Lesson Notes By Weeks and Term v3 - Primary 4
Multiplication
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Multiplication
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Subject: General Mathematics
Class: Primary 4
Term: 2nd Term
Week: 2
Theme: Basic Operations
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Watch on YouTubeSee Facebook postMultiply whole numbers by 2-digit number not exceeding 50; Solves quantitative aptitude problems in volving multiplication of whole numbers by 2-digit numbers; Multiply decimals numbers by 2-digit numbers; Solve quantitativeaptitude problems in volving multiplication of decimal numbers by 2 digit numbers. Calculate the squares of 1 and 2 digit numbers; Identify objects with perfect faces like cubes and Square shapes Solve quantitative aptitude problems in volving squares; Find square roots of perfect squares up to 400;
\times 5 = 25$ $6^2 = 6 \times 6 = 36$ $7^2 = 7 \times 7 = 49$ $8^2 = 8 \times 8 = 64$ $9^2 = 9 \times 9 = 81$ Example 6: Squares of 2-digit numbers $10^2 = 10 \times 10 = 100$ $11^2 = 11 \times 11 = 121$ $12^2 = 12 \times 12 = 144$ $15^2 = 15 \times 15 = 225$ $20^2 = 20 \times 20 = 400$ The 20x20 square chart can be used to quickly find these values by locating the intersection of the row and column corresponding to the number. For instance, to find $12^2$, locate '12' on the top row and '12' on the left column; their intersection will be '144'.
Objects with Perfect Square Faces: Learners should be able to identify real-world objects that have faces shaped like perfect squares. Dice Rubik's Cube Square tiles (on a floor or wall) A chessboard Some biscuits or crackers A square picture frame 2.
4. Square Roots of Perfect Squares The square root of a number is the value that, when multiplied by itself, gives the original number. It is denoted by the symbol $\sqrt{ }$. For example, $\sqrt{25}$ means "the square root of 25".
Concept: If a square has an area of 'A' square units, its side length is $\sqrt{A}$ units. This is the reverse operation of squaring a number. Finding Square Roots using a 20x20 Square Chart: To find the square root of a number using a chart:
1. Locate the number inside the grid of the chart.
2. Identify the corresponding number in the top row or leftmost column. This number is the square root.
Example: To find $\sqrt{144}$, locate 144 in the chart. Follow its row/column to the edge, where '12' will be found. So, $\sqrt{144} = 12$. Finding Square Roots using the Factor Method: This method is effective for perfect squares and helps in understanding the concept.
Steps:
1. Find the prime factors of the given number.
2. Group identical prime factors in pairs.
3. Take one factor from each pair.
4. Multiply these single factors together to get the square root.
Example 7: Find the square root of 36.
1. Prime factors of 36: $36 = 2 \times 18 = 2 \times 2 \times 9 = 2 \times 2 \times 3 \times 3$.
2. Group into pairs: $(2 \times 2) \times (3 \times 3)$.
3. Take one from each pair: $2 \times 3$.
4. Multiply: $2 \times 3 = 6$. So, $\sqrt{36} = 6$.
Example 8: Find the square root of 100.
1. Prime factors of 100: $100 = 2 \times 50 = 2 \times 2 \times 25 = 2 \times 2 \times 5 \times 5$.
2. Group into pairs: $(2 \times 2) \times (5 \times 5)$.
3. Take one from each pair: $2 \times 5$.
4. Multiply: $2 \times 5 = 10$. So, $\sqrt{100} = 10$.
Example 9: Find the square root of 225.
1. Prime factors of 225: $225 = 3 \times 75 = 3 \times 3 \times 25 = 3 \times 3 \times 5 \times 5$.
2. Group into pairs: $(3 \times 3) \times (5 \times 5)$.
3. Take one from each pair: $3 \times 5$.
4. Multiply: $3 \times 5 = 15$. So, $\sqrt{225} = 15$. This section provides a detailed explanation of the core concepts, supported by step-by-step examples relevant to the Nigerian context. 2.
1. Multiplication of Whole Numbers by 2-Digit Numbers Multiplication is a fundamental arithmetic operation that represents repeated addition. When multiplying by a 2-digit number, the process involves two steps: multiplying by the ones digit of the multiplier, then by the tens digit, and finally adding the partial products.
Steps:
1. Multiply the multiplicand by the ones digit of the multiplier.
2. Multiply the multiplicand by the tens digit of the multiplier. Remember to place a zero (or leave the space blank) in the ones column as a placeholder for the tens product.
3. Add the two partial products to get the final answer.
Example 1: Multiplying a 2-digit number by a 2-digit number A farmer sells a basket of mangoes for N
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5. If he sells 23 baskets, how much money does he make?
Calculation: 35 x 23 ``` 35 x 23 ----- 105 (35 x 3 - Multiply by the ones digit) 700 (35 x 20 - Multiply by the tens digit. Note the placeholder '0') ----- 805 (Add the partial products) ``` The farmer makes N
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5. Example 2: Multiplying a 3-digit number by a 2-digit number A school needs to buy 125 exercise books. If each book costs N24, how much will the school spend?
