Lesson Notes By Weeks and Term v3 - Primary 3
Subtraction
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Subtraction
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Subject: General Mathematics
Class: Primary 3
Term: 1st Term
Week: 3
Theme: Basic Operations
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Watch on YouTubesubtract 2-digit numbers with exchanging or renaming; subtract 3 - digit numbers; subtract 3 numbers taking two at a time; subtract fractions with the same denominator; mention the need for correct subtraction of numbers and fractions in everyday activities.
the Tens column. The Tens column has
0. So, we must first exchange from the Hundreds column.
Step 2: Exchange Hundreds to Tens. Take 1 Hundred from 7 Hundreds, leaving 6 Hundreds. Add 10 Tens to the 0 Tens, making 10 Tens. ``` H T U 6 110 3 7 0 3 - 4 8 5 --------- ``` Step 3: Now exchange Tens to Units. Take 1 Ten from the 10 Tens, leaving 9 Tens. Add 10 Units to the 3 Units, making 13 Units. Now, in the units column: 13 - 5 = 8. ``` H T U 6 9 113 7 0 3 - 4 8 5 --------- 8 ``` Step 4: Tens Column. Now, 9 Tens (after exchanging) - 8 Tens = 1 Ten. ``` H T U 6 9 113 7 0 3 - 4 8 5 --------- 1 8 ``` Step 5: Hundreds Column. 6 Hundreds (after exchanging) - 4 Hundreds = 2 Hundreds. ``` H T U 6 9 113 7 0 3 - 4 8 5 --------- 2 1 8 ``` Result:
2
1
8. D. Subtracting 3 Numbers Taking Two at a Time: This involves solving subtraction problems with three numbers by performing the operation in two steps. First, subtract the second number from the first, then subtract the third number from that result.
Example 5: Subtract 20 and 15 from
7
5. Step 1: Subtract the first two numbers. 75 - 20 Units: 5 - 0 = 5 Tens: 7 - 2 = 5 Result of first step: 55 Step 2: Subtract the third number from the result of Step 1. 55 - 15 Units: 5 - 5 = 0 Tens: 5 - 1 = 4 Final result:
4
0. Therefore, 75 - 20 - 15 =
4
0. E. Subtracting Fractions with the Same Denominator: When subtracting fractions that have the same denominator (the bottom number), subtract the numerators (the top numbers) and keep the denominator the same.
Example 6: Subtract 2/7 from 5/
7. We have 5 parts out of 7, and we want to take away 2 parts out of
7. Subtract the numerators: 5 - 2 =
3. Keep the denominator:
7. Result: 3/7. * This can be visualized with a cake divided into 7 equal slices. If 5 slices are available and 2 are eaten, 3 slices remain (3/7 of the cake).
A. Definition of Subtraction: Subtraction is the process of taking one number or quantity away from another. It helps to find the difference between two numbers, or how much is left.
Minuend: The number from which another number is subtracted (the larger number).
Subtrahend: The number that is being subtracted (the smaller number).
Difference: The result obtained after subtracting the subtrahend from the minuend.
Example: In 15 - 7 = 8, 15 is the minuend, 7 is the subtrahend, and 8 is the difference.
B. Subtraction of 2-Digit Numbers with Exchanging (Renaming/Borrowing): This involves situations where the digit in the units column of the minuend is smaller than the digit in the units column of the subtrahend. Exchanging means taking one ten from the tens column and converting it into ten units, which are then added to the units column.
Example 1: Subtract 43 from
7
2. Arrange the numbers vertically according to their place values: ``` T U 7 2 (Minuend) - 4 3 (Subtrahend) ----- ``` Step 1: Subtract the Units. In the units column, we have 2 -
3. Since 2 is smaller than 3, we cannot subtract directly. We need to exchange or rename. Take 1 Ten from the 7 Tens in the tens column. This leaves 6 Tens. The 1 Ten that was exchanged is converted into 10 Units and added to the 2 Units, making 10 + 2 = 12 Units. Now, in the units column, we have 12 - 3 = 9. ``` T U 6 112 7 2 - 4 3 ----- 9 ``` Step 2: Subtract the Tens. In the tens column, we now have 6 Tens (after exchanging) - 4 Tens = 2 Tens. ``` T U 6 112 7 2 - 4 3 ----- 2 9 ``` Therefore, 72 - 43 =
2
9. C.
Subtraction of 3-Digit Numbers: This follows the same principle as 2-digit subtraction, starting from the units column and moving to the left (tens, then hundreds). Exchanging may occur across multiple columns.
