Review of Adding and Subtracting Integers for 3rd Grade

Master integer operations: understanding positive and negative numbers, number line movements, and addition/subtraction with visual representations through these 3 detailed exercises.

Solution: Exercises 1 to 3
1 Adding Positive Integers
Exercise 1
Solve:
5 + 3 = ?
Definition:

Integer: A whole number that can be positive, negative, or zero. Positive integers are numbers greater than zero.

Number Line: A visual representation of numbers as points on a straight line.

Addition method for positive integers:
  1. Start at the first number on the number line
  2. Move to the right by the value of the second number
  3. The final position is the sum
Setup
5 + 3
Addition
8
Step 1: Start at 5

Locate 5 on the number line

Step 2: Move 3 spaces right

From 5, move 3 positions to the right

Step 3: Identify final position

We land on 8

5 + 3 = 8
Final answer:

5 + 3 = 8

Applied rules:

• Positive Addition: Adding positive numbers moves right on the number line

• Number Line Movement: Right movement increases value

• Sum Property: Adding two positive numbers results in a larger positive number

2 Subtracting Positive Integers
Exercise 2
Solve:
8 - 5 = ?
Definition:

Subtraction: The operation of finding the difference between two numbers.

Positive Integer: A number greater than zero.

Setup
8 - 5
Subtraction
3
Step 1: Start at 8

Locate 8 on the number line

Step 2: Move 5 spaces left

From 8, move 5 positions to the left

Step 3: Identify final position

We land on 3

8 - 5 = 3
Final answer:

8 - 5 = 3

Applied rules:

• Positive Subtraction: Subtracting positive numbers moves left on the number line

• Number Line Movement: Left movement decreases value

• Difference Property: Subtracting a smaller positive number from a larger one results in a positive number

3 Word Problem with Integers
Exercise 3
Tom had $10 in his piggy bank. He spent $4 on candy. Then he found $3 on the sidewalk. How much money does Tom have now?
Definition:

Word Problems: Real-life situations that require mathematical operations to solve. We identify key information and determine which operations to use.

Started with
$10
Spent
-$4
Found
+$3
Step 1: Identify the operations needed

Start with $10, subtract $4 (spent), add $3 (found)

Step 2: Set up the equation

10 - 4 + 3 = ?

Step 3: Calculate step by step

10 - 4 = 6, then 6 + 3 = 9

Step 4: Final answer

Tom has $9 now

Tom has $9 now
Final answer:

Tom has $9 now

Applied rules:

• Problem Solving: Read carefully, identify key information, determine operations

• Order of Operations: Work left to right when only addition and subtraction

• Real-world Context: Money can be represented as positive and negative integers

Key Concepts and Methods
a + b = c
Adding Positive Integers
Adding Integers
a + b = c
Positive + Positive
Subtracting Integers
a - b = c
Positive - Positive
Number Line
Right = Increase, Left = Decrease
Movement direction
Key definitions:

Integer: A whole number that can be positive, negative, or zero

Positive Integer: Any number greater than zero (1, 2, 3, ...)

Negative Integer: Any number less than zero (-1, -2, -3, ...)

Zero: Neither positive nor negative, represents no quantity

Adding Positive Integers Method:
  1. Combine the quantities of both numbers
  2. Move right on the number line by the second number's value
  3. The result is a larger positive number
Subtracting Positive Integers Method:
  1. Take away the second number from the first
  2. Move left on the number line by the second number's value
  3. The result may be positive or zero depending on values
Tip 1: Use a number line to visualize addition and subtraction
Tip 2: Right movement = addition, Left movement = subtraction
Tip 3: Adding always increases value, subtracting always decreases value (for positive numbers)
Common errors: Moving in wrong direction on number line, confusing addition and subtraction signs.
Number Line: Moving right increases value, moving left decreases value.
Detailed Summary: Adding and Subtracting Integers
Integer = {..., -2, -1, 0, 1, 2, ...}
Integer Set
Core Concepts:

Definition: Integers are whole numbers including positive numbers, negative numbers, and zero. They don't include fractions or decimals.

Positive Integers: Numbers greater than zero (1, 2, 3, ...)

Negative Integers: Numbers less than zero (-1, -2, -3, ...)

