# Concept of estimation and values , capacity ,volumes and mass

**Subject : **

Mathematics

**Term :**

First Term

**Week:**

Week Ten

**Class :**

Jss 1

**Previous lesson : **

The pupils have previous knowledge of **Fractions Continued: (a) Multiplication and Division of fractions (b) Prime numbers and factors**

**WEEK TEN**

**TOPIC: ESTIMATION**

**Estimation: **

**(i) Concept of estimation and reasons **

**(ii) Estimation of dimensions and reasons**

** (iii) Estimation of capacity(volumes) and mass of objects**

** (iv) Estimation of other things**

** (v) Quantitative reasoning involving estimation**

**CONTENT**

Rounding Off Numbers

Dimensions ,Distances, Capacity and Mass

**Costing **

Rounding off Number

Estimation is making guess of the nearly correct calculation in distance, weight, price or capacity of things without the actual measurement or calculation. Even though it is not accurately done, it gives a good idea of the correct answer.

Estimation help us to have a rough idea of the answer when we add, subtract, multiply or divides given quantity. Sometimes rounding off numbers and approximation are used in making estimation.

B.** Rounding Off Number**

Example;

1, Round 1234 to the nearest 10

II. Round 1834 to the nearest hundred

III. Round these numbers to the nearest thousands

- 3512 (b) 4265

Solution to the examples:

i. 1234 = 1230 to the nearest ten

ii. 1834 = 1800 to the nearest hundred

iii. 3512 = 4000 to the nearest thousand

iv. 4265 = 4000 to the nearest thousand.

2. Rounding Off Numbers to a Specific number of Decimal Places

Examples

Give 474.4547 correct to the nearest hundredth and thousandth

Solution to the example.

474.447 = 474.45 to the nearest tenth

=474.45 to the nearest hundredth

=474.455 to the nearest thousandth.

**3. Rounding Decimal number to the Nearest Whole Number.**

Examples

Round ( I ) 13.73 (ii)34.245 to the nearest whole number

Solution.

i. 13.73 = 14 to the nearest whole number

ii. 34.245 = 34 to the nearest whole number.

**3 Significant Figure**:The word significant means important and it is another way of approximating numbers. A figure position in a numbers. A figure’s position in a number show what the figure worth.

Note; That the first significant is always the first non-zero figure as you read a number from left. Again notice that zeros in the middle of a number are significant . Zero before or at the end of another are significant. Measurements and currencies are usually given to a specified number of significant figures.

Examples.

i. Give 5754 correct to

(a) 1. s.f (ii) 2. s.f (iii) 3. s.f.

ii. Give 147 .006 to

(a)1 s.f (ii) 2 s.f. (iii) 3. s.f. (iv) 4 s.f (e) 5 s.f

iii. Give 0.007025 to

(i) 1 s.f (ii)2 s.f (iii) 3.s.f (d) 4 s.f

iv. Give 0.0007004

(a) 2.s.f (b) 2.s.f.

Solution to the examples

i. 5754 = 60000 to 1 s.f

= 5800 to 2 sf

=5750 to 3s.f

ii. 147.006

= 100 correct to 1 s.f

= 150 correct to 2 s.f

=147 correct to 3s.f

= 147.0 correct 4 s.f

= 147.01 correct to 5 s.f

ii. 0.007025

= 0.007 correct to 1 s.f

=0.0070 correct to 2 s.f

= 0.00702 correct to 3 s.f

0.007025 correct to 4 s.f

iv.0.0007004

=0.00070 correct to 2 s.f

=0.000700 correct to 3 s.f

remember that the zeros at the end are necessary to show the number of significant figures.

**EVALUATION**

1. Read off to nearest ten (i) 95 (ii) 127

2. Give 3.9998 to (i) 1 s.f (ii) 2 s.f

Solution to evaluationquestions

1.i. 95 = 100 correct to nearest ten

ii. 127 = 13 correct to nearest ten

2. i. 4 = ( s.f)

ii. 4.0 ( s.f)

**READING ASSIGNMENT**

1. New General Mathematics JSS1 by J.B. Channonpg 152 Ex 24 a no 1a-e

2. Essential Mathematics by Oluwasanmipg 168 Ex 16.5 No.1 a,b, 2a,b,c.

II. **Dimension and Distances, Capacity and Mass**

The common units of length(i.e km, m,cm, mm) mass (i.etonne, kg. g ) capacity (i.e cl.ml) and time (hour, min. seconds ) are widely used. The most common unit for length are millimeter(mm) centimeter (cm). Meter(m) and centimeter for short length and the higher units (meter and kilometer) for larger distances.

