Lesson Notes By Weeks and Term v3 - Primary 4
Weight
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Weight
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Subject: General Mathematics
Class: Primary 4
Term: 3rd Term
Week: 5
Theme: Mensuration And Geometry
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Watch on YouTubeSee Facebook postcompute addition and subtraction of weights using Kg and g multiply and divide weight by whole numbers
A. Understanding Weight and Units: Weight: The measure of how heavy an object is. The standard unit of weight in the metric system is the kilogram (Kg).
Units of Weight: Kilogram (Kg): Used for heavier items like bags of rice, sacks of cement, or human body weight.
Gram (g): Used for lighter items like spices, medicines, or small quantities of ingredients.
Relationship between Units: 1 Kilogram (Kg) = 1000 Grams (g). This conversion factor is crucial for all operations involving mixed units. To convert Kg to g, multiply by 1000 (e.g., 2 Kg = 2 x 1000 g = 2000 g). To convert g to Kg, divide by 1000 (e.g., 3500 g = 3500 ÷ 1000 Kg = 3.5 Kg or 3 Kg 500 g).
B. Addition of Weights (Kg and g): Principle: Add grams to grams and kilograms to kilograms, similar to adding whole numbers, but with a crucial step of converting grams to kilograms when the sum of grams exceeds 999g.
Procedure:
1. Arrange the weights in two columns: one for kilograms (Kg) and one for grams (g).
2. Add the numbers in the grams column first.
3. If the sum of grams is 1000g or more, convert it to kilograms and grams (e.g., 1250g = 1 Kg 250g).
4. Write down the remaining grams in the grams column.
5. Carry over the kilograms obtained from the grams conversion to the kilograms column.
6. Add the numbers in the kilograms column, including any carried-over kilograms.
Worked Example 1 (Addition): A farmer bought 2 bags of fertilizer. One bag weighed 25 Kg 750 g and the other weighed 30 Kg 600 g. What is the total weight of the fertilizer?
Solution: ``` Kg g 25 750 + 30 600 ---------- ``` Step 1: Add the grams. 750 g + 600 g = 1350 g Step 2: Convert grams to kilograms. 1350 g = 1000 g + 350 g = 1 Kg 350 g Step 3: Write down the remaining grams and carry over kilograms. Write 350 g in the grams column. Carry over 1 Kg to the kilograms column.
Step 4: Add the kilograms. 25 Kg + 30 Kg + 1 Kg (carried over) = 56 Kg ``` Kg g 25 750 + 30 600 ---------- 56 350 ``` Answer: The total weight of the fertilizer is 56 Kg 350 g.
C. Subtraction of Weights (Kg and g): Principle: Subtract grams from grams and kilograms from kilograms. If the grams in the subtrahend are larger than the grams in the minuend, 'borrow' 1 Kg (which is 1000 g) from the kilograms column.
Procedure:
1. Arrange the weights in two columns: Kg and g.
2. Subtract the numbers in the grams column first.
3. If the number of grams to be subtracted is larger than the available grams, borrow 1 Kg from the kilograms column. Convert the borrowed 1 Kg to 1000 g and add it to the grams in the minuend.
4. Subtract the grams.
5. Subtract the numbers in the kilograms column, remembering to account for any borrowed kilograms.
Worked Example 2 (Subtraction): A trader had 15 Kg 200 g of rice. She sold 8 Kg 650 g. How much rice is left?
Solution: ``` Kg g 15 200 - 8 650 ---------- ``` Step 1: Look at the grams column. 200 g is less than 650 g. So, we need to borrow.
Step 2: Borrow from the kilograms column. Borrow 1 Kg from 15 Kg, leaving 14 Kg. Convert the borrowed 1 Kg to 1000 g.
Add the 1000 g to the existing 200 g: 1000 g + 200 g = 1200 g.
Step 3: Subtract the grams. 1200 g - 650 g = 550 g.
Step 4: Subtract the kilograms. 14 Kg (after borrowing) - 8 Kg = 6 Kg. ``` Kg g 14 1200 (after borrowing 1 Kg=1000g) 15 200 - 8 650 ---------- 6 550 ``` Answer: 6 Kg 550 g of rice is left.
D. Multiplication of Weights by Whole Numbers: * Principle: Kg. Convert the borrowed 1 Kg to 1000 g.
Add the 1000 g to the existing 200 g: 1000 g + 200 g = 1200 g.
Step 3: Subtract the grams. 1200 g - 650 g = 550 g.
Step 4: Subtract the kilograms. 14 Kg (after borrowing) - 8 Kg = 6 Kg. ``` Kg g 14 1200 (after borrowing 1 Kg=1000g) 15 200 - 8 650 ---------- 6 550 ``` Answer: 6 Kg 550 g of rice is left.
D. Multiplication of Weights by Whole Numbers: Principle: Multiply the grams by the whole number, then multiply the kilograms by the whole number. Convert any excess grams to kilograms and add to the kilograms product.
