Lesson Notes By Weeks and Term v3 - Junior Secondary 1
Addition and subtraction.
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Addition and subtraction.
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Subject: General Mathematics
Class: Junior Secondary 1
Term: 2nd Term
Week: 3
Theme: Basic Operations
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Add and subtract any given numbers correctly; State the place value of each numbers in the sum or difference; Draw and use number line to illustrate directed numbers; Add and subtract positive and negative in tegers correctly on the number line; In terpret and relate positive and negative numbers to everyday activities.
Step 3: Subtract the digits in the Tens column. 9 - 7 = 2. ``` Thousands Hundreds Tens Ones 3 4 9 10 - 1 2 7 5 ------------------------ 2 5 ``` Step 4: Subtract the digits in the Hundreds column. 4 - 2 = 2. ``` Thousands Hundreds Tens Ones 3 4 9 10 - 1 2 7 5 ------------------------ 2 2 5 ``` Step 5: Subtract the digits in the Thousands column. 3 - 1 = 2. ``` Thousands Hundreds Tens Ones 3 4 9 10 - 1 2 7 5 ------------------------ 2 2 2 5 ``` Result: 2,225 exercise books are left. Stating Place Value of Digits in Sum or Difference: After calculation, students should be able to state the place value of each digit. Example (from W.E. 1, sum = 4,221): The digit '1' is in the Ones place. The digit '2' (right) is in the Tens place. The digit '2' (left) is in the Hundreds place. The digit '4' is in the Thousands place.
B. Directed Numbers (Integers)
Definition: Directed numbers are whole numbers that have a direction, indicated by a positive (+) or negative (-) sign. Positive numbers are greater than zero (e.g., +1, +2, +3...). Often, the '+' sign is omitted (e.g., 5 means +5). Negative numbers are less than zero (e.g., -1, -2, -3...). The '-' sign must always be written. Zero is neither positive nor negative.
Real-life Interpretation in Nigeria: Temperature: Above freezing point (positive, e.g., 28°C in Lagos); Below freezing point (negative, e.g., -5°C in a freezer).
Money: Profit, credit, money received (positive); Loss, debt, money owed (negative). A balance of ₦5000 is +₦
5
0
0
0. A debt of ₦2000 is -₦
2
0
0
0. Elevation: Above sea level (positive, e.g., highest point in Plateau State); Below sea level (negative, e.g., depths of a well or mine).
Movement: Moving forward, climbing up (positive); Moving backward, descending (negative).
The Number Line: A visual representation of directed numbers. Draw a straight line. Mark a point in the middle as '0' (origin). Mark equal intervals to the right of '0' for positive numbers (+1, +2, +3...). Mark equal intervals to the left of '0' for negative numbers (-1, -2, -3...). Numbers increase in value as one moves to the right and decrease as one moves to the left. ``` -4 -3 -2 -1 0 +1 +2 +3 +4 +5 ``` Adding and Subtracting Directed Numbers on the Number Line: Rule for Addition: Start at the first number. To add a positive number, move to the right. To add a negative number, move to the left.
Worked Example 3: Adding Directed Numbers a) +3 + (+2) Start at +
3. Add (+2) means move 2 steps to the right.
Result: +5. ``` -1 0 +1 +2 +3 +4 +5 +6 ^ (start) ---> (move 2 right) ^ (end) ``` b) +5 + (-3) Start at +
5. Add (-3) means move 3 steps to the left.
Result: +2. ``` -1 0 +1 +2 +3 +4 +5 +6 ^ (start) -3 -2 -1 0 +1 +2 +3 +4 ^ (start) -----------------> (move 4 right) ^ (end) ``` d) -4 + (-1) Start at -
4. Add (-1) means move 1 step to the left.
Result: -5. ``` -5 -4 -3 -2 -1 0 +1 ^ ^ (start) -1 0 +1 +2 +3 +4 +5 +6 +7 ^ (start) ------------------> (move 4 right) ^ (end) ``` c) -3 - (+2)
Convert to addition: -3 + (-2) Start at -
3. Add (-2) means move 2 steps to the left.
Result: -5. ``` -5 -4 -3 -2 -1 0 +1 ^ ^ (start) -2 -1 0 +1 +2 +3 +4 +5 ^ (start) ---------------------------> (move 5 right) ^ (end) ``` This section provides a detailed breakdown of the core concepts related to addition and subtraction, including whole numbers and directed numbers, alongside practical examples relevant to the Nigerian context.
