Doubles or Near Doubles Addition Concepts for Grade 1 Students

Master the fundamental choice between doubles and near doubles: comprehensive exercises with step-by-step solutions, visual aids, and decision-making strategies.

Decision Making: Exercises 1 to 3
1 Identify Doubles vs Near Doubles
Exercise 1
Look at these addition problems and decide if they are doubles or near doubles:
3 + 3 = ?
4 + 5 = ?
6 + 6 = ?
2 + 3 = ?
Visual: 🟡🟡 + 🟡🟡 = 🟡🟡🟡🟡 (doubles) | 🔵🔵🔵 + 🔵🔵🔵🔵 = 🔵🔵🔵🔵🔵🔵🔵 (near doubles)
Definition:

Doubles: Addition facts where both addends are identical numbers (e.g., 3+3, 6+6)

Near Doubles: Addition facts where addends are consecutive numbers (e.g., 4+5, 2+3)

Identification Strategy:
  1. Look at both numbers: Are they the same? → Doubles
  2. If different: Are they consecutive (one apart)? → Near Doubles
  3. Count the difference: Same numbers = 0 difference (doubles), 1 difference (near doubles)
  4. Apply the appropriate strategy: Doubles rule or near doubles rule
Problem
3 + 3
Type
Doubles
Step 1: Examine both addends

Both numbers are 3, so this is a doubles fact: 3 + 3

Step 2: Apply the doubles strategy

When both numbers are the same: 3 + 3 = 6 (3 × 2 = 6)

Step 3: Analyze the next problem

4 + 5: Different numbers, but consecutive (4 and 5 differ by 1) → Near Doubles

Step 4: Continue with remaining problems

6 + 6: Both same → Doubles | 2 + 3: Consecutive → Near Doubles

3 + 3 = Doubles
4 + 5 = Near Doubles
6 + 6 = Doubles
2 + 3 = Near Doubles
Final answers:

Doubles: 3+3, 6+6 | Near Doubles: 4+5, 2+3

Applied rules:

• Identification Rule: Same numbers = Doubles, consecutive numbers = Near Doubles

• Decision-Making: Distinguish between problem types before calculating

• Pattern Recognition: Identifying the relationship between addends

2 Decision Making Process
Exercise 2
For each problem, identify the type and solve:
5 + 6 = ? (Type: Near Doubles)
7 + 7 = ? (Type: Doubles)
8 + 9 = ? (Type: Near Doubles)
4 + 4 = ? (Type: Doubles)
Visual: 🔴🔴🔴🔴 + 🔴🔴🔴🔴 = 🔴🔴🔴🔴🔴🔴🔴🔴 (doubles) | 🟢🟢🟢🟢🟢 + 🟢🟢🟢🟢🟢🟢 = 🟢🟢🟢🟢🟢🟢🟢🟢🟢 (near doubles)
Definition:

Decision Making: The process of identifying whether an addition problem is a doubles or near doubles fact before solving

Problem
5 + 6
Type
Near Doubles
Solution
11
Step 1: Identify the problem type

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

Step 2: Apply the near doubles strategy

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

Step 3: Analyze the next problem

7 + 7: Both numbers are the same → Doubles

Step 4: Apply the doubles strategy

7 + 7 = 14 (7 × 2 = 14)

Step 5: Repeat for all problems

Continue identifying type then applying appropriate strategy

5 + 6 = 11 (Near Doubles)
7 + 7 = 14 (Doubles)
8 + 9 = 17 (Near Doubles)
4 + 4 = 8 (Doubles)
Final answers:

5+6=11 (ND), 7+7=14 (D), 8+9=17 (ND), 4+4=8 (D)

Applied rules:

• Type Identification: Determine problem type before solving

• Strategy Selection: Use appropriate method for each type

• Sequential Processing: Apply consistent steps to each problem

3 Advanced Identification
Exercise 3
Circle the doubles and underline the near doubles:
1 + 1, 3 + 4, 5 + 5, 6 + 7, 8 + 8, 9 + 10, 2 + 2
Visual: 🟠 + 🟠 = 🟠🟠 (doubles) | 🟣🟣 + 🟣🟣🟣 = 🟣🟣🟣🟣🟣 (near doubles)
Definition:

Advanced Identification: Distinguishing between doubles and near doubles in mixed sets of problems

Problem Set
Mixed types
Doubles
1+1, 5+5, 8+8, 2+2
Near Doubles
3+4, 6+7, 9+10
Step 1: Examine each pair systematically

