Solved Exercises on Subtraction Facts Within 20 in Grade 2

Master subtraction facts within 20: counting back, fact families, missing addends, subtraction strategies, number line method through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Counting back strategy
Exercise 1
Solve 12 - 5 using the counting back strategy.
Definition:

Counting back: Starting with the larger number and counting backward by the smaller number.

Counting back method:
  1. Start with the minuend (larger number)
  2. Count backward by the subtrahend (smaller number)
  3. Keep track of counts
12
←
11
←
10
←
9
←
8
←
7
Step 1: Start with the minuend

Start with 12 (the number we're subtracting from)

Step 2: Count back by the subtrahend

Count back 5: 11, 10, 9, 8, 7

Step 3: Record the final number

12 - 5 = 7

Counting back: 12 - 5

Start at 12, count back 5: 11, 10, 9, 8, 7

12 - 5 = 7
Final answer:

12 - 5 = 7 using the counting back strategy.

Applied rules:

• Minuend first: Begin counting from the larger number

• Count backward: Move backward by the number of counts equal to the smaller number

• Track counts: Keep count of each step to ensure accuracy

2 Fact families
Exercise 2
Show the fact family for 8 + 7 = 15.
Definition:

Fact family: A group of related addition and subtraction facts using the same three numbers.

8 + 7 = 15
→
7 + 8 = 15
→
15 - 8 = 7
→
15 - 7 = 8
Step 1: Start with the given addition fact

8 + 7 = 15

Step 2: Write the related addition fact

7 + 8 = 15 (commutative property)

Step 3: Write the related subtraction facts

15 - 8 = 7 and 15 - 7 = 8

Step 4: Verify all facts are correct

Check: 8 + 7 = 15 ✓, 7 + 8 = 15 ✓, 15 - 8 = 7 ✓, 15 - 7 = 8 ✓

Fact family: 8, 7, 15

Two addition facts and two subtraction facts

15 - 8 = 7, 15 - 7 = 8
Final answer:

The fact family for 8 + 7 = 15 includes: 8 + 7 = 15, 7 + 8 = 15, 15 - 8 = 7, 15 - 7 = 8.

Applied rules:

• Fact family principle: Three numbers create four related facts

• Commutative property: Order doesn't matter in addition

• Relationship principle: Addition and subtraction are inverse operations

3 Missing addends
Exercise 3
Find the missing number: 14 - ? = 9.
Definition:

Missing addend: Finding the unknown number in a subtraction equation.

9
10
11
12
13
14
Step 1: Understand the problem

We know: 14 - ? = 9

We need to find what number subtracted from 14 gives 9

Step 2: Use the inverse operation

Instead of 14 - ? = 9, think: 9 + ? = 14

What number added to 9 gives 14?

Step 3: Solve the addition problem

9 + 5 = 14

So the missing number is 5

Step 4: Verify the answer

14 - 5 = 9 ✓

Missing addend: 14 - ? = 9

Think: 9 + ? = 14, so ? = 5

14 - 5 = 9
Final answer:

The missing number is 5. 14 - 5 = 9.

Applied rules:

• Inverse relationship: Subtraction and addition are inverse operations

• Missing addend strategy: Convert subtraction to addition problem

• Verification: Always check the answer by substituting back

Subtraction Facts Within 20 Rules and Methods
12 - 5 = 7
Counting Back
Strategy 1
Counting Back
Start with minuend
Strategy 2
Fact Families
Related addition/subtraction
Strategy 3
Missing Addends
Use inverse operation
Key definitions:

Subtraction facts: Basic subtraction equations with minuends within 20

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

Subtrahend: The number being subtracted (the second number)

Difference: The result of a subtraction problem

Fact family: Related addition and subtraction facts using the same numbers

Complete methodology:
  1. Counting back: Start with minuend, count backward by subtrahend
  2. Fact families: Use related addition facts to solve subtraction
  3. Missing addends: Convert to addition using inverse operation
  4. Number line: Visual representation of subtraction
Tip 1: Always start counting from the larger number in subtraction.
Tip 2: Use addition facts to help solve subtraction problems.
Tip 3: Use fingers or counters to visualize the subtraction.
Tip 4: Remember: subtraction undoes addition.
Common errors: Counting forward instead of backward, forgetting to stop at the right count, confusing minuend and subtrahend.
Memory aid: "Start big, count small" for subtraction strategy.
Rules to remember:

• Step 1: Identify the minuend and subtrahend

• Step 2: Apply the chosen subtraction strategy

• Step 3: Verify the result by checking

• Step 4: Practice regularly for fluency

15 - 8 = 7
Example Subtraction
Solution: Exercises 4 to 5
4 Number line method
Exercise 4
Solve 16 - 7 using the number line method.
Definition:

Number line method: Using a visual number line to show subtraction as movement backward.

9
10
11
12
13
14
15
16
17
18
Step 1: Start at the minuend

Start at 16 on the number line

Step 2: Move backward by the subtrahend

Move 7 steps backward: 15, 14, 13, 12, 11, 10, 9

Step 3: Land on the difference

You land on 9

Step 4: Write the answer

16 - 7 = 9

Number line: 16 - 7

Start at 16, move 7 steps backward to 9

16 - 7 = 9
Final answer:

16 - 7 = 9 using the number line method.

