Lesson Notes By Weeks and Term v3 - Primary 4
Open sentience
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Open sentience
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Subject: General Mathematics
Class: Primary 4
Term: 3rd Term
Week: 5
Theme: Algebraic Processes
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Watch on YouTubeSee Facebook postDefine open sentences; Find missing number in an open sentences; Solve related, quantitative aptitude problems on open sentences in volving multiplication and division.
2. 1. Definition of Open Sentences An open sentence in mathematics is a statement that contains an unknown number, often represented by a symbol such as an empty box (☐), a letter (e.g., 'x', 'y'), or a question mark (?). This unknown number needs to be found to make the statement true.
Example 1 (Addition): 5 + ☐ = 12 Here, '5' and '12' are known numbers. '☐' is the unknown. '+' is the operation. '=' is the equality sign.
Example 2 (Subtraction): 15 - x = 8 'x' is the unknown.
Example 3 (Multiplication): 3 × y = 21 'y' is the unknown.
Example 4 (Division): ☐ ÷ 4 = 6 '☐' is the unknown. 2.
2. Finding Missing Numbers in Open Sentences The core principle to solve open sentences is to isolate the unknown number using inverse operations. Inverse operations "undo" each other. Addition is the inverse of subtraction. Subtraction is the inverse of addition. Multiplication is the inverse of division. Division is the inverse of multiplication. 2.2.
1. Solving Open Sentences involving Addition and Subtraction Rule: To find the missing number, perform the inverse operation on the known numbers.
Case 1: Missing Addend Form: a + ☐ = c or ☐ + b = c Method: Subtract the known addend from the sum.
Example: Ade had ₦
2
0
0. After selling some groundnuts, he now has ₦
3
5
0. How much did he make from the groundnuts?
Open sentence: ₦200 + ☐ = ₦350 To find ☐, subtract ₦200 from ₦350: ☐ = ₦350 - ₦200 ☐ = ₦150 Check: ₦200 + ₦150 = ₦350 (True)
Case 2: Missing Subtrahend Form: a - ☐ = c Method: Subtract the difference from the minuend (the first number).
Example: A farmer had 45 yams. He sold some and was left with 18 yams. How many yams did he sell?
Open sentence: 45 - ☐ = 18 To find ☐, subtract 18 from 45: ☐ = 45 - 18 ☐ = 27 Check: 45 - 27 = 18 (True)
Case 3: Missing Minuend Form: ☐ - b = c Method: Add the subtrahend to the difference.
Example: A driver had some passengers. After dropping off 12 passengers at the market, he had 25 passengers left. How many passengers did he start with?
Open sentence: ☐ - 12 = 25 To find ☐, add 12 to 25: ☐ = 25 + 12 ☐ = 37 Check: 37 - 12 = 25 (True) 2.2.
2. Solving Open Sentences involving Multiplication and Division Rule: To find the missing number, perform the inverse operation on the known numbers.
Case 1: Missing Factor Form: a × ☐ = c or ☐ × b = c Method: Divide the product by the known factor.
Example: If 5 children share some pencils equally, and each child gets 7 pencils, how many pencils were there in total? (This example demonstrates finding the product from known factors, which is a direct multiplication. Let's adjust for a missing factor.) Adjusted
Example: Mama Ngozi bought some packets of biscuits. If each packet contains 8 biscuits and she has 40 biscuits in total, how many packets did she buy?
Open sentence: ☐ × 8 = 40 To find ☐, divide 40 by 8: ☐ = 40 ÷ 8 ☐ = 5 Check: 5 × 8 = 40 (True)
Case 2: Missing Dividend Form: ☐ ÷ b = c Method: Multiply the quotient by the divisor.
Example: Some oranges were shared equally among 6 friends. Each friend received 9 oranges. How many oranges were shared in total?
