Lesson Notes By Weeks and Term v3 - Primary 4
Addition and subtraction
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Addition and subtraction
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Subject: General Mathematics
Class: Primary 4
Term: 2nd Term
Week: 2
Theme: Basic Operations
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Watch on YouTubeSee Facebook postAdd and subtract whole numbers in Th. H. T. U with or with out renaming Carryout correct addition and subtraction in everyday life activities Add and subtract three 4-digit numbers taking two at a time Solve quantitative aptitude problems in volving addition and subtraction of whole numbers of four digit; Add and subtract:. two proper fractions. improper fractions and mixed fractions Correctly add and subtract proper and improper fractions in everyday life activities; Solves quantitative aptitude problems in volving addition and subtraction of fractions.
Steps:
1. Subtract Units: 6 - 4 =
2. Write 2 in the Units column.
2. Subtract Tens: 7 - 3 =
4. Write 4 in the Tens column.
3. Subtract Hundreds: 8 - 2 =
6. Write 6 in the Hundreds column.
4. Subtract Thousands: 4 - 1 =
3. Write 3 in the Thousands column.
Result: 3,642 exercise books are left. b.
With Renaming (Borrowing): This occurs when a digit in the minuend is smaller than the corresponding digit in the subtrahend. Borrow from the next higher place value.
Example 5: A shop had 5,342 loaves of bread. If 2,875 loaves were sold, how many are remaining? ``` Th H T U 5 3 4 2 - 2 8 7 5 ------------- ``` Steps:
1. Subtract Units: We cannot subtract 5 from
2. Borrow 1 Ten (10 units) from the Tens column. The 4 Tens become 3 Tens, and the 2 Units become 12 Units. Now, 12 - 5 =
7. Write 7 in the Units column.
2. Subtract Tens: We cannot subtract 7 from the remaining 3 Tens. Borrow 1 Hundred (10 Tens) from the Hundreds column. The 3 Hundreds become 2 Hundreds, and the 3 Tens become 13 Tens. Now, 13 - 7 =
6. Write 6 in the Tens column.
3. Subtract Hundreds: We cannot subtract 8 from the remaining 2 Hundreds. Borrow 1 Thousand (10 Hundreds) from the Thousands column. The 5 Thousands become 4 Thousands, and the 2 Hundreds become 12 Hundreds. Now, 12 - 8 =
4. Write 4 in the Hundreds column.
4. Subtract Thousands: 4 - 2 =
2. Write 2 in the Thousands column.
Result: 2,467 loaves of bread are remaining.
B. Addition and Subtraction of Fractions
1. Types of Fractions Review: Proper Fraction: Numerator is smaller than the denominator (e.g., 1⁄2, 3⁄4, 5⁄8).
Improper Fraction: Numerator is equal to or larger than the denominator (e.g., 3⁄3, 5⁄4, 10⁄3).
Mixed Fraction (Mixed Number): A whole number and a proper fraction combined (e.g., 1 1⁄2, 2 3⁄4).
Conversion: Improper to Mixed: Divide numerator by denominator. Quotient is whole number, remainder is new numerator over original denominator. (e.g., 5⁄2 = 2 1⁄2)
Mixed to Improper: Multiply whole number by denominator, add numerator. Result is new numerator over original denominator. (e.g., 2 1⁄2 = (2x2 + 1)/2 = 5⁄2)
2. Addition of Fractions: Rule: Fractions must have a common denominator before adding. Find the Least Common Multiple (LCM) of the denominators to create equivalent fractions. a.
Proper Fractions (Same Denominators): Add numerators, keep denominator.
Example 6: Musa ate 3⁄8 of a pizza, and his sister ate 2⁄8 of the same pizza. How much pizza did they eat in total? 3⁄8 + 2⁄8 = (3+2)⁄8 = 5⁄8 Result: They ate 5⁄8 of the pizza. b.
Proper Fractions (Different Denominators): Example 7: Adaku used 1⁄2 cup of flour for pancakes and 1⁄4 cup for puff-puff. How much flour did she use in total?
Step 1: Find LCM of denominators (2 and 4). LCM(2, 4) =
4. Step 2: Convert fractions to equivalent fractions with denominator 4. 1⁄2 = (1 x 2) / (2 x 2) = 2⁄4 1⁄4 remains 1⁄4 Step 3: Add the equivalent fractions. 2⁄4 + 1⁄4 = (2+1)⁄4 = 3⁄4 Result: Adaku used 3⁄4 cup of flour. c.
Improper Fractions: Convert to mixed numbers or add as improper, then simplify.
