Solved Exercises on Using Number Line to Add and Subtract in Grade 2

Master addition and subtraction using number lines: counting forward/backward, skip counting, and problem-solving strategies through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Basic addition
Exercise 1
Add: 12 + 5 using a number line
Definition:

Number line addition: A visual method of addition where you start at the first number and count forward by the amount of the second number.

Number line method:
  1. Draw a number line with numbers from 0 to 20
  2. Start at the first number (addend)
  3. Count forward by the second number (addend)
  4. Land on the answer (sum)
Addition: 12 + 5
10
11
12
13
14
15
16
17
18
19
20
1
2
3
4
5
1
Start at 12 (the first number)
2
Count forward 5 steps (the second number)
3
Land on 17 (the answer)
Step 1: Start at 12

Find 12 on the number line and mark it

Step 2: Count forward 5 steps

Move right: 13, 14, 15, 16, 17

Step 3: Read the answer

You land on 17, so 12 + 5 = 17

12 + 5 = 17
Final answer:

12 + 5 = 17

Applied rules:

• Start at first addend: Begin at the first number in the addition

• Move right: Count forward by the second number

• End at sum: The final position is the answer

2 Basic subtraction
Exercise 2
Subtract: 15 - 7 using a number line
Definition:

Number line subtraction: A visual method of subtraction where you start at the first number and count backward by the amount of the second number.

Subtraction: 15 - 7
10
11
12
13
14
15
16
17
18
19
20
1
2
3
4
5
6
7
Step 1: Start at 15

Find 15 on the number line and mark it

Step 2: Count backward 7 steps

Move left: 14, 13, 12, 11, 10, 9, 8

Step 3: Read the answer

You land on 8, so 15 - 7 = 8

Step 4: Verify the answer

Check: 8 + 7 = 15 ✓

15 - 7 = 8
Final answer:

15 - 7 = 8

Applied rules:

• Start at minuend: Begin at the first number in the subtraction

• Move left: Count backward by the second number

• End at difference: The final position is the answer

3 Comparing addition and subtraction
Exercise 3
Compare: 18 + 4 and 18 - 4 using number lines
Definition:

Comparison: Understanding the relationship between addition and subtraction operations on a number line.

Addition: 18 + 4 Addition
18
19
20
21
22
1
2
3
4
18 + 4 = 22
Subtraction: 18 - 4 Subtraction
14
15
16
17
18
1
2
3
4
18 - 4 = 14
Step 1: Addition 18 + 4

Start at 18, move right 4 steps: 19, 20, 21, 22

Step 2: Subtraction 18 - 4

Start at 18, move left 4 steps: 17, 16, 15, 14

Step 3: Compare the results

Addition makes the number larger (22 > 18), subtraction makes it smaller (14 < 18)

18 + 4 = 22 and 18 - 4 = 14
Final answer:

18 + 4 = 22, 18 - 4 = 14

Applied rules:

• Addition moves right: Forward on the number line increases the value

• Subtraction moves left: Backward on the number line decreases the value

• Same starting point: Both operations start at the same number

Rules and methods, laws,...
A + B = C (where C is found by starting at A and moving B units right on the number line)
A - B = C (where C is found by starting at A and moving B units left on the number line)
Number Line Operations Formula
Addition
Move Right
Forward on number line
Subtraction
Move Left
Backward on number line
Direction Rule
Right = Add, Left = Subtract
Key directional rule
Key definitions:

Number line: A straight line with numbers placed at equal intervals.

Addition: Finding the sum of two or more numbers by combining them.

Subtraction: Finding the difference between two numbers by taking one away from another.

Addend: Numbers being added together.

Sum: The result of addition.

Minuend: The number being subtracted from (the first number).

Subtrahend: The number being subtracted (the second number).

Difference: The result of subtraction (the answer).