A. Addition and Subtraction of Whole Numbers Definition: Addition is the process of combining two or more quantities to find their total sum. The symbol for addition is '+'. Subtraction is the process of finding the difference between two numbers or taking one quantity away from another. The symbol for subtraction is '-'.
Place Value Review: Understanding place value is critical for correctly adding and subtracting multi-digit numbers. Each digit in a number holds a specific value based on its position.
Example: In the number ₦4,752: 2 is in the Ones place (value = 2 x 1 = 2) 5 is in the Tens place (value = 5 x 10 = 50) 7 is in the Hundreds place (value = 7 x 100 = 700) 4 is in the Thousands place (value = 4 x 1000 = 4000) Column Method for Addition and Subtraction: This method aligns numbers vertically according to their place values, making the operation systematic.
Worked Example 1: Addition of Whole Numbers A trader at Onitsha Main Market bought 2,345 tubers of yam on Monday and 1,876 tubers on Tuesday. How many tubers did the trader buy in total?
Step 1: Write the numbers in columns, aligning by place value. ``` Thousands Hundreds Tens Ones 2 3 4 5 + 1 8 7 6 ------------------------ ``` Step 2: Add the digits in the Ones column. 5 + 6 =
1
1. Write down 1 in the Ones column and carry over 1 to the Tens column. ``` 1 2 3 4 5 + 1 8 7 6 ------------------------ 1 ``` Step 3: Add the digits in the Tens column, including the carried-over digit. 4 + 7 + 1 (carry-over) =
1
2. Write down 2 in the Tens column and carry over 1 to the Hundreds column. ``` 1 1 2 3 4 5 + 1 8 7 6 ------------------------ 2 1 ``` Step 4: Add the digits in the Hundreds column, including the carried-over digit. 3 + 8 + 1 (carry-over) =
1
2. Write down 2 in the Hundreds column and carry over 1 to the Thousands column. ``` 1 1 1 2 3 4 5 + 1 8 7 6 ------------------------ 2 2 1 ``` Step 5: Add the digits in the Thousands column, including the carried-over digit. 2 + 1 + 1 (carry-over) =
4. Write down 4 in the Thousands column. ``` 1 1 1 2 3 4 5 + 1 8 7 6 ------------------------ 4 2 2 1 ``` Result: The trader bought 4,221 tubers of yam in total.
Worked Example 2: Subtraction of Whole Numbers A school had 3,500 exercise books. If 1,275 books were distributed to JSS1 students, how many books are left?
Step 1: Write the numbers in columns, aligning by place value. ``` Thousands Hundreds Tens Ones 3 5 0 0 - 1 2 7 5 ------------------------ ``` Step 2: Subtract the digits in the Ones column. 0 - 5 is not possible. Borrow 1 from the Tens column. The Tens digit is 0, so borrow from the Hundreds column. The Hundreds digit (5) becomes
4. The Tens digit (0) becomes 10, then lends 1 to the Ones, becoming
9. The Ones digit (0) becomes 10. ``` Thousands Hundreds Tens Ones 3 4 9 10 - 1 2 7 5 ------------------------ 5 ``` Step 3: Subtract the digits in the Tens column. 9 - 7 = 2. ``` Thousands Hundreds Tens Ones 3 4 9 10 - 1 2 7 5 ------------------------ 2 5 ``` Step 4: Subtract the digits in the Hundreds column. 4 - 2 = 2. ``` Thousands Hundreds Tens Ones 3 4 9 10 - 1 2 7 5 ------------------------ 2 2 5 ``` * Step 5: Subtract the digits in the Thousands column. 3 - 1 = 2. ``` Thousands Hundreds Tens Ones 3 4 9 10 - This section outlines the step-by-step activities for both the teacher and the students to ensure an engaging and effective lesson delivery.