1+1: Same numbers → Doubles | 3+4: Consecutive → Near Doubles

Step 2: Continue analysis

5+5: Same → Doubles | 6+7: Consecutive → Near Doubles

Step 3: Complete the set

8+8: Same → Doubles | 9+10: Consecutive → Near Doubles | 2+2: Same → Doubles

Step 4: Organize results

Separate doubles from near doubles for clarity

Step 5: Verify identifications

Double-check each classification to ensure accuracy

Doubles: 1+1, 5+5, 8+8, 2+2
Near Doubles: 3+4, 6+7, 9+10
Final answer:

Doubles: 1+1, 5+5, 8+8, 2+2 | Near Doubles: 3+4, 6+7, 9+10

Applied rules:

• Systematic Analysis: Examine each problem individually

• Classification: Group problems by type for better organization

• Verification: Check classifications for accuracy

Doubles vs Near Doubles: Decision Making Guide
\text{Doubles: } n + n = 2n
Doubles Formula
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)

Decision Making: The process of identifying which strategy to use

Complete identification process:
  1. Examine both addends: Look at the two numbers being added
  2. Compare the numbers: Are they identical or different?
  3. Determine the difference: 0 difference = Doubles, 1 difference = Near Doubles
  4. Select strategy: Use appropriate method based on type
  5. Calculate: Apply the chosen strategy
Tip 1: Look for the same numbers in doubles (3+3, 7+7).
Tip 2: Look for consecutive numbers in near doubles (4+5, 8+9).
Tip 3: Count the difference between the numbers (0=doubles, 1=near doubles).
Tip 4: Practice identifying the type before calculating the answer.
Common errors: Misidentifying problem types, applying wrong strategies, skipping the identification step.
Key insight: Correct identification leads to faster, more accurate calculations.
Identification rules:

• Same numbers = Doubles (2+2, 5+5, 8+8)

• Consecutive numbers = Near Doubles (3+4, 6+7, 9+10)

• Non-consecutive different numbers = Neither (2+5, 3+8)

Doubles vs Near Doubles Decision Tree
🌳
Decision Steps

1. Look at both numbers

2. Are they the same?

3. If yes → Doubles

4. If no, are they consecutive?

5. If yes → Near Doubles

Visual Patterns

Doubles: Equal groups side by side

Near Doubles: One group has one more

Identification Process
1
Look
2
Compare
3
Decide
4
Solve
Decision Making Benefits

Improves calculation speed

Reduces errors

Builds number sense

Practice Decision Making! Identify First, Then Calculate!
Application: Exercises 4 to 5
4 Mixed Problem Solving
Exercise 4
Identify the type and solve:
7 + 8 = ? (Type: Near Doubles, Strategy: 7 + 7 + 1)
9 + 9 = ? (Type: Doubles, Strategy: 9 × 2)
5 + 6 = ? (Type: Near Doubles, Strategy: 5 + 5 + 1)
4 + 4 = ? (Type: Doubles, Strategy: 4 × 2)
Visual: ⚪⚪⚪⚪⚪ + ⚪⚪⚪⚪⚪⚪ = ⚪⚪⚪⚪⚪⚪⚪⚪⚪ (near doubles)
Definition:

Mixed Problem Solving: Applying identification skills to solve various types of problems in sequence

Problem
7 + 8
Type
Near Doubles
Solution
15
Step 1: Identify the problem type

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

Step 2: Apply the near doubles strategy

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

Step 3: Analyze the next problem

9 + 9: Both numbers are the same → Doubles

Step 4: Apply the doubles strategy

9 + 9 = 18 (9 × 2 = 18)

Step 5: Continue with remaining problems

Apply the same identification and solving process

7 + 8 = 15 (ND)
9 + 9 = 18 (D)
5 + 6 = 11 (ND)
4 + 4 = 8 (D)
Final answers:

7+8=15 (ND), 9+9=18 (D), 5+6=11 (ND), 4+4=8 (D)

Applied rules:

• Consistent Process: Apply the same identification steps to each problem

• Strategy Selection: Use appropriate method for each identified type

• Sequential Execution: Work through problems systematically

5 Word Problems with Type Identification
Exercise 5
Sarah has 6 stickers. Her friend gives her 7 more stickers. How many stickers does Sarah have now? (Type: Near Doubles)
Tom has 8 toy cars. He gets 8 more toy cars. How many toy cars does Tom have now? (Type: Doubles)
Visual: 🚗🚗🚗🚗🚗🚗 + 🚗🚗 = 🚗🚗🚗🚗🚗🚗🚗🚗 (doubles) | 📝📝📝📝📝 + 📝📝📝 = 📝📝📝📝📝📝 (near doubles)
Definition:

Word Problems with Type Identification: Translating real-world scenarios to mathematical operations and identifying the problem type

Problem 1
6 + 7
Type
Near Doubles
Solution
13
Step 1: Translate the word problem

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

Step 2: Identify the problem type

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

Step 3: Apply the near doubles strategy

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

Step 4: Interpret the result in context

Sarah has 13 stickers in total

Step 5: Solve the doubles problem

Tom: 8 + 8 = 16 toy cars (doubles fact)

Sarah: 6 + 7 = 13 stickers (ND)
Tom: 8 + 8 = 16 cars (D)
Final answers:

Sarah has 13 stickers (Near Doubles). Tom has 16 toy cars (Doubles).

