Lesson Notes By Weeks and Term v3 - Primary 3
Multiplication
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Multiplication
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Subject: General Mathematics
Class: Primary 3
Term: 1st Term
Week: 3
Theme: Basic Operations
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Watch on YouTubemultiply from1 x 1 to 9 x 9 multiply 2-digit number by 1-digit number; multiply three 1-digit numbers taking two at a time; carry out correct multiplication in everyday activities.
2.1 Definition of Multiplication Multiplication is a quick way of performing repeated addition of the same number. It is represented by the symbol 'x' (read as "times" or "multiplied by").
Example: 3 x 4 means "3 groups of 4" or "4 added to itself 3 times" (4 + 4 + 4). The result is 12. 2.2 Key Terms Multiplicand: The number being multiplied (the number of groups in "groups of"). In 3 x 4, 4 is the multiplicand.
Multiplier: The number by which another number is multiplied (the number of groups). In 3 x 4, 3 is the multiplier.
Product: The result obtained from multiplying two or more numbers. In 3 x 4 = 12, 12 is the product. 2.3 Multiplication Facts (1 x 1 to 9 x 9) Learners are expected to memorize the basic multiplication facts up to 9 x
9. This forms the foundation for all subsequent multiplication skills.
Strategies for learning: Skip Counting: Counting by 2s, 3s, 4s, etc. (e.g., for 3 x 5, count by 3 five times: 3, 6, 9, 12, 15).
Repeated Addition: Explicitly writing out the addition (e.g., 6 x 4 = 4 + 4 + 4 + 4 + 4 + 4).
Using patterns: For example, the 9 times table (digits sum to 9, finger trick). Flashcards and chants.
Example Facts: 4 x 5 = 20 7 x 6 = 42 9 x 8 = 72 2.4 Multiplying a 2-Digit Number by a 1-Digit Number This involves applying place value understanding and basic multiplication facts.
There are two common methods: 2.4.1 Vertical Method (Column Multiplication) This method aligns numbers by their place values (Ones under Ones, Tens under Tens).
Steps:
1. Write the numbers vertically, aligning the ones digits.
2. Multiply the ones digit of the 2-digit number by the 1-digit number.
3. If the product is 10 or more, write down the ones digit of the product and carry over the tens digit to the tens column.
4. Multiply the tens digit of the 2-digit number by the 1-digit number.
5. Add any carried-over tens to this product. Write the result in the tens and hundreds columns as needed.
Worked Example 1 (Without Carrying): Calculate 23 x 3 ``` 23 (2 tens, 3 ones) x 3 (3 ones) ---- 9 (3 x 3 ones = 9 ones) 60 (3 x 2 tens = 6 tens or 60) ---- 69 ``` Step-by-step breakdown: Multiply 3 (ones in 23) by 3 (multiplier): 3 x 3 =
9. Write 9 in the ones place.
Multiply 2 (tens in 23) by 3 (multiplier): 2 x 3 =
6. Write 6 in the tens place. The product is
6
9. Worked Example 2 (With Carrying): Calculate 38 x 4 ``` 38 x 4 ---- ``` Step-by-step breakdown: Step 1: Multiply the Ones digit.
Multiply 8 (ones in 38) by 4 (multiplier): 8 x 4 =
3
2. Write down 2 in the ones place of the product. Carry over 3 (from 3 tens) to the tens column. ``` 38 x 4 ---- 2 ``` Step 2: Multiply the Tens digit and Add Carry-over.
Multiply 3 (tens in 38) by 4 (multiplier): 3 x 4 =
1
2. Add the carried-over 3: 12 + 3 =
1
5. Write 15 in the tens and hundreds places. ``` 38 x 4 ---- 152 ``` The product is
1
5
2. This could be applied to calculate the cost of 4 bags of garri at N38 per bag (if garri was very cheap!). 2.4.2 Horizontal Method (Expanded Form/Distributive Property) This method breaks down the 2-digit number into its expanded form (tens and ones) and then multiplies each part by the 1-digit number.
