3-Digit Subtraction With Exchanging: Missing Numbers and Word Problems for Primary 2

Class: Primary 2
Term: First Term
Week: 9
Age: 7 years
Duration: 40 minutes
Subject: Mathematics
Curriculum Theme: Not separately stated in the scheme
Previous Lesson: 3-Digit Column Subtraction Without Exchanging
Topic: Subtraction of 3-Digit Numbers with and without Exchanging
Subject Matter: Subtraction with and without exchanging, missing numbers and subtraction word problems.

Specific Objectives

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

Cognitive Domain

• subtract three-digit numbers using correct H-T-U arrangement
• solve three-digit calculations with and without exchanging
• find a missing number in a simple number sentence
• solve a simple word problem and state the answer correctly

Affective Domain

• show patience and accuracy when checking calculations

Psychomotor Domain

• arrange counters or sticks in hundreds, tens and units to model an operation

Social Domain

• compare methods and correct work respectfully with a partner

Reference Materials

The following resources were used in planning this lesson:

• 9 Years Basic Education Curriculum.
• Relevant State Unified Scheme of Work.
• An approved Primary School textbook or teaching resource for the subject.

Instructional Materials

The teacher will teach this lesson with the aid of:

• Bottle tops
• sticks
• seeds
• pebbles
• place-value chart
• bundled counting sticks
• worksheet

Rationale for the Lesson

This lesson helps pupils understand and use subtraction of 3-digit numbers with and without exchanging through familiar objects, clear examples and guided practice. It builds a foundation for accurate mathematical thinking in school and daily life.

Prerequisite/Previous Knowledge

Pupils can count familiar objects, follow simple instructions and use basic number language needed for the lesson. The teacher should check this quickly with concrete materials before introducing the new work.

Lesson Content/Board Summary

Subtraction of 3-Digit Numbers with and without Exchanging

Place-Value Arrangement

Write each number in Hundreds, Tens and Units columns. Units must be under units, tens under tens and hundreds under hundreds. Work from the units column to the hundreds column.

Subtraction without Exchanging

Subtraction without exchanging is used when every top digit is greater than or equal to the digit below it. Each column is subtracted from units to hundreds.

Example 1: 786 − 243

Solution

Step 1: Units: 6 − 3 = 3.
Step 2: Tens: 8 − 4 = 4.
Step 3: Hundreds: 7 − 2 = 5.
Answer: 543.

Example 2: 954 − 321

Solution

Step 1: Units: 4 − 1 = 3.
Step 2: Tens: 5 − 2 = 3.
Step 3: Hundreds: 9 − 3 = 6.
Answer: 633.

Subtraction with Exchanging

When the top digit is too small, exchange one ten for 10 units or one hundred for 10 tens.

Example 1: 532 − 178

Solution

Step 1: Exchange 1 ten: 12 − 8 = 4 units.
Step 2: Exchange 1 hundred: 12 − 7 = 5 tens.
Step 3: Hundreds: 4 − 1 = 3.
Answer: 354.

Example 2: 704 − 286

Solution

Step 1: Exchange through the zero so that 14 − 6 = 8 units.
Step 2: There are now 9 tens; 9 − 8 = 1 ten.
Step 3: Hundreds: 6 − 2 = 4.
Answer: 418.

Missing Numbers

Use the inverse operation to find a missing number.

• 650 − __ = 225. Since 650 − 225 = 425, the missing number is 425.
• __ − 214 = 330. Since 330 + 214 = 544, the missing number is 544.

Subtraction Word Problems

Example: A library had 725 books and lent 214 books. How many books remained?

Solution

Number sentence: 725 − 214

Step 1: Units: 5 − 4 = 1.
Step 2: Tens: 2 − 1 = 1.
Step 3: Hundreds: 7 − 2 = 5.
Answer: 511 books remained.

Suggested Lesson Video

The teacher may use this short video after the practical activity to reinforce the lesson.

Teaching Methods/Instructional Techniques

Explanation, Demonstration, Question and Answer, Guided Practice and Problem Solving.

Instructional Procedures

Step 1: Introduction with Place-Value Materials

Time: 4 minutes

Teaching Skill: Set Induction/Questioning

Teacher’s Activity: The teacher shows bundled sticks, seeds and pebbles, forms one three-digit quantity and removes part of it while pupils identify − as the sign for finding what remains.

