Open Sentences, Missing Numbers and Quantitative Reasoning for Primary 4

Class: Primary Four
Term: Second Term
Week: 7
Age: 9 years
Duration: 45 minutes
Subject: General Mathematics
Curriculum Theme: Basic Operations
Focal competence: Solving open sentences related problems
Key competencies/values: Collaboration
Skills:

• Generating open-sentence problems and solving them

Previous Lesson: Estimation, Rounding Numbers and Estimating Sums and Products
Topic: Open Sentence
Subject Matter: Meaning of an open sentence, finding missing numbers in addition/subtraction open sentences, quantitative reasoning

Specific Objectives

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

Cognitive Domain

• explain the meaning of an open sentence;
• find missing numbers in an open sentence involving addition and subtraction operations;
• solve quantitative reasoning involving open sentences.

Affective Domain

• collaborate with peers to solve open sentence problems.

Psychomotor Domain

• create simple open sentence problems.

Reference Materials

The following resources were used in planning this lesson:

• 2025 Revised 9 Years Basic Education Curriculum
• Relevant State Unified Scheme of Work
• New General Mathematics for Primary Schools, Book 4
• The HeadTeacher Scheme of work

Instructional Materials

The teacher will teach this lesson with the aid of:

• Objects (e.g., counters, stones)
• Boxes or empty containers
• Charts showing examples of open sentences
• Number cards

Rationale for the Lesson

This lesson helps pupils develop foundational algebraic thinking by introducing them to unknown quantities in mathematical statements. Understanding open sentences improves problem-solving skills and prepares them for more complex mathematical concepts in higher classes. It also strengthens their grasp of inverse operations.

Prerequisite/Previous Knowledge

Pupils should have a good understanding of basic addition and subtraction operations, including sums and differences up to 1000.

Lesson Content/Board Summary

Open Sentence

Meaning of an Open Sentence

An open sentence is a mathematical statement that contains an unknown value, represented by a symbol, letter, or an empty box. It is like a puzzle where you need to find the missing piece to make the statement true.

Examples:

1. (5 + text{?} = 12)
2. (x – 3 = 7)
3. (15 – square = 8)

Finding Missing Numbers in Addition Open Sentences

To find a missing number in an addition open sentence, we use the inverse operation, which is subtraction.

Rule for Addition

If (a + b = c), then (b = c – a) or (a = c – b).

Example 1

Question: Find the missing number in (6 + text{?} = 15).

Solution:

Step 1: Identify the known sum and one of the addends.

Here, the sum is 15 and one addend is 6.

Step 2: Subtract the known addend from the sum.

(15 – 6 = 9)

Step 3: Write the answer and check.

The missing number is 9.

Check: (6 + 9 = 15). The statement is true.

Answer: (9)

Example 2

Question: Find the missing number in (square + 7 = 20).

Solution:

Step 1: Identify the known sum and one of the addends.

Here, the sum is 20 and one addend is 7.

Step 2: Subtract the known addend from the sum.

(20 – 7 = 13)

Step 3: Write the answer and check.

The missing number is 13.

Check: (13 + 7 = 20). The statement is true.

Answer: (13)

Finding Missing Numbers in Subtraction Open Sentences

To find a missing number in a subtraction open sentence, we use the inverse operation, which is addition or subtraction, depending on the position of the missing number.

Rule for Subtraction

1. If (a – b = c), and (b) is missing, then (b = a – c).
2. If (a – b = c), and (a) is missing, then (a = b + c).

Example 1

Question: Find the missing number in (10 – text{?} = 4).

Solution:

Step 1: Identify the known minuend and difference.

Here, the minuend is 10 and the difference is 4. The subtrahend is missing.

Step 2: Subtract the difference from the minuend.

(10 – 4 = 6)

Step 3: Write the answer and check.

The missing number is 6.

Check: (10 – 6 = 4). The statement is true.

