Lesson Notes By Weeks and Term v5 - Grade 5
Whole numbers and operations (Grade 5) – Week 1 focus
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Whole numbers and operations (Grade 5) – Week 1 focus
Download the Lessonotes Mobile South Africa app for faster lesson access on Android and iPhone.
Subject: Mathematics
Class: Grade 5
Term: 1st Term
Week: 1
Theme: General lesson support
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This week, we will be diving into whole numbers and operations. Understanding whole numbers and how to add, subtract, multiply, and divide them is crucial.
Think about it: whether you're sharing sweets with friends, calculating the cost of groceries at the shop, or figuring out how many bricks you need to build a small wall, whole numbers are essential! In South Africa, we use these skills every day in our homes, schools, and communities. Imagine planning a braai and needing to calculate how much meat to buy for everyone – that's maths in action! This week lays the foundation for more complex math concepts in the future.
2.1 Understanding Whole Numbers Whole numbers are the numbers 0, 1, 2, 3, 4, and so on. They don't include fractions or decimals. We use a place value system to represent these numbers. Each digit in a number has a specific value based on its position.
Place Value: In the number 345 678: 8 is in the Units place (value = 8) 7 is in the Tens place (value = 70) 6 is in the Hundreds place (value = 600) 5 is in the Thousands place (value = 5 000) 4 is in the Ten Thousands place (value = 40 000) 3 is in the Hundred Thousands place (value = 300 000)
Reading Numbers: We read the number 345 678 as "Three hundred and forty-five thousand, six hundred and seventy-eight." Comparing Numbers: To compare numbers, start by comparing the digits in the largest place value. For example, 567 890 is greater than 499 999 because 5 (in the hundred thousands place) is greater than 4. 2.2 Rounding Numbers Rounding makes numbers simpler to work with. We round to the nearest 10, 100, or
1
0
0
0. Rounding to the Nearest 10: Look at the units digit. If it's 5 or more, round up to the next
1
0. If it's less than 5, round down.
Example: 47 rounds up to 50. 23 rounds down to
2
0. Rounding to the Nearest 100: Look at the tens digit. If it's 5 or more, round up to the next
1
0
0. If it's less than 5, round down.
Example: 362 rounds up to 400. 718 rounds up to 800. 549 rounds down to
5
0
0. Rounding to the Nearest 1000: Look at the hundreds digit. If it's 5 or more, round up to the next
1
0
0
0. If it's less than 5, round down.
Example: 1580 rounds up to 2000. 2300 rounds down to 2000. 2.3 Addition and Subtraction We use column addition and subtraction to add and subtract large numbers.
Example (Addition): A school collected 12 345 cans for recycling in January and 23 789 cans in February. How many cans did they collect in total? ``` 1 2 3 4 5 + 2 3 7 8 9 ----------------- 3 6 1 3 4 ``` So, they collected 36 134 cans in total. Remember to carry over when the sum of digits in a column is 10 or more.
Example (Subtraction): A farmer harvested 45 678 oranges. He sold 21 934 oranges at the market. How many oranges are left? ``` 4 5 6 7 8 2 1 9 3 4 ----------------- 2 3 7 4 4 ``` So, there are 23 744 oranges left. Remember to borrow when the digit being subtracted is larger than the digit above it. 2.4 Multiplication We use column multiplication to multiply larger numbers.
Example: A bakery sells 35 loaves of bread each day. How many loaves do they sell in 24 days? ``` 3 5 x 2 4 ------- 1 4 0 (35 x 4) + 7 0 0 (35 x 20) -------- 8 4 0 ``` The bakery sells 840 loaves of bread in 24 days. 2.5 Division We use long division to divide larger numbers.
Example: A group of 135 children is going on a school trip. If each bus can hold 30 children, how many buses are needed? ``` 4 R 15 30| 135 -120 ----- 15 ``` We need 4 buses, and there will be 15 children left over on the last bus. (4 buses can fit 120 children (30x4), leaving 15 children remaining.) Guided Practice (With Solutions)
Question 1: Write the number 234 567 in words.
Solution: Two hundred and thirty-four thousand, five hundred and sixty-seven.
Commentary: This tests understanding of place value and how to translate numerical values into written form.
Question 2: Round 678 to the nearest
1
0
0. Solution: 700
Commentary: The tens digit is 7, which is 5 or more, so we round up to the next hundred.
Question 3: Calculate 3 456 + 1
7
8
9. Solution: ``` 3 4 5 6 + 1 7 8 9 ----------- 5 2 4 5 ``` The answer is 5
2
4
5. Commentary: This involves column addition with carrying over. Each column must be added carefully, starting from the units place.
Question 4: Calculate 234 x
1
2. Solution: ``` 2 3 4 x 1 2 -------- 4 6 8 (234 x 2) + 2 3 4 0 (234 x 10) -------- 2 8 0 8 ``` The answer is 2
8
0
8. Commentary: This involves column multiplication. Multiply each digit of 234 by 2 and then by 10, and add the results.
Question 5: Calculate 456 ÷
3. Solution: ``` 1 5 2 3| 4 5 6 -3 --- 1 5 -1 5 ---- 0 6 6 --- 0 ``` The answer is
1
5
2. Commentary: This is a long division problem. Divide each digit of 456 by 3, bringing down the next digit after each subtraction. Independent Practice (Questions Only) Write the number 506 082 in words. Round 1 234 to the nearest 10, 100, and
1
0
0
0. Calculate 12 345 + 6
7
8
9. Calculate 9 876 - 5
4
3
2. Calculate 456 x
2
3. Calculate 1 234 x
3
4. Calculate 789 ÷ 4. (Include the remainder) Calculate 1 025 ÷
5. A shop has 345 apples. They sell 123 apples on Monday and 98 apples on Tuesday. How many apples are left? A farmer plants 12 rows of mielies, with 45 mielies in each row. How many mielies does the farmer plant in total?