Year 4 Maths: Estimating and Approximating

Introduction to Estimating and Approximating

Hello, Year 4! Today, we are going to learn about estimating and approximating. These are important skills that help us to quickly find out about numbers without having to do all the hard calculations. Let’s break it down!

What is Estimating?

Estimating means making a good guess about a number. It helps us to understand how big or small a number is without calculating the exact answer.

Example:

If you want to buy 3 packets of sweets that cost £2.50 each, you can estimate the total cost by rounding £2.50 to £3. That makes it easier to say, “Oh, I will need about £9 for the sweets!”

What is Approximating?

Approximating is similar to estimating. It means we find a number that is close to the exact number. We often round numbers to make them easier to work with.

Example:

If you have 47 apples and you want to know how many apples you have without counting each one, you can approximate by rounding 47 to 50.

Key Rules for Estimating and Approximating

1. Rounding Numbers:
   • If a number is 5 or more, round up.
   • If a number is less than 5, round down.
   For example:
   • 34 rounds to 30 (down)
   • 38 rounds to 40 (up)
2. Use Friendly Numbers:
   • Friendly numbers are easier to add, subtract, multiply, or divide.
   • For example, instead of 29 + 34, you can estimate using 30 + 30 = 60.
3. Check Your Work:
   • After estimating, you can do a quick check with the actual numbers to see if your estimate was close.

Tips and Tricks

• Look for Patterns:Sometimes you can find patterns in numbers that help with estimating.
• Use Benchmarks:Knowing common numbers can help. For example, you know that 50 is halfway between 0 and 100, so use it as a guide.
• Practice with Real-Life Examples:Look at prices in shops or distances on maps, and try to estimate the totals or how far things are.

Practice Questions

Easy Level Questions

1. Estimate the sum: 23 + 18
2. Round 75 to the nearest ten.
3. What is 4.7 rounded to the nearest whole number?
4. Estimate the product: 6 × 7
5. Round 52 to the nearest ten.
6. Estimate how many sweets are in 15 packets if each packet has about 6 sweets.
7. What is 24 rounded to the nearest ten?
8. Estimate the sum: 45 + 29
9. Round 89 to the nearest ten.
10. What is 9.2 rounded to the nearest whole number?
11. Estimate the difference: 100 – 34
12. Round 64 to the nearest ten.
13. How many people are at a party if there are 23 adults and 19 children? Estimate.
14. What is 3.8 rounded to the nearest whole number?
15. Estimate the sum: 18 + 32
16. Round 91 to the nearest ten.
17. Estimate how many balloons are in 9 bags with 4 balloons each.
18. What is 2.5 rounded to the nearest whole number?
19. Estimate the total cost if 5 books cost £7.50 each.
20. Round 47 to the nearest ten.

Medium Level Questions

1. Estimate the sum: 76 + 34
2. Round 145 to the nearest hundred.
3. What is 6.8 rounded to the nearest whole number?
4. Estimate the product: 9 × 5
5. Round 157 to the nearest ten.
6. Estimate how many biscuits are in 12 boxes if each box has about 8 biscuits.
7. What is 93 rounded to the nearest ten?
8. Estimate the sum: 58 + 29
9. Round 234 to the nearest hundred.
10. What is 4.6 rounded to the nearest whole number?
11. Estimate the difference: 200 – 86
12. Round 162 to the nearest ten.
13. How many apples are in a basket with 32 red apples and 27 green apples? Estimate.
14. What is 7.3 rounded to the nearest whole number?
15. Estimate the sum: 45 + 56
16. Round 198 to the nearest hundred.
17. Estimate how many pencils are in 10 packs with 6 pencils each.
18. What is 5.5 rounded to the nearest whole number?
19. Estimate the total cost if 4 shirts cost £12.99 each.
20. Round 65 to the nearest ten.

Hard Level Questions

1. Estimate the sum: 189 + 276
2. Round 345 to the nearest hundred.
3. What is 12.6 rounded to the nearest whole number?
4. Estimate the product: 13 × 8
5. Round 499 to the nearest hundred.
6. Estimate how many toys are in 15 boxes if each box has about 9 toys.
7. What is 245 rounded to the nearest ten?
8. Estimate the sum: 112 + 89
9. Round 378 to the nearest hundred.
10. What is 8.7 rounded to the nearest whole number?
11. Estimate the difference: 500 – 236
12. Round 421 to the nearest ten.
13. How many books are on a shelf if there are 54 mystery books and 49 adventure books? Estimate.
14. What is 9.4 rounded to the nearest whole number?
15. Estimate the sum: 129 + 276
16. Round 672 to the nearest hundred.
17. Estimate how many marbles are in 20 bags with 5 marbles each.
18. What is 6.7 rounded to the nearest whole number?
19. Estimate the total cost if 6 games cost £19.99 each.
20. Round 839 to the nearest ten.

Answers and Explanations

Easy Level Answers

1. 40 (Estimate: 20 + 20)
2. 80
3. 5
4. 42 (Estimate: 6 × 7 = 42)
5. 50
6. 90 (Estimate: 15 × 6 = 90)
7. 20
8. 70 (Estimate: 40 + 30)
9. 90
10. 9
11. 100 (Estimate: 100 – 30 = 70)
12. 60
13. 40 (Estimate: 20 + 20)
14. 3
15. 50 (Estimate: 20 + 30)
16. 90
17. 60 (Estimate: 10 × 6 = 60)
18. 3
19. £70 (Estimate: 5 × 8 = £40)
20. 50

Medium Level Answers

1. 110 (Estimate: 80 + 30)
2. 100
3. 7
4. 45 (Estimate: 10 × 5)
5. 160
6. 96 (Estimate: 12 × 8 = 96)
7. 90
8. 80 (Estimate: 60 + 20)
9. 200
10. 5
11. 200 (Estimate: 200 – 80 = 120)
12. 160
13. 60 (Estimate: 30 + 30)
14. 7
15. 100 (Estimate: 40 + 60)
16. 200
17. 120 (Estimate: 20 × 6 = 120)
18. 6
19. £50 (Estimate: 4 × 10 = £40)
20. 70

Hard Level Answers

1. 460 (Estimate: 200 + 300)
2. 300
3. 13
4. 100 (Estimate: 10 × 10)
5. 500
6. 135 (Estimate: 15 × 9 = 135)
7. 240
8. 200 (Estimate: 100 + 100)
9. 400
10. 9
11. 300 (Estimate: 500 – 200)
12. 420
13. 100 (Estimate: 50 + 50)
14. 9
15. 400 (Estimate: 100 + 300)
16. 700
17. 100 (Estimate: 20 × 5 = 100)
18. 7
19. £120 (Estimate: 6 × 20 = £120)
20. 840

Now that you have learned about estimating and approximating, try to use these skills in your everyday life! Happy estimating!