Lesson Notes By Weeks and Term v3 - Primary 5
Multiplication
Download the Lessonotes Mobile Nigeria 2025 app for faster lesson access on Android and iPhone.
Multiplication
Download the Lessonotes Mobile Nigeria 2025 app for faster lesson access on Android and iPhone.
Subject: General Mathematics
Class: Primary 5
Term: 1st Term
Week: 3
Theme: Numbers And Numeration
This page supports the lesson note with a companion video and a short classroom-ready summary.
For class groups and homework, share this lesson page so learners also get the summary, objectives, and full lesson context.
multiply a 3-digit number by a 3-digit number solve quantitative aptitude problems on multiplication apply “of‟ as multiplication when dealing with fractions of whole numbers multiply numbers by zero and one multiply decimals by whole numbers multiply decimal fractions by whole numbers calculate squares of whole numbers more than 50 and square roots of perfect squares greater than 400 solve quantitative aptitude problems in volving squares of numbers more than 50 and square root of numbers greater than 400
This section provides the foundational knowledge and step-by-step procedures for each learning objective. A. Multiplication of a 3-Digit Number by a 3-Digit Number This involves extending the long multiplication method learned for smaller numbers. The key is careful alignment of digits according to their place values and accurate addition of partial products.
Steps: Arrange the numbers: Write the numbers vertically, aligning the ones, tens, and hundreds digits.
Multiply by the ones digit: Multiply the top number by the ones digit of the bottom number. Write the result as the first partial product. Remember to carry over when necessary.
Multiply by the tens digit: Multiply the top number by the tens digit of the bottom number. Write the result as the second partial product, starting directly under the tens place (i.e., add a zero as a placeholder in the ones place).
Multiply by the hundreds digit: Multiply the top number by the hundreds digit of the bottom number. Write the result as the third partial product, starting directly under the hundreds place (i.e., add two zeros as placeholders in the ones and tens places).
Add the partial products: Sum the three partial products to obtain the final product.
Example 1: Multiply ₦245 by 132. ``` 245 (Multiplicand) x 132 (Multiplier) 490 (245 x 2 400, the square roots will be > 20 (since 202 = 400).
Steps: Estimate: Start by estimating which whole number, when squared, would be close to the given number. (e.g., if √441, know 202=400, so the answer is slightly above
2
0. Look at the last digit: if it ends in 1, the root might end in 1 or 9).
Test: Test the estimated number or numbers ending with the appropriate digit.
Verify: Multiply the tested number by itself to confirm if it yields the original perfect square.
Example 13: Find the square root of 441 (√441).
Solution: Estimate: We know 20 x 20 =
4
0
0. So the answer is a bit more than
2
0. Last digit check: The number 441 ends in
1. Numbers that square to end in 1 are those ending in 1 (1x1=1) or 9 (9x9=81).
Trial: Let's try 21. 21 x 21 = 441 Answer: √441 =
2
1. Example 14: Find the square root of 625 (√625).
Solution: Estimate: We know 20 x 20 = 400, and 30 x 30 =
9
0
0. So the answer is between 20 and
3
0. Last digit check: The number 625 ends in
5. Numbers that square to end in 5 are those ending in 5 (5x5=25).
Trial: Let's try 25. 25 x 25 = 625 Answer: √625 =
2
5. H. Quantitative Aptitude Problems Involving Squares and Square Roots These problems integrate the concepts of squaring and square roots into word problems.
Steps: Read and understand: Identify what is given and what needs to be found.
Determine the operation: Decide if squaring or finding the square root is required. Keywords like "area of a square," "square plot," "find the side of a square" are clues.
Formulate and solve: Apply the appropriate calculation. State the answer with units.
Example 15: A square plot of land has a side length of 60 meters. What is the area of the land?
Solution: Side of the square = 60 m Area of a square = side x side = side2 Area = 60 m x 60 m = 3600 m2 Answer: The area of the land is 3600 square meters.