A. Introduction (10 minutes)
Teacher Activity: Begin by eliciting prior knowledge on basic addition and subtraction. Ask questions like, "If you buy a sachet of water for ₦20 and a biscuit for ₦50, how much do you spend?" Introduce the concept of positive and negative numbers by discussing real-life scenarios familiar to students in Nigeria.
Examples: Temperature: "The temperature in Jos can drop to 10°C, but in Kano, it might be 35°C. What if we talk about temperatures below freezing point?" (Use a large thermometer drawing if available).
Money: "If you have ₦500 (positive) but owe your friend ₦200 (negative), what is your financial standing?" Elevation: "Some towns are on hills (positive height), others are in valleys (negative height relative to a reference point)." Briefly explain the idea of a number line as a tool to visualise these numbers.
Student Activity: Respond to questions on basic addition and subtraction. Share their understanding of "gain" and "loss" or "above" and "below" in various contexts. Observe and participate in discussions about real-life examples of directed numbers.
B. Development - Part 1: Addition and Subtraction of Whole Numbers (20 minutes)
Teacher Activity: Review place values (ones, tens, hundreds, thousands) using a place value chart or by writing numbers on the board. Demonstrate the column method for addition with a 4-digit number example, emphasising carrying over. Use an example like calculating total school fees collected from two classes. Demonstrate the column method for subtraction with a 4-digit number example, emphasising borrowing. Use an example like calculating remaining items in a shop. Guide students to state the place value of each digit in the calculated sum or difference.
Student Activity: Practice identifying place values of digits in given numbers. Work through guided examples of 4-digit addition and subtraction using the column method on their notebooks. Practise stating the place value of digits in the results.
C. Development - Part 2: Directed Numbers and Number Line (30 minutes)
Teacher Activity: Clearly draw a number line on the board, marking '0' and showing positive numbers to the right and negative numbers to the left with equal spacing. Explain how to locate any given integer on the number line. Demonstrate step-by-step how to add directed numbers on the number line: Start at the first number.
Movement rule: right for '+' (positive number), left for '-' (negative number). Use examples like a student walking forward 3 steps, then 2 steps backward. Demonstrate step-by-step how to subtract directed numbers on the number line: Introduce the rule: "Subtracting a positive is adding a negative" (move left), and "Subtracting a negative is adding a positive" (move right). Emphasise conversion of subtraction to addition of the opposite.
Use examples like a change in debt: "You had a debt of ₦
5
0
0. Your friend removed ₦200 from your debt. How much is your debt now?" (-500 - (-200)).
Student Activity: Draw their own number lines in their notebooks. Practice locating various positive and negative integers on their number lines. Work through guided examples of adding directed numbers on the number line. Work through guided examples of subtracting directed numbers on the number line, paying attention to the conversion rule. Act out simple movements (forward/backward) to reinforce the concept of directed numbers and their operations.
D. Conclusion (5 minutes)
Teacher Activity: Summarise the key learning points: addition/subtraction of whole numbers using column method, understanding directed numbers, and using the number line for integer operations. Reiterate the importance of these concepts in everyday Nigerian life. Assign homework.
Student Activity: Participate in a brief recap session. Ask clarifying questions. Note down homework assignment. These questions are designed to be worked through collaboratively with the teacher's guidance. A farmer in Benue State harvested 3,487 bags of maize in the first season and 2,935 bags in the second season. a) Calculate the total number of bags harvested. b) State the place value of each digit in your answer.
Solution: a)
Total bags harvested: ``` 3 4 8 7 + 2 9 3 5 6 4 2 2 ``` Calculation Steps: Ones: 7 + 5 = 12 (Write 2, carry 1)
Tens: 8 + 3 + 1 (carry-over) = 12 (Write 2, carry 1)
Hundreds: 4 + 9 + 1 (carry-over) = 14 (Write 4, carry 1)
Thousands: 3 + 2 + 1 (carry-over) = 6 (Write 6)
Result: The farmer harvested 6,422 bags of maize. b) Place Value of digits in 6,422: The digit '2' (rightmost) is in the Ones place. The digit '2' (middle) is in the Tens place. The digit '4' is in the Hundreds place. The digit '6' is in the Thousands place. A commercial bank in Lagos had ₦5,200,000 in its vault. After a customer withdrew ₦3,548,250, how much money was left in the vault?
