Number & Operations in Base Ten
Place Value to 1000 and Operations
Grade 2
- ✓By the end of this lesson students will be able to understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones.
- ✓By the end of this lesson students will be able to read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
- ✓By the end of this lesson students will be able to compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits.
- ✓By the end of this lesson students will be able to fluently add and subtract within 1000 using strategies based on place value and properties of operations.
Key concepts
Place value tells us the value of each digit in a number based on its position. In a three-digit number, we have the hundreds place, the tens place, and the ones place.
The digit in the hundreds place tells us how many groups of one hundred there are. For example, in the number 345, the digit 3 is in the hundreds place, meaning 3 hundreds, or 300.
The digit in the tens place tells us how many groups of ten there are. For example, in the number 345, the digit 4 is in the tens place, meaning 4 tens, or 40.
The digit in the ones place tells us how many single units there are. For example, in the number 345, the digit 5 is in the ones place, meaning 5 ones, or 5.
This is the usual way we write numbers using digits. For example, 728.
This is a way to write a number by showing the sum of the value of each digit. For example, 728 in expanded form is 700 + 20 + 8.
This is a way to write a number using words. For example, 728 in word form is seven hundred twenty-eight.
To add numbers within 1000, we can use place value strategies. This means adding the ones digits, then the tens digits, then the hundreds digits. Sometimes we need to regroup (carry) if the sum in a place value column is 10 or more.
To subtract numbers within 1000, we can use place value strategies. This means subtracting the ones digits, then the tens digits, then the hundreds digits. Sometimes we need to regroup (borrow) if a digit in the top number is smaller than the digit below it in the same place value column.
Key facts to remember
- 1The value of a digit depends on its place in the number.
- 210 ones make 1 ten.
- 310 tens make 1 hundred.
- 4Numbers can be written in standard form (digits), expanded form (sum of values), and word form (words).
- 5When adding or subtracting, always line up the digits by their place value.
- 6Regrouping (carrying or borrowing) is a key strategy for addition and subtraction when a column's sum is 10 or more, or when a digit is too small to subtract from.
Worked examples
Example 1
What is the value of the digit 6 in the number 637? Write 637 in expanded form and word form.
Answer
The value of the digit 6 is 600.\nExpanded Form: 600 + 30 + 7\nWord Form: six hundred thirty-seven
Remember, the 'value' of a digit is different from its 'place'.
Example 2
Add 458 + 235.
Answer
693
Always start adding from the ones place and move to the left.
Example 3
Subtract 763 - 328.
Answer
435
When you regroup a ten, you are taking 10 ones from the tens place and adding them to the ones place.
Common mistakes
- ✗Not lining up digits correctly by place value when adding or subtracting.
- ✗Confusing the place of a digit (e.g., tens place) with its value (e.g., 30 for 3 tens).
- ✗Forgetting to regroup (carry) when the sum of a column is 10 or more.
- ✗Forgetting to regroup (borrow) when a digit in the top number is smaller than the digit below it.
- ✗Incorrectly reading or writing numbers in word form, especially with 'and' (e.g., 'one hundred AND twenty-three' instead of 'one hundred twenty-three').
Exam tips
- ★Use a place value chart to help organize your numbers, especially for addition and subtraction.
- ★Break down numbers into hundreds, tens, and ones to understand their value before performing operations.
- ★Always double-check your regrouping steps in addition and subtraction.
- ★Practice writing numbers in all three forms (standard, expanded, word) to build fluency.
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