Solved Exercises on Repeated Addition Sentences in Grade 2

Master repeated addition: connecting addition to multiplication, recognizing patterns, and building foundational skills through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Basic Repeated Addition
Exercise 1
Write a repeated addition sentence for 3 groups of 4 stars.
Definition:

Repeated Addition Sentence: An addition equation where the same number is added multiple times, showing how multiplication works.

Repeated Addition Method:
  1. Identify how many groups there are
  2. Identify how many items are in each group
  3. Write the same number added multiple times
  4. Find the total sum
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Group 1
⭐⭐⭐⭐
Group 2
⭐⭐⭐⭐
Group 3
Pattern: Same number (4) added 3 times
Step 1: Count the groups

There are 3 groups

Step 2: Count items per group

Each group has 4 stars

Step 3: Write repeated addition

Add 4 three times: 4 + 4 + 4

Step 4: Calculate the sum

4 + 4 + 4 = 12

4 + 4 + 4 = 12
↓
3 × 4 = 12
Final answer:

The repeated addition sentence is: 4 + 4 + 4 = 12

Applied rules:

• Repeated Addition: Same number added multiple times

• Grouping: Number of groups × Items per group

• Connection to Multiplication: 3 groups of 4 = 3 × 4

2 Connecting to Multiplication
Exercise 2
There are 5 rows of flowers. Each row has 3 flowers. Write the repeated addition sentence and show the multiplication connection.
Definition:

Array Model: Objects arranged in rows and columns, representing multiplication as repeated addition.

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Row 1
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Row 2
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Row 3
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Row 4
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Row 5
Pattern: 3 flowers added 5 times
Step 1: Count the rows

There are 5 rows

Step 2: Count flowers per row

Each row has 3 flowers

Step 3: Write repeated addition

3 + 3 + 3 + 3 + 3

Step 4: Calculate the sum

3 + 3 + 3 + 3 + 3 = 15

3 + 3 + 3 + 3 + 3 = 15
↓
5 × 3 = 15
Final answer:

Repeated addition: 3 + 3 + 3 + 3 + 3 = 15

Multiplication equivalent: 5 × 3 = 15

Applied rules:

• Array Model: Rows × Columns

• Repeated Addition: Same number added for each row

• Multiplication Connection: Faster way to add equal groups

3 Identifying Patterns
Exercise 3
Which of these are repeated addition sentences? Explain why or why not.
a) 5 + 5 + 5
b) 2 + 3 + 4
c) 7 + 7 + 7 + 7
d) 6 + 6 + 8
Definition:

Pattern Recognition: Identifying when the same number is added repeatedly versus different numbers being added.

Step 1: Analyze option a) 5 + 5 + 5

The number 5 is added 3 times → YES, repeated addition

Step 2: Analyze option b) 2 + 3 + 4

Different numbers (2, 3, 4) → NO, not repeated addition

Step 3: Analyze option c) 7 + 7 + 7 + 7

The number 7 is added 4 times → YES, repeated addition

Step 4: Analyze option d) 6 + 6 + 8

Numbers 6 and 8 are different → NO, not repeated addition

Key Rule: All addends must be identical
a) 5 + 5 + 5 = 15 ✓
c) 7 + 7 + 7 + 7 = 28 ✓
Final answer:

a) Yes: 5 + 5 + 5 is repeated addition (same number 3 times)

b) No: 2 + 3 + 4 has different numbers

c) Yes: 7 + 7 + 7 + 7 is repeated addition (same number 4 times)

d) No: 6 + 6 + 8 has different numbers

Applied rules:

• Repetition Rule: All addends must be the same number

• Pattern Recognition: Look for identical numbers being added

• Verification: Check each addend is identical

Repeated Addition Concepts & Connections
4 + 4 + 4 = 3 × 4
Addition to Multiplication
Addition Sentence
4 + 4 + 4 = 12
Adding same number repeatedly
Multiplication
3 × 4 = 12
Faster way to add equal groups
Groups
3 groups of 4
Visual representation
Key Definitions:

Repeated Addition: Adding the same number multiple times

Addend: Numbers being added together

Sum: Result of addition

Equal Groups: Sets containing the same number of items

Array: Rectangular arrangement of objects in rows and columns

Pattern Recognition Steps:
  1. Look for identical numbers: Check if all addends are the same
  2. Count repetitions: How many times the same number appears
  3. Connect to multiplication: Number of repetitions × the repeated number
  4. Verify: Calculate both addition and multiplication to confirm
Tip 1: Look for the same number appearing multiple times in an addition sentence.
Tip 2: Draw circles or boxes to group repeated numbers visually.
Tip 3: Practice counting by 2s, 3s, 4s, etc. to understand repeated addition.
Tip 4: Remember that multiplication is a shortcut for repeated addition.
Key Concepts: Repeated addition connects addition to multiplication, patterns help identify multiplication situations, arrays provide visual models.
Benefits: Builds conceptual understanding, prepares for multiplication facts, strengthens number sense.
Solution: Exercises 4 to 5
4 Converting Addition to Multiplication
Exercise 4
Convert these repeated addition sentences to multiplication sentences:
a) 6 + 6 + 6 + 6
b) 8 + 8 + 8
c) 2 + 2 + 2 + 2 + 2 + 2
Definition:

Conversion Process: Changing from repeated addition to multiplication by identifying the number of groups and items per group.

Step 1: Analyze a) 6 + 6 + 6 + 6

Number 6 appears 4 times → 4 groups of 6 → 4 × 6

Step 2: Calculate a) 6 + 6 + 6 + 6

6 + 6 + 6 + 6 = 24

Step 3: Verify a) 4 × 6

4 × 6 = 24 ✓

Step 4: Analyze b) 8 + 8 + 8

Number 8 appears 3 times → 3 groups of 8 → 3 × 8

Step 5: Calculate b) 8 + 8 + 8

8 + 8 + 8 = 24

Step 6: Verify b) 3 × 8

3 × 8 = 24 ✓

Step 7: Analyze c) 2 + 2 + 2 + 2 + 2 + 2

Number 2 appears 6 times → 6 groups of 2 → 6 × 2

Step 8: Calculate c) 2 + 2 + 2 + 2 + 2 + 2

2 + 2 + 2 + 2 + 2 + 2 = 12

Step 9: Verify c) 6 × 2

6 × 2 = 12 ✓

a) 6 + 6 + 6 + 6 = 24
b) 8 + 8 + 8 = 24
c) 2 + 2 + 2 + 2 + 2 + 2 = 12
↓
a) 4 × 6 = 24
b) 3 × 8 = 24
c) 6 × 2 = 12
Final answer:

a) 6 + 6 + 6 + 6 = 4 × 6 = 24

b) 8 + 8 + 8 = 3 × 8 = 24

c) 2 + 2 + 2 + 2 + 2 + 2 = 6 × 2 = 12

Applied rules:

• Count Repetitions: How many times the number appears

• Identify the Number: What number is being repeated

• Convert Format: Number of repetitions × repeated number

5 Word Problems with Repeated Addition
Exercise 5
A classroom has 4 tables. Each table seats 5 students. Write the repeated addition sentence to find the total number of students that can sit in the classroom.
Definition:

Word Problem Application: Using repeated addition to solve real-world scenarios involving equal groups.

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Table 1
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Table 2
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Table 3
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Table 4
Pattern: 5 students added 4 times
Step 1: Identify the scenario

4 tables, each seating 5 students

Step 2: Identify the equal groups

Each table is a group with 5 students

Step 3: Count the groups

There are 4 groups (tables)

Step 4: Identify items per group

Each group has 5 students

Step 5: Write repeated addition

5 + 5 + 5 + 5 (adding 5 four times)

Step 6: Calculate the sum

5 + 5 + 5 + 5 = 20

Step 7: Connect to multiplication

4 groups of 5 = 4 × 5 = 20

5 + 5 + 5 + 5 = 20
↓
4 × 5 = 20
Final answer:

The repeated addition sentence is: 5 + 5 + 5 + 5 = 20

This means 20 students can sit in the classroom.

Applied rules:

• Word Problem Strategy: Identify equal groups in the scenario

• Repeated Addition: Same number added for each group

• Real-World Connection: Math applies to everyday situations

Complete Summary: Repeated Addition Sentences
n + n + n ... (k times) = k × n
General Formula
Comprehensive Definitions:

Repeated Addition Sentence: An addition equation where the same number (addend) is added multiple times, such as 3 + 3 + 3 + 3 = 12. This represents the foundation for multiplication.

