Solved Exercises on Subtraction Within Ten in 1st Grade

Master subtraction within ten: basic concepts, counting backwards, and visual methods through these 3 detailed exercises.

Solution: Exercises 1 to 3
1 Basic subtraction
Exercise 1
Solve:
\(8 - 3 = ?\)
Definition:

Subtraction: Taking away objects from a group. Start with 8 objects, take away 3, count what remains.

Subtraction method:
  1. Start with the first number (8)
  2. Take away the second number (3)
  3. Count what remains
8
-
3
=
5
Start with 8
A
B
O
G
S
C
V
A
Take away 3
A
B
O
G
S
C
V
A
Remain 5
G
S
C
V
A
Step 1: Start with 8 objects

We have 8 apples: 🍎🍎🍎🍎🍎🍎🍎🍎

Step 2: Take away 3 objects

We remove 3 apples: 🍎🍎🍎~~🍎🍎🍎🍎~~

Step 3: Count remaining objects

We have 5 apples left: 🍎🍎🍎🍎🍎

\(8 - 3 = 5\)
Final answer:

\(8 - 3 = 5\)

Applied rules:

• Subtraction: Taking away objects from a group

• Counting: Count what remains after taking away

• Visual method: Using objects to represent numbers

2 Counting backwards
Exercise 2
Solve:
\(7 - 4 = ?\)
Definition:

Counting backwards: Start from the first number and count backwards the amount of the second number.

7
6
5
4
3
0
1
2
3
4
5
6
7
↓
Step 1: Start at 7

We begin at the number 7

Step 2: Count backwards 4 steps

From 7, we move back 4 steps: 7 → 6 → 5 → 4 → 3

Step 3: The answer is 3

We land on the number 3

\(7 - 4 = 3\)
Final answer:

\(7 - 4 = 3\)

Applied rules:

• Counting backwards: Move left on the number line

• Subtraction: Each step backward represents taking away 1

• Number line: Visual representation of numbers in order

3 Subtraction facts
Exercise 3
Solve:
\(10 - 6 = ?\)
Definition:

Subtraction facts: Knowing subtraction combinations automatically. Use counting backwards or think of addition.

10
-
6
=
4
Start with 10
A
B
O
G
S
C
V
A
B
O
Take away 6
A
B
O
G
S
C
V
A
B
O
Remain 4
V
A
B
O
Step 1: Start with 10 objects

We have 10 stars: ⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐

Step 2: Take away 6 objects

We remove 6 stars: ⭐⭐⭐⭐⭐⭐~~⭐⭐⭐⭐~~

Step 3: Count remaining objects

We have 4 stars left: ⭐⭐⭐⭐

\(10 - 6 = 4\)
Final answer:

\(10 - 6 = 4\)

Applied rules:

• Subtraction: Taking away objects from a group

• Counting backwards: From 10, count backwards 6 steps

• Think addition: What number added to 6 makes 10? (6 + 4 = 10)

Worksheet Practice Problems
\(a - b = c\)
Subtraction Within Ten
Subtract 0
\(a - 0 = a\)
Any number minus 0 stays the same
Subtract itself
\(a - a = 0\)
Any number minus itself equals 0
Count backwards
\(a - 1\)
Move one step back on number line
7-2
5
9-4
5
6-1
5
8-5
3
10-7
3
5-2
3
9-3
6
8-2
6
10-4
6
All Subtraction Facts within 10:
  • 10 - 0 = 10, 10 - 1 = 9, 10 - 2 = 8, 10 - 3 = 7, 10 - 4 = 6, 10 - 5 = 5, 10 - 6 = 4, 10 - 7 = 3, 10 - 8 = 2, 10 - 9 = 1, 10 - 10 = 0
  • 9 - 0 = 9, 9 - 1 = 8, 9 - 2 = 7, 9 - 3 = 6, 9 - 4 = 5, 9 - 5 = 4, 9 - 6 = 3, 9 - 7 = 2, 9 - 8 = 1, 9 - 9 = 0
  • 8 - 0 = 8, 8 - 1 = 7, 8 - 2 = 6, 8 - 3 = 5, 8 - 4 = 4, 8 - 5 = 3, 8 - 6 = 2, 8 - 7 = 1, 8 - 8 = 0
  • 7 - 0 = 7, 7 - 1 = 6, 7 - 2 = 5, 7 - 3 = 4, 7 - 4 = 3, 7 - 5 = 2, 7 - 6 = 1, 7 - 7 = 0
  • 6 - 0 = 6, 6 - 1 = 5, 6 - 2 = 4, 6 - 3 = 3, 6 - 4 = 2, 6 - 5 = 1, 6 - 6 = 0
  • 5 - 0 = 5, 5 - 1 = 4, 5 - 2 = 3, 5 - 3 = 2, 5 - 4 = 1, 5 - 5 = 0
Key Subtraction Rules:

• Subtraction is not commutative: \(a - b ≠ b - a\)

• Subtraction makes numbers smaller: \(a - b < a\) when \(b > 0\)

• You cannot subtract a larger number from a smaller number: In 1st grade, we only subtract equal or smaller numbers

Visual Methods for Subtraction
\(8 - 3 = 5\)
Visual Subtraction
Visual methods:

Finger counting: Use fingers to represent numbers and fold down fingers to subtract.

Object manipulation: Use physical objects like blocks or counters.

Number lines: Move backwards on a number line to subtract.