Example 8: Add 5⁄4 + 3⁄2 Step 1: Find LCM of denominators (4 and 2). LCM(4, 2) =
4. Step 2: Convert fractions. 5⁄4 remains 5⁄4 3⁄2 = (3 x 2) / (2 x 2) = 6⁄4 Step 3: Add. 5⁄4 + 6⁄4 = (5+6)⁄4 = 11⁄4 Step 4: Convert to mixed fraction (optional, but good practice). 11⁄4 = 2 3⁄4 Result: 2 3⁄4 d.
Mixed Fractions: Add whole numbers separately, then add the fraction parts.
Example 9: Add 1 1⁄2 + 2 3⁄4 Method 1 (Separate whole and fraction parts): * Add (4 and 2). LCM(4, 2) =
4. Step 2: Convert fractions. 5⁄4 remains 5⁄4 3⁄2 = (3 x 2) / (2 x 2) = 6⁄4 Step 3: Add. 5⁄4 + 6⁄4 = (5+6)⁄4 = 11⁄4 Step 4: Convert to mixed fraction (optional, but good practice). 11⁄4 = 2 3⁄4 Result: 2 3⁄4 d.
Mixed Fractions: Add whole numbers separately, then add the fraction parts.
Example 9: Add 1 1⁄2 + 2 3⁄4 Method 1 (Separate whole and fraction parts): Add whole numbers: 1 + 2 = 3 Add fractions: 1⁄2 + 3⁄
4. LCM(2, 4) = 4. 1⁄2 = 2⁄4 2⁄4 + 3⁄4 = 5⁄
4. Convert 5⁄4 to mixed: 1 1⁄4 Combine whole number sum and mixed fraction: 3 + 1 1⁄4 = 4 1⁄4 Method 2 (Convert to improper fractions first): 1 1⁄2 = 3⁄2 2 3⁄4 = 11⁄4 Add: 3⁄2 + 11⁄
4. LCM(2, 4) = 4. 3⁄2 = 6⁄4 6⁄4 + 11⁄4 = 17⁄4 Convert to mixed: 17⁄4 = 4 1⁄4 Result: 4 1⁄4
3. Subtraction of Fractions: Rule: Fractions must have a common denominator before subtracting. a.
Proper Fractions (Same Denominators): Subtract numerators, keep denominator.
Example 10: A baker used 7⁄10 of a bag of flour. If he had 3⁄10 remaining, how much did he start with? (Oops, this is addition implied, "how much did he use?" is better for subtraction here, or "how much more did he use than what remained?").
Let's rephrase: A baker had 7⁄10 of a bag of flour. He used 3⁄10 of it. How much is left? 7⁄10 - 3⁄10 = (7-3)⁄10 = 4⁄10 Simplify: 4⁄10 = 2⁄5 Result: 2⁄5 of the flour is left. b.
Proper Fractions (Different Denominators): Example 11: Chiamaka had 3⁄4 of a cake. She gave 1⁄2 of it to her friend. How much cake is left?
Step 1: Find LCM of denominators (4 and 2). LCM(4, 2) =
4. Step 2: Convert fractions. 3⁄4 remains 3⁄4 1⁄2 = 2⁄4 Step 3: Subtract. 3⁄4 - 2⁄4 = (3-2)⁄4 = 1⁄4 Result: 1⁄4 of the cake is left. c.
Mixed Fractions: Example 12: Subtract 2 1⁄2 from 4 1⁄4 Method 1 (Separate whole and fraction parts - may require borrowing): 4 1⁄4 - 2 1⁄2 Can't subtract 1⁄2 from 1⁄4 directly. Borrow 1 whole from 4. 4 1⁄4 becomes 3 (1 + 1⁄4) = 3 (4⁄4 + 1⁄4) = 3 5⁄4 Now subtract: 3 5⁄4 - 2 1⁄2 Convert 1⁄2 to 2⁄4. 3 5⁄4 - 2 2⁄4 = (3-2) + (5⁄4 - 2⁄4) = 1 + 3⁄4 = 1 3⁄4 Method 2 (Convert to improper fractions first): 4 1⁄4 = (4x4 + 1)⁄4 = 17⁄4 2 1⁄2 = (2x2 + 1)⁄2 = 5⁄2 Subtract: 17⁄4 - 5⁄
2. LCM(4, 2) = 4. 5⁄2 = 10⁄4 17⁄4 - 10⁄4 = (17-10)⁄4 = 7⁄4 Convert to mixed: 7⁄4 = 1 3⁄4 Result: 1 3⁄4
C. Addition and Subtraction of Decimals
1. Place Value for Decimals Review: Decimal point separates whole numbers from fractional parts. Tenths (0.1): First digit after the decimal point (e.g., 0.5 means 5⁄10). Hundredths (0.01): Second digit after the decimal point (e.g., 0.05 means 5⁄100). Thousandths (0.001): Third digit after the decimal point (e.g., 0.005 means 5⁄1000).