Addend: The numbers being added together in an addition sentence.

Sum: The result obtained when adding numbers together.

Equal Groups: Collections that contain the exact same number of items.

Array: A rectangular arrangement of objects in rows and columns that visually represents multiplication.

Step-by-Step Methodology:
  1. Identify Equal Groups: Look for situations where the same number of items appears multiple times
  2. Count Repetitions: Determine how many times the same number is being added
  3. Write Addition Sentence: Express the situation as the same number added repeatedly
  4. Calculate Sum: Add all the numbers to find the total
  5. Connect to Multiplication: Recognize that repeated addition equals multiplication (e.g., 4 + 4 + 4 = 3 × 4)
  6. Verify Answer: Check that both addition and multiplication give the same result
Tip 1: Look for clue words like "each," "per," "groups of," and "rows of" in word problems.
Tip 2: Draw pictures or use manipulatives to visualize equal groups.
Tip 3: Practice skip counting (2, 4, 6, 8...) to understand repeated addition.
Tip 4: Remember: multiplication is just a faster way to write repeated addition!
Core Rules: All addends must be identical in a repeated addition sentence. The number of addends tells you the first factor in multiplication. The repeated number is the second factor.
Examples: 2 + 2 + 2 + 2 = 4 × 2 = 8; 5 + 5 + 5 = 3 × 5 = 15; 7 + 7 = 2 × 7 = 14.
Key Takeaways:

• Foundation Concept: Repeated addition is the bridge between addition and multiplication

• Pattern Recognition: Identifying when the same number appears multiple times

• Efficiency: Multiplication is a shortcut for repeated addition

• Visualization: Equal groups and arrays help understand the concept

• Real Applications: Many real-world situations involve equal groups

Questions & Answers

Question: Why do we learn repeated addition when multiplication seems easier?

Answer: Great question! Actually, multiplication IS the easier way once you know it, but repeated addition teaches you WHY multiplication works:

  • Understanding: Repeated addition shows you what multiplication really means - equal groups
  • Foundation: It builds your number sense and understanding of operations
  • Backup Strategy: If you forget a multiplication fact, you can always add repeatedly
  • Connection: It helps you see that 4 × 3 is the same as 3 + 3 + 3 + 3

Think of it like learning to walk before running - addition is walking, multiplication is running. Both are important!

For example: If you don't remember 6 × 4, you can think "4 + 4 + 4 + 4 + 4 + 4 = 24". Now you know 6 × 4 = 24!

Question: How can I tell if an addition sentence is repeated addition or not?

Answer: Look for this simple rule: ALL the numbers being added must be IDENTICAL!

YES, repeated addition:

  • 5 + 5 + 5 (all 5s)
  • 2 + 2 + 2 + 2 + 2 (all 2s)
  • 7 + 7 (all 7s)

NO, not repeated addition:

  • 3 + 4 + 5 (different numbers)
  • 6 + 6 + 8 (not all the same)
  • 1 + 3 + 1 + 3 (mixed numbers)

The key is the PATTERN - look for the same number appearing over and over again. That's your clue that it's repeated addition!

Question: Can you give me more examples of real things that use repeated addition?

Answer: Absolutely! Here are many real-life examples of repeated addition:

  • Eggs in cartons: 2 rows of 6 eggs = 6 + 6 = 12 (or 2 × 6)
  • Shelves of books: 4 shelves with 5 books each = 5 + 5 + 5 + 5 = 20
  • Boxes of crayons: 3 boxes with 8 crayons each = 8 + 8 + 8 = 24
  • Pack of stickers: 5 sheets with 4 stickers each = 4 + 4 + 4 + 4 + 4 = 20
  • Classroom desks: 6 rows with 3 desks each = 3 + 3 + 3 + 3 + 3 + 3 = 18
  • Toy cars: 4 bags with 7 cars each = 7 + 7 + 7 + 7 = 28

You'll notice that in each case, the SAME number appears multiple times - that's repeated addition! This happens whenever things are organized in equal groups.

Next time you see objects arranged in groups, try writing the repeated addition sentence!