Solution: Money left in the vault: ``` ₦5 200 000 ₦3 548 250 ₦1 651 750 ``` Calculation Steps: (Perform column subtraction with borrowing from left to right as needed) 0 - 0 = 0 (Ones) 0 - 5 (borrow from 0, then 0, then 0, then 2) -> 10 - 5 = 5 (Tens) 9 - 2 = 7 (Hundreds) (from previous borrowing) 9 - 8 = 1 (Thousands) (from previous borrowing) 9 - 4 = 5 (Ten Thousands) (from previous borrowing) 1 - 5 (borrow from 5) -> 11 - 5 = 6 (Hundred Thousands) 4 - 3 = 1 (Millions)
Result: ₦1,651,750 was left in the vault. Illustrate and calculate the following using a number line: a) -3 + (+5) b) +4 - (+6)
Solution: a) -3 + (+5) Draw a number line. Start at -
3. Move 5 steps to the right (because we are adding a positive number). ``` -3 -2 -1 0 +1 +2 +3 +4 ^ (start) ---------------------> (move 5 right) ^ (end) ``` Result: +2 b) +4 - (+6)
Convert to addition: +4 + (-6). Draw a number line. Start at +
4. Move 6 steps to the left (because we are adding a negative number). ``` -3 -2 -1 0 +1 +2 +3 +4 +5 ^ (start) <-------------------------------- (move 6 left) ^ (end) ``` Result: -2 A divers goes 15 metres below sea level. If she then rises 8 metres, what is her new position relative to sea level? Relate this to directed numbers.
Solution: Interpretation: "15 metres below sea level" can be represented as -15. "Rises 8 metres" can be represented as +
8. Calculation: -15 + (+8)
Using Number Line/Mental Calculation: Start at -
1
5. Move 8 units to the right. -15, -14, -13, -12, -11, -10, -9, -8, -7 Result: The diver's new position is -7 metres, which means 7 metres below sea level.
This topic is deeply integrated into various aspects of daily life in Nigeria, making it highly relevant to students. Financial Management (Market, Business, Personal Finance): Community/Economy: Individuals in local markets (e.g., Balogun Market, Ariaria International Market) constantly use addition and subtraction to calculate the total cost of goods, determine change, and keep track of daily sales. A small business owner must add expenses and subtract them from income to determine profit or loss. For example, calculating the total cost of ingredients for making 'akara' (bean cakes) and subtracting it from the total sales to find the profit.
Personal: Managing 'kolo' (piggy bank) savings involves adding deposits and subtracting withdrawals. Understanding debt (negative balance) and credit (positive balance) in local cooperative societies or informal lending groups.
Temperature and Environment: Environment: Interpreting weather reports from the Nigerian Meteorological Agency (NiMet) often involves understanding temperature changes. For instance, if the temperature in Abuja is 30°C and it drops by 5°C overnight, students can calculate the new temperature. Discussions about cold rooms for preserving agricultural produce (e.g., tomatoes, fish) or vaccines involve understanding temperatures below 0°C (negative values) and their implications. Measurement and Position (Geography, Sports): Geography: Understanding elevation and depression. Nigeria has diverse topography; students can relate heights above sea level (e.g., Mambilla Plateau) to positive numbers and depths below a reference point (e.g., digging a well or a bore hole) to negative numbers.
Sports: In football, goal difference is calculated by subtracting goals conceded from goals scored. If a team scores 5 goals (+5) and concedes 3 goals (-3), their goal difference is +
2. This helps in understanding league standings. A climber ascending (positive) and descending (negative) a mountain like Chappal Waddi (Nigeria's highest peak) can track their position using directed numbers.