Procedure:
1. Multiply the grams by the given whole number.
2. If the product of grams is 1000g or more, convert it to kilograms and grams.
3. Write down the remaining grams and carry over the kilograms.
4. Multiply the kilograms by the given whole number.
5. Add any carried-over kilograms to the product of kilograms.
Worked Example 3 (Multiplication): A baker needs 1 Kg 300 g of sugar for one cake. How much sugar is needed for 4 such cakes?
Solution: ``` Kg g 1 300 x 4 ---------- ``` Step 1: Multiply the grams. 300 g x 4 = 1200 g Step 2: Convert grams to kilograms. 1200 g = 1 Kg 200 g Step 3: Write down the remaining grams and carry over kilograms. Write 200 g in the grams column. Carry over 1 Kg to the kilograms column.
Step 4: Multiply the kilograms. 1 Kg x 4 = 4 Kg Step 5: Add the carried-over kilograms. 4 Kg + 1 Kg (carried over) = 5 Kg ``` Kg g 1 300 x 4 ---------- 5 200 ``` Answer: 5 Kg 200 g of sugar is needed.
E. Division of Weights by Whole Numbers: Principle: Divide the kilograms first. Convert any remainder kilograms to grams and add them to the existing grams. Then divide the total grams by the whole number.
Procedure:
1. Divide the kilograms by the given whole number.
2. If there is a remainder in kilograms, convert this remainder to grams (multiply by 1000) and add it to the existing grams.
3. Divide the total grams (original grams + converted remainder grams) by the given whole number.
Worked Example 4 (Division): A bag of beans weighing 9 Kg 600 g is to be shared equally among 3 families. How much beans will each family get?
Solution: ``` Kg g 9 600 ÷ 3 ---------- ``` Step 1: Divide the kilograms. 9 Kg ÷ 3 = 3 Kg. (No remainder). Write 3 Kg in the kilograms column.
Step 2: Divide the grams. 600 g ÷ 3 = 200 g. Write 200 g in the grams column. ``` Kg g 3 200 ---------- 3 | 9 600 -9 --- 0 6 -6 --- 00 ``` Answer: Each family will get 3 Kg 200 g of beans. Worked Example 5 (Division with Remainder in Kg): A large sack of garri weighing 7 Kg 500 g is to be packed into 2 smaller bags equally. What is the weight of garri in each bag?
Solution: ``` Kg g 7 500 ÷ 2 ---------- ``` Step 1: Divide the kilograms. 7 Kg ÷ 2 = 3 Kg with a remainder of 1 Kg. Write 3 Kg in the kilograms column.
Step 2: Convert the remainder Kg to grams and add to existing grams. Remainder 1 Kg = 1000 g.
Add to existing grams: 1000 g + 500 g = 1500 g. * Step 3: Divide the total grams. 1500 g ÷ 2 = 750 g. Write 750 g in the grams column. ``` Kg g 3 750 ---------- 2 | 7 500 -6 --- 1 Kg (remainder) -> 1000g + 500g = 1500g -14 ---- 10 -10 ---- 0 ``` Answer: Each bag will contain 3 Kg 750 g of garri.
Teacher Activities: Introduction and Review: Begin by asking students about their experiences with measuring weight in daily life (e.g., "Who has been to the market with their parents? What kind of things do they buy by weight?"). Review the concept of weight and the units Kg and g, and their relationship (1 Kg = 1000 g). Use visual aids like an actual weighing scale, a 1 Kg bag of sugar/rice, and perhaps smaller items to represent grams. Demonstrate conversion between Kg and g (e.g., "If I have 2.5 Kg of salt, how many grams is that?"). Explicit Instruction (Addition & Subtraction): Present the procedures for addition and subtraction of weights, emphasizing the column arrangement and the conversion/borrowing steps. Work through the provided examples (or similar Nigerian-context examples) step-by-step on the board, explaining each stage clearly. Encourage student participation by asking questions at each step. Explicit Instruction (Multiplication & Division): Present the procedures for multiplication and division of weights, again emphasizing the column arrangement, unit conversion, and carrying/remainder handling. Work through the provided examples (or similar Nigerian-context examples) step-by-step on the board. Highlight common errors, especially in carrying over Kg from grams in multiplication, and handling remainder Kg in division. Demonstration with Physical Objects (if available): If a simple kitchen or bathroom scale is available, demonstrate measuring weights of various classroom objects (books, pencils, bags). This makes the concept tangible. If not, use hypothetical scenarios with realistic weights.
Guided Practice Facilitation: Provide guided practice questions (from section 4) for students to attempt in pairs or small groups. Circulate around the classroom, providing support, clarification, and immediate feedback. Review solutions as a class, addressing any misconceptions.
Student Activities: Participatory Discussions: Students actively respond to teacher's questions about weight, units, and real-life applications.
Unit Conversion Practice: Students practice converting grams to kilograms and vice-versa verbally and in their notebooks.
Collaborative Problem Solving: Students work in pairs or small groups to solve guided practice problems on addition, subtraction, multiplication, and division of weights.
Individual Practice: Students attempt independent practice questions from the board or worksheets.