Pupils’ Activity: Pupils identify the − sign and state what the operation does to the quantities.

Learning Point: Subtraction is connected to a clear joining or taking-away situation.

Step 2: Arranging Numbers in H-T-U Columns

Time: 5 minutes

Teaching Skill: Explanation/Observation

Teacher’s Activity: The teacher draws an H-T-U chart and places the digits of 532 − 178 so that hundreds, tens and units are vertically aligned.

Pupils’ Activity: Pupils place matching digit cards in the correct columns and identify the column where calculation begins.

Learning Point: Correct place-value alignment prevents digits of unlike values from being combined.

Step 3: Demonstrating the Operation and Exchanging

Time: 5 minutes

Teaching Skill: Demonstration/Modelling

Teacher’s Activity: The teacher models 532 − 178 and physically exchanges ten units for one ten where required, writes each column result and obtains 354.

Pupils’ Activity: Pupils manipulate the bundles with the teacher and state each units, tens and hundreds calculation.

Learning Point: The subtraction method is carried out from units to hundreds with correct exchanging.

Step 4: Guided Column Practice

Time: 6 minutes

Teaching Skill: Guided Practice

Teacher’s Activity: The teacher writes 704 − 286, invites pupils to supply each column result and records 418 only after the class checks the working.

Pupils’ Activity: Pupils copy the H-T-U arrangement, calculate each column and compare their answer with the model.

Learning Point: Pupils apply the column method with guided checking.

Step 5: Applying the Operation to a Word Problem

Time: 5 minutes

Teaching Skill: Practical Activity/Problem Solving

Teacher’s Activity: The teacher reads: “A store had 650 exercise books and sold 275. How many remained?” and underlines the quantities before writing and solving the matching number sentence.

Pupils’ Activity: Pairs state the required operation, solve 650 − 275 and give the answer as 375 exercise books.

Learning Point: A word problem is solved by choosing the operation, calculating and naming the quantity in the answer.

Step 6: Independent Calculation

Time: 5 minutes

Teaching Skill: Independent Practice

Teacher’s Activity: The teacher gives one fresh column calculation and one missing-number item based on subtraction, then supports pupils who still need the H-T-U chart.

Pupils’ Activity: Pupils align and solve both items independently, showing any carried or exchanged value above the correct column.

Learning Point: Pupils complete subtraction accurately without copying the worked example.

Step 7: Evaluation/Review

Time: 5 minutes

Teaching Skill: Questioning/Assessment

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

1. Arrange 865 − 243 in H-T-U columns.
2. Calculate 865 − 243.
3. Calculate 732 − 458.
4. Find the missing number: 600 − __ = 275.
5. A library had 725 books and lent 214. How many books remained?

Pupils’ Activity: Pupils arrange and solve the evaluation calculations, explain any exchange and solve the word-problem item with its correct unit or object name.

Learning Point: Pupils demonstrate correct H-T-U alignment, operation choice and calculation with exchanging.

Step 8: Conclusion

Time: 5 minutes

Teaching Skill: Summary/Feedback

Teacher’s Activity: The teacher reconstructs the key H-T-U calculation, asks why work starts from units and corrects one common alignment error.

Pupils’ Activity: Pupils explain the first column step and complete a final oral calculation using the − sign.

Learning Point: Accurate subtraction depends on correct place-value alignment and orderly working.

Lesson Keywords

• addition – joining numbers to find a total
• subtraction – taking away or finding a difference
• exchange – changing one larger place-value group into ten smaller groups
• sum – the answer to an addition
• difference – the answer to a subtraction

Differentiation

Support: Use real objects, larger pictures, teacher modelling, paired work and fewer examples at a time. Allow pupils who need help to point, match, count or demonstrate before writing.

Extension: Ask faster pupils to create one additional correct example, explain their method independently or apply the same idea to another familiar situation without moving to a new topic.

Note for teachers using this lesson plan

Use the supplied counters as units and bundled sticks for tens and hundreds. Check column alignment before allowing pupils to calculate; for exchanging, make pupils exchange physical bundles before using carried or borrowed digits. Use the suggested video only after the concrete explanation or as a short reinforcement; pause it for questions. Understanding is shown when pupils can complete the evaluation task with the correct language, method and unit where required.