Complete methodology:
  1. Draw the number line: Create a line with numbers at equal intervals
  2. Identify the operation: Determine if it's addition (move right) or subtraction (move left)
  3. Mark the starting point: Locate and mark the first number on the number line
  4. Count in the correct direction: Move right for addition, left for subtraction
  5. Mark the ending point: The position you land on is the answer
  6. Read the answer: Identify the number at your ending position
  7. Verify: Check your answer by performing the inverse operation
Tip 1: Always start at the first number in the operation.
Tip 2: Move right (forward) when adding, move left (backward) when subtracting.
Tip 3: Count each step carefully to avoid mistakes.
Tip 4: Use skip counting for larger numbers (count by 2s, 5s, or 10s).
Tip 5: Break larger numbers into tens and ones for easier counting.
Tip 6: Always verify your answer by using the inverse operation.
Common errors: Starting at the wrong number, moving in the wrong direction, miscounting steps, forgetting to verify the answer.
Key insight: Moving right on a number line represents addition, while moving left represents subtraction.
Rules to remember:

• Addition direction: Move right (forward) on the number line

• Subtraction direction: Move left (backward) on the number line

• Start at first number: Begin at the first number in the operation

• Equal intervals: Keep consistent spacing between numbers

• Verify answer: Check by using the inverse operation

Solution: Exercises 4 to 5
4 Word problem with mixed operations
Exercise 4
Tom had 25 marbles. His friend gave him 8 more marbles. Then Tom lost 6 marbles. How many marbles does Tom have now? Use a number line to solve.
Definition:

Mixed operations: Problems that involve both addition and subtraction operations.

Mixed Operations: 25 + 8 - 6
20
22
24
26
28
30
32
34
36
38
1
2
3
4
5
6
7
8
-1
-2
-3
-4
-5
-6
Step 1: Identify the operations

Tom starts with 25, adds 8, then subtracts 6: 25 + 8 - 6

Step 2: First operation - Addition

Start at 25, move right 8 steps: 26, 27, 28, 29, 30, 31, 32, 33

Step 3: Second operation - Subtraction

From 33, move left 6 steps: 32, 31, 30, 29, 28, 27

Step 4: Read the answer

You land on 27, so Tom has 27 marbles.

Step 5: Verify the answer

Check: 25 + 8 = 33, then 33 - 6 = 27 ✓

25 + 8 - 6 = 27
Final answer:

Tom has 27 marbles.

Applied rules:

• Sequence of operations: Perform operations in order given

• Direction changes: Addition moves right, subtraction moves left

• Contextual answer: Provide the answer in context of the problem

5 Skip counting for larger numbers
Exercise 5
Add: 34 + 16 using skip counting on a number line
Definition:

Skip counting: Counting by equal intervals (by 2s, 5s, or 10s) to make addition/subtraction faster.

Skip Counting: 34 + 16 (count by 10s then 6s)
30
32
34
36
38
40
42
44
46
48
50
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Step 1: Start at 34

Find 34 on the number line and mark it

Step 2: Break 16 into tens and ones

16 = 10 + 6, so we can count forward 10 then 6 more

Step 3: Count forward 16 steps

Move right: 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50

Step 4: Read the answer

You land on 50, so 34 + 16 = 50

Step 5: Verify the answer

Check: 50 - 16 = 34 ✓

34 + 16 = 50
Final answer:

34 + 16 = 50

Applied rules:

• Breaking into parts: Split the addend into manageable chunks

• Sequential counting: Count forward by each part separately

• Verification: Always check your answer by using the inverse operation

Complete Summary: Using Number Line to Add and Subtract
A + B = C (where C is found by starting at A and moving B units right on the number line)
A - B = C (where C is found by starting at A and moving B units left on the number line)
Number Line Operations Formula
Key definitions:

Number line: A straight line with numbers placed at equal intervals.

Addition: Finding the sum of two or more numbers by combining them.

Subtraction: Finding the difference between two numbers by taking one away from another.

Addend: Numbers being added together.

Sum: The result of addition.

Minuend: The number being subtracted from (the first number).

Subtrahend: The number being subtracted (the second number).

Difference: The result of subtraction (the answer).

Skip counting: Counting by equal intervals (by 2s, 5s, or 10s) to make operations faster.