Example 2: Subtract 234 from 579 (No Exchanging). ``` H T U 5 7 9 - 2 3 4 --------- 3 4 5 ``` Units: 9 - 4 = 5 Tens: 7 - 3 = 4 Hundreds: 5 - 2 = 3 Result:
3
4
5. Example 3: Subtract 283 from 645 (With Exchanging). ``` H T U 6 4 5 - 2 8 3 --------- ``` Step 1: Units Column. 5 - 3 =
2. No exchanging needed here. ``` H T U 6 4 5 - 2 8 3 --------- 2 ``` Step 2: Tens Column. 4 -
8. Since 4 is smaller than 8, we exchange 1 Hundred from the 6 Hundreds. This leaves 5 Hundreds. The 1 Hundred is converted into 10 Tens and added to the 4 Tens, making 10 + 4 = 14 Tens. Now, 14 - 8 = 6. ``` H T U 5 114 5 6 4 5 - 2 8 3 --------- 6 2 ``` Step 3: Hundreds Column. Now, 5 Hundreds (after exchanging) - 2 Hundreds = 3 Hundreds. ``` H T U 5 114 5 6 4 5 - 2 8 3 --------- 3 6 2 ``` Result:
3
6
2. Example 4: Subtract 485 from 703 (Multiple Exchanging). ``` H T U 7 0 3 - 4 8 5 --------- ``` Step 1: Units Column. 3 -
5. Cannot subtract. We need to exchange from the Tens column. The Tens column has
0. So, we must first exchange from the Hundreds column.
Step 2: Exchange Hundreds to Tens. Take 1 Hundred from 7 Hundreds, leaving 6 Hundreds. Add 10 Tens to the 0 Tens, making 10 Tens. ``` H T U 6 110 3 7 0 3 - 4 8 5 --------- ``` Step 3: Now exchange Tens to Units. Take 1 Ten from the 10 Tens, leaving 9 Tens. * Add 10 Units to the 3 Units, making 13 Units.
Teacher Activities: Introduction & Review: Begin with a brief review of place value (Units, Tens, Hundreds) and basic subtraction without exchanging. Engage students by asking simple subtraction questions related to classroom items (e.g., "If we have 10 chalks and I use 3, how many are left?").
Demonstration of Exchanging (2-digit): Using concrete materials: Represent 2-digit numbers using bundles of 10 sticks (tens) and single sticks (units), or bottle caps/Naira notes (N10 notes for tens, N1 coins for units). Demonstrate a problem like 32 -
1
5. Show taking 1 ten (a bundle of 10 sticks) and unbundling it into 10 single sticks, then adding to the units before subtracting. Use a place value chart drawn on the board to guide the process.
Transition to abstract: Write the vertical subtraction problem on the board and explain the renaming process numerically, clearly showing the crossing out and writing new digits.
Demonstration of 3-Digit Subtraction: Present an example with no exchanging, then one with single exchanging, and finally one with multiple exchanges (as in Examples 2, 3, and 4 above). Emphasize starting from the units column and moving left. Continuously refer back to the concept of exchanging 1 Ten for 10 Units, or 1 Hundred for 10 Tens. Demonstration of Subtracting Three Numbers: Present a word problem or a numerical example (e.g., 80 - 25 - 10). Guide students to perform the first subtraction, then use that result for the second subtraction. Highlight the step-by-step nature.
Demonstration of Fraction Subtraction: Use visual aids: draw a circle or rectangle divided into equal parts (e.g., 7 parts for 5/7 - 2/7). Shade the initial fraction, then cross out the parts being subtracted. Explain that only the top numbers (numerators) are subtracted when the bottom numbers (denominators) are the same.
