Estimation : Round up of numbers (Addition and Subtraction)

SECOND TERM E NOTES FOR PRIMARY 4 MATHEMATICS

SUBJECT: MATHEMATICS

CLASS: BASIC FOUR / / PRIMARY 4

WEEK 6

TOPICS : Estimation : Round up of numbers (Addition and Subtraction) 

Importance :

• It is used in budget
  writing.
• To estimate the total cost
  of items at a
  departmental store

Learning Objectives

Pupils should be able to:

• identify actual numbers.
• solve round-up numbers.
• calculate addition and
  subtraction of round-up of
  numbers.
• interpret and solve real life
  problems on estimation.
• solve quantitative
  reasoning.

Learning Activities

• Pupils in a group fill an empty jar with pebbles,
• count the number of pebbles that will fill the jar.
• Then estimate the number.
• Pupils use a ruler and cardboard to prepare scale chart for estimation.

Embedded Core Skills 

• Critical thinking and problem solving skills
• Communication and Collaboration
• Leadership skills and Personal Development
• Creativity and Imagination

Audio Resources

• Empty jar
• Pebbles
• Hands

Content

Estimation is a way to make a guess about a number that is close to the actual answer. It can help you do math problems faster, and it can also help you check if your answer is reasonable.

One way to estimate is to round numbers up or down. When you round a number, you change it to the nearest multiple of 10, 100, 1000, and so on. Here are some examples:

1. Rounding up for addition: Suppose you want to add 46 and 22. To estimate the answer, you can round up both numbers to the nearest ten, which would be 50 and 20. Then you can add these rounded numbers together: 50 + 20 = 70. This is an estimate of the answer. The actual answer is 68, so your estimate is a little bit higher.
2. Rounding up for subtraction: Suppose you want to subtract 28 from 49. To estimate the answer, you can round up both numbers to the nearest ten, which would be 30 and 50. Then you can subtract the rounded numbers: 50 – 30 = 20. This is an estimate of the answer. The actual answer is 21, so your estimate is a little bit lower.

Remember, estimation is not always exact, but it can help you get a sense of what the answer should be.

To use empty jars and pebbles for estimation, you can follow these steps:

1. Start by pouring some pebbles into an empty jar. Count how many pebbles there are and record this number.
2. For example, if you count 32 pebbles, you can round this number to the nearest ten by rounding up to 40.
3. Now take another jar with some pebbles, let’s say you count 17 pebbles. You can round this number to the nearest ten by rounding down to 10.
4. Add the rounded numbers together: 40 + 10 = 50. This is an estimate of the answer.
5. If you want to check your answer, you can count the pebbles in both jars and add them together. The actual answer may be different, but you can see how close your estimate was.

To use your hands for estimation, you can follow these steps:

1. Hold up both of your hands and count how many fingers you have in total.
2. For example, if you count 8 fingers on one hand and 7 fingers on the other hand, you can round this number to the nearest ten by rounding up to 20.
3. Now suppose you want to subtract 4 from this rounded number. You can estimate the answer by rounding 4 down to 0, and subtracting from the rounded number: 20 – 0 = 20.
4. This is an estimate of the answer. If you want to check your answer, you can count your fingers and subtract 4 from the actual number. The actual answer may be different, but you can see how close your estimate was.

Remember, estimation is not always exact, but it can help you get a sense of what the answer should be. Using jars, pebbles, and your hands can make estimation more fun and interactive!

ESTIMATION

Rules for rounding off decimals to the nearest whole number

When the rounding off decimals to the nearest whole number, look at the digit in the tenths place.

1. If this digit is 5 or greater than 5, replace the digits after the decimal point by zero and add 1 to the digit in the units place
2. If this digit is less than 5, replace the digits after the decimal point by zero.

Note: ‘≈’ means ‘is approximately equal to’

ROUNDING WHOLE NUMBERS

Consider these numbers:

10 20 30 40 50 60 70 80 90

Each of these numbers are multiples of 10 and each number has zero in its unit place. These numbers (i.e. multiples of 10) are round numbers.

Consider these numbers:

11 12 13 14 15 16 17 18 19 21 24 25 etc

These numbers are called non-rounded because the digits in the unit place is greater than zero.

