Class: Primary 6
Term: 2nd Term
Week: 4
Age: 11 years
Duration: 45 minutes
Subject: General Mathematics
Curriculum Theme: Algebraic Thinking
Previous Lesson: Ratio and Percentages, Class Ratio and Profit or Loss Percent.
Topic: OPEN SENTENCES
Subject Matter: Open sentences from word problems, interpreting division word problems into open sentences, solving quantitative aptitude with three or more operations, multi-step open sentence problems

Specific Objectives

By the end of the lesson, pupils should be able to:

Cognitive Domain:

Define an open sentence.
Interpret simple word problems into open sentences.
Solve open sentences involving one or two operations.
Solve quantitative aptitude problems with three or more operations.

Affective Domain:

Appreciate the use of open sentences in solving real-life problems.
Show interest in converting word problems into mathematical expressions.
Develop confidence in solving multi-step open sentence problems.

Psychomotor Domain:

Accurately write open sentences from given word problems.
Correctly calculate the unknown value in an open sentence.
Demonstrate the steps for solving multi-step open sentences.

Collaborate with peers to interpret and solve word problems.
Communicate their solutions and strategies effectively to others.

Reference Materials

The following resources were used in planning this lesson:

9 Years Basic Education Curriculum (Primary 4-6)
Lagos State Unified Scheme of Work for Primary Schools (Mathematics)
New Method Mathematics for Primary Schools Book 6
https://www.mathisfun.com/algebra/open-sentences.html
https://www.splashlearn.com/math-vocabulary/algebra/open-sentence

Instructional Materials

The teacher will teach this lesson with the aid of:

Textbook
Workbook
Posters showing examples of open sentences
Charts with steps for solving open sentences

Rationale for the Lesson

This lesson helps pupils understand how to translate everyday problems into mathematical statements. It enables them to use mathematical thinking to find unknown values, which is important for problem-solving in daily life and in higher mathematics.

Prerequisite/Previous Knowledge

Pupils are expected to have a basic understanding of number operations (addition, subtraction, multiplication, division) and the concept of equality.

Lesson Content/Board Summary

OPEN SENTENCES

Definition of Open Sentences

An open sentence is a mathematical statement that contains one or more variables (unknowns). It becomes true or false depending on the value substituted for the variable. Open sentences are usually equations or inequalities.

Examples of open sentences:

x + 7 = 15
y – 3 > 10
2m = 18
p ÷ 4 < 5

Interpreting Word Problems into Open Sentences

To interpret a word problem into an open sentence, identify the unknown quantity and represent it with a variable (e.g., x, y, m). Then, translate the words into mathematical operations and symbols.

Common words and their mathematical equivalents:

“a number”, “some number”, “what number” -> variable (x)
“sum”, “increased by”, “added to”, “more than” -> +
“difference”, “decreased by”, “subtracted from”, “less than” -> –
“product”, “times”, “multiplied by” -> × or *
“quotient”, “divided by” -> ÷ or /
“is”, “equals”, “results in” -> =

Solving Open Sentences from Word Problems

After converting a word problem into an open sentence (equation), use inverse operations to find the value of the unknown variable.

Example 1: “A number increased by 5 is 12.”

Let the number be x.
Open sentence: x + 5 = 12
To solve: x = 12 – 5
x = 7

Example 2: “When a number is divided by 3, the result is 9.”

Let the number be y.
Open sentence: y ÷ 3 = 9
To solve: y = 9 × 3
y = 27

Solving Quantitative Aptitude Problems with Three or More Operations

These problems involve multiple steps and operations. It is important to translate each part of the problem carefully into an open sentence and then solve it step-by-step.

Example: “Double a number, then add 10, and finally divide the result by 4. If the final answer is 7, what is the number?”

Let the number be n.
Double a number: 2n
Then add 10: 2n + 10
Divide the result by 4: (2n + 10) ÷ 4
If the final answer is 7: (2n + 10) ÷ 4 = 7
To solve:
2n + 10 = 7 × 4
2n + 10 = 28
2n = 28 – 10
2n = 18
n = 18 ÷ 2
n = 9

Teaching Methods/Instructional Techniques

Discussion, Lecture, Demonstration, Question and Answer, Visual Aids

Instructional Procedures

Step 1: Introduction

Time: 5 minutes
Teaching Skill: Set Induction
Teacher’s Activity: The teacher greets the pupils and asks them to recall what they know about finding missing numbers in simple calculations like “____ + 5 = 10”. The teacher then introduces the topic “Open Sentences” as a way to solve such problems systematically.
Pupils’ Activity: Pupils respond to questions about missing numbers and listen attentively to the introduction.
Learning Point: Pupils connect prior knowledge to the new topic and understand the relevance of open sentences.

