Understanding consecutive numbers

3 Challenging Near Doubles
Exercise 3
Solve: 8 + 9 using the near doubles strategy
Challenging Near Doubles Definition:

Challenging Near Doubles: Addition facts with largest consecutive numbers (7+8 to 8+9)

Challenging Near Doubles Strategy:

Use the closest advanced doubles fact and adjust accordingly

For 8 + 9: Think of 8 + 8 = 16, then add 1 more = 17

1
2
3
4
5
6
7
8
+
9
10
11
12
13
14
15
16
17
=
17
Step 1: Identify the near double

8 and 9 are consecutive numbers

Step 2: Think of the doubles fact

8 + 8 = 16

Step 3: Add the extra amount

Since 9 is 1 more than 8, add 1 more to 16 = 17

8 + 9 = 17
Final answer:

8 + 9 = 17

Applied rules:

• Challenging Near Doubles Pattern: Use advanced doubles facts to solve nearby problems

• Adjustment: Add or subtract the difference from the doubles fact

• Number Relationships: Understanding consecutive numbers

Advanced Doubles and Near Doubles Practice
6 + 6
12
7 + 7
14
8 + 8
16
9 + 9
18
6 + 7
13
7 + 8
15
8 + 9
17
5 + 6
11
4 + 5
9
3 + 4
7
2 + 3
5
1 + 2
3
9 + 8
17
6 + 5
11
7 + 6
13
8 + 7
15
Advanced Doubles and Near Doubles Concepts
n + (n+1) = 2n + 1
Advanced Near Doubles Formula
Doubles
7 + 7 = 14
Larger numbers
Near Doubles
7 + 8 = 15
Consecutive numbers
Strategy
14 + 1 = 15
Use doubles + 1
Key definitions:

Advanced Doubles: Addition facts where both addends are 6 or greater (6+6, 7+7, etc.)

Advanced Near Doubles: Addition facts where larger numbers differ by 1 (6+7, 7+8, etc.)

Strategy: Using known facts to solve unknown problems

Advanced Doubles Strategy Steps:
  1. Recognize: Identify if both numbers are the same
  2. Double: Multiply the number by 2
  3. Recall: Use memorized advanced doubles facts
  4. Verify: Count to confirm the answer
Tip 1: Practice advanced doubles facts until they're automatic.
Tip 2: Use near doubles to solve tricky problems.
Tip 3: Visualize equal groups to understand doubles.
Tip 4: Count on from the doubles fact for near doubles.
Common errors: Confusing doubles with near doubles, forgetting the pattern.
Success strategies: Regular practice, visual aids, connecting to real life.
Comprehensive Advanced Doubles and Near Doubles Summary
Key Definitions and Concepts
  • Advanced Doubles: Addition facts where both addends are 6 or greater (e.g., 6+6, 7+7, 8+8). These facts follow the pattern n+n=2n and are foundational math facts that students should memorize.
  • Advanced Near Doubles: Addition facts where the two numbers differ by 1 and are 6 or greater (e.g., 6+7, 7+8, 8+9). These facts can be solved by using the closest advanced doubles fact and adjusting by 1.
  • Advanced Doubles Strategy: A mental math technique that uses known advanced doubles facts to solve addition problems efficiently. This strategy builds fluency and number sense.
  • Advanced Near Doubles Strategy: A mental math technique that uses advanced doubles facts to solve problems with consecutive numbers by adding or subtracting 1 from the doubles result.
Core Rules and Principles
  • Advanced Doubles Rule: When both addends are the same and 6 or greater, the sum is double the number (n+n=2n).
  • Advanced Near Doubles Rule: Use the closest advanced doubles fact and adjust by the difference (if numbers differ by 1, add or subtract 1).
  • Pattern Recognition: Identifying when numbers are the same or consecutive in the advanced range.
  • Mental Math: Using known facts to solve unknown problems quickly.
Step-by-Step Methods
  1. Step 1: Look at both numbers in the addition problem.
  2. Step 2: Determine if they are the same (advanced doubles) or differ by 1 (advanced near doubles).
  3. Step 3: For advanced doubles, double the number (multiply by 2).
  4. Step 4: For advanced near doubles, think of the closest advanced doubles fact.
  5. Step 5: Adjust by adding or subtracting the difference.
  6. Step 6: State the final answer.
Examples: Simple to Advanced
  • Simple Doubles: 1+1=2, 2+2=4, 3+3=6
  • Intermediate Doubles: 4+4=8, 5+5=10, 6+6=12
  • Advanced Doubles: 7+7=14, 8+8=16, 9+9=18
  • Advanced Near Doubles: 6+7=13 (think 6+6=12, then +1), 7+8=15 (think 7+7=14, then +1)
Tips, Tricks, and Common Pitfalls
  • Tip: Practice advanced doubles facts daily until they become automatic.
  • Trick: Remember that advanced doubles are like mirrors (same numbers).
  • Pitfall: Confusing advanced doubles with other addition facts.
  • Warning: Don't try to use the strategy when numbers aren't consecutive.
Memorization Aids and Takeaways
  • Memory Aid: "Advanced doubles are twins, they look the same!"
  • Takeaway 1: Advanced doubles facts build on basic doubles facts.
  • Takeaway 2: Advanced near doubles use advanced doubles as a stepping stone.
  • Takeaway 3: These strategies develop mental math skills for larger numbers.
Essential Advanced Doubles Components:

• Pattern Recognition: Identifying when numbers are the same or consecutive in the advanced range

• Mental Math: Using known facts to solve unknown problems

• Number Relationships: Understanding how larger numbers connect and relate

• Fluency: Automatic recall of advanced addition facts

Questions & Answers

Question: Why do I need to learn advanced doubles? Are they different from regular doubles?

Answer: Great question! Advanced doubles are just like regular doubles but with larger numbers:

  • Regular doubles: 1+1, 2+2, 3+3, 4+4, 5+5
  • Advanced doubles: 6+6, 7+7, 8+8, 9+9

Learning advanced doubles is important because:

  • They help you solve bigger math problems faster
  • They prepare you for second grade math
  • They build confidence with larger numbers
  • They help with advanced near doubles (like 7+8)

Think of advanced doubles as the next step in your math journey!

Question: My child is comfortable with basic doubles but struggles with advanced ones. How can I help?

Answer: Here are strategies to help your child with advanced doubles:

  • Build on basics: Connect advanced doubles to basic ones (if 3+3=6, then 6+6=12)
  • Use manipulatives: Counters, blocks, or toys to physically show the relationship
  • Visual connections: Draw pictures showing the advanced doubles
  • Verbalize: Say "7+7 is like 3+3 but bigger" to make connections
  • Practice regularly: Short, daily practice sessions work better than long ones

Focus on the patterns and connections between basic and advanced doubles.

Remember, advanced doubles are just regular doubles with bigger numbers!

Question: How does practicing advanced doubles prepare students for second grade?

Answer: Practicing advanced doubles prepares students for second grade in several ways:

  • Builds fluency: Students develop automaticity with larger basic facts
  • Develops number sense: Students understand relationships between larger numbers
  • Improves mental math: Students learn to think flexibly about larger numbers
  • Creates problem-solving tools: Students learn to use known facts for unknown problems
  • Prepares for advanced math: Builds foundation for multi-digit addition

Advanced doubles help students transition smoothly to working with larger numbers in second grade.

They also promote mathematical reasoning and pattern recognition skills needed for future math success.