Practical Estimation (Optional): Students estimate the weight of various objects and, if scales are available, compare their estimations with actual measurements.
Presentation of Solutions: Selected students present their solutions to the class, explaining their steps.
Question 1 (Addition): A caterer bought a bag of semovita weighing 10 Kg 850 g and another bag of flour weighing 12 Kg 500 g. What is the total weight of the grains bought?
Solution 1: ``` Kg g 10 850 + 12 500 ``` Step 1: Add the grams: 850 g + 500 g = 1350 g.
Step 2: Convert 1350 g to Kg and g: 1350 g = 1 Kg 350 g.
Step 3: Write 350 g in the grams column and carry over 1 Kg to the kilograms column.
Step 4: Add the kilograms: 10 Kg + 12 Kg + 1 Kg (carried over) = 23 Kg. ``` Kg g 10 850 + 12 500 23 350 ``` Answer: The total weight of the grains bought is 23 Kg 350 g.
Commentary: This question tests addition with regrouping, requiring students to convert excess grams to kilograms.
Question 2 (Subtraction): A container initially held 20 Kg 150 g of palm oil. If 13 Kg 700 g was used for cooking, how much palm oil is remaining in the container?
Solution 2: ``` Kg g 20 150 13 700 ``` Step 1: In the grams column, 150 g is less than 700 g. Borrow 1 Kg from the kilograms column.
Step 2: 20 Kg becomes 19 Kg. The borrowed 1 Kg becomes 1000 g.
Add this to 150 g: 1000 g + 150 g = 1150 g.
Step 3: Subtract the grams: 1150 g - 700 g = 450 g.
Step 4: Subtract the kilograms: 19 Kg - 13 Kg = 6 Kg. ``` Kg g 19 1150 (after borrowing) 20 150 13 700 6 450 ``` Answer: 6 Kg 450 g of palm oil is remaining.
Commentary: This question tests subtraction with borrowing from the kilogram column, a common point of difficulty.
Question 3 (Multiplication): A carpenter bought 5 planks of wood. Each plank weighed 3 Kg 250 g. What is the total weight of all the planks?
Solution 3: ``` Kg g 3 250 x 5 ``` Step 1: Multiply the grams: 250 g x 5 = 1250 g.
Step 2: Convert 1250 g to Kg and g: 1250 g = 1 Kg 250 g.
Step 3: Write 250 g in the grams column and carry over 1 Kg to the kilograms column.
Step 4: Multiply the kilograms: 3 Kg x 5 = 15 Kg.
Step 5: Add the carried-over Kg: 15 Kg + 1 Kg = 16 Kg. ``` Kg g 3 250 x 5 16 250 ``` Answer: The total weight of all the planks is 16 Kg 250 g.
Commentary: This question involves multiplying both units and requires conversion and carrying over kilograms.
Question 4 (Division): A total of 12 Kg 800 g of cassava flour is to be divided equally into 4 small bags. How much cassava flour will each bag contain?
Solution 4: ``` Kg g ? ? 4 | 12 800 ``` Step 1: Divide the kilograms: 12 Kg ÷ 4 = 3 Kg. (No remainder).
Step 2: Write 3 Kg in the kilograms column of the quotient.
Step 3: Divide the grams: 800 g ÷ 4 = 200 g.
Step 4: Write 200 g in the grams column of the quotient. ``` 3 Kg 200 g 4 | 12 Kg 800 g -12 Kg 0 Kg 800 g -800 g 0 g ``` Answer: Each bag will contain 3 Kg 200 g of cassava flour.
Commentary: This problem is a straightforward division where both Kg and g are perfectly divisible.
Market Transactions and Budgeting: Application: When parents or guardians go to the market (e.g., Balogun Market in Lagos or Onitsha Main Market), they often buy food items by weight. Students can apply these skills to help calculate the total weight of different items purchased (e.g., 2 Kg of rice, 500 g of beans, 1.5 Kg of garri). They can also estimate total weight for transport purposes (e.g., if a taxi has a weight limit).
Integration: Students can be given a hypothetical shopping list with weights and asked to calculate the total weight, or calculate how much more of an item they can buy within a certain weight limit. Cooking, Baking, and Food Preparation: Application: In Nigerian homes, recipes often involve specific weights of ingredients (flour for akara, sugar for kunu, ingredients for stews). Understanding operations with weight helps in scaling recipes up or down. For instance, if a recipe calls for 750 g of yam flour for 10 servings, and one needs to prepare for 30 servings, multiplication of weight is required.
Integration: Ask students to find a simple Nigerian recipe that uses weights and discuss how they would adjust the ingredients for a larger or smaller family.
Local Trade and Packaging: Application: Small-scale traders in Nigeria often repackage goods (e.g., sugar, rice, beans, detergents) from large sacks into smaller, more affordable quantities for sale. They need to calculate how many small bags can be obtained from a large sack (division) or the total weight of several small bags (multiplication).
Integration: Present a scenario where a trader buys a 50 Kg bag of rice and needs to package it into 2 Kg and 500 g portions. Students can calculate how many of each portion can be made, applying both division and conversion skills.