Solved Exercises on Using Number Line for Subtraction in Grade 2

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

Solution: Exercises 1 to 3
1 Basic subtraction
Exercise 1
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.

Number line method:
  1. Draw a number line with numbers from 0 to 20
  2. Start at the first number (minuend)
  3. Count backward by the second number (subtrahend)
  4. Land on the answer (difference)
Subtraction: 15 - 7
10
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12
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15
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18
19
20
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7
1
Start at 15 (the first number)
2
Count backward 7 steps (the second number)
3
Land on 8 (the answer)
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

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

2 Skip counting subtraction
Exercise 2
Subtract: 24 - 6 using skip counting on a number line
Definition:

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

Subtraction: 24 - 6 (Skip counting by 1s)
18
19
20
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23
24
25
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28
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30
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6
Step 1: Start at 24

Find 24 on the number line and mark it

Step 2: Count backward 6 steps

Move left: 23, 22, 21, 20, 19, 18

Step 3: Read the answer

You land on 18, so 24 - 6 = 18

Step 4: Verify the answer

Check: 18 + 6 = 24 ✓

24 - 6 = 18
Final answer:

24 - 6 = 18

Applied rules:

• Equal intervals: Count by 1s when subtracting small numbers

• Consistent movement: Move left by the same amount each step

• Verification: Add the answer to the subtracted number to check

3 Place value understanding
Exercise 3
Subtract: 35 - 12 using a number line
Definition:

Place value: The value of a digit based on its position in a number (tens, ones).

Subtraction: 35 - 12 (Break into tens and ones)
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22
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34
36
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42
44
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12
Step 1: Start at 35

Find 35 on the number line and mark it

Step 2: Break 12 into tens and ones

12 = 10 + 2, so count back 10 then 2 more

Step 3: Count backward 12 steps

Move left: 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23

Step 4: Read the answer

You land on 23, so 35 - 12 = 23

35 - 12 = 23
Final answer:

35 - 12 = 23

Applied rules:

• Place value breakdown: Split the subtrahend into tens and ones

• Step-by-step counting: Count backward by the total amount

• Visual tracking: Mark your starting and ending positions

Rules and methods, laws,...
A - B = C (where C is found by starting at A and moving B units left on the number line)
Number Line Subtraction Formula
Starting Point
A
Minuend (first number)
Movement
B units left
Subtrahend (second number)
Ending Point
C
Difference (answer)
Key definitions:

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

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

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

Difference: The result of subtraction (the answer).

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

Complete methodology:
  1. Draw the number line: Create a line with numbers at equal intervals
  2. Mark the starting point: Locate and mark the minuend on the number line
  3. Count backward: Move left by the number of spaces equal to the subtrahend
  4. Mark the ending point: The position you land on is the difference
  5. Read the answer: Identify the number at your ending position
  6. Verify: Add the difference to the subtrahend to check your answer
Tip 1: Always start at the first number in the subtraction.
Tip 2: 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 adding it back to the subtrahend.
Common errors: Starting at the wrong number, moving right instead of left, miscounting steps, forgetting to verify the answer.
Key insight: Moving left on a number line represents subtraction, while moving right represents addition.
Rules to remember:

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

• Move left: Count backward by the second number

• Equal intervals: Keep consistent spacing between numbers

• Verify answer: Check by adding difference + subtrahend = minuend

• Visual confirmation: The distance between numbers represents the subtraction

Solution: Exercises 4 to 5
4 Word problem
Exercise 4
Sarah had 28 stickers. She gave 13 stickers to her friend. How many stickers does Sarah have left? Use a number line to solve.
Definition:

Word problem: A mathematical problem presented in everyday language requiring translation to numerical operations.

Word Problem: 28 - 13
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23
24
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28
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Step 1: Identify the numbers

Sarah starts with 28 stickers and gives away 13 stickers.

Step 2: Set up the subtraction

28 - 13 (start at 28 and count back 13)

Step 3: Start at 28

Find 28 on the number line and mark it

Step 4: Count backward 13 steps

Move left: 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15

Step 5: Read the answer

You land on 15, so Sarah has 15 stickers left.

Step 6: Verify the answer

Check: 15 + 13 = 28 ✓

28 - 13 = 15
Final answer:

Sarah has 15 stickers left.