Complete methodology:
  1. Draw the number line: Create a line with numbers at equal intervals covering the range needed
  2. Identify the operation: Determine if it's addition (move right) or subtraction (move left)
  3. Mark the starting point: Locate and mark the first number on the number line
  4. Count in the correct direction: Move right for addition, left for subtraction
  5. Mark the ending point: The position you land on is the answer
  6. Read the answer: Identify the number at your ending position
  7. Verify: Check your answer by using the inverse operation
Tip 1: Always start at the first number in the operation.
Tip 2: Move right (forward) when adding, move left (backward) when subtracting.
Tip 3: Count each step carefully to avoid mistakes.
Tip 4: Use skip counting for larger numbers (count by 2s, 5s, or 10s).
Tip 5: Break larger numbers into tens and ones for easier counting.
Tip 6: Always verify your answer by using the inverse operation.
Tip 7: Use different colors or marks to distinguish starting and ending points.
Tip 8: Practice with small numbers first before moving to larger ones.
Common errors: Starting at the wrong number, moving in the wrong direction, miscounting steps, forgetting to verify the answer, drawing uneven intervals on the number line.
Key insight: Moving right on a number line represents addition, while moving left represents subtraction.
Memory aid: Think of addition as "going forward" and subtraction as "going backward" on the number line.
Checking method: Always verify by using the inverse operation (addition to check subtraction, subtraction to check addition).
Rules to know by heart:

• Addition direction: Move right (forward) on the number line

• Subtraction direction: Move left (backward) on the number line

• Start at first number: Begin at the first number in the operation

• Equal intervals: Keep consistent spacing between numbers

• Verify answer: Check by using the inverse operation

• Break large numbers: For numbers greater than 10, break into tens and ones

• Consistent direction: Always move in the correct direction for each operation

Multiple Examples

Basic addition: 12 + 5 (count forward 5 steps from 12)

Basic subtraction: 15 - 7 (count backward 7 steps from 15)

Comparison: 18 + 4 vs 18 - 4 (same starting point, opposite directions)

Word problem: 25 + 8 - 6 (mixed operations in sequence)

Skip counting: 34 + 16 (break 16 into 10 + 6)

Verification: 12 + 5 = 17, so 17 - 5 = 12 ✓

Questions & Answers

Question: Why do I move right when adding and left when subtracting? How do I remember which direction to go?

Answer: Great question! The direction represents what happens to the number:

  • Adding: Makes numbers bigger, so we move right (toward larger numbers)
  • Subtracting: Makes numbers smaller, so we move left (toward smaller numbers)

Here's a memory trick:

  • Add = "go forward" (move right on the number line)
  • Subtract = "go backward" (move left on the number line)

Think of it like walking: if you're standing at 10 and you "add" 3 steps forward, you walk right to 13. If you "subtract" 3 steps, you walk left to 7.

Question: My child gets confused when doing mixed operations like 25 + 8 - 6. How can I help them keep track of the direction changes?

Answer: For mixed operations, break the problem into separate steps:

  1. First operation: 25 + 8 (start at 25, move right 8 steps to reach 33)
  2. Second operation: 33 - 6 (start at 33, move left 6 steps to reach 27)

You can also use different colored markers or arrows to represent each operation:

  • Use green arrows for addition (moving right)
  • Use red arrows for subtraction (moving left)

Another helpful strategy is to think of it as a story: "I start with 25 marbles, get 8 more (move right), then lose 6 (move left)." This helps visualize the sequence of events.

Question: How can I check if my answer is correct when using the number line?

Answer: There are two good ways to check your answer:

  1. Use the inverse operation: If you did addition, check by subtracting. If you did subtraction, check by adding.
  2. Double-check on the number line: Repeat the steps to make sure you counted correctly.

For example:

  • If you found that 12 + 5 = 17, check by doing 17 - 5 = 12 ✓
  • If you found that 15 - 7 = 8, check by doing 8 + 7 = 15 ✓

You can also do a quick mental check: Does the answer make sense? If I start with 15 and take away 7, should I get a number that's about 8? Yes, because 15 - 5 = 10, and taking away 2 more gives 8.

Checking your work is an important habit that will help you catch mistakes early!