Key Takeaways
- Place value determines a digit's worth based on position
- PEMDAS: Parentheses, Exponents, Multiply/Divide, Add/Subtract
- Same signs multiply/divide to positive; different signs to negative
- Round up if the next digit is 5 or more
- Use manipulatives to help students visualize numbers
Number Sense and Basic Operations
The Mathematics section of the ParaPro tests your ability to work with numbers at a K-8 level. Strong number sense is the foundation for all math skills.
Place Value
Understanding place value is essential for working with whole numbers and decimals.
Whole Number Place Values:
| Millions | Hundred Thousands | Ten Thousands | Thousands | Hundreds | Tens | Ones |
|---|---|---|---|---|---|---|
| 1,000,000 | 100,000 | 10,000 | 1,000 | 100 | 10 | 1 |
Example: In 4,523, the 4 is in the thousands place (value = 4,000).
Decimal Place Values:
| Ones | . | Tenths | Hundredths | Thousandths |
|---|---|---|---|---|
| 1 | . | 0.1 | 0.01 | 0.001 |
Example: In 3.45, the 5 is in the hundredths place (value = 0.05).
Operations with Whole Numbers
Addition: Combining quantities
- 234 + 567 = 801
Subtraction: Finding the difference
- 567 - 234 = 333
Multiplication: Repeated addition
- 23 × 4 = 92
Division: Splitting into equal groups
- 92 ÷ 4 = 23
Order of Operations (PEMDAS)
When a problem has multiple operations, follow this order:
| Order | Operation | Example |
|---|---|---|
| P | Parentheses | (2 + 3) first |
| E | Exponents | 2² = 4 |
| M/D | Multiply/Divide (left to right) | 4 × 3, then ÷ 2 |
| A/S | Add/Subtract (left to right) | 5 + 3, then - 2 |
Example: 3 + 4 × 2 = 3 + 8 = 11 (multiply first!)
Working with Negative Numbers
Rules for Addition/Subtraction:
- Same signs: Add and keep the sign → (-3) + (-5) = -8
- Different signs: Subtract and keep sign of larger → (-7) + 4 = -3
Rules for Multiplication/Division:
- Same signs = Positive → (-3) × (-4) = 12
- Different signs = Negative → (-3) × 4 = -12
Rounding Numbers
Steps to Round:
- Find the place to round to
- Look at the digit to the right
- If 5 or more, round up; if 4 or less, round down
Example: Round 3,847 to the nearest hundred
- Hundreds place: 8
- Digit to the right: 4
- 4 < 5, so round down → 3,800
Classroom Application
Help students with number operations by:
- Using manipulatives (base-ten blocks, counters)
- Teaching place value with visual charts
- Practicing PEMDAS with color-coding
- Creating number lines for negative numbers
- Using estimation to check reasonableness
What is the value of 5 + 3 × 2?
In the number 45.123, what is the place value of the digit 2?