Answer: (6)

Example 2

Question: Find the missing number in (square – 5 = 12).

Solution:

Step 1: Identify the known subtrahend and difference.

Here, the subtrahend is 5 and the difference is 12. The minuend is missing.

Step 2: Add the subtrahend and the difference.

(5 + 12 = 17)

Step 3: Write the answer and check.

The missing number is 17.

Check: (17 – 5 = 12). The statement is true.

Answer: (17)

Quantitative Reasoning involving Open Sentences

Quantitative reasoning problems often present patterns or relationships that can be expressed as open sentences. Solving them requires identifying the rule and then finding the missing number.

Example 1

Question: Look at the pattern and find the missing number:

If (3 + 4 = 7)

And (5 + 2 = 7)

Then (8 + text{?} = 11)

Solution:

Step 1: Identify the operation in the pattern.

The pattern uses addition.

Step 2: Form an open sentence for the last part.

(8 + text{?} = 11)

Step 3: Solve the open sentence.

(text{?} = 11 – 8)

(text{?} = 3)

Answer: (3)

Example 2

Question: Find the missing number in the sequence:

(20, 18, text{?}, 14, 12)

Solution:

Step 1: Identify the pattern or rule.

The numbers are decreasing by 2 each time. ( (20 – 2 = 18), (14 – 2 = 12) )

Step 2: Form an open sentence for the missing number.

(18 – 2 = text{?})

Step 3: Solve the open sentence.

(text{?} = 16)

Answer: (16)

Teaching Methods/Instructional Techniques

Discussion, Demonstration, Guided Practice, Question and Answer, Explanation, Individual Practice

Instructional Procedures

Step 1: Introduction

Time: 5 minutes

Teaching Skill: Recalling/Engaging

Teacher’s Activity: The teacher begins by reviewing basic addition and subtraction facts. The teacher asks pupils to complete simple statements like “5 + 3 = ?” and “10 – 4 = ?”. Then, the teacher introduces the idea of a missing number by saying, “What if we don’t know one of the numbers? Like 5 + ? = 8.”

Pupils’ Activity: Pupils answer the basic addition and subtraction questions. They think about the missing number problem posed by the teacher.

Learning Point: Activating prior knowledge

Step 2: Explanation of Open Sentences

Time: 8 minutes

Teaching Skill: Explaining/Illustrating

Teacher’s Activity: The teacher explains what an open sentence is using number cards and an empty box or symbol. For example, the teacher writes (7 + square = 10) on the board and explains that the box represents an unknown number. The teacher shows other examples like (x – 4 = 6) and (12 – y = 5).

Pupils’ Activity: Pupils listen attentively, observe the examples, and identify the unknown parts in the statements.

Learning Point: Meaning of open sentence

Step 3: Finding Missing Numbers in Addition

Time: 8 minutes

Teaching Skill: Demonstrating/Modeling

Teacher’s Activity: The teacher demonstrates how to find missing numbers in addition open sentences using inverse operations. For (6 + text{?} = 15), the teacher explains that to find the missing number, we subtract 6 from 15. The teacher works through Example 1 and 2 from the Board Summary, showing the step-by-step process and how to check the answer.

Pupils’ Activity: Pupils observe the demonstration, ask questions, and follow the steps to understand the method.

Learning Point: Solving addition open sentences

Step 4: Finding Missing Numbers in Subtraction

Time: 8 minutes

Teaching Skill: Demonstrating/Modeling

Teacher’s Activity: The teacher demonstrates how to find missing numbers in subtraction open sentences. For (10 – text{?} = 4), the teacher explains subtracting the difference from the minuend. For (square – 5 = 12), the teacher explains adding the subtrahend and the difference. The teacher works through Example 1 and 2 from the Board Summary, emphasizing the checking method.

Pupils’ Activity: Pupils pay attention to the different approaches for subtraction problems and practice the inverse operations mentally.