Example 16: A farmer wants to fence a square farm with an area of 900 square meters. What is the length of one side of the farm?
Solution: Area of the square farm = 900 m2 Side of a square = √Area Side = √900 Estimate: 30 x 30 =
9
0
0. Side = 30 m Answer: The length of one side of the farm is 30 meters. --- Phase 1: Introduction and Review (10 minutes)
Teacher Activity: Begins by reviewing basic multiplication facts and the concept of multiplication as repeated addition. Recalls long multiplication for 2-digit numbers by 2-digit numbers through a quick example on the board (e.g., 23 x 15). States the lesson objectives clearly in simple terms, relating them to real-life situations like market transactions or land measurement.
Student Activity: Respond to teacher's questions on basic multiplication. Observe and recall previous knowledge during the review. Listen attentively to the stated objectives and their relevance.
Phase 2: Concept Development and Guided Practice (40 minutes)
Teacher Activity: Objective 1 & 2 (3-digit by 3-digit multiplication & quantitative aptitude): Demonstrates the steps for multiplying a 3-digit number by a 3-digit number using "Example 1" (₦245 x 132) on the chalkboard, emphasizing place value alignment and carrying over. Explains how to approach quantitative aptitude problems, using "Example 2" (farmer's maize) to show how to translate words into a multiplication problem. Engages students in a choral response for smaller multiplication steps during the demonstration. Objective 3 ("of" as multiplication): Explains the meaning of "of" in mathematical context using "Example 3" (3⁄4 of ₦800) and "Example 4" (ripe oranges). Shows how to convert the word problem into a fractional multiplication.
Objective 4 (Multiplication by 0 and 1): States and explains the identity property (n x 1 = n) and the zero property (n x 0 = 0) of multiplication with simple numerical examples ("Examples 5, 6, 7, 8"). Asks students to provide quick examples. Objective 5 & 6 (Multiplying decimals by whole numbers): Demonstrates the process of multiplying decimals by whole numbers using "Example 9" (₦12.50 x 4) and "Example 10" (fabric for dresses). Emphasizes the crucial step of counting decimal places in the multiplicand and placing them correctly in the product. Objective 7 & 8 (Squares and Square Roots & quantitative aptitude): Introduces the concept of squaring a number (n x n) and its notation (n2). Uses "Example 11" (552) and "Example 12" (722) to demonstrate. Explains the concept of square root (√n) as the inverse of squaring. Guides students through finding square roots of perfect squares greater than 400 using estimation and trial-and-error (e.g., "Example 13" (√441) and "Example 14" (√625)), starting with known squares like 20x20, 30x
3
0. Applies these concepts to quantitative aptitude problems using "Example 15" (area of square land) and "Example 16" (side length from area). Checks for understanding frequently by asking targeted questions.
Student Activity: Actively participate by observing, asking questions, and attempting guided practice problems with teacher's help. Work along with the teacher on their individual slates or notebooks during demonstrations. Contribute to discussions and provide quick responses to conceptual questions. Practice identifying keywords for quantitative aptitude problems. Practice placing decimal points correctly. Engage in the estimation and trial-and-error process for square roots.
Phase 3: Collaborative Practice (15 minutes)
Teacher Activity: Divides students into small groups (e.g., 4-5 students per group). Provides each group with a few practice questions covering different objectives (one question per objective). Monitors group work, providing guidance, clarifying misconceptions, and ensuring all members participate. Encourages peer learning within groups.
Student Activity: Work collaboratively in groups to solve the assigned practice problems. Discuss strategies and solutions with group members. Present their group's solutions to the class when called upon.
Phase 4: Conclusion and Summary (5 minutes)
Teacher Activity: Summarizes the key concepts covered in the lesson: 3-digit multiplication, "of" as multiplication, properties of 0 and 1, decimal multiplication, squares, and square roots. Reiterates the real-life importance of these skills. Assigns independent practice questions as homework.