Step-by-step approach:
  1. Identify the starting number: Show this many objects or fingers
  2. Identify how many to take away: This is the number being subtracted
  3. Remove the specified number: Cross out or physically take away objects
  4. Count remaining objects: This is your answer
Tip 1: Use fingers to solve subtraction problems up to 10.
Tip 2: Draw circles and cross out to visualize subtraction.
Tip 3: Practice counting backwards from any number.
Tip 4: Remember: bigger number comes first in subtraction.
Common errors: Subtracting the wrong way, forgetting to count what remains, counting the removed items instead of the remaining ones.
Practice strategies: Use manipulatives, draw pictures, count on fingers, relate to addition facts.
Important concepts to remember:

• Subtraction means taking away or finding the difference

• The answer to a subtraction problem is called the difference

• Always start with the bigger number first in 1st grade problems

• You can check your answer by adding the difference back to the subtracted number

Detailed Summary: Subtraction Within Ten
Complete Learning Guide
Definition of Subtraction: Subtraction is the mathematical operation that involves taking away objects from a group. It finds the difference between two numbers. The symbol "-" is used for subtraction.
Key Terms:
  • Minuend: The first number in a subtraction problem (the number being subtracted from)
  • Subtrahend: The second number in a subtraction problem (the number being subtracted)
  • Difference: The answer to a subtraction problem
  • Example: In 8 - 3 = 5, 8 is the minuend, 3 is the subtrahend, and 5 is the difference
Core Rules of Subtraction:
  • Zero Rule: Any number minus 0 equals the same number (a - 0 = a)
  • Identity Rule: Any number minus itself equals 0 (a - a = 0)
  • Non-commutative: Order matters in subtraction (a - b ≠ b - a)
  • Subtraction makes numbers smaller: a - b < a when b > 0
Step-by-Step Method:
  1. Identify the minuend (starting number)
  2. Identify the subtrahend (number to subtract)
  3. Use visual aids, fingers, or counting backwards
  4. Count the remaining objects
  5. Write the difference
Visual Methods:
  • Finger Counting: Use fingers to represent the minuend, then fold down fingers equal to the subtrahend
  • Drawing Objects: Draw circles or shapes representing the minuend, cross out the number of shapes equal to the subtrahend
  • Number Line: Start at the minuend and move backwards by the number of spaces equal to the subtrahend
  • Manipulatives: Use physical objects like blocks, counters, or toys
Examples (Simple to Advanced):
  • Simple: 5 - 1 = 4 (start with 5, take away 1, get 4)
  • Medium: 7 - 3 = 4 (start with 7, take away 3, get 4)
  • Advanced: 10 - 6 = 4 (start with 10, take away 6, get 4)
Tips and Tricks:
  • Always check your answer by adding the difference to the subtrahend to get the minuend
  • Think of subtraction as "how many are left?"
  • Practice counting backwards to improve mental subtraction
  • Memorize subtraction facts within 10 for faster calculations
  • Use the "think addition" strategy: if 7 - 3 = ?, think "what number added to 3 equals 7?"
Common Pitfalls:
  • Subtracting the wrong way (smaller number minus larger number)
  • Counting the removed objects instead of the remaining ones
  • Forgetting to count zero when all objects are taken away
  • Mixing up the minuend and subtrahend
Memory Aids:
  • "Subtraction means take away!"
  • "The answer gets smaller!"
  • "Bigger number first, smaller number second!"
  • Practice with hands-on materials to build conceptual understanding
Checking Your Work: Always verify your subtraction by adding the difference to the number you subtracted. For example, if 8 - 3 = 5, check: 5 + 3 = 8 ✓

Questions & Answers

Question: I don't understand how to do subtraction when the numbers are close together like 7 - 6. Can you explain how to think about it?

Answer: Great question! When numbers are close together like 7 - 6, here are helpful ways to think about it:

  • Count backwards: Start at 7 and count backwards 6 steps: 7, 6, 5, 4, 3, 2, 1. You land on 1.
  • Use your fingers: Hold up 7 fingers, put down 6 fingers. How many are still up? 1 finger!
  • Think of it as "what's left": If you have 7 cookies and eat 6, how many are left? 1 cookie.
  • Think addition: What number added to 6 makes 7? 6 + 1 = 7, so 7 - 6 = 1.

For 7 - 6 specifically, you're just taking away 6 out of 7 things, leaving 1 thing behind. It's like having 7 toys and giving 6 to a friend - you keep 1 toy.

The key is recognizing that when the second number is close to the first number, the answer will be small!

Question: Why can't I do 3 - 8? My older sibling says it's impossible, but why?

Answer: You're asking an excellent question! In 1st grade math, we focus on subtraction where we take away fewer objects than we start with. Let me explain:

  • If you have 3 apples, you can't give away 8 apples because you don't have 8 apples to begin with!
  • It's like trying to eat 8 cookies when you only have 3 cookies - impossible!
  • In 1st grade, we learn subtraction where the first number is always equal to or bigger than the second number.

Later in school, you'll learn about negative numbers which allow us to do 3 - 8, but for now, we stick to problems where we don't take away more than we have.

So for now, always make sure the first number is bigger than or equal to the second number!

Question: How do I know if my subtraction answer is right? Sometimes I'm not sure about my answer.

Answer: Checking your subtraction is a smart habit! Here are ways to verify your answer:

  • Addition check: Take your answer and add back the number you subtracted. For 8 - 3 = 5, check: 5 + 3 = 8 ✓
  • Draw pictures: Draw 8 circles, cross out 3, count the remaining ones.
  • Use objects: Count out 8 blocks, take away 3, count what's left.
  • Count up: From your answer, count up by the subtracted number to see if you reach the original number.

For example, if you calculated 9 - 4 = 5, check by adding: 5 + 4 = 9 ✓ That confirms your answer is correct!

This checking method helps build confidence and catches mistakes early!