### ESTIMATION AND APPROXIMATION MATHEMATICS LESSON NOTE AND PLAN FOR BOTH PRIMARY AND SECONDARY SCHOOL

Monday
Understand estimation and approximation

Round whole numbers to the nearest ten
Resources
Inside out
mathematics Book 4, page  181 and 6 page 106
flashcards,  beads, jelly bean, glass jar,  currency note biscuits, books, pencils.

Introduction to estimation and approximation
Estimation is a way of saying a sum is nearly about a figure or find something close to the correct answer. If we write 99, we say that it is nearly or about 100. Another word for estimation is approximation.  this sign means “approximately equal to”.

When rounding numbers, do notice the following:
a. digits that are less than 5 are rounded down, I.e replaced by zero.
b. digits that are 5 or greater than 5 are rounded up. i.e 1 added to the original digit.

Rounding whole Numbers to the Nearest Ten
When rounding whole numbers to the nearest ten, simply round up or down the last whole number
Note
a. numbers like 20, 30,40,90, 100 200, 300, 800, 1000, 2000
b. numbers like 21, 22, 23, 24, are all rounded down to the nearest ten (20). Since they are nearer to 20 than 30.
c. numbers like 25, 26, 28, 29 are all rounded up to the nearest ten (30), since they are nearer to 30 than 20.

Examples
1. round 72 and 287 to the nearest ten:
Solution

a. 72 = 70 to nearest ten. (since the last digit is 2 and not up to 5, so it is rounded down)

b. 297  = 300 to the nearest ten. ( since 7 is the last digit and is greater than 4 so one is added to the previous number)
Begin the lesson by quickly showing them items like 20 books placed on top of the other. Then I ask each and pupil to make a rough guess or estimate of the number of books.
Pupils should be able to understand the concept of approximation and estimation. And they should be able to round off whole numbers to the nearest ten.

seat work: Inside out mathematics Book 4, page  182, exercise 21.1 (1 i – x)
Inside out
mathematics Book 4, page  182 , exercise 21.1 (2 - 3)

Tuesday
Round whole numbers to the nearest hundred.

Approximate whole numbers to the nearest thousand
Resources
Inside out
Learn
Mathematics, book 4 page 183 and  Book 6, page  107
flashcards,  beads, jelly bean, glass jar,  currency note biscuits, books, pencils.

Round whole numbers to the nearest hundred
When rounding whole numbers to the nearest hundred, you only need to round up or down the last but one digit. The answer should end with two zeros

Examples
1. express each of these numbers to the nearest hundreds:
i. 423              ii. 5468

solution
i. 423 = 400 to the nearest hundred (since digit 2 is rounded down)

ii. 5468 = 5500 to the nearest hundred (since digit 6 is rounded up)

rounding whole numbers to the nearest thousand

when rounding whole numbers to the nearest thousand, you should round up or down the third digit from the right (the number in the hundred’s place) the answer should end with three zeros)

Examples
1. approximate these numbers to the nearest thousand:
a. 2462                       b. 7972

Solution
a. 2462  = 2000 to the nearest thousand (it is rounded down since digit 4 is not up to 5)

b. 7972 = 8000 to the nearest thousand (it is rounded up since 9 is more than 4)

Start the lesson by playing the guessing and estimation game. That is I bring out a quantity of items and ask them to guess its amount
Pupils should be able to
a.  round whole numbers to the nearest hundred. B. approximate whole numbers to the nearest thousand

seat work: Inside out mathematics Book 4, page  183, exercise 21.1 (1 a – j)

seat work: Inside out mathematics Book 6, page  107, exercise 13.1 (1a – j) and (2a- j)

Wednesday
Estimate decimal numbers to the nearest tenth or 1 decimal places.

Estimate decimal numbers to the nearest hundredth or 2 decimal places.

Resources
Inside out
Learn
mathematics Book 6, page  110
flashcards,  beads, jelly bean, glass jar,  currency note biscuits, books, pencils.

Estimate decimal numbers to the nearest tenth or 1 decimal places.
To approximate decimal numbers to the nearest tenth, or 1 decimal place round up or down the second digit after the decimal point (the number in the hundredths’ place). The answer should end with one decimal place.

Examples

1. approximate these numbers to one decimal places:
a. 2.93                            b. 0.56

solution
a. 2.93 =  2.9 to the nearest tenth or 1 decimal place.
(Since the second digit after the decimal point is 3 and it is not up to 5, then we round down when approximating to 1 decimal place.)

b. 0.56  = 0.6  to the nearest tenth
(Since the second digit after the decimal point is 6 and it is more than 4, then we round up when approximating to 1 decimal place.)

Estimate decimal numbers to the nearest hundredth or 2 decimal places.

To approximate decimals to the nearest hundredth or 2 decimal places, round up or down the third digit after the decimal point (the number in the thousandths place), the answer should end with two decimal places.

Examples
1. approximate 0.273 and 2.509 to the nearest hundredth or 2 decimal places

Solution
a. 0.273 = 0.27 to the nearest hundredths or 2 decimal places.
(since the third digit after the decimal point is 3 and it is not up to 5, then we round down when approximating it to 2 decimal places.)

Begin the lesson by doing the first example for them.

Pupils should be able to
a. estimate decimal numbers to one decimal places

b. estimate decimal numbers to 2 decimal places

Thursday
Rounding off decimal  to the nearest whole number
Resources
inside out mathematics book 4
page 187
Rounding off decimal to the nearest whole number
Content
To round off decimal numbers to the nearest whole numbers, numbers that are 5 or greater than 5 are rounded up and replaced by zero and 1 is added to the previous digit. But, if however, the digit is less than 5, it is rounded down. That is, replace the digit after the decimal point with zero.

Examples
1. estimate these numbers to the nearest whole numbers:
a. 9.2                      b. 15.8
solution
a. 9.2 =  9 to the nearest whole number.
(Since 2 which is the number after the decimal point is not up to 5, then we round down)

b. 15.8 = 16 to the nearest whole number
(since 8 which is the number after the decimal point is more than 4, then we round up)

Begin the lesson by showing them a video of guessing games which they are to tell you the answer before the result is revealed.

Pupils should be able to
a. round off decimal number to the nearest whole number.