Student Activity: Listen to the summary and ask any remaining questions. Copy down homework assignments. --- The teacher should present these questions and guide students through solving them step-by-step, ensuring understanding at each stage. Question 1 (3-digit by 3-digit multiplication): A large shop in Lagos ordered 356 cartons of soft drinks. If each carton contains 144 bottles, how many bottles of soft drinks were ordered in total?
Solution: Understanding the problem: This requires finding the total number of bottles given the number of cartons and bottles per carton. This is a multiplication problem.
Setup: ``` 356 x 144 ``` Step 1: Multiply by the ones digit (4) 4 x 356 = 1424 ``` 356 x 144 1424 (356 x 4) ``` Step 2: Multiply by the tens digit (40) 40 x 356 = 14240 (Remember the zero placeholder) ``` 356 x 144 1424 14240 (356 x 40) ``` Step 3: Multiply by the hundreds digit (100) 100 x 356 = 35600 (Remember two zero placeholders) ``` 356 x 144 1424 14240 35600 (356 x 100) ``` Step 4: Add the partial products ``` 356 x 144 1424 14240 35600 51264 ``` Answer: The shop ordered a total of 51,264 bottles of soft drinks. Question 2 ("of" as multiplication): Mrs. Adebayo earns ₦1,200,000 per year. She spends 2⁄5 of her earnings on food. How much does she spend on food annually?
Solution: Understanding the problem: The phrase "2⁄5 of her earnings" implies multiplication.
Setup: Food spending = 2⁄5 of ₦1,200,000 Calculation: (2/5) x 1,200,000 = (2 x 1,200,000) / 5 = 2,400,000 / 5 = 480,000 Answer: Mrs. Adebayo spends ₦480,000 on food annually. Question 3 (Multiplying decimals by whole numbers): A trader buys 5.5 kg of garri from a local market. If she buys 7 such quantities for her customers, what is the total mass of garri she bought?
Solution: Understanding the problem: This involves multiplying a decimal number (mass of garri) by a whole number (number of quantities).
Setup: Total mass = 5.5 kg x 7 Calculation: Ignore the decimal point initially: 55 x 7 55 x 7 = 385 Count decimal places in 5.5: There is one decimal place. Place the decimal point in 385, one place from the right: 38.5 Answer: The total mass of garri she bought is 38.5 kg. Question 4 (Squares of numbers > 50): A square farmland has a side length of 85 meters. Calculate the area of the farmland.
Solution: Understanding the problem: The area of a square is found by squaring its side length (side x side).
Setup: Area = 852 = 85 x 85 Calculation: ``` 85 x 85 425 (85 x 5) 6800 (85 x 80) 7225 ``` Answer: The area of the farmland is 7225 square meters (m2). Question 5 (Square roots of perfect squares > 400): A community well is located in the exact centre of a square market square with an area of 1024 m
2. What is the length of one side of this market square?
Solution: Understanding the problem: To find the side length of a square given its area, we need to find the square root of the area.
Setup: Side length = √1024 Calculation (Trial and Error): We know 30 x 30 = 900 and 40 x 40 =
1
6
0
0. So the answer is between 30 and
4
0. The last digit of 1024 is
4. A number ending in 2 or 8, when squared, ends in 4 (2x2=4, 8x8=64).
Let's try 32: 32 x 32 = 1024 Answer: The length of one side of the market square is 32 meters. ---
A. Remediation (for struggling learners): Focus on Prerequisite Skills: Before tackling complex multiplication, ensure mastery of basic multiplication facts (times tables). Use flashcards, multiplication charts, or online games.
Visual Aids: Utilize grid paper for 3-digit multiplication to help students align digits correctly and manage place values. Use manipulatives (like base ten blocks if available, or locally sourced items like bottle caps) to demonstrate the concept of carrying over.
Break Down Steps: For long multiplication, break it into smaller, manageable steps. Provide partially completed problems for students to finish. For decimals, initially work with whole numbers, then introduce placing the decimal point in the final product as a separate step.