Calculation: 125 x 24 ``` 125 x 24 ----- 500 (125 x 4) 2500 (125 x 20) ----- 3000 ``` The school will spend N3,000. 2.
2. Multiplication of Decimal Numbers by 2-Digit Numbers When multiplying decimal numbers by whole numbers, the process is similar to multiplying whole numbers. The main difference lies in placing the decimal point in the final product.
Steps:
1. Perform the multiplication as if the numbers were whole numbers, ignoring the decimal point initially.
2. Count the total number of decimal places in the decimal number (the multiplicand).
3. Place the decimal point in the product by counting from the right the same number of places determined in step
2. Example 3: Multiplying a decimal by a 2-digit number A tailor uses 1.75 meters of fabric for one dress. How much fabric will she use for 12 such dresses?
Calculation: 1.75 x 12 ``` 1.75 (2 decimal places) x 12 ----- 350 (175 x 2) 1750 (175 x 10) ----- 2100 ``` Since there are 2 decimal places in 1.75, count 2 places from the right in the product (2100) and place the decimal point. The result is 21.
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0. The tailor will use 21.00 meters of fabric.
Example 4: Multiplying a smaller decimal by a 2-digit number A sachet of sugar weighs 0.25 kg. What is the total weight of 15 sachets?
Calculation: 0.25 x 15 ``` 0.25 (2 decimal places) x 15 ----- 125 (25 x 5) 250 (25 x 10) ----- 375 ``` Count 2 decimal places from the right: 3.
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5. The total weight of 15 sachets is 3.75 kg. 2.
3. Squares of 1 and 2-Digit Numbers The square of a number is the result of multiplying a number by itself. It is denoted by a small '2' written above and to the right of the number (e.g., $5^2$).
Concept: If a square has a side length of 's' units, its area is $s \times s = s^2$ square units. This visual representation helps in understanding squares.
Example 5: Squares of 1-digit numbers $1^2 = 1 \times 1 = 1$ $2^2 = 2 \times 2 = 4$ $3^2 = 3 \times 3 = 9$ $4^2 = 4 \times 4 = 16$ $5^2 = 5 \times 5 = 25$ $6^2 = 6 \times 6 = 36$ $7^2 = 7 \times 7 = 49$ $8^2 = 8 \times 8 = 64$ $9^2 = 9 \times 9 = 81$ Example 6: Squares of 2-digit numbers $10^2 = 10 \times 10 = 100$ $11^2 = 11 \times 11 = 121$ $12^2 = 12 \times 12 = 144$ $15^2 = 15 \times 15 = 225$ $20^2 = 20 \times 20 = 400$ The 20x20 square chart can be used to quickly find Materials: Multiplication charts, flashcards (multiplication facts, squares), 20x20 square chart (printed or drawn on a large cardboard), unit cubes or blocks, real-life objects with square faces (e.g., a dice, a small square tile), chalk, blackboard/whiteboard.
Introduction (10 minutes): Teacher Activity: Begin with a quick revision of basic multiplication facts (up to 10x10) using oral drills or flashcards. Pose a simple word problem that requires multiplication (e.g., "If one pen costs N10, how much do 5 pens cost?"). Elicit responses and relate to real-life transactions.
Student Activity: Participate in oral drills, answer questions, and solve the simple multiplication problem.
Phase 1: Multiplication by 2-Digit Numbers (Whole Numbers and Decimals) (25 minutes)
Teacher Activity: Introduce multiplication by 2-digit numbers using vertical column method. Demonstrate Example 1 (35 x 23) step-by-step on the board, emphasizing the partial products and placeholder zero. Provide another example (e.g., 215 x 15) and guide learners through it, asking questions at each step. Introduce multiplication of decimal numbers by 2-digit numbers. Explain the process of ignoring the decimal point during multiplication and then placing it correctly in the final product. Demonstrate Example 3 (1.75 x 12). Stress the importance of counting decimal places accurately.
Student Activity: Copy the examples from the board. Solve practice problems provided by the teacher in their notebooks. Participate in Q&A sessions, clarifying doubts.
Phase 2: Squares of Numbers and Objects with Square Faces (20 minutes)
Teacher Activity: Introduce the concept of "squaring a number" by demonstrating with physical objects (e.g., arranging 3x3 unit blocks to form a square, asking for the total number of blocks). Explain the notation $N^2$. List squares of 1-digit numbers (Example 5) and some 2-digit numbers (Example 6) on the board. Present the 20x20 square chart and explain how to use it to find the square of a number. Ask learners to identify objects in the classroom or from their homes that have perfect square faces (e.g., dice, a book cover, a window pane).
