Subtraction Within 20 Assessment for 1st Grade

Master subtraction concepts: counting back, number lines, fact families, and word problems through these 3 detailed exercises.

Subtraction Exercises 1 to 3
1 Counting Back Method
Exercise 1
Solve: 15 - 7 = ?
Use the counting back method.
Definition:

Subtraction: Taking away a number from another number to find the difference.

Counting Back Method:
  1. Start with the larger number (15)
  2. Count backwards by the smaller number (7 steps)
  3. Land on the answer
Starting Number
15
Steps Back
7
Answer
8
Step 1: Start with 15

15, 14, 13, 12, 11, 10, 9, 8

Step 2: Count back 7 numbers

15 - 1 = 14, 14 - 1 = 13, 13 - 1 = 12, 12 - 1 = 11, 11 - 1 = 10, 10 - 1 = 9, 9 - 1 = 8

Step 3: Final Answer

15 - 7 = 8

15 - 7 = 8
Final answer:

15 - 7 = 8

Applied rules:

• Counting Back: Subtract by counting backwards from the starting number

• Number Line Concept: Moving left on the number line

• Verification: Add the answer to the subtracted number to check: 8 + 7 = 15

2 Number Line Strategy
Exercise 2
Solve: 18 - 9 = ?
Use the number line strategy.
Definition:

Number Line Strategy: Using a visual number line to move backwards from the starting number.

Starting Number
18
Steps Back
9
Answer
9
Step 1: Start at 18 on the number line

Visual representation: ← ← ← ← ← ← ← ← ← 18

Step 2: Move 9 spaces to the left

18 → 17 → 16 → 15 → 14 → 13 → 12 → 11 → 10 → 9

Step 3: Land on 9

18 - 9 = 9

18 - 9 = 9
Final answer:

18 - 9 = 9

Applied rules:

• Number Line: Moving left represents subtraction

• Equal Groups: 9 and 9 make 18, so 18 - 9 = 9

• Verification: Add the answer to the subtracted number: 9 + 9 = 18

3 Fact Family Approach
Exercise 3
Solve: 16 - 8 = ?
Use fact family relationships.
Definition:

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

Numbers
8, 8, 16
Related Facts
8+8=16
Result
16-8=8
Step 1: Identify the fact family

For 8, 8, and 16: 8 + 8 = 16

Step 2: Apply the inverse operation

If 8 + 8 = 16, then 16 - 8 = 8

Step 3: Verify the answer

8 + 8 = 16, so 16 - 8 = 8

Step 4: Complete the fact family

16 - 8 = 8, 16 - 8 = 8, 8 + 8 = 16, 8 + 8 = 16

16 - 8 = 8
Final answer:

16 - 8 = 8

Applied rules:

• Fact Families: Addition and subtraction are inverse operations

• Part-Part-Whole: 8 and 8 are parts that make the whole 16

• Verification: Use addition to check subtraction: 8 + 8 = 16

Subtraction Methods and Strategies
Minuend - Subtrahend = Difference
Subtraction Structure
Method 1
Counting Back
Start with larger number, count backward
Method 2
Number Line
Move left on number line
Method 3
Fact Families
Use related addition facts
Key definitions:

Minuend: The number being subtracted from (top number)

Subtrahend: The number being subtracted (bottom number)

Difference: The result of subtraction

Subtraction Strategies:
  1. Counting Back: Start with the larger number and count backward
  2. Number Line: Move left on a visual number line
  3. Fact Families: Use related addition facts
  4. Make Ten: Break apart numbers to make subtraction easier
Tip 1: Always start with the larger number in subtraction.
Tip 2: Use your fingers to count back when needed.
Tip 3: Check your answer by adding the result to the subtracted number.
Tip 4: Look for doubles facts to help with subtraction.
Common errors: Forgetting to count the starting number, mixing up minuend and subtrahend, incorrect counting.
Key concepts: Subtraction means taking away, finding difference, or comparing quantities.
Important Subtraction Facts:

• Any number minus itself equals zero: n - n = 0

• Any number minus zero equals itself: n - 0 = n

• Subtraction is not commutative: a - b ≠ b - a

• Subtraction is the inverse of addition: a - b = c means c + b = a

Visual Aids and Practice Problems
4 Visual Representation
Exercise 4
Show 14 - 6 using pictures or dots.
Definition:

Visual Subtraction: Representing subtraction using physical objects, drawings, or pictures.