Simplified Numbers: Start with smaller 2-digit by 1-digit multiplications, gradually increasing complexity. For squares and square roots, work with smaller perfect squares (e.g., 22, 32, √9, √16) before moving to larger numbers.
One-on-One Support: Provide direct, individualized instruction to address specific areas of difficulty.
Peer Tutoring: Pair struggling learners with more advanced students for peer support during practice sessions.
B. Extension (for high-achieving learners): Multi-step Word Problems: Provide complex quantitative aptitude problems that require multiple operations (e.g., multiplication, addition, subtraction).
Larger Numbers/More Decimals: Challenge them with multiplying 4-digit numbers by 3-digit numbers, or decimals with more decimal places (e.g., 1.234 x 56).
Introduction to Cubes/Cube Roots: Briefly introduce the concept of cubing a number (n3) and finding cube roots of perfect cubes.
Mental Math Strategies: Encourage and teach mental multiplication techniques (e.g., for multiplying by 5, 10, 25, or numbers close to 100).
Inverse Operations: Explore how division is the inverse of multiplication, and how squaring and square roots are inverse operations, using examples.
Problem Creation: Ask advanced students to create their own challenging word problems for their peers, fostering deeper understanding and creativity.
C. Differentiation during Activities: Varying Group Roles: In group activities, assign roles that cater to different strengths (e.g., "scribe" for good handwriting, "checker" for accuracy, "presenter" for communication, "calculator" for numerical operations).
Tiered Worksheets: Prepare different versions of practice worksheets with varying levels of complexity for independent practice.
Flexible Grouping: Periodically reassess and regroup students based on their progress and needs for specific objectives.
Open-ended Tasks: Provide opportunities for students to explore alternative solutions or present their reasoning in different ways (e.g., drawing diagrams for word problems).
Market Transactions and Budgeting (Commerce/Personal Finance): Application: When buying multiple items at a market stall in Onitsha or Lagos, students can calculate the total cost. For example, if a "mudu" (local unit of measure) of beans costs ₦850, a trader buying 120 mudus needs to quickly calculate 850 x
1
2
0. Similarly, understanding "of" as multiplication helps in budgeting, like calculating 1⁄2 of one's monthly income for food or 1⁄5 for transport fares.
Integration: The teacher can bring empty cartons or pictures of market scenes. Students can create a shopping list with prices and quantities (e.g., 3 bags of rice @ ₦45,000 each, 2 cartons of Maggi @ ₦2,500 each, 0.5 kg of groundnut @ ₦1,200 per kg) and calculate the total cost. Land Measurement and Construction (Agriculture/Engineering): Application: Farmers or builders in rural or urban areas frequently deal with land areas. Calculating the area of a square farm plot (e.g., 70m by 70m, requiring 702) to determine how many crops can be planted or how many building blocks are needed. Conversely, if a village elder designates a square plot of land with a certain area (e.g., 900 m2) for a communal garden, community members need to know how to find the side length (√900) to measure it out.
Integration: The teacher can use a square object (e.g., a square piece of cardboard representing a farm plot). Students can be given dimensions and asked to calculate the area, or given the area and asked to find the side, connecting mathematics to local land tenure and development. Resource Allocation and Community Sharing (Social Studies/Home Economics): Application: In many Nigerian communities, resources are often shared. For instance, if a donor provides 500 bags of rice to a community, and a local leader decides that 1⁄5 of the bags should go to internally displaced persons (IDPs), students can calculate this amount (1⁄5 of 500). If a local government wants to share 1200 textbooks among schools, and each school receives 150 books, the total number of books can be verified through multiplication.
Integration: Students can work in groups to solve hypothetical problems about sharing resources (e.g., sharing 200 sachets of pure water amongst 50 students, where each student gets 4 sachets, or sharing an amount of money). This helps them see the practical utility of multiplication in fair distribution and resource management. ---