Student Activity: Count blocks to understand the concept of a square. Recite squares of 1-digit numbers. Practice finding squares of 2-digit numbers using the 20x20 square chart. Share examples of objects with square faces.
Phase 3: Square Roots of Perfect Squares (20 minutes)
Teacher Activity: Introduce the concept of square root as the reverse of squaring a number. Explain the $\sqrt{ }$ symbol. Demonstrate how to find square roots of perfect squares up to 400 using the 20x20 square chart (reverse lookup). Introduce the factor method for finding square roots (Examples 7, 8, 9). Guide learners through the steps of prime factorization and pairing. Emphasize that this method is robust for perfect squares.
Student Activity: Practice finding square roots using the 20x20 square chart. Work through examples of the factor method for square roots, actively participating in identifying prime factors and forming pairs.
Conclusion (5 minutes): Teacher Activity: Summarize the key concepts covered: multiplication of whole numbers and decimals by 2-digit numbers, squares of numbers, identification of square-faced objects, and finding square roots. Provide a brief recap of the methods taught.
Student Activity: Ask clarifying questions, participate in a quick Q&A session to test understanding.
Question 1 (Whole Number Multiplication): A trader buys 48 bags of rice. If each bag costs N2,500, how much does he pay in total? (
Note: The actual calculation will be 2500 x 48, which exceeds the "2-digit number not exceeding 50" for the multiplicand, but the multiplier (48) fits. The prompt says "multiply whole numbers by 2-digit number not exceeding 50", implying the 2-digit limit applies to the multiplier. For Primary 4, 2500 x 48 is a bit large, but we can simplify to 25 x 48 for demonstration purposes if sticking strictly to primary 4 numbers, or assume they can handle larger numbers with careful instruction). Let's use a simpler example suitable for the primary 4 context and the 'not exceeding 50' for the multiplier: A box contains 24 oranges. How many oranges are in 32 such boxes?
Solution 1: To find the total number of oranges, multiply 24 by 32. ``` 24 x 32 48 (24 x 2) 720 (24 x 30) 768 ``` There are 768 oranges in 32 boxes.
Commentary: This problem reinforces the concept of multiplying a 2-digit number by another 2-digit number using the standard column method.
Question 2 (Decimal Multiplication): A painter uses 0.75 litres of paint for one small wall. How much paint will he use for 25 similar walls?
Solution 2: To find the total paint used, multiply 0.75 by 25. ``` 0.75 (2 decimal places) x 25 375 (75 x 5) 1500 (75 x 20) 1875 ``` Count 2 decimal places from the right in the product: 18.
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5. The painter will use 18.75 litres of paint.
Commentary: This question tests the ability to multiply decimals by 2-digit numbers, ensuring correct placement of the decimal point. Question 3 (Squares and Square-faced Objects): a) Calculate the square of 14. b) Name two objects found in a typical Nigerian home or school that have perfect square faces.
Solution 3: a) The square of 14 means $14 \times 14$. ``` 14 x 14 56 (14 x 4) 140 (14 x 10) 196 ``` The square of 14 is 196. b) Two objects with perfect square faces could be: A dice (from a board game) A square floor tile A square picture frame A Rubik's Cube
Commentary: This question covers calculating squares and applying knowledge of geometric shapes to real-world objects.
Question 4 (Square Roots): Find the square root of 196 using the factor method.
Solution 4: To find $\sqrt{196}$ using the factor method: Find the prime factors of 196: $196 = 2 \times 98$ $98 = 2 \times 49$ $49 = 7 \times 7$ So, $196 = 2 \times 2 \times 7 \times 7$. Group the identical prime factors in pairs: $(2 \times 2) \times (7 \times 7)$.
Take one factor from each pair: $2 \times 7$.
Multiply these factors: $2 \times 7 = 14$.
Therefore, $\sqrt{196} = 14$.
Commentary: This question assesses the understanding and application of the factor method for finding square roots of perfect squares.
Market Transactions and Budgeting: Learners can apply multiplication when calculating the total cost of multiple items at a market. For instance, if one tuber of yam costs N850, a learner can calculate the cost of 15 tubers for a family event ($850 \times 15$). This also relates to budgeting for household expenses.
Construction and Tiling: The concept of squares and square roots is essential in construction. If a builder needs to tile a square room, knowing the side length allows them to calculate the area using squaring. Conversely, if the area is known, they can find the side length using square roots to determine how many tiles are needed along one edge. For example, if a room has an area of $144 \text{ m}^2$, the side length is $\sqrt{144} = 12 \text{ m}$.
Measurements and Quantities: Multiplication with decimals is vital when dealing with quantities that aren't whole numbers, such as fuel consumption (e.g., a car uses 0.8 litres of fuel per km; how much for a 25 km journey?), weighing produce (e.g., buying 1.5 kg of fish at N1,800 per kg), or measuring fabric for sewing (e.g., 2.75 metres of fabric for 12 school uniforms). These scenarios are common in Nigerian daily life.