Step 2: Definition of Open Sentences

Time: 5 minutes
Teaching Skill: Explanation/Definition
Teacher’s Activity: The teacher defines an open sentence, explaining what a variable is and how an open sentence becomes true or false. The teacher writes simple examples on the board.
Pupils’ Activity: Pupils listen, take notes, and ask questions for clarification.
Learning Point: Pupils understand the definition and basic structure of an open sentence.

Step 3: Interpreting Word Problems into Open Sentences

Time: 8 minutes
Teaching Skill: Demonstration/Guidance
Teacher’s Activity: The teacher presents various word problems and guides pupils on how to identify the unknown, choose a variable, and translate key words into mathematical symbols to form an open sentence. Examples will include addition, subtraction, multiplication, and division scenarios.
Pupils’ Activity: Pupils participate in translating word problems, suggesting variables and operations.
Learning Point: Pupils learn to convert verbal statements into algebraic expressions and open sentences.

Step 4: Solving Open Sentences from Word Problems

Time: 8 minutes
Teaching Skill: Problem-solving/Illustration
Teacher’s Activity: The teacher demonstrates how to solve the open sentences formed in Step 3, using inverse operations to find the value of the unknown. The teacher emphasizes checking the answer by substituting it back into the original word problem or open sentence.
Pupils’ Activity: Pupils observe the solving process, ask questions, and practice solving simple open sentences.
Learning Point: Pupils acquire the skill of solving open sentences to find unknown values.

Step 5: Solving Quantitative Aptitude Problems with Multiple Operations

Time: 8 minutes
Teaching Skill: Step-by-step instruction
Teacher’s Activity: The teacher introduces more complex word problems involving three or more operations. The teacher guides pupils through the process of setting up the multi-step open sentence and solving it systematically, emphasizing the order of operations and inverse operations.
Pupils’ Activity: Pupils work through the examples with the teacher, identifying each step in forming and solving the open sentence.
Learning Point: Pupils can interpret and solve multi-step word problems using open sentences.

Step 6: Classwork/Practice

Time: 6 minutes
Teaching Skill: Activity/Application
Teacher’s Activity: The teacher gives pupils a few practice problems to solve independently or in pairs, covering interpretation and solving of open sentences, including multi-step problems.
Pupils’ Activity: Pupils attempt to solve the practice problems. The teacher moves around to provide assistance.
Learning Point: Pupils apply their understanding and practice problem-solving independently.

Step 7: Evaluation/Review

Time: 5 minutes

Teaching Skill: Questioning/Assessment

Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

What is an open sentence?
Convert the following word problem into an open sentence: “A number decreased by 7 is 15.”
Solve the open sentence: 3x + 4 = 19.
Explain how to solve a word problem that requires three operations to find the unknown number.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Pupils demonstrate understanding of the lesson.

Step 8: Conclusion

Time: 2 minutes
Teaching Skill: Summarization
Teacher’s Activity: The teacher summarises the key points of the lesson, reinforcing the importance of open sentences in solving everyday problems and in mathematics. The teacher gives homework.
Pupils’ Activity: Pupils listen to the summary and copy down the homework.
Learning Point: Pupils recall the main concepts learned in the lesson.

Home Task: Solve three new exercises on OPEN SENTENCES. Show each step and check each answer.

Lesson Keywords

Open Sentence – A mathematical statement containing a variable, which can be true or false depending on the value of the variable.
Variable – A symbol (usually a letter) used to represent an unknown number or quantity.
Equation – A mathematical statement that shows two expressions are equal.
Inverse Operation – An operation that reverses the effect of another operation (e.g., addition is the inverse of subtraction).
Word Problem – A mathematical problem presented in a narrative form.

Differentiation

For pupils who grasp concepts quickly, the teacher will provide more complex multi-step word problems or introduce simple inequalities. For pupils who need additional support, the teacher will offer one-on-one guidance, simplify the word problems, and provide visual aids with step-by-step instructions for forming and solving open sentences.

Note for teachers using this lesson plan

Encourage pupils to use various letters as variables to avoid the misconception that ‘x’ is the only variable. Emphasize the importance of reading word problems carefully to correctly identify operations and relationships. Provide ample practice for both interpreting and solving open sentences.