Open sentence: ☐ ÷ 6 = 9 To find ☐, multiply 9 by 6: ☐ = 9 × 6 ☐ = 54 Check: 54 ÷ 6 = 9 (True)
Case 3: Missing Divisor Form: a ÷ ☐ = c * Method: Divide the dividend Case 2: Missing Dividend Form: ☐ ÷ b = c Method: Multiply the quotient by the divisor.
Example: Some oranges were shared equally among 6 friends. Each friend received 9 oranges. How many oranges were shared in total?
Open sentence: ☐ ÷ 6 = 9 To find ☐, multiply 9 by 6: ☐ = 9 × 6 ☐ = 54 Check: 54 ÷ 6 = 9 (True)
Case 3: Missing Divisor Form: a ÷ ☐ = c Method: Divide the dividend by the quotient.
Example: Mr. Emeka had 72 mangoes. He packed them into some baskets, with 9 mangoes in each basket. How many baskets did he use?
Open sentence: 72 ÷ ☐ = 9 To find ☐, divide 72 by 9: ☐ = 72 ÷ 9 ☐ = 8 Check: 72 ÷ 8 = 9 (True) 2.
3. Quantitative Aptitude Problems Quantitative aptitude problems often present open sentences in a pictorial or word problem format that requires the learner to first identify the underlying mathematical operation and then solve for the missing number. These problems test logical reasoning along with arithmetic skills. They often involve number patterns, sequences, or simple operations presented in a less direct way.
Example: (Diagram showing three circles in a row, with numbers 3, 7, and a blank circle, connected by arrows indicating "x 2" from 3 to 7, and then " + 5" from 7 to the blank. Wait, this isn't an open sentence example, but a pattern. Let's use a clear open sentence QA problem.) Better QA
Example: A diagram shows: `[5] --> [x 4] --> [☐] --> [÷ 2] --> [10]` Question: What number should be in the empty box?
Solution Approach: Work forwards from the start or backwards from the end.
Working forwards: 5 x 4 =
2
0. So, ☐ =
2
0. Then 20 ÷ 2 = 10 (True).
Working backwards: From 10, the inverse of ÷ 2 is x
2. So, 10 x 2 =
2
0. Therefore, ☐ = 20. 3.
1. Introduction (5 minutes)
Teacher Activity: Begins by writing simple incomplete number sentences on the board (e.g., 3 + \_ = 7; 10 - \_ = 4; 2 x \_ = 10). Asks learners to fill in the missing numbers. Introduces the term "open sentence" for these kinds of problems, explaining that the missing number makes the sentence "open" or incomplete. States the lesson's objectives.
Student Activity: Learners mentally or verbally complete the simple number sentences. They listen attentively and ask clarifying questions. 3.
2. Development 1: Defining Open Sentences (10 minutes)
Teacher Activity: Formally defines an open sentence, explaining that it's a mathematical statement with an unknown quantity, represented by a box (☐), a letter (x, y), or a question mark. Provides various examples involving all four basic operations, highlighting the unknown. Emphasises the concept of inverse operations as the tool to find the unknown.
Examples: ₦500 - ☐ = ₦250; 7 × y = 63; ☐ ÷ 5 =
1
2. Student Activity: Learners listen to the definition and identify the unknown in given examples. They brainstorm where they might encounter missing numbers in their daily lives (e.g., buying things, sharing). 3.
3. Development 2: Finding Missing Numbers (Addition and Subtraction) (15 minutes)
Teacher Activity: Reviews finding missing numbers in addition and subtraction open sentences. Uses Nigerian-centric word problems. Demonstrates step-by-step using inverse operations.
Example 1 (Addition): "A Lagos bus had some passengers. 15 more passengers joined at Oshodi, making a total of 40 passengers. How many passengers were on the bus initially?" (☐ + 15 = 40).