Real-life Application Discussion: Lead a short discussion on why subtraction is important (e.g., giving change, knowing how many items are left in a shop).
Guided Practice Facilitation: Provide problems for students to solve in class, circulating to offer support and correct misconceptions.
Student Activities: Active Participation: Respond to review questions and engage in discussions.
Manipulative Practice: Use concrete materials (sticks, bottle caps, local currency if available) to model 2-digit and 3-digit subtraction problems, especially those involving exchanging, under teacher guidance.
Problem Solving: Work individually, in pairs, or small groups to solve subtraction problems written on the board or given on worksheets.
Step-by-Step Recording: Accurately record their solutions, showing the exchanging process (crossing out and writing new digits).
Fraction Drawing: Draw simple diagrams to represent fraction subtraction problems.
Presentation: Some students may be called upon to present their solutions and explanations on the board.
Questioning: Ask questions when they encounter difficulties. The teacher should guide students through these examples, encouraging them to try independently first, then reviewing step-by-step. Question 1 (2-digit subtraction with exchanging): A market woman had 85 oranges. She sold 39 of them. How many oranges are left?
Solution: ``` T U 7 115 8 5 3 9 4 6 ``` Units: 5 -
9. Cannot subtract. Exchange 1 Ten from 8 Tens, leaving 7 Tens. Add 10 Units to 5 Units, making 15 Units. Now, 15 - 9 =
6. Tens: 7 - 3 =
4. Answer: 46 oranges are left. Question 2 (3-digit subtraction with exchanging): Mr. Emeka had N524 in his savings. He spent N178 to buy foodstuffs. How much money does he have left?
Solution: ``` H T U 4 111 114 5 2 4 1 7 8 3 4 6 ``` Units: 4 -
8. Cannot subtract. Exchange 1 Ten from 2 Tens, leaving 1 Ten. Add 10 Units to 4 Units, making 14 Units. Now, 14 - 8 =
6. Tens: We now have 1 Ten - 7 Tens. Cannot subtract. Exchange 1 Hundred from 5 Hundreds, leaving 4 Hundreds. Add 10 Tens to 1 Ten, making 11 Tens. Now, 11 - 7 =
4. Hundreds: 4 - 1 =
3. Answer: Mr. Emeka has N346 left. Question 3 (Subtracting 3 numbers taking two at a time): There were 95 sachet water packs in a cooler. A hawker sold 25 packs in the morning and 30 packs in the afternoon. How many sachet water packs are left?
Solution: Step 1: Subtract the morning sales. 95 - 25 = 70 packs (95 minus 25 equals 70).
Step 2: Subtract the afternoon sales from the remaining. 70 - 30 = 40 packs (70 minus 30 equals 40).
Answer: 40 sachet water packs are left. Question 4 (Subtracting fractions with the same denominator): Subtract 3/8 from 7/
8. Solution: Both fractions have the same denominator (8).
Subtract the numerators: 7 - 3 =
4. Keep the denominator the same:
8. Answer: 4/8 (which can be simplified to 1/2, but 4/8 is acceptable at this level).
Market Transactions (Economy): Application: When a parent goes to the market and buys items (e.g., N350 for yam, N120 for tomatoes) with a N500 note, subtraction is used to calculate the change received (N500 - (N350 + N120)).
Integration: Students can role-play buying and selling local items like garri, plantain, or akara, using play money (Naira notes and coins) and practicing calculating change. Resource Management and Sharing (Community/Culture): Application: If a family cooks a pot of jollof rice divided into 10 equal portions, and 3 portions are eaten, subtraction (10/10 - 3/10 = 7/10) helps to determine how much is left.
Integration: Discuss scenarios like sharing kola nuts or garden produce. If a farmer harvests 150 tubers of cassava and uses 60 for garri, the remaining are for sale. Students can calculate the difference.
Time and Event Planning (Daily Life): Application: If an event is scheduled to last 90 minutes and 35 minutes have passed, subtraction helps to find out how many minutes are remaining.
Integration: Students can calculate time differences for classroom activities, e.g., "If break time is 30 minutes and 10 minutes have already passed, how many more minutes until break is over?"