Applied rules:

• Number line principle: Moving left represents subtraction

• Counting steps: Each step represents subtracting 1

• Visual tracking: See the distance between numbers

5 Word problem
Exercise 5
Sarah had 18 stickers. She gave 6 to her friend. How many stickers does Sarah have left?
Definition:

Word problem: A real-world scenario requiring subtraction to solve.

18
←
17
←
16
←
15
←
14
←
13
←
12
Step 1: Identify the numbers in the problem

Sarah started with 18 stickers

She gave away 6 stickers

Step 2: Set up the subtraction equation

18 - 6 = ?

Step 3: Solve using counting back

Start at 18, count back 6: 17, 16, 15, 14, 13, 12

Step 4: Write the answer in context

Sarah has 12 stickers left

Word problem: 18 - 6

Start with 18, take away 6, remaining is 12

18 - 6 = 12
Final answer:

Sarah has 12 stickers left after giving 6 to her friend.

Applied rules:

• Problem identification: Find the numbers and operation needed

• Context application: Apply mathematical solution to real situation

• Complete answer: Include units and context in final answer

Subtraction Facts Within 20 Laws, Methods, and Definitions
a - b ≠ b - a
Non-commutative Property
Key definitions:

Subtraction facts: Basic subtraction equations with minuends within 20 that should be memorized

Minuend: The number being subtracted from (first number in subtraction)

Subtrahend: The number being subtracted (second number in subtraction)

Difference: The result of a subtraction problem

Counting back: A strategy starting with the minuend and counting backward by the subtrahend

Fact family: A set of related addition and subtraction facts using the same three numbers

Complete methodology:
  1. Counting back: Start with minuend, count backward by subtrahend
  2. Fact families: Use related addition facts to solve subtraction
  3. Missing addends: Convert subtraction to addition using inverse operation
  4. Number line: Visual representation of subtraction as backward movement
  5. Verification: Always check the answer using addition
Tip 1: Always start counting from the larger number in subtraction.
Tip 2: Use addition facts to help solve subtraction problems.
Tip 3: Use the number line to visualize subtraction as moving backward.
Tip 4: Check your answer by adding the difference and subtrahend.
Common errors: Counting forward instead of backward, confusing minuend and subtrahend, forgetting to stop at the correct count.
Memory aids: "Start big, count small" for subtraction strategy.
Essential laws and rules:

• Non-commutative property: a - b ≠ b - a (order matters)

• Identity property: a - 0 = a (subtracting zero doesn't change the number)

• Subtraction principle: Take away the subtrahend from the minuend

• Inverse relationship: a - b = c means c + b = a

• Counting back rule: Start with minuend, count backward by subtrahend

15 - 8 = 7
Example Subtraction
Visual representation: Using counters or fingers helps students understand the concept of taking away quantities.
Real-world connection: Subtraction represents taking away or finding the difference between quantities.

Questions & Answers

Question: Why do we count backwards for subtraction? Why not count forwards?

Answer: Great question! Subtraction means taking away or removing:

  • Counting back: If you have 12 apples and take away 5, you go backward: 11, 10, 9, 8, 7
  • Counting forward: Would mean adding, not subtracting!

Think of it like walking backward on a number line - when you subtract, you move to smaller numbers!

It's like going down a staircase - you go from step 12 to step 11 to step 10, etc.

Question: What's a fact family? How does it help with subtraction?

Answer: A fact family uses 3 numbers to make 4 facts! It shows how addition and subtraction are related:

  • With numbers 8, 7, and 15: 8 + 7 = 15 and 7 + 8 = 15
  • Also: 15 - 8 = 7 and 15 - 7 = 8

It helps with subtraction because:

  • If you know 8 + 7 = 15, then you know 15 - 8 = 7
  • It connects addition and subtraction facts
  • You can use addition facts to solve subtraction problems

All four facts belong together like a family!

Question: My child gets confused with missing number problems like 14 - ? = 9. How can I help them?

Answer: Missing number problems can be solved by using the inverse operation:

  • For 14 - ? = 9: Think "what number added to 9 equals 14?"
  • Convert to addition: 9 + ? = 14
  • Solve: 9 + 5 = 14, so ? = 5

You can also use a number line:

  • Start at 9, count up to 14
  • Count how many steps: 10, 11, 12, 13, 14 (5 steps)
  • So the missing number is 5

Always check: 14 - 5 = 9 ✓

Question: What's the difference between minuend and subtrahend? They sound the same!

Answer: They sound similar but have different meanings:

  • Minuend: The first number in subtraction (the number you start with)
  • Subtrahend: The second number in subtraction (the number you take away)

In 15 - 8 = 7:

  • 15 is the minuend (what you start with)
  • 8 is the subtrahend (what you take away)
  • 7 is the difference (what's left)

Think of it like: "MINU-end is what you MINU-s from!"

Question: Why can't we switch the numbers in subtraction like we can in addition?

Answer: Addition and subtraction behave differently:

  • Addition is commutative: 5 + 3 = 3 + 5 = 8
  • Subtraction is not commutative: 5 - 3 ≠ 3 - 5

Think of it practically:

  • If you have 5 apples and take away 3, you have 2 left
  • If you have 3 apples and try to take away 5, you can't!

In subtraction, the order matters because you can't take away more than you have!