Total Objects
●●●●●●●●●●●●●●
Take Away
●●●●●●
Left Over
●●●●●●●●
Step 1: Draw 14 circles

●●●●●●●●●●●●●●

Step 2: Cross out 6 circles

●●●●●●●●●●●●●● → ●●●●●●●●

Step 3: Count remaining circles

There are 8 circles left

14 - 6 = 8
Final answer:

14 - 6 = 8

Applied rules:

• Concrete Representation: Physical objects help visualize subtraction

• One-to-One Correspondence: Each circle represents one unit

• Conservation of Number: Total changes when items are removed

5 Word Problem
Exercise 5
Sarah had 17 stickers. She gave 9 to her friend. How many does she have left?
Definition:

Word Problem: A real-life situation that requires mathematical operations to solve.

Initial Amount
17
Given Away
9
Remaining
8
Step 1: Identify the total amount

Sarah started with 17 stickers

Step 2: Identify what was taken away

She gave 9 stickers to her friend

Step 3: Set up the subtraction

17 - 9 = ?

Step 4: Solve using counting back

17, 16, 15, 14, 13, 12, 11, 10, 9 → That's 8 steps back

Sarah has 8 stickers left
Final answer:

Sarah has 8 stickers left

Applied rules:

• Keywords: "gave" indicates subtraction

• Real-Life Context: Connect math to everyday situations

• Verification: Check if 8 + 9 = 17

Subtraction Within 20: Laws, Methods, and Definitions
A - B = C
Basic Subtraction
Key definitions:

Subtraction: An operation that finds the difference between two numbers.

Minuend: The number being subtracted from (A in A-B=C).

Subtrahend: The number being subtracted (B in A-B=C).

Difference: The result of subtraction (C in A-B=C).

Subtraction Methods:
  1. Counting Back: Start with the larger number and count backward by the smaller number
  2. Number Line: Move left on a number line from the starting number
  3. Fact Families: Use related addition facts to find subtraction answers
  4. Draw Pictures: Draw objects and cross out the number being subtracted
  5. Think Addition: Think "What number added to the subtrahend equals the minuend?"
Tip 1: Use your fingers to count back when solving subtraction problems.
Tip 2: Remember that subtraction is the opposite of addition.
Tip 3: Always check your answer by adding the difference to the subtrahend.
Tip 4: Practice doubles facts (like 6+6=12) to help with subtraction (12-6=6).
Common errors: Starting with the wrong number, counting incorrectly, forgetting to count the starting number when counting back.
Exam preparation: Practice all methods, memorize basic subtraction facts, work on word problems.
Subtraction Properties:

• Identity Property: n - 0 = n (any number minus zero equals itself)

• Zero Property: n - n = 0 (any number minus itself equals zero)

• Inverse Property: If a - b = c, then c + b = a

• Non-Commutative: a - b ≠ b - a (order matters in subtraction)

Questions & Answers

Question: I don't understand how to do subtraction when the number I'm subtracting is bigger than the number I'm starting with. Like 5 - 8. Is that possible?

Answer: Great question! In 1st grade math, we focus on subtraction where the starting number (minuend) is larger than the number we're subtracting (subtrahend). This ensures we get positive answers.

So for 5 - 8, we would say "we can't take 8 away from 5" because we don't have enough to take away. We'll learn about negative numbers later in school!

For now, always make sure the first number is bigger than the second number in subtraction. For example: 8 - 5 = 3 is okay, but 5 - 8 is too advanced for now.

Question: My child gets confused when doing subtraction. They sometimes subtract the wrong way around. How can I help them remember which number to start with?

Answer: This is very common! Here are some helpful strategies:

  • Tell your child "start with the bigger number" - in 12 - 5, start with 12
  • Use the phrase "take away" - "take 5 away from 12" means start with 12
  • Use manipulatives like blocks or counters - physically remove items from the larger group
  • Point to the first number in the problem and emphasize "this is where we start"

You can also create stories: "I had 12 cookies and ate 5. How many are left?" The larger number (12) is what we start with.

Question: I sometimes forget if subtraction is the same as addition. Are they different?

Answer: Yes, they are completely different operations! Here's how to remember:

  • Addition (+): Joining groups together to make a bigger number
  • Subtraction (-): Taking away from a group to make a smaller number

Think of it this way: Addition is like getting more toys (making more), and subtraction is like giving away toys (making less).

They are actually opposites, or "inverse operations." If 5 + 3 = 8, then 8 - 3 = 5 and 8 - 5 = 3.