Shows: ☐ = 40 - 15 =
2
5. Example 2 (Subtraction): "Mama Bimbo had ₦1,
2
0
0. She spent some money at the market and was left with ₦
7
5
0. How much did she spend?" (₦1,200 - ☐ = ₦750).
Shows: ☐ = ₦1,200 - ₦750 = ₦
4
5
0. Provides more practice questions for students to solve on their individual whiteboards or exercise books.
Student Activity: Learners observe the teacher's examples and actively participate in solving practice problems. They share their answers and methods with the class. 3.
4. Development 3: Finding Missing Numbers (Multiplication and Division) (20 minutes)
Teacher Activity: Focuses on open sentences involving multiplication and division, as per the performance objective. Explains and demonstrates the use of inverse operations for these.
Example 1 (Multiplication): "If 6 boys collected 'x' coconuts each, and they collected 48 coconuts in total, how many coconuts did each boy collect?" (6 × x = 48).
Shows: x = 48 ÷ 6 =
8. Example 2 (Division - Missing Dividend): "Some bags of rice were shared equally among 7 families. Each family received 5 bags. How many bags of rice were there initially?" (☐ ÷ 7 = 5).
Shows: ☐ = 5 × 7 =
3
5. Example 3 (Division - Missing Divisor): "72 kolanuts were shared equally among some elders, and each elder received 8 kolanuts. How many elders were there?" (72 ÷ ☐ = 8).
Shows: ☐ = 72 ÷ 8 =
9. Provides classwork exercises for learners to solve independently or in pairs.
Student Activity: Learners pay close attention to the inverse operations for multiplication and division. They work through the examples and complete assigned practice problems. 3.
5. Development 4: Solving Quantitative Aptitude Problems (15 minutes)
Teacher Activity: Presents quantitative aptitude problems involving multiplication and division, often presented in a less direct or diagrammatic format. Explains how to extract the open sentence from the problem.
Example 1 (Diagram): Shows a sequence like `[4] --(x 3)--> [A] --(÷ 2)--> [B]`. Asks learners to find A and B. (A=12, B=6). This leads to open sentences 4 x 3 = A, and A ÷ 2 =
B. Example 2 (Word problem): "A vendor sells oranges in nets. Each net contains 12 oranges. If a customer bought 'x' nets and got 60 oranges, how many nets did they buy?" (x × 12 = 60). Guides learners through the process of identifying the operation and solving. * Student Activity: Learners analyze the quantitative aptitude problems, discuss potential strategies in small groups, and apply their knowledge of to find A and B. (A=12, B=6). This leads to open sentences 4 x 3 = A, and A ÷ 2 =
B. Example 2 (Word problem): "A vendor sells oranges in nets. Each net contains 12 oranges. If a customer bought 'x' nets and got 60 oranges, how many nets did they buy?" (x × 12 = 60). Guides learners through the process of identifying the operation and solving. * Student Activity: Learners analyze the quantitative aptitude problems, discuss potential strategies in small groups, and apply their knowledge of open sentences to solve them. They present their solutions and explanations.
Market Stalls and Trading: Learners can apply open sentences when helping parents or guardians at local markets. For example, if a mother gives her child ₦2,000 to buy rice and asks how much change she expects if a bag of rice costs ₦1,
8
0
0. The open sentence would be ₦1,800 + ☐ = ₦2,
0
0
0. Or, if a trader sells yam tubers at ₦500 each and earned ₦4,500, how many tubers did they sell (☐ x ₦500 = ₦4,500).
Community Resource Management: In rural communities, resources like planting seedlings, distributing relief materials, or sharing tools for a communal task often involve unknown quantities. For instance, if 60 seedlings need to be planted, and each farmer can plant 12 seedlings a day, how many farmers are needed to complete the task in one day (☐ x 12 = 60)?
Family Budgeting and Savings: Children can use open sentences to understand family finances. If their parents save ₦5,000 monthly and need to buy a bicycle that costs ₦20,000, they can determine how many more months of saving are needed (₦5,000 x ☐ = ₦20,000, or a variation of it). Similarly, if they have saved ₦3,500 and need ₦5,000, how much more do they need (₦3,500 + ☐ = ₦5,000)?