Number Sense and Operations for Grade 4
Understanding Place Value
Place value is the value of each digit in a number based on its position. For example, in the number 345, the digit 3 is in the hundreds place, 4 is in the tens place, and 5 is in the ones place.
Example: In the number 789, the digit 7 is in the hundreds place, so it represents 700. The digit 8 is in the tens place, representing 80, and the digit 9 is in the ones place, representing 9.
Comparing and Ordering Numbers
Comparing numbers helps us understand which number is greater or smaller. We use symbols like > (greater than), < (less than), and = (equal to) to compare numbers.
Example: To compare 456 and 465, we first look at the hundreds place. Both have 4 in the hundreds place. Next, we look at the tens place. Since 5 (in 456) is less than 6 (in 465), we can say 456 < 465.
Rounding Numbers
Rounding numbers makes them easier to work with. We round numbers to the nearest ten, hundred, or thousand. To round, we look at the digit to the right of the place we are rounding to.
Example: To round 378 to the nearest ten, we look at the digit in the ones place, which is 8. Since 8 is greater than 5, we round up to 380.
Basic Operations: Addition, Subtraction, Multiplication, and Division
These are the four basic operations in mathematics. They help us solve problems involving numbers.
Example: Addition combines two or more numbers to find their total. For example, 23 + 45 = 68. Subtraction finds the difference between two numbers. For example, 78 - 34 = 44. Multiplication is repeated addition. For example, 5 × 6 = 30. Division is the process of splitting a number into equal parts. For example, 48 ÷ 6 = 8.
Properties of Operations
Understanding properties like the commutative, associative, and distributive properties helps us solve problems more efficiently.
Example: The commutative property of addition states that the order of numbers does not change the sum. For example, 3 + 5 = 5 + 3. The associative property of addition states that the way numbers are grouped does not change the sum. For example, (2 + 3) + 4 = 2 + (3 + 4). The distributive property involves multiplication and addition. For example, 3 × (4 + 5) = (3 × 4) + (3 × 5).