Non-rounded numbers can be replaced by the nearest multiples of 10, 100. This is called rounding.

We can use the number line to round numbers to the nearest 10 and 100. We can also round without using the number line.

Rounding to the nearest 10

Examples

Round to the nearest 10.

1. 46 2. 22

Rounding decimals to nearest whole numbers

Decimals can also be rounded to the nearest whole numbers with and without using a number line.

Examples

Example: round off the following decimal numbers to the nearest whole numbers.

6.7 ≈ 7 to the nearest whole number

6.3 ≈ 6 to the nearest whole number

17 ≈20 to the nearest ten

EXERCISE 1.

Write to the nearest whole number

1. 4.7
2. 1.1
3. 7.9
4. 8.6
5. 0.9
6. 13.2

Evaluation

1. What is the rounded-up estimate of 53 + 27? (a) 60 (b) 70 (c) 80 (d) 90
2. What is the rounded-up estimate of 198 + 74? (a) 260 (b) 270 (c) 280 (d) 290
3. What is the rounded-down estimate of 492 – 223? (a) 200 (b) 250 (c) 270 (d) 300
4. What is the rounded-down estimate of 837 – 453? (a) 300 (b) 350 (c) 380 (d) 400
5. What is the rounded-up estimate of 99 + 28? (a) 110 (b) 120 (c) 130 (d) 140
6. What is the rounded-up estimate of 67 + 44? (a) 100 (b) 110 (c) 120 (d) 130
7. What is the rounded-down estimate of 745 – 568? (a) 100 (b) 150 (c) 170 (d) 200
8. What is the rounded-down estimate of 933 – 671? (a) 200 (b) 250 (c) 260 (d) 300
9. What is the rounded-up estimate of 348 + 198? (a) 500 (b) 540 (c) 580 (d) 620
10. What is the rounded-down estimate of 576 – 238? (a) 200 (b) 250 (c) 270 (d) 300

Lesson Presentation

Introduction:

• Begin by asking students if they’ve ever had to make a guess about how many objects are in a jar or container.
• Explain that today, we’ll be learning about a way to make educated guesses, or estimates, when we do math problems.
• Define estimation as making a guess about a number that is close to the actual answer.
• Explain that we’ll be focusing on rounding up numbers to the nearest ten to make estimation easier.

Body:

• Write the numbers 27 and 44 on the whiteboard.
• Ask students to round each number to the nearest ten and record their answers.
• Check student answers and review the process of rounding up to the nearest ten.
• Write the problem 27 + 44 on the whiteboard.
• Ask students to estimate the answer by rounding up each number to the nearest ten and adding.
• Model how to solve the problem using this method.
• Repeat the process with subtraction problems, using the same numbers.
• Explain that we can also use empty jars and pebbles to estimate addition and subtraction problems.
• Demonstrate how to use pebbles to round up and add or subtract numbers.
• Ask students to try it on their own, using the empty jars and pebbles.
• Explain that we can also use our hands to estimate addition and subtraction problems.
• Model how to use hands to round up and add or subtract numbers.
• Ask students to try it on their own, using their hands.

Conclusion:

• Review the steps for rounding up to the nearest ten and using this skill to estimate addition and subtraction problems.
• Ask students to share any questions they have or examples of how they might use this skill in everyday life.
• Summarize the importance of estimation as a way to make math problems easier and more manageable.

Assessment:

• Students will be assessed on their ability to round up numbers to the nearest ten and use this skill to estimate addition and subtraction problems, through class participation and independent practice

Weekly Assessment /Test

1. Rounding a number means changing it to the nearest __________.
2. To round up to the nearest ten, we look at the __________ digit in the number.
3. The rounded-up estimate of 38 + 27 is __________.
4. The rounded-down estimate of 379 – 228 is __________.
5. To use empty jars and pebbles for estimation, we count the number of __________ in each jar.
6. The rounded-up estimate of 64 + 28 is __________.
7. The rounded-down estimate of 931 – 689 is __________.
8. To use your hands for estimation, you count the number of __________ on each hand.
9. The rounded-up estimate of 87 + 36 is __________.
10. The rounded-down estimate of 652 – 447 is __________.