2. Addition of Decimals: Rule: Align the decimal points vertically. Add zeros to the end of numbers to ensure they have the same number of decimal places for easier calculation.
Example 13: Add 3.45 + 0.789 ``` 3.450 (Added a zero to 3.45 to match 3 decimal places) + 0.789 ------- 4.239 ------- ``` Steps:**
1. Align decimal points.
2. Add zeros to 3.45 to make it 3.450.
3. Add from right to left (thousandths, hundredths, tenths, then whole numbers), carrying over as needed. 0 + 9 = 9 (thousandths) 5 + 8 = 13 (hundredths). Write 3, carry This section provides detailed explanations and step-by-step procedures for teaching addition and subtraction of whole numbers, fractions, and decimals.
A. Addition and Subtraction of Whole Numbers (Th.
H. T. U)
1. Place Value Review: Before proceeding, ensure learners understand place values up to Thousands. Units (ones) Tens (10 units) Hundreds (10 tens) Thousands (10 hundreds) A number like 3,456 means 3 Thousands, 4 Hundreds, 5 Tens, and 6 Units.
2. Addition of Whole Numbers: Rule: Always start adding from the Units column, then Tens, Hundreds, and Thousands. Align numbers vertically by their place values. a.
Without Renaming (Carrying): This occurs when the sum of digits in any column is 9 or less.
Example 1: A farmer harvested 2,345 yams and later harvested another 1,234 yams. How many yams did he harvest in total? ``` Th H T U 2 3 4 5 + 1 2 3 4 ------------- 3 5 7 9 ------------- ``` Steps:
1. Add Units: 5 + 4 =
9. Write 9 in the Units column.
2. Add Tens: 4 + 3 =
7. Write 7 in the Tens column.
3. Add Hundreds: 3 + 2 =
5. Write 5 in the Hundreds column.
4. Add Thousands: 2 + 1 =
3. Write 3 in the Thousands column.
Result: 3,579 yams. b.
With Renaming (Carrying): This occurs when the sum of digits in any column is 10 or more. The "extra" value is carried over to the next higher place value.
Example 2: A marketer sold 1,875 bags of garri in January and 2,368 bags in February. How many bags were sold in total? ``` Th H T U 1 8 7 5 + 2 3 6 8 ------------- ``` Steps:
1. Add Units: 5 + 8 =
1
3. Write 3 in the Units column and carry-over 1 to the Tens column.
2. Add Tens: 7 + 6 + (carried 1) =
1
4. Write 4 in the Tens column and carry-over 1 to the Hundreds column.
3. Add Hundreds: 8 + 3 + (carried 1) =
1
2. Write 2 in the Hundreds column and carry-over 1 to the Thousands column.
4. Add Thousands: 1 + 2 + (carried 1) =
4. Write 4 in the Thousands column.
Result: 4,243 bags of garri. c. Adding Three 4-Digit Numbers (taking two at a time): Example 3: Three villages contributed to a project: Village A gave N1,250, Village B gave N2,580, and Village C gave N1,
8
7
5. What is the total contribution?
Step 1: Add Village A and Village B's contributions. ``` Th H T U 1 2 5 0 (Village A) + 2 5 8 0 (Village B) ------------- 3 8 3 0 ------------- ``` Step 2: Add the sum from Step 1 to Village C's contribution. ``` Th H T U 3 8 3 0 (Sum A+B) + 1 8 7 5 (Village C) ------------- 5 7 0 5 ------------- ``` Result: Total contribution is N5,705.
3. Subtraction of Whole Numbers: Rule: Always start subtracting from the Units column, then Tens, Hundreds, and Thousands. Align numbers vertically by their place values. a.
Without Renaming (Borrowing): This occurs when each digit in the top number (minuend) is greater than or equal to the corresponding digit in the bottom number (subtrahend).
Example 4: A school had 4,876 exercise books. If 1,234 were given out, how many are left? ``` Th H T U 4 8 7 6 - 1 2 3 4 ------------- 3 6 4 2 ------------- ``` Steps:
1. Subtract Units: 6 - 4 =
2. Write 2 in the Units column.
2. Subtract Tens: 7 - 3 =
4. Write 4 in the Tens column.
3. Subtract Hundreds: 8 - 2 =
6. Write 6 in the Hundreds column.
4. Subtract Thousands: 4 - 1 =
3. Write 3 in the Thousands column.
Result: 3,642 exercise books are left. * b.
