Class 4 Exam > Class 4 Notes > Year 4 Mathematics IGCSE (Cambridge) > Chapter Notes: Addition and Subtraction of Whole Numbers
Addition and Subtraction of Whole Numbers Chapter Notes | Year 4 Mathematics IGCSE (Cambridge) - Class 4 PDF Download
Using a symbol to represent a missing number or operation
Math Puzzle- Focuses on using a symbol to represent a missing number or operation sign in addition or subtraction calculations.
- Introduces solving missing number puzzles, which are engaging for both children and adults, similar to jigsaw puzzles.
- A symbol (e.g., a blank, square, or circle) represents the unknown in equations like:
- 30 − _ = 27
- 650 + _ = 1000
- 3 + _ = 15
- 10 _ 2 = 20
- Methods to find the missing number include:
- Number line: Count on from the known number to the target (e.g., for 650 + _ = 1000, count from 650 to 1000, adding 50 to 700, then 300 to 1000, totaling 350).
- Subtraction: Rewrite the equation as a subtraction problem (e.g., 1000 − 650 = 350).
- Mental calculation: Use known facts to compute directly (e.g., recognize that 650 + 350 = 1000).
- Addition and subtraction are inverse operations, allowing equations to be rewritten (e.g., 650 + _ = 1000 can be solved as 1000 − 650 = 350).
- Key terminology:
- Symbol: A placeholder for an unknown number or operation.
- Symbol: A placeholder for an unknown number or operation.
Addition and subtraction of whole numbers
Math Fundamentals- Focuses on performing addition and subtraction with whole numbers through various strategies.
- Students learn to:
- Compose: Put together parts to form a whole number.
- Decompose: Split a number into its place value components (e.g., hundreds, tens, ones).
- Regroup: Reorganize numbers during calculations to facilitate addition or subtraction.
- Choose appropriate mental or written methods for calculations.
- Estimate the size of the answer before calculating to check reasonableness.
- Addition and subtraction are applied in everyday contexts, such as calculating total costs or change when shopping.
- Written method for addition example: 235 + 174
- Estimate: 200 + 200 = 400
- Decompose: 235 = 200 + 30 + 5, 174 = 100 + 70 + 4
- Add parts: 200 + 100 = 300, 30 + 70 = 100, 5 + 4 = 9
- Compose: 300 + 100 + 9 = 409
- Written method for subtraction examples:
- For 459 − 318:
- Estimate: 500 − 300 = 200
- Decompose: 459 = 400 + 50 + 9, 318 = 300 + 10 + 8
- Subtract parts: 400 − 300 = 100, 50 − 10 = 40, 9 − 8 = 1
- Compose: 100 + 40 + 1 = 141
- For 424 − 179:
- Estimate: 400 − 200 = 200
- Decompose with regrouping: 424 = 300 + 110 + 14, 179 = 100 + 70 + 9
- Subtract parts: 300 − 100 = 200, 110 − 70 = 40, 14 − 9 = 5
- Compose: 200 + 40 + 5 = 245
- For 459 − 318:
- Key terminology:
- Compose: Combine parts to form a number.
- Decompose: Break a number into its place value components.
- Difference: The result of subtraction.
- Regroup: Reorganize numbers for calculations (e.g., borrowing or carrying).
- Emphasis on estimating first to ensure calculations are reasonable (e.g., for235 + 174, estimate 200 +200 = 400, close to 409).
Generalising with odd and even numbers
- Focuses on making and testing general statements about the addition and subtraction of odd and even numbers.
- Uses visual aids like "L-shapes" to show that odd numbers have a remainder when divided by 2, while combining two L-shapes forms a rectangle with an even number of dots.
- Examples of combining odd numbers:
- 3 + 3 = 6
- 5 + 5 = 10
- 7 + 7 = 14
- General statement: odd + odd = even, which holds for all cases.
- Additional general statements:
- even + even = even
- odd + odd + odd = odd
- even + even + even = even
- even + odd = odd
- Students test these statements by trying examples and identifying counter-examples to disprove incorrect claims.
- Example: Adding three odd numbers always results in an odd number (e.g., 1 + 3 + 5 = 9, 11 + 23 + 35 = 69), so a claim of getting an even number like 50 is incorrect.
- Key terminology:
- Counter-example: An example that disproves a statement.
- Even: A number divisible by 2 with no remainder.
- Generalisation (general statement): A rule that applies to all cases of a specific type.
- Odd: A number not divisible by 2, leaving a remainder of 1.
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FAQs on Addition and Subtraction of Whole Numbers Chapter Notes - Year 4 Mathematics IGCSE (Cambridge) - Class 4
| 1. What are the basic rules of addition and subtraction of whole numbers? |  |
Ans. The basic rules of addition state that when you combine two or more whole numbers, their total increases. For example, 5 + 3 = 8. The rules of subtraction state that when you take a number away from another, the total decreases. For instance, 8 - 3 = 5. Additionally, addition is commutative (order doesn't matter: a + b = b + a) and associative (grouping doesn't matter: (a + b) + c = a + (b + c)), while subtraction is neither.
| 2. How do you perform addition and subtraction with larger whole numbers? | |
Ans. To perform addition and subtraction with larger whole numbers, you can use the column method. Write the numbers one under the other, aligning the digits by place value (units, tens, hundreds, etc.). For addition, start from the rightmost column and move left, carrying over if necessary. For subtraction, start from the rightmost column as well, borrowing from the next column if needed.
| 3. What is the significance of zero in addition and subtraction? | |
Ans. Zero plays a crucial role in addition and subtraction. In addition, adding zero to any whole number does not change its value (e.g., 5 + 0 = 5). In subtraction, subtracting zero from any whole number also leaves it unchanged (e.g., 5 - 0 = 5). Zero acts as the identity element for addition and shows that there is no change in value.
| 4. Can you explain the concept of 'borrowing' in subtraction? | |
Ans. 'Borrowing' in subtraction is a technique used when the top digit in a column is smaller than the bottom digit. To borrow, you take 1 from the next left column, which reduces that number by 1 and increases the current column's top digit by 10. This allows you to complete the subtraction. For example, in 52 - 27, you would borrow from the 5 (making it 4) to turn the 2 into 12, allowing you to subtract 7 from 12.
| 5. How can I check my addition and subtraction calculations for accuracy? | |
Ans. To check your addition, you can use the inverse operation of subtraction. For example, if you calculated 5 + 3 = 8, you can verify by doing 8 - 3 to see if you return to 5. For subtraction, you can check by adding the result to the subtracted number. If 8 - 3 = 5, then 5 + 3 should return to 8. Additionally, you can estimate the results by rounding the numbers to the nearest ten for a quick check.
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