Example: 23 x 3 Break 23 into 20 +
3. Multiply each part by 3: (20 x 3) + (3 x 3) 60 + 9 69
Example: 38 x 4 Break 38 into 30 +
8. Multiply each part by 4: (30 x 4) + (8 per bag (if garri was very cheap!). 2.4.2 Horizontal Method (Expanded Form/Distributive Property) This method breaks down the 2-digit number into its expanded form (tens and ones) and then multiplies each part by the 1-digit number.
Example: 23 x 3 Break 23 into 20 +
3. Multiply each part by 3: (20 x 3) + (3 x 3) 60 + 9 69
Example: 38 x 4 Break 38 into 30 +
8. Multiply each part by 4: (30 x 4) + (8 x 4) 120 + 32 152 2.5 Multiplying Three 1-Digit Numbers (taking two at a time) This involves using the associative property of multiplication, which states that the way numbers are grouped in multiplication does not change the product (a x b) x c = a x (b x c).
Steps:
1. Multiply the first two numbers.
2. Multiply the result from step 1 by the third number.
Example: Calculate 2 x 3 x 4 Method 1: Grouping (2 x 3) first First, multiply 2 x 3 =
6. Then, multiply the result by the third number: 6 x 4 =
2
4. Method 2: Grouping (3 x 4) first First, multiply 3 x 4 =
1
2. Then, multiply the result by the first number: 2 x 12 =
2
4. Both methods yield the same product,
2
4. This skill is useful in situations like calculating the number of items in a box, where each box has a certain number of layers, each layer has a certain number of rows, and each row has a certain number of items (e.g., 2 rows of 3 items, in 4 layers). 2.6 Properties of Multiplication (Brief Introduction)
Commutative Property: The order of numbers being multiplied does not affect the product. a x b = b x a (e.g., 5 x 3 = 15, and 3 x 5 = 15).
Identity Property: Any number multiplied by 1 is the number itself. a x 1 = a (e.g., 7 x 1 = 7).
Zero Property: Any number multiplied by 0 is 0. a x 0 = 0 (e.g., 9 x 0 = 0). 3.1 Introduction (5 minutes)
Teacher Activity: Begin by reviewing skip counting (e.g., count by 2s, 5s, 10s). Ask learners to define repeated addition. Connect repeated addition to multiplication (e.g., "If we add 3 to itself 4 times, that's 3 + 3 + 3 + 3, which is also 4 times 3"). Introduce the 'x' symbol.
Student Activity: Learners participate in skip counting drills and orally define repeated addition. 3.2 Activity 1: Mastering Multiplication Facts (1x1 to 9x9) (15 minutes)
Teacher Activity: Display a large multiplication chart or use flashcards for quick recall. Lead a chant or song for specific multiplication tables (e.g., "Two times one is two, two times two is four..."). Conduct a quick "quiz" where the teacher calls out a multiplication fact (e.g., "6 x 7") and learners shout out the answer. Use physical objects (e.g., bottle caps, stones, beans) to demonstrate multiplication as groups of items. For example, "Show me 3 groups of 5 bottle caps." Student Activity: Learners recite multiplication tables collectively. Learners practice with flashcards in pairs, quizzing each other. Learners use physical counters to model multiplication facts. 3.3 Activity 2: Multiplying 2-Digit Numbers by 1-Digit Numbers (20 minutes)
Teacher Activity: Demonstrate the vertical multiplication method on the chalkboard using clear step-by-step instructions, first without carrying, then with carrying. Emphasize place value alignment. Use concrete materials like base-ten blocks (or drawings of them) to illustrate the concept of multiplying tens and ones. For example, to multiply 13 x 2, show 1 ten block and 3 unit blocks, then duplicate them to show two sets. Provide examples relevant to Nigerian daily life (e.g., "A sachet of water costs N
2
0. How much do 4 sachets cost?"). Guide learners through examples on their individual whiteboards or slates.
Student Activity: Learners observe the teacher's demonstration. Learners practice solving problems on their slates/notebooks, guided by the teacher. Learners can use drawn base-ten representations to solve simpler problems. Volunteer learners solve problems on the chalkboard for peer review. 3.4 Activity 3: Multiplying Three 1-Digit Numbers (15 minutes)
Teacher Activity: Explain the concept of multiplying three numbers by taking two at a time. Write examples like 2 x 3 x 4 on the board. Demonstrate both grouping methods (e.g., (2x3)x4 and 2x(3x4)) to show that the answer remains the same.
