Lesson Notes By Weeks and Term v5 - Grade 3
Numbers 0–999: place value and operations (Grade 3) – Week 2 focus
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Numbers 0–999: place value and operations (Grade 3) – Week 2 focus
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Subject: Mathematics
Class: Grade 3
Term: 1st Term
Week: 2
Theme: General lesson support
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This week, we continue our exciting journey with numbers up to 999! Building on what we learned last week, we will be focusing on understanding the place value of each digit in a 3-digit number (hundreds, tens, and ones) and using this knowledge to perform addition and subtraction operations. This is incredibly important because numbers are everywhere in our daily lives. Whether you are counting your pocket money to buy a cool drink at the spaza shop, figuring out how many sweets you need to share with your friends, or even understanding the scores in a soccer match, understanding place value and operations helps us make sense of the world around us.
Place Value: Hundreds, Tens, and Ones Remember that each digit in a number has a special place, and that place tells us its value. In a 3-digit number, we have the hundreds place, the tens place, and the ones place.
Hundreds: The digit in the hundreds place tells us how many groups of one hundred there are. For example, in the number 325, the 3 is in the hundreds place, so it represents 300 (three hundred).
Tens: The digit in the tens place tells us how many groups of ten there are. In the number 325, the 2 is in the tens place, so it represents 20 (twenty).
Ones: The digit in the ones place tells us how many single units there are. In the number 325, the 5 is in the ones place, so it represents 5 (five). Decomposing Numbers Breaking a number down into its hundreds, tens, and ones components helps us understand its value and makes addition and subtraction easier.
Example: The number 478 can be decomposed as: 400 (four hundred) + 70 (seventy) + 8 (eight) Addition with Regrouping (Carrying Over) Sometimes, when we add the digits in the ones or tens place, the sum is greater than
9. In this case, we need to "regroup" or "carry over".
Example: Let's add 256 + 175: Write the numbers vertically, aligning the place values: ``` 256 + 175 ------ ``` Add the ones place: 6 + 5 =
1
1. Since 11 is more than 9, we write down the 1 (in the ones place) and carry over the 1 (representing 10) to the tens place. ``` 1 256 + 175 ------ 1 ``` Add the tens place, including the carried-over 1: 1 + 5 + 7 =
1
3. Write down the 3 (in the tens place) and carry over the 1 (representing 100) to the hundreds place. ``` 1 1 256 + 175 ------ 31 ``` Add the hundreds place, including the carried-over 1: 1 + 2 + 1 =
4. Write down the 4 in the hundreds place. ``` 1 1 256 + 175 ------ 431 ``` Therefore, 256 + 175 =
4
3
1. Subtraction with Regrouping (Borrowing) Sometimes, when we subtract, the digit we are subtracting from is smaller than the digit we are subtracting. In this case, we need to "regroup" or "borrow" from the next higher place value.
Example: Let's subtract 324 - 158: Write the numbers vertically, aligning the place values: ``` 324 158 ------ ``` Subtract the ones place: We can't subtract 8 from 4, so we need to borrow from the tens place. We borrow 1 ten from the 2, leaving 1 ten. We add the borrowed 10 to the 4, making it
1
4. Now we can subtract: 14 - 8 = 6. ``` 3 1(14) 1 5 8 ------ 6 ``` Subtract the tens place: We can't subtract 5 from 1, so we need to borrow from the hundreds place. We borrow 1 hundred from the 3, leaving 2 hundreds. We add the borrowed 10 tens to the 1 ten, making it 11 tens.
Now we can subtract: 11 - 5 = 6. ``` 2(11)(14) 1 5 8 ------ 6 6 ``` Subtract the hundreds place: 2 - 1 = 1. ``` 2(11)(14) 1 5 8 ------ 1 6 6 ``` Therefore, 324 - 158 =
1
6
6. Using Expanded Notation Using expanded notation can help to visualize and check calculations.
Let's use the previous addition example: 256 + 175 256 = 200 + 50 + 6 175 = 100 + 70 + 5 Adding the hundreds: 200 + 100 = 300 Adding the tens: 50 + 70 = 120 Adding the ones: 6 + 5 = 11 Therefore: 300 + 120 + 11 = 431 Guided Practice (With Solutions)
Question 1: What is the place value of the digit 7 in the number 672?
Solution: The digit 7 is in the tens place, so its value is 70 (seventy).
Commentary: This question tests the basic understanding of place value. Make sure you know which digit is in which position (hundreds, tens, ones).
Question 2: Decompose the number 539 into its hundreds, tens, and ones.
Solution: 539 = 500 + 30 + 9
Commentary: This question reinforces understanding of how a 3-digit number is built from its components.
Question 3: Calculate 487 +
2
3
5. Solution: ``` 1 1 487 + 235 722 ``` Therefore, 487 + 235 =
7
2
2. Commentary: This is an addition problem with regrouping. Remember to carry over when the sum of the digits in a place value column is greater than
9. Question 4: Calculate 642 -
2
7
8. Solution: ``` 5(13)(12) 2 7 8 3 6 4 ``` Therefore, 642 - 278 =
3
6
4. Commentary: This is a subtraction problem with regrouping (borrowing). Remember to borrow from the next higher place value when needed.
Question 5: Sipho has 325 marbles, and Thandi has 148 marbles. How many marbles do they have together?
Solution: This is an addition word problem. We need to add the number of marbles Sipho has and the number of marbles Thandi has: 325 + 148. ``` 325 + 148 473 ``` Therefore, Sipho and Thandi have a total of 473 marbles.
Commentary: This question combines both addition and problem-solving skills. It is important to identify what operation needs to be carried out to answer the problem. Independent Practice (Questions Only) What is the place value of the digit 4 in the number 941? Decompose the number 706 into its hundreds, tens, and ones. Calculate 358 +
2
6
4. Calculate 813 -
3
4
5. Maria has 247 beads, and she gives 89 beads to her friend. How many beads does Maria have left? A farmer has 156 chickens and buys 278 more. How many chickens does the farmer have now?