Applied rules:

• Problem Translation: Convert words to mathematical expressions

• Type Identification: Determine if it's doubles or near doubles

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

Complete Summary: Doubles or Near Doubles Decision Making
\text{Doubles: } n + n = 2n \quad \text{Near Doubles: } n + (n+1) = 2n + 1
Type Identification 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)

Decision Making: The process of identifying which strategy to use

Type Identification: Recognizing problem categories before solving

Complete identification process:
  1. Examine both addends: Look at the two numbers being added
  2. Compare the numbers: Are they identical or different?
  3. Determine the difference: 0 difference = Doubles, 1 difference = Near Doubles
  4. Select strategy: Use appropriate method based on type
  5. Calculate: Apply the chosen strategy
Tip 1: Look for the same numbers in doubles (3+3, 7+7).
Tip 2: Look for consecutive numbers in near doubles (4+5, 8+9).
Tip 3: Count the difference between the numbers (0=doubles, 1=near doubles).
Tip 4: Practice identifying the type before calculating the answer.
Common errors: Misidentifying problem types, applying wrong strategies, skipping the identification step.
Key insight: Correct identification leads to faster, more accurate calculations.
Identification rules:

• Same numbers = Doubles (2+2, 5+5, 8+8)

• Consecutive numbers = Near Doubles (3+4, 6+7, 9+10)

• Non-consecutive different numbers = Neither (2+5, 3+8)

Decision Making Mastery
🎯
Doubles Patterns

Same numbers added together

Results are always even

Formula: n + n = 2n

Near Doubles Patterns

Consecutive numbers added

Results are always odd

Formula: n + (n+1) = 2n + 1

Decision Making Process
1
Examine
2
Compare
3
Classify
4
Apply
5
Solve
Decision Making Benefits

Improves calculation speed

Reduces errors

Builds number sense

Develops strategy selection skills

Master Decision Making! Identify Before You Calculate!

Questions & Answers

Question: My child sometimes confuses doubles with near doubles. How can I help them distinguish between the two?

Answer: This is a common challenge! Here's a systematic approach to help your child distinguish:

  • Visual comparison: Show them that doubles have the same number of objects in both groups (3+3: three objects in each group)
  • Counting strategy: Teach them to ask "Are both numbers the same?" for doubles, "Are the numbers one apart?" for near doubles
  • Physical objects: Use counters or fingers to physically demonstrate the difference
  • Pattern recognition: Doubles always result in even numbers, near doubles always result in odd numbers

Practice with a simple identification game: give them problems and ask them to sort into "same numbers" (doubles) vs "consecutive numbers" (near doubles) before solving.

Focus on the identification step first, then the calculation. This builds the foundational skill of recognizing problem types.

Question: How can I teach students to identify the problem type before solving?

Answer: Teaching problem identification involves explicit instruction and consistent practice:

  • Model the process: Think aloud as you examine problems, verbalizing your thought process
  • Create a checklist: "Look at both numbers, are they the same? If yes, it's doubles. If they're one apart, it's near doubles."
  • Use visual cues: Color-code or circle the numbers to emphasize the comparison
  • Practice identification separately: Give students problems just to classify as doubles or near doubles without solving

Start with simple numbers and gradually increase complexity. The goal is to make identification automatic before moving to calculation.

Emphasize that taking time to identify the type actually saves time in the long run by allowing them to use efficient strategies.

Question: What activities help students master the decision-making process?

Answer: Effective activities for decision-making include:

  • Type sorting games: Students sort problem cards into "doubles" and "near doubles" piles
  • Quick identification drills: Flash cards with problems, students call out "doubles" or "near doubles"
  • Problem analysis sheets: Students write the type before solving
  • Partner activities: One student identifies the type, another solves
  • Self-check activities: Students identify, solve, then verify their type identification

Incorporate movement by having students raise hands for doubles and stomp for near doubles. This kinesthetic approach reinforces the distinction.

Regular practice with mixed problem types helps students develop automatic recognition skills.