Applied rules:

• Problem identification: Recognize when to subtract

• Number line setup: Properly draw and label the number line

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

5 Multi-step subtraction
Exercise 5
Subtract: 42 - 18 using a number line (break into tens and ones)
Definition:

Multi-step subtraction: Breaking the subtrahend into tens and ones for easier counting on the number line.

Multi-step: 42 - 18 (18 = 10 + 8)
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42
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18
Step 1: Start at 42

Find 42 on the number line and mark it

Step 2: Break 18 into tens and ones

18 = 10 + 8, so we can count back 10 then 8 more

Step 3: Count backward 18 steps

Move left: 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24

Step 4: Read the answer

You land on 24, so 42 - 18 = 24

Step 5: Verify the answer

Check: 24 + 18 = 42 ✓

42 - 18 = 24
Final answer:

42 - 18 = 24

Applied rules:

• Breaking into parts: Split the subtrahend into manageable chunks

• Sequential counting: Count backward by each part separately

• Verification: Always check your answer by adding back

Complete Summary: Using Number Line for Subtraction
A - B = C (where C is found by starting at A and moving B units left on the number line)
Number Line Subtraction Formula
Key definitions:

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

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

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

Difference: The result of subtraction (the answer).

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

Counting backward: Moving from a higher number to a lower number on the number line.

Complete methodology:
  1. Draw the number line: Create a line with numbers at equal intervals covering the range needed
  2. Mark the starting point: Locate and mark the minuend (first number) on the number line
  3. Count backward: Move left by the number of spaces equal to the subtrahend (second number)
  4. Mark the ending point: The position you land on is the difference
  5. Read the answer: Identify the number at your ending position
  6. Verify: Add the difference to the subtrahend to check your answer
Tip 1: Always start at the first number in the subtraction.
Tip 2: 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 adding it back to the subtrahend.
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 right instead of left, miscounting steps, forgetting to verify the answer, drawing uneven intervals on the number line.
Key insight: Moving left on a number line represents subtraction, while moving right represents addition.
Memory aid: Think of subtraction as "going backward" on the number line.
Checking method: Always verify by adding your answer to the subtracted number to see if you get the original number.
Rules to know by heart:

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

• Move left: Count backward by the second number

• Equal intervals: Keep consistent spacing between numbers

• Verify answer: Check by adding difference + subtrahend = minuend

• Visual confirmation: The distance between numbers represents the subtraction

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

• Consistent direction: Always move in the same direction (left) for subtraction

Multiple Examples

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

Place value breakdown: 35 - 12 (break 12 into 10 + 2)

Word problem: 28 - 13 (contextual subtraction)

Multi-step: 42 - 18 (break 18 into 10 + 8)

Verification: 28 - 13 = 15, so 15 + 13 = 28 ✓

Questions & Answers

Question: Why do I need to move left on the number line when subtracting? It seems backwards.

Answer: Great question! Moving left on the number line represents getting smaller, which is what subtraction does. Think of it like this:

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

For example, if you have 10 cookies and eat 3, you now have fewer cookies. On the number line, you go from 10 to 7, which means moving left.

You can also think of it as "taking away" - when you take away from a number, you end up with less, so you move toward the smaller numbers on the left side of the number line.

Question: My child gets confused when subtracting larger numbers like 24 - 17. How can I help them use the number line effectively?

Answer: For larger numbers, it's helpful to break the subtraction into smaller, more manageable parts:

  1. Start at 24 on the number line
  2. Break 17 into 10 + 7 (or 15 + 2, or another combination that works)
  3. Count back 10 first: 24 → 23 → 22 → 21 → 20 → 19 → 18 → 17 → 16 → 15 → 14
  4. Then count back 7 more: 14 → 13 → 12 → 11 → 10 → 9 → 8 → 7

Alternatively, you can teach them to "jump" by tens first, then count the remaining ones. This makes the process faster and less prone to counting errors.

You can also use different colors to mark the starting point (red) and ending point (green) to make the visual clearer.

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. Addition Check: Take your answer and add the number you subtracted. You should get back to your starting number.
  2. Reverse Operation: If you did 24 - 17 = 7, check by doing 7 + 17 = 24

For example, if you found that 35 - 12 = 23 using the number line, you can check: 23 + 12 = 35 ✓

You can also do a quick mental check: Does the answer make sense? If I start with 35 and take away 12, should I get a number that's about 23? Yes, because 35 - 10 = 25, and taking away 2 more gives 23.

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