Number
Number Sense and Place Value
Grade 1 · Grade 2 · Grade 3
- ✓By the end of this lesson students will be able to count forwards and backwards to 1000 by various amounts.
- ✓By the end of this lesson students will be able to identify the place value of digits in numbers up to 1000.
- ✓By the end of this lesson students will be able to represent numbers using concrete materials and standard notation.
- ✓By the end of this lesson students will be able to add two-digit and three-digit numbers with and without regrouping.
- ✓By the end of this lesson students will be able to subtract two-digit and three-digit numbers with and without regrouping.
Key concepts
Counting is how we find out 'how many' there are. We can count forwards (getting bigger) or backwards (getting smaller). We can count by 1s, 2s, 5s, 10s, 25s, or 100s. This is called skip counting. For example, counting by 10s from 100 would be 100, 110, 120, 130, and so on, all the way to 1000.
Place value tells us how much each digit in a number is worth based on its position. In Canada, we use a base-ten system. This means that every place to the left is worth ten times more than the place to its right.\n\n- **Ones Place**: The digit on the far right. It tells us how many single units we have (e.g., 7 in 237 means 7 ones).\n- **Tens Place**: The digit to the left of the ones place. It tells us how many groups of ten we have (e.g., 3 in 237 means 3 tens, which is 30).\n- **Hundreds Place**: The digit to the left of the tens place. It tells us how many groups of one hundred we have (e.g., 2 in 237 means 2 hundreds, which is 200).\n\nWe can use base ten blocks to show place value: small cubes for ones, rods for tens, and flats for hundreds.
Addition is when we combine two or more numbers to find a total. The answer to an addition problem is called the 'sum'. We use the plus sign (+) for addition. When adding larger numbers, we often line them up by place value (ones under ones, tens under tens, etc.). Sometimes, when the digits in a place value column add up to 10 or more, we need to 'regroup' or 'carry over' to the next place value column.
Subtraction is when we take one number away from another to find out how many are left, or to find the difference between two numbers. The answer to a subtraction problem is called the 'difference'. We use the minus sign (-) for subtraction. When subtracting larger numbers, we line them up by place value. Sometimes, if a digit in the top number is smaller than the digit below it, we need to 'regroup' or 'borrow' from the next place value column to the left.
Key facts to remember
- 1Numbers are made up of digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9).
- 2The position of a digit in a number determines its place value (ones, tens, hundreds).
- 3Counting by 1s, 2s, 5s, 10s, 25s, and 100s helps us understand number patterns.
- 4Addition means combining numbers to find a total (sum).
- 5Subtraction means taking away or finding the difference between numbers.
- 6Regrouping (carrying over in addition, borrowing in subtraction) is essential when working with larger numbers.
Worked examples
Example 1
What is the value of the digit '4' in the number 472?
Answer
The value of the digit '4' in 472 is 4 hundreds, or 400.
Remember, the position of a digit changes its value!
Example 2
Add 38 + 25.
Answer
38 + 25 = 63
Always start adding from the ones place and move to the left.
Example 3
Subtract 63 - 27.
Answer
63 - 27 = 36
When you can't subtract, remember to 'borrow' from the next place value to the left!
Common mistakes
- ✗Mixing up place values, for example, thinking the '3' in 345 means 3 ones instead of 3 hundreds.
- ✗Not regrouping correctly in addition or subtraction, leading to incorrect answers.
- ✗Subtracting the smaller digit from the larger digit in a column, even if the larger digit is on the bottom (e.g., in 43 - 17, doing 7-3 instead of regrouping).
- ✗Counting errors when skip counting, especially when crossing hundreds (e.g., 90, 100, 110 instead of 90, 100, 110).
- ✗Not lining up numbers by place value when adding or subtracting, which causes errors.
Exam tips
- ★Always read the question carefully to understand what is being asked.
- ★Use concrete materials like base ten blocks or draw pictures to help you visualize the numbers and operations.
- ★Show all your steps clearly, especially when regrouping, so your teacher can see your thinking.
- ★Check your work! You can use addition to check subtraction, and vice versa (e.g., if 63 - 27 = 36, then 36 + 27 should equal 63).
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