Lesson Notes By Weeks and Term v3 - Primary 1
Open Sentences
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Open Sentences
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Subject: General Mathematics
Class: Primary 1
Term: 1st Term
Week: 10
Theme: Algebraic Processes
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Watch on YouTubefind missing numbers in an open sentence; solve simple related open sentences.
Definition of an Open Sentence: An open sentence is a mathematical statement that has a missing part, usually a number, represented by a symbol. Common symbols used for the missing number in Primary 1 are a box (\[]), a circle (O), a blank line (_), or sometimes a simple letter like 'n' or 'x'. The goal is to find the value of this missing number that makes the statement true.
Types of Open Sentences (for Primary 1): At this level, open sentences primarily involve simple addition and subtraction within the number range already familiar to students (typically up to 10 or 20).
1. Missing sum/difference (straightforward calculation): 3 + 2 = [] (Already covered in basic addition/subtraction, serves as a bridge) 5 - 1 = []
2. Missing addend (number being added): 4 + [] = 7 [] + 2 = 6
3. Missing subtrahend (number being subtracted): 8 - [] = 3
4. Missing minuend (number from which subtraction is made): [] - 3 = 5 Methods for Finding Missing Numbers:
1. Counting On/Counting Back (Concrete Method): For Addition (e.g., 4 + [] = 7): Students can start at the given number (4) and count on using fingers, beads, or drawings until they reach the total (7). The number of counts made is the missing number. _Teacher explanation:_ "Start at
4. Count 5 (one finger), 6 (two fingers), 7 (three fingers). You counted 3 fingers. So, the missing number is 3." For Subtraction (e.g., 8 - [] = 3): Students can start at the total (8) and count back until they reach the remaining number (3). The number of counts made is the missing number. _Teacher explanation:_ "Start at
8. Count back 7 (one finger), 6 (two fingers), 5 (three fingers), 4 (four fingers), 3 (five fingers). You counted 5 fingers. So, the missing number is 5."
2. Inverse Operations (Conceptual Method - simplified for P1): This method teaches students to think of addition as the opposite of subtraction, and vice versa. While the term 'inverse operation' might not be explicitly used with P1 students, the concept is taught. If the open sentence is addition (e.g., 4 + [] = 7): To find the missing number, subtract the known addend from the sum. _Teacher explanation:_ "If 4 plus something gives us 7, we can find that 'something' by taking 4 away from
7. So, 7 - 4 = 3." If the open sentence is subtraction with a missing subtrahend (e.g., 8 - [] = 3): To find the missing number, subtract the difference from the minuend. _Teacher explanation:_ "If 8 minus something gives us 3, we can find that 'something' by taking 3 away from
8. So, 8 - 3 = 5." If the open sentence is subtraction with a missing minuend (e.g., [] - 3 = 5): To find the missing number, add the difference to the subtrahend. _Teacher explanation:_ "If some number minus 3 gives us 5, we can find that original number by adding 3 and 5 together. So, 5 + 3 = 8." Worked Examples (Nigerian Context): Example 1: Missing Addend (Addition) A vulcanizer patched 5 bicycle tyres. He patched some more, and now he has patched a total of 9 tyres. How many more tyres did he patch?
Open Sentence: 5 + \[ ] = 9 Solution (using counting on): Start at
5. Count 6 (1), 7 (2), 8 (3), 9 (4). The missing number is
4. Solution (using inverse operation): Since it's an addition problem, we can subtract. 9 - 5 =
4. Answer: He patched 4 more tyres.
Example 2: Missing Subtrahend (Subtraction) There were 10 mangoes in a basket. Children ate some mangoes, and 4 mangoes were left. How many mangoes did the children eat?
Open Sentence: 10 - \[ ] = 4 Solution (using counting back): Start at
1
0. Count back 9 (1), 8 (2), 7 (3), 6 (4), 5 (5), 4 (6). The missing number is 6. * Solution (using inverse operation): Since we know the starting number and problem, we can subtract. 9 - 5 =
4. Answer: He patched 4 more tyres.
Example 2: Missing Subtrahend (Subtraction) There were 10 mangoes in a basket. Children ate some mangoes, and 4 mangoes were left. How many mangoes did the children eat?
Open Sentence: 10 - \[ ] = 4 Solution (using counting back): Start at
1
0. Count back 9 (1), 8 (2), 7 (3), 6 (4), 5 (5), 4 (6). The missing number is
6. Solution (using inverse operation): Since we know the starting number and the ending number, we can find the number eaten by subtracting. 10 - 4 =
6. Answer: The children ate 6 mangoes.
Example 3: Missing Minuend (Subtraction) A farmer sold 3 bags of maize and had 5 bags left. How many bags of maize did the farmer have at first?
Open Sentence: \[ ] - 3 = 5 Solution (using inverse operation): Since 3 bags were sold and 5 were left, we add them together to find the original amount. 5 + 3 =
8. Answer: The farmer had 8 bags of maize at first.
Materials: Counters (bottle tops, stones, seeds, sticks), number line, chalk and chalkboard, pupils' slates/notebooks.
