Approximation and Estimation Basic 6 Mathematics Lesson Note

What is Approximation?

Approximation means finding a value that is close to the exact answer but easier to work with. We use approximation to make quick calculations and check if our answers are reasonable.

What is Estimation?

Estimation is making a sensible guess about the size, amount, or value of something without calculating the exact answer.

1. Approximation of Whole Numbers

Rounding to Nearest 10

Rule: Look at the units digit

• If 5 or more, round up
• If less than 5, round down

Examples:

• 27 → 30 (7 ≥ 5, round up)
• 43 → 40 (3 < 5, round down)
• 65 → 70 (5 = 5, round up)

Rounding to Nearest 100

Rule: Look at the tens digit

Examples:

• 156 → 200 (5 ≥ 5, round up)
• 234 → 200 (3 < 5, round down)
• 289 → 300 (8 ≥ 5, round up)

Rounding to Nearest 1000

Rule: Look at the hundreds digit

Examples:

• 2,567 → 3,000 (5 ≥ 5, round up)
• 4,234 → 4,000 (2 < 5, round down)
• 8,750 → 9,000 (7 ≥ 5, round up)

Exercise A – Rounding Whole Numbers

Round to the nearest 10:

1. 34 → ______
2. 67 → ______
3. 125 → ______
4. 89 → ______
5. 156 → ______

Round to the nearest 100:

1. 267 → ______
2. 834 → ______
3. 450 → ______
4. 1,678 → ______
5. 2,349 → ______

Round to the nearest 1000:

1. 3,456 → ______
2. 7,890 → ______
3. 12,567 → ______
4. 25,234 → ______
5. 48,750 → ______

1. Approximation of Decimal Numbers

Rounding to Nearest Whole Number

Rule: Look at the first decimal place (tenths)

Examples:

• 4.7 → 5 (7 ≥ 5, round up)
• 8.3 → 8 (3 < 5, round down)
• 12.5 → 13 (5 = 5, round up)

Rounding to 1 Decimal Place

Rule: Look at the second decimal place (hundredths)

Examples:

• 3.46 → 3.5 (6 ≥ 5, round up)
• 7.23 → 7.2 (3 < 5, round down)
• 9.85 → 9.9 (5 = 5, round up)

Rounding to 2 Decimal Places

Rule: Look at the third decimal place (thousandths)

Examples:

• 5.678 → 5.68 (8 ≥ 5, round up)
• 2.453 → 2.45 (3 < 5, round down)
• 8.235 → 8.24 (5 = 5, round up)

Exercise B – Rounding Decimal Numbers

Round to the nearest whole number:

1. 6.8 → ______
2. 12.3 → ______
3. 9.5 → ______
4. 15.7 → ______
5. 23.2 → ______

Round to 1 decimal place:

1. 4.67 → ______
2. 8.34 → ______
3. 12.85 → ______
4. 6.92 → ______
5. 18.46 → ______

Round to 2 decimal places:

1. 7.456 → ______
2. 3.789 → ______
3. 15.234 → ______
4. 9.675 → ______
5. 11.928 → ______

Estimation in Calculations

Addition Estimation

Example: 267 + 189 + 345 Estimate: 300 + 200 + 300 = 800 Exact: 801

Subtraction Estimation

Example: 856 – 234 Estimate: 900 – 200 = 700 Exact: 622

Multiplication Estimation

Example: 23 × 47 Estimate: 20 × 50 = 1,000 Exact: 1,081

Division Estimation

Example: 789 ÷ 19 Estimate: 800 ÷ 20 = 40 Exact: 41.5

Exercise C – Estimation Practice

Estimate first, then calculate exactly:

1. 234 + 567 Estimate: ______ Exact: ______
2. 789 – 345 Estimate: ______ Exact: ______
3. 34 × 28 Estimate: ______ Exact: ______
4. 645 ÷ 21 Estimate: ______ Exact: ______
5. 156 + 289 + 367 Estimate: ______ Exact: ______

Exercise D – Decimal Estimation

Estimate these decimal calculations:

1. 12.7 + 8.9 Estimate: ______ Exact: ______
2. 25.6 – 8.4 Estimate: ______ Exact: ______
3. 7.8 × 4.2 Estimate: ______ Exact: ______
4. 56.8 ÷ 7.9 Estimate: ______ Exact: ______
5. 23.4 + 16.8 – 9.7 Estimate: ______ Exact: ______

iii. Quantitative Reasoning

Estimation in Real Life

Money Estimation

Example: Shopping Bill

• Item 1: ₦1,890 ≈ ₦2,000
• Item 2: ₦3,450 ≈ ₦3,500
• Item 3: ₦780 ≈ ₦800 Estimated Total: ₦6,300

Time Estimation

Example: Journey Time

• Distance: 387 km ≈ 400 km
• Speed: 58 km/h ≈ 60 km/h Estimated Time: 400 ÷ 60 ≈ 7 hours

Exercise E – Money Problems

Estimate the total cost:

1. Market Shopping:
   1. Rice: ₦2,340
   2. Oil: ₦1,870
   3. Fish: ₦3,560
2. Estimated Total: ₦______
3. School Supplies:
   1. Books: ₦4,890
   2. Uniform: ₦6,750
   3. Shoes: ₦3,290
4. Estimated Total: ₦______
5. Family Budget:
   1. Rent: ₦45,600
   2. Food: ₦28,900
   3. Transport: ₦12,450
6. Estimated Total: ₦______

Exercise F – Measurement Estimation

Solve these estimation problems:

1. Classroom Size: A classroom is 8.7m long and 6.3m wide. Estimate the area. Estimate: ______ square meters
2. Journey Distance: Three towns are 67km, 89km, and 124km apart. Estimate the total distance traveling through all three. Estimate: ______ km
3. Water Usage: A family uses 347 liters on Monday, 289 liters on Tuesday, and 456 liters on Wednesday. Estimate their total usage. Estimate: ______ liters

Exercise G – Population and Large Numbers

Estimate these calculations:

1. School Population: Primary section: 1,234 students Secondary section: 1,789 students Estimated Total: ______
2. City Growth: Lagos had 12,550,000 people in 2015. If it grows by 2,340,000, estimate the new population. Estimate: ______
3. Production: A factory produces 4,567 items per day. Estimate production for 30 days. Estimate: ______

Exercise H – Reasonableness Check

Check if these answers are reasonable using estimation:

1. Problem: 789 + 567 = 1,356 Estimate Check: ______ Reasonable? Yes/No
2. Problem: 45 × 23 = 1,035 Estimate Check: ______ Reasonable? Yes/No
3. Problem: 1,200 ÷ 25 = 48 Estimate Check: ______ Reasonable? Yes/No
4. Problem: 67.8 – 23.4 = 44.4 Estimate Check: ______ Reasonable? Yes/No

Answer Key

Exercise A: 1-5: 30, 70, 130, 90, 160 6-10: 300, 800, 500, 1,700, 2,300 11-15: 3,000, 8,000, 13,000, 25,000, 49,000

Exercise B: 1-5: 7, 12, 10, 16, 23 6-10: 4.7, 8.3, 12.9, 6.9, 18.5 11-15: 7.46, 3.79, 15.23, 9.68, 11.93

Exercise C:

1. Est: 800, Exact: 801
2. Est: 450, Exact: 444
3. Est: 900, Exact: 952
4. Est: 30, Exact: 30.7
5. Est: 800, Exact: 812

Exercise D:

1. Est: 22, Exact: 21.6
2. Est: 17, Exact: 17.2
3. Est: 32, Exact: 32.76
4. Est: 7, Exact: 7.19
5. Est: 30, Exact: 30.5

Exercise E:

1. ₦8,000
2. ₦15,000
3. ₦87,000

Exercise F:

1. 54 square meters
2. 280 km
3. 1,100 liters

Exercise G:

1. 3,000
2. 15,000,000
3. 135,000

Exercise H:

1. 1,400, Yes
2. 900, Yes
3. 50, Yes
4. 44, Yes