Use a real-life scenario: "Imagine you have 3 rows of 2 mangoes, and you have 4 such arrangements. How many mangoes altogether?" Provide additional practice questions on the board.
Student Activity: Learners observe and follow along as the teacher demonstrates. Learners practice solving similar problems in their notebooks. Learners explain in their own words why the order of grouping doesn't change the product. 3.5 Activity 4: Everyday Activities (10 minutes)
Teacher Activity: Present simple word problems based on Nigerian contexts that require multiplication (e.g., "A farmer planted 5 rows of maize, with 9 maize plants in each row. How many maize plants did he plant in total?"). Encourage learners to identify the multiplication operation required.
Student Activity: Learners solve the word problems presented by the teacher. Learners share their answers and methods with the class. Learners brainstorm other real-life scenarios where multiplication is used in their community. The teacher should guide learners through these questions, providing immediate feedback and clarification.
Question: Multiply 7 x
9. Solution: 7 x 9 = 63
Commentary: This targets the recall of basic multiplication facts (Performance Objective 1). Learners should aim for quick recall.
Question: Calculate 14 x 5 using the vertical method.
Solution: ``` 14 x 5 20 (5 x 4 =
2
0. Write 0, carry 2.) 50 (5 x 1 =
5. Add carried 2: 5+2 =
7. Write 7 in tens place) 70 ``` Step-by-step: Multiply 5 x 4 (ones digit) =
2
0. Write down 0, carry over 2 to the tens column. Multiply 5 x 1 (tens digit) =
5. Add the carried over 2: 5 + 2 =
7. Write down
7. The product is
7
0. Commentary: This assesses the ability to multiply a 2-digit by a 1-digit number with carrying, demonstrating proper column alignment and carrying over (Performance Objective 2). This could represent the cost of 5 sachets of pure water at N14 each.
Question: There are 6 children in a small group. Each child has 3 pencils, and each pencil costs N
1
0. How much did all the pencils for one child cost?
Solution: This question requires multiplying two 1-digit numbers to find the cost per child. Cost per child = Number of pencils x Cost per pencil Cost per child = 3 x N10 = N
3
0. Commentary: This is a simple word problem targeting the application of 1-digit multiplication in a real-life context (Performance Objective 4).
Question: Multiply 2 x 4 x
5. Solution: Method 1: (2 x 4) x 5 = 8 x 5 = 40 Method 2: 2 x (4 x 5) = 2 x 20 = 40
Commentary: This question assesses the multiplication of three 1-digit numbers, emphasizing the 'taking two at a time' approach (Performance Objective 3).
Question: A local bakery bakes 24 loaves of bread every hour. How many loaves will it bake in 3 hours?
Solution: Number of loaves = 24 x 3 ``` 24 x 3 2 (3 x 4 =
1
2. Write 2, carry 1.) 7 (3 x 2 =
6. Add carried 1: 6+1 = 7.) 72 ``` The bakery will bake 72 loaves in 3 hours.
Commentary: This integrates 2-digit by 1-digit multiplication into a practical scenario, demonstrating its use in everyday activities (Performance Objective 4).
Multiplication is a cornerstone of daily numerical reasoning in Nigeria.
Market Transactions and Budgeting: Learners can apply multiplication to calculate the total cost of multiple identical items. For instance, if a learner is sent to buy 3 sachets of seasoning at N80 each, they multiply 3 x N80 to get N
2
4
0. Or calculating how many oranges a hawker has if they packed 7 rows of 5 oranges each.
Counting and Inventory: In homes or small businesses, multiplication helps count items efficiently. For example, if a shopkeeper arranges mineral drinks in 4 rows with 6 bottles in each row, they can quickly determine there are 4 x 6 = 24 bottles. Similarly, counting kola nuts or garden eggs bought in groups.
Time and Quantity Management: Multiplication helps in scheduling and calculating quantities over time. If a child spends 2 hours reading every day for 5 days, they can use multiplication (2 x 5 = 10 hours) to find the total reading time for the week.