Teacher Activities: Introduction & Review: Begin by reviewing simple addition and subtraction problems using concrete objects (e.g., "If I have 3 stones and add 2 more, how many do I have?"). Introduce the idea of a "missing number" in a story context: "I have 4 oranges, and I need 7 oranges for my family. How many more oranges do I need?" Introducing Open Sentences: Write a simple problem on the board like 4 + \[ ] =
7. Explain that the box represents the missing number we need to find.
Use counters to demonstrate: place 4 counters, then add more until the total is
7. Count the added counters.
Demonstrate using a number line: start at 4, jump forward until 7, count the jumps.
Explaining Solving Strategies: For addition (missing addend): Demonstrate both counting on and the inverse operation (subtraction) using various examples. Emphasize that subtracting the known part from the total gives the missing part.
For subtraction (missing subtrahend): Demonstrate counting back and the inverse operation (subtracting the remainder from the original amount).
For subtraction (missing minuend): Demonstrate the inverse operation (adding the part taken away to the part remaining). Use stories to make it clear (e.g., "If I ate 3 biscuits and have 5 left, how many did I have? I add the 3 I ate to the 5 I have left.").
Guided Practice: Write various open sentences on the board (e.g., 6 + \[ ] = 10, 9 - \[ ] = 5, \[ ] - 4 = 3). Call on individual students to come forward and solve using counters or drawing on the board. Guide the whole class through solving problems on their slates, providing immediate feedback.
Word Problem Translation: Read simple word problems aloud (e.g., "A farmer had 7 chickens. Some ran away, and 4 chickens were left. How many ran away?"). Guide students to identify the known numbers, the unknown number, and to formulate the open sentence (7 - \[ ] = 4). Guide them to solve the open sentence.
Recap: Review the different types of open sentences and the strategies used to solve them.
Student Activities: Active Participation: Respond to teacher questions and participate in demonstrations.
Manipulative Use: Use counters (stones, bottle caps) to model and solve open sentences, especially during initial learning.
Drawing and Visualisation: Draw pictures or use a number line to represent and solve problems.
Oral Responses: Orally state missing numbers and explain their reasoning.
Written Practice: Solve open sentences on their slates or in their notebooks, both numerical and from simple word problems.
Pair Work: Work with a partner to solve problems, discussing their strategies.
Problem Creation (Extension): High-achieving students may create simple open sentences for their peers to solve. The teacher guides students through these problems, encouraging them to use counters, fingers, or drawing as needed, then introduces the inverse operation concept.
Question 1: A mother bought 5 oranges. Her friend gave her some more, and now she has 8 oranges. How many oranges did her friend give her?
Open Sentence: 5 + \[ ] = 8 Solution: Method 1 (Counting on): Start at
5. Count on: 6 (1), 7 (2), 8 (3). The number of counts is
3. Method 2 (Inverse Operation): To find the missing number, subtract the known part from the total. 8 - 5 =
3. Commentary: This targets objective 1 (finding missing numbers) and objective 2 (solving a simple related open sentence from a word problem involving addition).
Question 2: There were 9 children playing under a mango tree. Some children went home, and 4 children were left. How many children went home?
Open Sentence: 9 - \[ ] = 4 Solution: Method 1 (Counting back): Start at
9. Count back until 4: 8 (1), 7 (2), 6 (3), 5 (4), 4 (5). The number of counts is
5. Method 2 (Inverse Operation): To find the missing number (what was taken away), subtract the remainder from the original amount. 9 - 4 =
5. Commentary: This targets objective 1 (finding missing numbers) and objective 2 (solving a simple related open sentence from a word problem involving subtraction where the subtrahend is missing).
Question 3: A tailor had some fabrics. She used 3 pieces to sew clothes and had 6 pieces left. How many pieces of fabric did she have at first?
Open Sentence: \[ ] - 3 = 6 Solution: Method (Inverse Operation): If 3 pieces were used and 6 were left, the original number of pieces must be the sum of what was used and what was left. So, 6 + 3 =
9. Commentary: This targets objective 1 (finding missing numbers) and objective 2 (solving a simple related open sentence from a word problem involving subtraction where the minuend is missing).
Market Stalls and Trade: When a market vendor starts with a certain number of yams, sells some, and has some left, open sentences can help calculate how many were sold. For instance, "A woman brought 15 tubers of yam to the market. By afternoon, she had 7 tubers left. How many tubers did she sell?" (15 - \[ ] = 7). This directly applies to daily commerce in Nigerian markets. Community Projects and Resource Management: In rural communities, counting resources for a project often involves missing numbers. If a community needs 10 bags of cement for a building project and they already have 6 bags, an open sentence (6 + \[ ] = 10) helps determine how many more bags are needed. This integrates mathematics with local development and planning.
Family Sharing and Inventory: At home, open sentences are used for managing daily items. For example, if a family had a certain number of boiled eggs, some were eaten, and 2 are left. If 4 eggs were eaten, how many were there initially? (\[ ] - 4 = 2). This helps children understand practical situations involving food distribution and tracking items.