Solved Exercises on Repeated Addition and Subtraction in Grade 2

Master repeated addition and subtraction: understanding operations, number patterns, and foundational arithmetic skills through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Repeated Addition Patterns
Exercise 1
Complete the pattern: 2, 4, 6, 8, ___, ___, ___
Definition:

Repeated Addition Pattern: Adding the same number repeatedly to create a sequence.

Pattern Recognition Method:
  1. Identify the number being added repeatedly
  2. Continue the pattern by adding the same number
  3. Verify the sequence makes sense
  4. Check that the pattern continues consistently
2
4
6
8
10
12
14
2
+
2
=
4
4
+
2
=
6
6
+
2
=
8
8
+
2
=
10
Pattern
+2 each time
Next
10 + 2 = 12
Next
12 + 2 = 14
Step 1: Identify the pattern

2 → 4 → 6 → 8: Each number increases by 2

Step 2: Continue adding 2

8 + 2 = 10, then 10 + 2 = 12, then 12 + 2 = 14

Step 3: Verify the sequence

2, 4, 6, 8, 10, 12, 14 - all numbers are 2 apart

Step 4: Check the pattern

Each number is 2 more than the previous one

2, 4, 6, 8, 10, 12, 14
Final answer:

The completed pattern is: 2, 4, 6, 8, 10, 12, 14

Applied rules:

• Pattern recognition: Identify the constant difference

• Consistency: Apply the same operation throughout

• Verification: Check that the pattern continues logically

Pattern Tip: Look for the difference between consecutive numbers!
Sequence Tip: Write down the operation to see the pattern clearly.
2 Repeated Subtraction Patterns
Exercise 2
Complete the pattern: 20, 18, 16, 14, ___, ___, ___
Definition:

Repeated Subtraction Pattern: Subtracting the same number repeatedly to create a decreasing sequence.

20
18
16
14
12
10
8
20
-
2
=
18
18
-
2
=
16
16
-
2
=
14
14
-
2
=
12
Pattern
-2 each time
Next
14 - 2 = 12
Next
12 - 2 = 10
Next
10 - 2 = 8
Step 1: Identify the pattern

20 → 18 → 16 → 14: Each number decreases by 2

Step 2: Continue subtracting 2

14 - 2 = 12, then 12 - 2 = 10, then 10 - 2 = 8

Step 3: Verify the sequence

20, 18, 16, 14, 12, 10, 8 - all numbers are 2 apart

Step 4: Check the pattern

Each number is 2 less than the previous one

20, 18, 16, 14, 12, 10, 8
Final answer:

The completed pattern is: 20, 18, 16, 14, 12, 10, 8

Applied rules:

• Decreasing pattern: Same number subtracted repeatedly

• Consistency: Apply the same operation throughout

• Verification: Check that the pattern continues logically

Subtraction Tip: Look for the difference between consecutive numbers!
Pattern Tip: Numbers decrease when subtracting repeatedly.
3 Addition and Subtraction Together
Exercise 3
Start with 10. Add 3, then subtract 1, repeat this pattern 3 times. What is the final number?
Definition:

Alternating Operations: Performing different operations in a repeating sequence.

10
+3
=13
-1
=12
+3
=15
-1
=14
+3
=17
-1
=16
10
+
3
=
13
13
-
1
=
12
12
+
3
=
15
15
-
1
=
14
Start
10
Pattern
+3, -1
Repeat
3 times
Step 1: Start with 10

Begin with the number 10

Step 2: First cycle (+3, -1)

10 + 3 = 13, then 13 - 1 = 12

Step 3: Second cycle (+3, -1)

12 + 3 = 15, then 15 - 1 = 14

Step 4: Third cycle (+3, -1)

14 + 3 = 17, then 17 - 1 = 16

Step 5: Final result

After 3 cycles, the final number is 16

Final number: 16
Final answer:

The final number after 3 cycles is 16

Applied rules:

• Sequential operations: Perform each operation in order

• Pattern repetition: Follow the same sequence multiple times

• Step-by-step calculation: Track each result carefully

Sequence Tip: Write down each step to avoid confusion!
Pattern Tip: Track the result after each operation.
Operation Patterns & Properties
a + a + ... + a = n × a
Repeated Addition Formula
Repeated Addition
a + a + a = 3a
Increases value
Repeated Subtraction
a - b - b - b = a - 3b
Decreases value
Alternating Operations
a + b - c = result
Combines effects
+
-
n
0
Key definitions:

Repeated Addition: Adding the same number multiple times (increases value)

Repeated Subtraction: Subtracting the same number multiple times (decreases value)

Pattern: A predictable sequence of numbers or operations

Pattern benefits: Develops number sense, improves mental math, recognizes sequences
Arithmetic foundation: Builds skills for multiplication and division
Operation Methods:
  1. Identify the pattern: Recognize the sequence of operations
  2. Apply systematically: Perform each operation in order
  3. Track results: Keep track of each intermediate result
  4. Verify accuracy: Check that each step is correct
  5. Look for shortcuts: Find efficient ways to calculate
Solution: Exercises 4 to 5
4 Word Problem with Operations
Exercise 4
Sarah starts with 15 candies. She eats 2 each day for 4 days. Then she gets 3 more candies. How many does she have now?
Definition:

Multi-step Word Problem: A real-world scenario requiring multiple operations to solve.