With Renaming (Borrowing): This occurs when a digit in the minuend is smaller than the corresponding digit in the subtrahend. Borrow from the next higher zeros to the end of numbers to ensure they have the same number of decimal places for easier calculation.
Example 13: Add 3.45 + 0.789 ``` 3.450 (Added a zero to 3.45 to match 3 decimal places) + 0.789 ------- 4.239 ------- ``` Steps:
1. Align decimal points.
2. Add zeros to 3.45 to make it 3.450.
3. Add from right to left (thousandths, hundredths, tenths, then whole numbers), carrying over as needed. 0 + 9 = 9 (thousandths) 5 + 8 = 13 (hundredths). Write 3, carry 1. 4 + 7 + (carried 1) = 12 (tenths). Write 2, carry 1. 3 + 0 + (carried 1) = 4 (whole numbers).
4. Place the decimal point in the answer directly below the aligned decimal points.
Result: 4.239 Example 14: A tailor bought 2.5 meters of Ankara fabric and 3.75 meters of lace fabric. How many meters of fabric did he buy in total? ``` 2.50 (Added a zero to 2.5) + 3.75 ------ 6.25 ------ ``` Result: 6.25 meters of fabric.
3. Subtraction of Decimals: Rule: Align the decimal points vertically. Add zeros to the end of numbers to ensure they have the same number of decimal places.
Example 15: Subtract 1.234 from 5.000 ``` 5.000 - 1.234 ------- 3.766 ------- ``` Steps:
1. Align decimal points.
2. Subtract from right to left (thousandths, hundredths, tenths, then whole numbers), borrowing as needed. Cannot subtract 4 from 0 (thousandths). Borrow from the next place value. In this case, we need to borrow all the way from the 5 in the Units place. The 5 becomes
4. The first 0 (tenths) becomes 10, then borrows 1 for hundredths (becomes 9). The second 0 (hundredths) becomes 10, then borrows 1 for thousandths (becomes 9). The third 0 (thousandths) becomes 10. 10 - 4 = 6 (thousandths) 9 - 3 = 6 (hundredths) 9 - 2 = 7 (tenths) 4 - 1 = 3 (whole numbers)
3. Place the decimal point in the answer directly below the aligned decimal points.
Result: 3.766 Example 16: A bag of rice weighs 50.75 kg. If 15.25 kg was removed, what is the new weight of the rice? ``` 50.75 - 15.25 ------- 35.50 ------- ``` Result: The new weight is 35.50 kg (or 35.5 kg). D. Quantitative Aptitude Problems These problems combine addition and subtraction within a word problem context. They require careful reading to identify the operations needed.
Example: A trader bought 1,500 oranges. He sold 850 in the morning and 420 in the afternoon. How many oranges are left?
Step 1: Total sold. 850 + 420 = 1,270 oranges.
Step 2: Remaining oranges. 1,500 - 1,270 = 230 oranges. * Result: 230 oranges are left.
Market Transactions and Budgeting: Application: Learners can apply addition and subtraction when simulating market scenarios. For instance, calculating the total cost of buying bags of rice, tubers of yam, and baskets of tomatoes (4-digit whole numbers). They can also determine the change received from a specific denomination of Naira. When dealing with smaller items or precise measurements (e.g., buying 0.75 kg of meat or adding N150.50 for transport), decimal addition and subtraction become crucial. This directly integrates with financial literacy and everyday commerce in Nigeria.
Example: A mother bought N4,500 worth of garri, N2,850 worth of beans, and N1,200 worth of palm oil. What is her total expenditure? If she paid with N10,000, how much change did she get?
Resource Sharing and Allocation: Application: Fractions are essential for understanding how to divide resources fairly. Whether it's sharing a piece of land among family members, distributing food items, or allocating portions of work, fractions provide a mathematical framework. Learners can calculate how much of a shared resource each person gets or how much is left after distribution.
Example: A community land measures 5 1⁄2 hectares. If 2 3⁄4 hectares are allocated for farming, how much land remains for other purposes? Or, if a mother bakes a loaf of bread and her three children eat 1⁄4, 1⁄3, and 1⁄6 of it respectively, how much bread is left for her?
Measurement and Construction: Application: Decimals are extensively used in measurements for tailoring, carpentry, and construction projects. Carpenters measure wood lengths (e.g., 2.5 meters), tailors measure fabric (e.g., 3.75 meters), and builders calculate quantities of cement or sand (e.g., 50.5 kg). Addition and subtraction of these decimal quantities ensure accuracy in projects, preventing wastage and ensuring correct dimensions.
Example: A carpenter needs two pieces of wood measuring 1.25 metres and 0.875 metres. What is the total length of wood he needs? If he has a plank of 3.000 metres, how much will be left after cutting the required pieces?