The common units of mass are the gramme(g), kilogramme kg and tone (t). The common units of capacity and the milliliter (ml) centiliter (cl) and litre (l) as unit length, we use the lower units for smaller quantities.

It is important to be able to choose the most appropriate meter units of measurement to use. For example to measure distance less than a metre,smaller such as millimeter (mm) and centimeters are used. To measure a large distance metres (m) a kilometers (km) are used.

For example;

i. to measure the distance between Lagos and Benin City, we use km.

ii. to measure the height of a man, we use meters and centimeter.

iii. to measure the time it will take to run 200m, we use seconds etc.

Examples

1.State the metric units at length you would use to measure the following;

(a) length of your classroom (b) length of your fingernail

2. State the appropriate metric units of mass (weight) you would use to measure the following;

(a) your weight (b) the weight of a diary.

3. State the appropriate metric unit capacity you would use to measure the following;

a. the amount of water in a glass cup b. the amount of medicine in a tea spoon

4. State the appropriate metric unit of time you would use to estimate the following :

a . the time it takes a sportman to run 100m b. the time it takes to walk or travel to your school.

Solution to the examples.

1. (a) m (b)mm

2. (a) kg (b) g

3. (a) ml (b) ml

4. (a) second (b) min.

**EVALUATION**

1. State the units of length you would use to measure the following:

(a) height of a desk (b) height of yourself

2. State the units of mass you would use to measure the mass of the following

(a) a parcel (b) a large land

3. State the units of capacity you would use to measure the capacity of the following ;

(a) cup (b) car petrol tank (c)a tin of peak milk (d) the amount of water in a reservoir

4. State the appropriate metric units of time you would use to measure the following:

a time it takes to fill an empty tank b. the time it takes to travel from Lagos to Ado Ekiti.

Solution

1. a. cm b. cm

2. a. g or kg b. t

3. a. ml b. liter c. ml d. ml

4. a. min b. hour.

**READING ASSIGNMENT**

New General Mathematics by J.B Channonpg 24 Ex 24C nos 2 c-d

Essential Mathematics pg. 170 Ex.16. 7 nos 1 c-d.

**Costing: **

It is important to know the prices of items or goods in your area. This will enable you know the best place to buy a particular item at a reasonable price. In general, the more you buy the more you must pay.

Examples.

1.James bought 5 exercise books at a bookshop at N50.50 each> How much did he spend.

Solution

1. 1 exercise book cost = N50.50

therefore 5 exercise books will cost N50.50 x 5 = N225.50.

That means he spent N252.25

2. one candle cost 19C. Calculate the cost of five candles.

Solution

1 candle cost 19C

therefore 5 candles will cost 19C x 5 =95C

3. Find the cost of three tins of margarine at N48.00per tin

Solution

1 tin costs N48.00

Therefore 3 tins will cost N48.000 x 3 = N144.00

**EVALUATION**

1. Eggs cost N6.00 each. How much will one dozen of eggs cost?

2. 30 mangoes cost N150. What would be the cost of N140 similar margarine/

Solution

1 egg cost 12 eggs will cos N6.00

1 dozen (12) eggs will cost N6.00 x 12 eggs = N72.00

one dozen = N72.00

2. 30 mangoes cost N150.00

therefore 1 mango will cost 150.00/30 mangoes =N5

therefore 140 similar mangoes will cost N5 x 140 = N700.00

140 mangoes will cost N700.00

**READING ASSIGNMENT**

1. New General Mathematics JSS 1 by J.bChannonpg 159 Ex 23C No 4.

2. Essential Maths by AJS Oluwasanmipg 172 Ex 16 No 3

**WEEKEND ASSIGNMENT**

1. Round 567 to the nearest hundred

(a)500 (b)520 (c )540 (d) 580 (e) 600

2. What is 1.99961 correct to 2 d.p

(a) 1.99 (b) 2.00 (c ) 3.00 (d) 4.00 (e) 5.00

3. Write 7.0149 correct to the nearest thousandth

(a) 7.000 (b)7.014 (c ) 7.015 (d) 7.0145 (e) 7.0146

4. Give 0.000057891 to 4 s.f.

(a)0.00005789 (b)0.00005790 (c) 0.00005781 (d)0.000057892 (e)0.00005793.

5. Give 45698 correct to 3 s.f.

(a) 45600 (b)45700 (c )45800 (d)45690 (e) 45000.

**THEORY**

1. A sack of rice holds 64 basins of rice. How much will a woman get if she sells each basin of rice for N48.50.

2.Calculate the total cost of the following :

i. 3 textbooks at N400.00 each

ii.9 mathematical set at N2500.50

iii. 3 pens at 120.25 each

iv. 5 pencils at N20.00 each.