Start: 15
Day 1: -2
=13
Day 2: -2
=11
Day 3: -2
=9
Day 4: -2
=7
+3
=10
15
-
2
-
2
-
2
-
2
+
3
=
10
Start
15
Subtract
4 × 2 = 8
Add
+ 3
Total
15 - 8 + 3 = 10
Step 1: Start with 15 candies

Sarah begins with 15 candies

Step 2: Subtract 2 each day for 4 days

Day 1: 15 - 2 = 13, Day 2: 13 - 2 = 11, Day 3: 11 - 2 = 9, Day 4: 9 - 2 = 7

Step 3: Add 3 more candies

7 + 3 = 10

Step 4: Final count

Sarah has 10 candies

Sarah has 10 candies now
Final answer:

Sarah has 10 candies now

Applied rules:

• Sequential operations: Perform operations in the order given

• Real-world connection: Math applies to everyday situations

• Step-by-step tracking: Keep track of each change

Word Problem Tip: Break the problem into smaller steps!
Tracking Tip: Write down each step to follow the changes.
5 Alternating Pattern Challenge
Exercise 5
Start with 1. Add 2, subtract 1, add 2, subtract 1, and continue this pattern 5 times. What is the final number?
Definition:

Complex Alternating Pattern: A sequence of operations that alternates between different operations.

1
+2
=3
-1
=2
+2
=4
-1
=3
+2
=5
-1
=4
+2
=6
-1
=5
+2
=7
-1
=6
1
+
2
-
1
+
2
-
1
+
2
-
1
+
2
-
1
+
2
-
1
Start
1
Pattern
+2, -1
Repeat
5 times
Net effect
+1 each cycle
Step 1: Start with 1

Begin with the number 1

Step 2: Cycle 1 (+2, -1)

1 + 2 = 3, then 3 - 1 = 2

Step 3: Cycle 2 (+2, -1)

2 + 2 = 4, then 4 - 1 = 3

Step 4: Cycle 3 (+2, -1)

3 + 2 = 5, then 5 - 1 = 4

Step 5: Cycle 4 (+2, -1)

4 + 2 = 6, then 6 - 1 = 5

Step 6: Cycle 5 (+2, -1)

5 + 2 = 7, then 7 - 1 = 6

Final number: 6
Final answer:

The final number after 5 cycles is 6

Applied rules:

• Pattern recognition: Each cycle adds a net of 1 (+2 - 1 = +1)

• Sequential operations: Perform each operation in order

• Shortcuts: After 5 cycles: 1 + (5 × 1) = 6

Pattern Tip: Look for the net effect of each complete cycle!
Shortcut Tip: Find patterns that allow quicker calculations.
Detailed Summary: Repeated Addition and Subtraction
a + a + ... + a (n times) = n × a
a - b - b - ... - b (n times) = a - n × b
Fundamental Operation Formulas
Key definitions:

Repeated Addition: Adding the same number multiple times (e.g., 3 + 3 + 3 = 9)

Repeated Subtraction: Subtracting the same number multiple times (e.g., 10 - 2 - 2 - 2 = 4)

Pattern: A predictable sequence of numbers or operations

Alternating Operations: Performing different operations in a repeating sequence

Operation Methods:
  1. Identify the pattern: Recognize what operation(s) are being repeated
  2. Apply systematically: Perform each operation in the correct order
  3. Track intermediate results: Keep track of each step's outcome
  4. Verify accuracy: Check that each calculation is correct
  5. Look for shortcuts: Find efficient ways to calculate the final result
  6. Check the final answer: Ensure it makes sense in the context
Tip 1: Repeated addition leads to multiplication (3 + 3 + 3 = 3 × 3 = 9).
Tip 2: Repeated subtraction can be thought of as adding negative numbers.
Tip 3: Look for the net effect when operations alternate (+2, -1 = net +1).
Tip 4: Write down each step to avoid losing track of your calculations.
Tip 5: Check if your answer makes sense in the real-world context.
Common errors: Forgetting to continue the pattern, miscalculating intermediate steps.
Practice advice: Start with simple patterns, use visual aids, practice regularly.
Essential operation facts:

• Repeated addition: a + a + ... + a (n times) = n × a

• Repeated subtraction: a - b - b - ... - b (n times) = a - n × b

• Patterns help predict future values in sequences

• Alternating operations can be simplified by finding net effects

• Operations build number sense and mental math skills

• These concepts are foundational for multiplication and division

Pattern Recognition Path
1
Identify Pattern
2
Apply Operations
3
Track Results
4
Verify Answer

Questions & Answers

Question: Why do we learn repeated addition and subtraction? When will I use this?

Answer: These skills are very useful in daily life:

  • Shopping: Counting money, adding prices, making change
  • Time: Adding minutes, calculating elapsed time
  • Recipes: Doubling or halving ingredient amounts
  • Sports: Keeping score, calculating points
  • Foundation: Prepares you for multiplication and division

These patterns help you become better at math and solve real-world problems!

Question: How can I help my child practice these patterns at home?

Answer: Try these fun activities:

  • Counting games: Count by 2s, 5s, 10s while walking or driving
  • Money math: Add coins in patterns, make change
  • Calendar patterns: Count days, weeks, months
  • Recipe math: Double or halve measurements
  • Number lines: Move forward (add) and backward (subtract)

Make it a game and keep practice sessions short and positive!

Question: What if I get confused with alternating operations? It's hard to keep track!

Answer: Here are strategies to stay organized:

  • Write it down: Keep track of each step on paper
  • Use objects: Counters, blocks, or fingers to visualize
  • Take it slow: Do one operation at a time
  • Find patterns: Look for shortcuts like net effects
  • Check work: Go back and verify each step

Practice with simple numbers first, then work up to harder problems!