Number Line: A visual tool where numbers are placed at equal intervals along a straight line.

Step-by-Step Process:
  1. Identify the operation: Determine if you're adding or subtracting
  2. Locate the starting point: Find the first number on the number line
  3. Determine direction: Add = move right, Subtract = move left
  4. Move the distance: Move by the value of the second number
  5. Read the result: The final position is your answer
Example 1 (Simple): 3 + 4 = 7 (start at 3, move 4 right to 7)
Example 2 (Subtraction): 8 - 3 = 5 (start at 8, move 3 left to 5)
Example 3 (Real world): Temperature: 5°C - 8°C = -3°C (temperature drops below zero)
Key Rules: 1) Adding positive numbers moves right 2) Subtracting positive numbers moves left 3) Result depends on starting point and movement
Common Mistakes: Moving in wrong direction, not accounting for sign changes, misreading the number line
Memory Aids:

• Remember: "Add = Right, Subtract = Left" on the number line

• Remember: Adding increases value, subtracting decreases value (with positive numbers)

• Always Check: Does your answer make sense compared to the original numbers?

• Visualization: Imagine walking forward (add) or backward (subtract)

Properties and Advanced Strategies
a + b = b + a
Commutative Property
Key properties:

Commutative Property: Order doesn't matter in addition (a + b = b + a)

Identity Property: Adding zero doesn't change the number (a + 0 = a)

Subtraction as Addition: a - b is the same as a + (-b)

Closure Property: Adding or subtracting integers always results in an integer

Mental Math Strategies:
  1. Counting On: Start with the larger number and count up
  2. Make Tens: Break apart numbers to make multiples of 10
  3. Compensation: Adjust one number to make the calculation easier
Tip 1: To add 9, add 10 and subtract 1 (e.g., 15 + 9 = 15 + 10 - 1 = 24)
Tip 2: To subtract 9, subtract 10 and add 1 (e.g., 23 - 9 = 23 - 10 + 1 = 14)
Tip 3: Look for doubles (e.g., 6 + 6 = 12) to make mental math faster
Tip 4: Use fact families (e.g., if 5 + 3 = 8, then 8 - 3 = 5)
Subtraction Facts: Remember that subtraction is the inverse of addition.
Estimation: Round numbers to check if your answer is reasonable.
Important Patterns:

• Adding Positive Numbers: Always increases the total

• Subtracting Positive Numbers: Always decreases the total

• Adding Zero: Doesn't change the number

• Subtracting Zero: Doesn't change the number

Questions & Answers

Question: My students struggle with understanding the number line concept. How can I make it more concrete for them?

Answer: Number lines can be challenging! Here are concrete strategies:

  • Physical Movement: Have students walk along a large number line drawn on the floor
  • Thermometer Model: Use temperature changes to show positive and negative movement
  • Elevator Model: Floors above and below ground level demonstrate integer movement
  • Money Model: Earning money (positive) and spending money (negative) on a timeline

Start with small numbers and gradually increase complexity. Use manipulatives like counters or chips to represent movement on the number line.

Question: How can I help my child understand when to add or subtract in word problems?

Answer: Word problems can be tricky! Here's a strategy to identify operations:

  • Addition Keywords: altogether, combined, total, sum, in all, increased by, more than, gained
  • Subtraction Keywords: difference, fewer, less than, decreased by, take away, left, remaining, lost
  • Visual Representation: Draw pictures or use objects to model the situation
  • Context Clues: Ask "Are we putting things together?" (addition) or "Are we taking some away?" (subtraction)

For example, "Tom had $10 and spent $4" → spending means subtracting. Practice identifying keywords and drawing models to reinforce understanding.

Question: I sometimes get confused about which direction to move on the number line. How do I remember?

Answer: This is very common! Here's a simple memory device:

  • RIGHT = ADDITION: Adding makes numbers bigger, so we move right toward larger numbers
  • LEFT = SUBTRACTION: Subtracting makes numbers smaller, so we move left toward smaller numbers
  • Memory Device: "Add to the right, subtract to the left!"
  • Real Example: If you have 5 cookies and get 3 more, you have more (right). If you eat 2, you have fewer (left).

Practice with small numbers first, then gradually increase complexity. The more you practice, the more natural it becomes!