Lesson Notes By Weeks and Term v5 - Grade 4

Lesson Video

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Performance objectives

• Identify the place value of digits up to 9999.
• Break down (decompose) numbers.
• Add whole numbers up to 9999.
• Subtract whole numbers up to 9999.
• Solve real-life word problems.

Lesson summary

This week, we will delve deeper into understanding whole numbers, focusing specifically on place value up to at least thousands and performing basic operations (addition and subtraction) with larger numbers. Understanding place value is crucial because it's the foundation for all other mathematical concepts. Imagine you are helping your family manage their monthly budget – you need to understand the value of each digit in the amounts of money you're spending and saving. Similarly, when calculating distances on a road trip, or measuring ingredients for a vetkoek recipe, a strong understanding of place value and operations is essential.

Lesson notes

Place Value: Place value refers to the value of a digit based on its position in a number. In the number 3456, the digit 3 is in the thousands place, the digit 4 is in the hundreds place, the digit 5 is in the tens place, and the digit 6 is in the units/ones place.

Units/Ones: The rightmost digit represents the number of individual units.

Tens: The digit to the left of the units represents the number of groups of ten.

Hundreds: The digit to the left of the tens represents the number of groups of one hundred.

Thousands: The digit to the left of the hundreds represents the number of groups of one thousand.

Decomposing Numbers: Decomposing a number means breaking it down into its place value components. This helps us understand the value of each digit and is crucial for performing operations like addition and subtraction.

Example: The number 5289 can be decomposed as 5000 + 200 + 80 +

9. Addition of Whole Numbers: Addition involves combining two or more numbers to find their total, or sum. We can use column addition, which involves aligning the numbers vertically according to their place value and adding each column separately, starting from the units/ones place. When the sum of a column is greater than 9, we need to regroup (carry over) the tens digit to the next column.

Example: 2345 + 1876 ``` 2 3 4 5 + 1 8 7 6 ----------- 4 2 2 1 ``` Step 1 (Units): 5 + 6 =

1

1. Write down 1 in the units place and carry over 1 to the tens place.

Step 2 (Tens): 1 (carried over) + 4 + 7 =

1

2. Write down 2 in the tens place and carry over 1 to the hundreds place.

Step 3 (Hundreds): 1 (carried over) + 3 + 8 =

1

2. Write down 2 in the hundreds place and carry over 1 to the thousands place.

Step 4 (Thousands): 1 (carried over) + 2 + 1 =

4. Write down 4 in the thousands place.

Subtraction of Whole Numbers: Subtraction involves finding the difference between two numbers. We can use column subtraction, which involves aligning the numbers vertically according to their place value and subtracting each column separately, starting from the units/ones place. When the digit in the top number is smaller than the digit in the bottom number, we need to regroup (borrow) from the next column to the left.

Example: 4221 - 1876 ``` 4 2 2 1 1 8 7 6 ----------- 2 3 4 5 ``` Step 1 (Units): 1 -

6. We can't subtract 6 from 1, so we borrow 1 from the tens place. The 2 in the tens place becomes 1, and the 1 in the units place becomes

1

1. Now we have 11 - 6 =

5. Step 2 (Tens): 1 -

7. We can't subtract 7 from 1, so we borrow 1 from the hundreds place. The 2 in the hundreds place becomes 1, and the 1 in the tens place becomes

1

1. Now we have 11 - 7 =

4. Step 3 (Hundreds): 1 -

8. We can't subtract 8 from 1, so we borrow 1 from the thousands place. The 4 in the thousands place becomes 3, and the 1 in the hundreds place becomes

1

1. Now we have 11 - 8 =

3. Step 4 (Thousands): 3 - 1 =

2. Guided Practice (With Solutions)

Question 1: What is the place value of the digit 7 in the number 6732?

Solution: The digit 7 is in the hundreds place.

Therefore, its place value is

7

0

0. Question 2: Decompose the number 8405 into its place value components.

Solution: 8405 = 8000 + 400 + 0 +

5. Notice that we include the 0 in the tens place.

Question 3: Calculate 3567 + 2984 using column addition.

Solution: ``` 3 5 6 7 + 2 9 8 4 6 5 5 1 ``` 7 + 4 = 11 (Write down 1, carry over 1) 1 + 6 + 8 = 15 (Write down 5, carry over 1) 1 + 5 + 9 = 15 (Write down 5, carry over 1) 1 + 3 + 2 = 6 Question 4: Calculate 7235 - 4618 using column subtraction.

Solution: ``` 7 2 3 5 4 6 1 8 2 6 1 7 ``` 5 - 8 (Borrow 1 from the tens place): 15 - 8 = 7 2 - 1 (Remember we borrowed 1 from the tens place so its 2 instead of 3) : 2 - 1 =1 2 - 6 (Borrow 1 from the thousands place): 12 - 6 = 6 6 - 4 = 2 (Remember we borrowed 1 from the thousands place so its 6 instead of 7) Independent Practice (Questions Only) What is the place value of the digit 5 in the number 9513? Decompose the number 6072 into its place value components. Calculate 4829 +

3

1

7

5. Calculate 9000 -

5

4

3

2. A tuck shop owner buys 1250 sweets. He then buys another 875 sweets. How many sweets does he have in total? Sarah has saved R

3

4

5

0. She spends R1875 on a new bicycle. How much money does Sarah have left? What number is 1000 more than 5678? What number is 500 less than 8234?

Arrange these numbers in ascending order: 2345, 2435, 2354,

2

4

5

3. Arrange these numbers in descending order: 7890, 7980, 7098, 7089.