Lesson Notes By Weeks and Term v3 - Primary 5
Use of Number line in addition and subtraction
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Use of Number line in addition and subtraction
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Subject: General Mathematics
Class: Primary 5
Term: 2nd Term
Week: 2
Theme: Basic Operations
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Add and subtract numbers using number line Solve problems on quantitative aptitude in volving addition and subtraction on the number line
number line. ``` 0 1 2 3 4 5 6 7 8 (9) 10 ```
3. Move 5 steps to the left from '9'. 1st step: lands on 8 2nd step: lands on 7 3rd step: lands on 6 4th step: lands on 5 5th step: lands on 4 ``` 0 1 2 3 (4) 7 -> 8 -> 9 -> 10 -> 11). The final position is
1
1. Therefore, 6 + 5 =
1
1. Commentary: This checks the basic understanding of addition on a number line. Ensure students clearly show the starting point and the 5 distinct jumps.
2. Question: Subtract 7 from 13 using a number line.
Solution: Draw a number line from 0 to
1
5. Start at
1
3. Move 7 steps to the left from 13 (13 -> 12 -> 11 -> 10 -> 9 -> 8 -> 7 -> 6). The final position is
6. Therefore, 13 - 7 =
6. Commentary: This checks the basic understanding of subtraction on a number line. Emphasize moving left.
3. Question (Quantitative Aptitude): A _keke napep_ started its journey with 7 passengers. At the next bus stop, 4 more passengers boarded. How many passengers are now in the _keke napep_? Use a number line to show your working.
Solution: Identify Operation: "4 more passengers boarded" indicates addition.
Problem: 7 + 4 = ? Draw a number line from 0 to
1
5. Start at 7 (initial passengers). Move 4 steps to the right from 7 (7 -> 8 -> 9 -> 10 -> 11). The final position is
1
1. Therefore, there are 11 passengers in the _keke napep_.
Commentary: This assesses the ability to interpret a word problem and apply addition on a number line in a relevant Nigerian context.
4. Question (Quantitative Aptitude): Emeka had ₦1000 in his savings box. He spent ₦400 to buy a new school bag. How much money does he have left? Illustrate with a number line.
Solution: Identify Operation: "spent ₦400" indicates subtraction.
Problem: 1000 - 400 = ? Draw a number line with intervals of 100 (e.g., 0, 100, 200, ..., 1000). Start at 1000 (initial savings). Move 4 steps (of 100 each) to the left from 1000 (1000 -> 900 -> 800 -> 700 -> 600). The final position is
6
0
0. Therefore, Emeka has ₦600 left.
Commentary: This tests the application of subtraction on a number line using larger numbers (scaled intervals) in a financial context. A. What is a Number Line? A number line is a straight line on which numbers are marked at equal intervals or distances.
Key Features: It extends indefinitely in both directions (indicated by arrows at the ends). It has an origin, which is usually zero (0). Numbers to the right of zero are positive and increase in value. Numbers to the left of zero are negative and decrease in value (though Primary 5 largely focuses on positive integers and results). The intervals between consecutive numbers are uniform (e.g., 0, 1, 2, 3... or 0, 2, 4, 6...). For this topic, focus on unit intervals (1, 2, 3...). B. Representing Numbers on a Number Line To represent a number on a number line, simply locate its position. For instance, to represent '5', find the mark corresponding to 5 on the line.
C. Addition on a Number Line Addition on a number line involves moving to the right.
Steps:
1. Start at the position of the first number in the addition problem.
2. To add a second number, move a specific number of steps to the right from your starting point. The number of steps you move is equal to the second number.
3. The point where you land is the sum (the answer).
Worked Example 1: Basic Addition Problem: Add 3 and 4 using a number line. (i.e., 3 + 4)
Solution:
1. Draw a number line and mark numbers, for example, from 0 to 10. ``` 0 1 2 3 4 5 6 7 8 9 10 ```
2. Start at '3' on the number line. ``` 0 1 2 (3) 4 5 6 7 8 9 10 ```
3. Move 4 steps to the right from '3'. 1st step: lands on 4 2nd step: lands on 5 3rd step: lands on 6 4th step: lands on 7 ``` 0 1 2 3 --(1)-->(4)--(2)-->(5)--(3)-->(6)--(4)-->(7) 8 9 10 ^ ^ Start (3) End (7) ```
4. The landing point is '7'.
Therefore, 3 + 4 =
7. Worked Example 2: Nigerian Context (Quantitative Aptitude)
Problem: Mallam Garba sold 5 _gari_ measures in the morning. In the afternoon, he sold 6 more measures. How many _gari_ measures did he sell in total? Use a number line.
