🔵Understanding the Equal Sign
What is the Equal Sign (=)?
The equal sign shows that two quantities have the same value. It means "is the same as" or "balances".
Important Idea:
The equal sign does NOT mean "the answer is coming". It means the left side and the right side are equal (the same amount).
True or False? (Understanding Equality)
| Equation | True or False? | Why? |
|---|---|---|
| 3 + 2 = 5 | True | 3+2 equals 5 |
| 4 + 1 = 6 | False | 4+1 equals 5, not 6 |
| 2 + 3 = 1 + 4 | True | Both sides equal 5 |
| 5 = 5 | True | Same number on both sides |
| 7 – 2 = 5 | True | 7–2 equals 5 |
Balance Scale Model:
Think of the equal sign as a balance scale. Both sides must weigh the same to be balanced.
👀 See a worked example
Is this equation true or false? 4 + 3 = 7
- Left side: 4 + 3 = 7
- Right side: 7
- Both sides equal 7
-
Answer: True **Example 2:** Is this equation true or false? 8 – 2 = 5 *Solution:* - Left side: 8 – 2 = 6 - Right side: 5 - 6 ≠ 5, so false - **Answer:** False **Example 3:** Fill in the blank to make a true equation: 3 + 4 = ___ + 2 *Solution:* - Left side: 3 + 4 = 7 - Right side must also equal 7 - So ___ + 2 = 7 - The missing number is 5 (because 5 + 2 = 7) - **Answer:** 5
🤖 Vidi's Key Points
- The equal sign means both sides have the same value
- Equal sign is like a balance scale
- Equations can be true or false
- Many different expressions can equal the same number
- Always check both sides before deciding true or false
🟢Missing Number Problems
What are Missing Number Problems?
A missing number problem is an equation with a blank or a box. We need to find what number goes in the blank to make the equation true.
Types of Missing Number Problems:
| Type | Example | What to Do |
|---|---|---|
| _ + 3 = 7 | Find the missing addend | 4 + 3 = 7 |
| 8 – _ = 5 | Find the missing subtrahend | 8 – 3 = 5 |
| 2 + 3 = _ + 4 | Find missing number on either side | 5 = 1 + 4, so 1 |
| 10 = _ + 4 | Missing number at start | 6 + 4 = 10 |
Strategies for Finding Missing Numbers:
| Strategy | How It Works | Example |
|---|---|---|
| **Count On** | Start at first number, count to total | _ + 3 = 7 → count from 3 to 7 (4 steps) → answer 4 |
| **Think Addition** | Use related addition fact | 8 – _ = 5 → think 5 + _ = 8 → _ = 3 |
| **Use Fact Families** | Related facts help | 6 + 4 = 10, so 10 – 4 = 6, 10 – 6 = 4 |
| **Balance Both Sides** | Make left equal right | 3 + 4 = _ + 2 → 7 = 5 + 2 → _ = 5 |
Fact Families for Addition and Subtraction:
For numbers 3, 4, 7:
- 3 + 4 = 7
- 4 + 3 = 7
- 7 – 3 = 4
- 7 – 4 = 3
👀 See a worked example
Find the missing number: _ + 5 = 12
- Think: What plus 5 equals 12?
- Count up from 5 to 12: 5→6(1),7(2),8(3),9(4),10(5),11(6),12(7)
- 7 jumps, so answer is 7
- Check: 7 + 5 = 12 ✓
-
Answer: 7 **Example 2:** Find the missing number: 15 – _ = 9 *Solution:* - Think: 15 minus what equals 9? - Use fact family: 9 + _ = 15 - 9 + 6 = 15, so _ = 6 - Check: 15 – 6 = 9 ✓ - **Answer:** 6 **Example 3:** Find the missing number: 4 + 7 = 5 + ___ *Solution:* - Left side: 4 + 7 = 11 - Right side: 5 + ___ must also be 11 - 5 + 6 = 11, so ___ = 6 - **Answer:** 6
🤖 Vidi's Key Points
- Missing number problems have a blank to fill
- Use counting up for missing addend
- Use fact families to find related facts
- Both sides must be equal after filling the blank
- Check your answer by plugging it back into the equation
🟣Simple Mathematical Relationships and Balancing Equations
What is a Mathematical Relationship?
A mathematical relationship shows how numbers are connected. For example, "4 is 2 more than 2" or "6 is double 3".
Types of Relationships:
| Relationship | Meaning | Example |
|---|---|---|
| **Greater than (>)** | Bigger than | 7 > 3 |
| **Less than (<)** | Smaller than | 2 < 5 |
| **Equal to (=)** | Same as | 4 = 4 |
| **More than** | Adding | 5 is 2 more than 3 |
| **Less than** | Subtracting | 3 is 2 less than 5 |
What is a Balanced Equation?
A balanced equation has the same value on both sides of the equal sign. We can add or subtract numbers as long as we do the same thing to both sides.
Balancing Equations (Keeping Equality):
| Action | Example | Result |
|---|---|---|
| Start with true equation | 5 + 3 = 8 | True |
| Add 2 to both sides | 5 + 3 + 2 = 8 + 2 | Still true (10=10) |
| Subtract 1 from both sides | 5 + 3 – 1 = 8 – 1 | Still true (7=7) |
Key Idea: If you change both sides the same way, the equation stays balanced!
👀 See a worked example
Fill in the blank with <, >, or = : 7 + 2 ___ 10
- Left side: 7 + 2 = 9
- Compare 9 and 10
- 9 is less than 10
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Answer: < (less than) **Example 2:** Complete the balanced equation: 8 + 3 = 9 + ___ *Solution:* - Left side: 8 + 3 = 11 - Right side: 9 + ___ must equal 11 - 9 + 2 = 11 - **Answer:** 2 **Example 3:** If 5 + 3 = 8, what is 5 + 3 + 2? Write a balanced equation. *Solution:* - Start with 5 + 3 = 8 - Add 2 to both sides: 5 + 3 + 2 = 8 + 2 - Left: 10, Right: 10 - **Answer:** 5 + 3 + 2 = 8 + 2 (or 10 = 10)
🤖 Vidi's Key Points
- Mathematical relationships describe how numbers compare
- > means greater than, < means less than, = means equal
- A balanced equation has the same value on both sides
- Adding or subtracting the same number to both sides keeps the equation balanced
- Finding missing numbers helps us understand relationships
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