Learning Point: Solving subtraction open sentences

Step 5: Introduction to Quantitative Reasoning

Time: 5 minutes

Teaching Skill: Guiding/Connecting

Teacher’s Activity: The teacher introduces quantitative reasoning problems related to open sentences. The teacher presents simple patterns or sequences and guides pupils to identify the rule and form an open sentence to find the missing number, using Example 1 from the Board Summary.

Pupils’ Activity: Pupils analyze the patterns, identify the rules, and suggest ways to represent the missing numbers using open sentences.

Learning Point: Open sentences in reasoning

Step 6: Guided Practice and Problem Creation

Time: 5 minutes

Teaching Skill: Facilitating/Encouraging

Teacher’s Activity: The teacher gives pupils simple open sentences to solve individually or in pairs. The teacher then encourages pupils to create their own simple open sentence problems involving addition or subtraction, using objects or number cards. The teacher provides support as needed.

Pupils’ Activity: Pupils solve practice problems. They create and share their own simple open sentence problems with their peers.

Learning Point: Generating and solving problems

Step 7: Evaluation/Review

Time: 5 minutes

Teaching Skill: Questioning/Assessment

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

1. What is an open sentence?
2. Find the missing number: (8 + text{?} = 17).
3. Find the missing number: (14 – square = 6).
4. If (x – 7 = 10), what is (x)?

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Assessing problem-solving skills

Step 8: Note-Taking

Time: 4 minutes

Teaching Skill: Guided Writing

Teacher’s Activity: The teacher guides pupils/students to copy the essential Board Summary notes on the meaning of open sentences and how to find missing numbers into their notebooks.

Pupils’ Activity: Pupils/students copy the notes carefully into their notebooks.

Learning Point: Recording lesson content

Step 9: Conclusion

Time: 2 minutes

Teaching Skill: Consolidating/Summarizing

Teacher’s Activity: The teacher briefly summarizes the key points of the lesson, reinforcing that open sentences are like puzzles with missing numbers that can be solved using inverse operations. The teacher commends pupils for their participation.

Pupils’ Activity: Pupils listen and confirm their understanding of the lesson.

Learning Point: Consolidating main concepts

Continuous Assessment/Further Study

Type: Homework

Instruction: Solve the following open sentences in your notebook:

1. (12 + text{?} = 25)
2. (square – 9 = 11)
3. (18 – x = 7)
4. (y + 6 = 21)
5. If (5, 10, text{?}, 20, 25) is a pattern, find the missing number.

Lesson Keywords

• Open Sentence – A mathematical statement with an unknown value.
• Missing Number – The unknown value in an open sentence.
• Inverse Operation – The opposite operation used to undo another (e.g., addition and subtraction).
• Quantitative Reasoning – Solving problems by understanding patterns and relationships.

Differentiation

For weaker learners, the teacher will provide more concrete examples using physical objects and counters to model the missing numbers. They will focus on simpler addition and subtraction open sentences. For faster learners, the teacher can introduce slightly more complex open sentences or encourage them to create more challenging quantitative reasoning problems for their peers.

Suggested Lesson Videos

For further understanding, search on YouTube for: open sentences missing numbers primary 4 mathematics

Teacher Guide for Using This Lesson Plan

Teachers should prepare number cards, small objects (like bottle caps or stones), and an empty box or container to visually represent the unknown in open sentences. Begin by ensuring pupils are comfortable with basic addition and subtraction before introducing the concept of an unknown. When teaching missing numbers, clearly demonstrate the use of inverse operations for both addition and subtraction, emphasizing the “checking” method to verify answers. Encourage pupils to actively participate by creating their own simple problems. During the note-taking step (Step 8), ensure pupils copy the Board Summary accurately. Pay close attention to pupils who might struggle with identifying the correct inverse operation, providing individual guidance and simplified examples. For advanced learners, encourage them to explain the reasoning behind their solutions and explore more complex number patterns.