Solution:
1. Draw a number line (e.g., 0 to 15).
2. Start at '5' (measures sold in the morning).
3. Move 6 steps to the right (measures sold in the afternoon). 5 + 1 = 6 6 + 1 = 7 7 + 1 = 8 8 + 1 = 9 9 + 1 = 10 10 + 1 = 11
4. The final position is '11'.
5. Therefore, Mallam Garba sold 11 _gari_ measures in total.
D. Subtraction on a Number Line Subtraction on a number line involves moving to the left.
Steps:
1. Start at the position of the first number (the number from which you are subtracting).
2. To subtract a second number, move a specific number of steps to the left from your starting point. The number of steps you move is equal to the second number.
3. The point where you land is the difference (the answer).
Worked Example 3: Basic Subtraction Problem: Subtract 5 from 9 using a number line. (i.e., 9 - 5)
Solution:
1. Draw a number line (e.g., 0 to 10). ``` 0 1 2 3 4 5 6 7 8 9 10 ```
2. Start at '9' on the number line. ``` 0 1 2 3 4 5 6 7 8 (9) 10 ```
3. Move 5 steps to the left from '9'. 1st step: lands on 8 2nd step: lands on 7 3rd step: lands on 6 4th step: lands on 5 5th step: lands on 4 ``` 0 1 2 3 (4) 7 -> 8 -> 9 -> 10 -> 11). The final position is
1
1. Therefore, 6 + 5 =
1
1. Commentary: This checks the basic understanding of addition on a
A. Differentiation (Remediation for Struggling Learners): Concrete Number Line: Provide a physical number line on the classroom floor or a long strip of paper. Students can physically walk or use small objects to move along the line, making the abstract concept more concrete.
Pre-drawn Number Lines: For students who struggle with drawing, provide worksheets with pre-drawn number lines where they only need to mark the movements.
Smaller Numbers: Start with very small numbers (e.g., 1-5) and gradually increase the range as confidence grows.
Peer Support: Pair struggling learners with more confident peers who can offer gentle guidance and explanation.
Focus on One Operation: Master addition on the number line first, then introduce subtraction. Avoid combining operations until basic understanding is firm.
B. Extension for High-Achieving Learners: Larger Numbers and Scaled Intervals: Challenge them with problems involving larger numbers that require them to choose appropriate intervals for their number line (e.g., intervals of 5, 10, 50, or 100).
Example:* "Calculate 250 + 150 using a number line, choosing appropriate intervals." Multi-step Problems: Introduce word problems that involve both addition and subtraction in sequence.
Example:* "A farmer had 10 goats. He sold 3, then bought 5 more. How many goats does he have now? Show your steps on a number line." Introduction to Negative Numbers (Conceptual): Briefly introduce the concept of moving left past zero, only if they grasp positive operations very quickly and are curious. Emphasize it's an advanced concept.
Example:* "What happens if you start at 3 and move 5 steps to the left?" (To land on -2).
C. Remediation Activities: Re-demonstration: Re-demonstrate basic addition and subtraction steps on the board or physical number line, inviting the student to guide the steps.
Tracing Exercises: Provide worksheets with dotted lines or arrows indicating the movement on a number line, and have students trace them and identify the final answer.
Number Line Race Game: Create a simple game where students roll a dice, move forward (add) or backward (subtract) on a number line game board, reinforcing the concept in a fun way.
Individualized Feedback: Spend one-on-one time with the student to identify specific points of confusion (e.g., always moving right, miscounting steps, difficulty drawing the line). Basic Operations
Market Transactions: Teachers can pose scenarios where a seller has a certain number of yams and a customer buys some, requiring subtraction. Or, a customer buys oranges from one vendor and then more from another, requiring addition.
Example:* "If Mama Ngozi has 15 plantains and sells 8, how many are left? Show it on a number line."
Example:* "Musa collected ₦500 from his mother and ₦300 from his father. How much money does he have in total? Use a number line with ₦100 intervals." Journey Planning and Distance: Students can apply number lines to understand distances travelled and distances remaining.
Example:* "A _danfo_ bus is going from Lagos to Ibadan, a total of 120km. If it has covered 70km, how many more kilometres are left? (Using intervals of 10km on the number line)." Local Sport Scores and Counting: Many Nigerian children play games like Ludo, _ayo_ (Mancala), or local football. The number line can help track scores.
Example:* "In a game of Ludo, If Segun had 6 points and gained 4 more, what is his total score? Illustrate this on a number line."
Example:* "A group of children were playing football. They started with 10 balls, but 3 rolled away into a bush. How many balls are left?"