WORKING ON MATHS IN ENGLISH
UNIT 7
Isabel Leo de Blas
MEASUREMENTS
SUMMARY
INTRODUCTION
1. DEFINITION
I. THE METRIC SYSTEM
1 LENGTH
1.2 CONVERTION OF METRIC UNITS
1.3 PRACTICES of Length
2 MASS
2.1 PRACTICES of Mass
3. CAPACITY
3.1 PRACTICES of capacity
4. VOLUME
4.1 RELATING METRIC UNITS
5. AREA
2.1 PRACTICES of surface
II. IMPERIAL UNITS
III. MEASURING TEMPERATURE
- EXERCISES AND PRACTICE
IV. TEST AND DAILY LIFE PROBLEMS
V. PROJECTS: SHOPPING
1
1 ST LEVEL
WORKING ON MATHS IN ENGLISH
Isabel Leo de Blas
Webs for more practice:
- http://www.bbc.co.uk/skillswise/numbers/measuring/lwc/ Facts and worksheets
http://www.bbc.co.uk/apps/ifl/schools/ks2bitesize/maths/quizengine?quiz=measures&temp
lateStyle=maths TEST
- http://www.bbc.co.uk/skillswise/numbers/measuring/lwc/flash0.shtml games
- http://www.bbc.co.uk/schools/ks2bitesize/maths/shape_space/measures/read1.shtml
Theory
- http://cybersleuth-kids.com/sleuth/Math/Measurement/index.htm
units of measure
- http://www.aaamath.com/mea.html
NOTE: THERE ARE pdf files: with more activities, problems and test of evaluation.
convert_fahrenheit_celsius_002.pdf
convert_celsius_fahrenheit_003.pdf
convert_inches_to_centimeters_001.pdf
convert_inches_to_centimeters_010.pdf
convert_between_celsius_fahrenheit_001.pdf
BBCmeasuresScales.pdf
InstrumentsMEASURworksheet.pdf
Measuring lines in cm (2).doc
convert_between_celsius_fahrenheit_negatives_001.pdf
telling_temperature_004.pdf
measurements length.pdf
measuresEXERC.pdf
EvaTESTmeasure.pdf
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WORKING ON MATHS IN ENGLISH
UNIT 7
Isabel Leo de Blas
MEASUREMENTS
1ST LEVEL
“A cynic is a man who knows the price
of everything, and the value of nothing.”
Oscar Wilde
INTRODUCTION
Measurements connect the real world to the
numbers systems. In this section we are going to
apply the previous learning of arithmetic to daily
life situations. To solve many problems we will
manage different operations with fractions,
decimals, powers, negative numbers, etc.
The purpose of this unit is to understand clearly
units of measurements, the metric system and
conversion, and practise them into a class project.
1. DEFINITION
How tall are you? How fat are you? How old are you? How far is the school from your
house? To answer these data questions we need to make measurements.
What we can measure is a magnitude: length, capacity, weight, time…
When we measure something we get concrete information about its size and we ask
questions like:
How long is it? How fat is it? How far? How tall? How much is it?...
And we get answers in numbers plus a unit of measurement.
I am 1,56 metres tall, I am 45,5 kg fat and I am 13 years old. The school is at 2
km from my house.
What do you do when you measure the weight of a package or the length of a room? We
just compare a unit of measurement with the object using some instruments: a metre, a
scale…
To measure is to compare the magnitude with a unit.
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WORKING ON MATHS IN ENGLISH
Isabel Leo de Blas
Can you think about more examples of measurements in daily life? For example at
shopping, or building something…
Research old units to measure: ask to your grandparents what is a hand span, “an arroba”,
acre, quintal, etc.
To check your previous knowledge work out together on this matching:
MATCH THE FOLLOWING MEASUREMENTS
1. Capacity of a tablespoon
3. Mass of a stamp
pool
2. Length of a shoe
4. Length of a swimming
5. Temperature of the fire
6. Capacity of a cup
7. Mass of a concert piano
hot
8. Temperature of the
chocolate
9. Width of a door
10. Mass of a sandwich
a) 250 ml b) 2ml c) 36cm
d) 100 mg
e) 125 g
f) 90 cm
g) 1500C
h) 500C
i) 1 t
j) 5 m
I. THE METRIC SYSTEM
In the above exercise: cm, l, m, mg, g … are units included in the metric system.
It is important to use standard units of measure to best understand each other.
The metric system is an international decimal measuring system used to simplify trade
and commerce among countries. It works as a decimal system.
There are basic units with multiples and submultiples of ten to measure magnitudes as
length, mass, capacity, volume and surface.
Do you know who founded the metric system?
In which country was he born?
In which century was it established?
What important revolution happens in that time?
Search on Internet to answer the above questions: http://lamar.colostate.edu/~hillger/origin.html
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WORKING ON MATHS IN ENGLISH
Isabel Leo de Blas
Which are the basic units in the metric system?
MAGNITUDE
BASIC UNIT
SYMBOL
LENGTH
metre
m
MASS
gram
g
CAPACITY
litre
L
VOLUME
cube metre
m3
SURFACE
square metre
m2
Note: you can write meter or metre, liter or litre; it depends if it is American or British English.
Work in groups to find objects you can measure with these units:
a) metre: a table, _________________________________________
b) gram: sugar pot, ____________________________________________
c) litre: oil, _______________________________________________
d) cube metre: a swimming pool, __________________________________
e) square metre: a room, ___________________________________________
For multiples and submultiples we use prefixes that multiply or divide the basic unit by
powers of 10
Meanings of metric prefixes:
1000 = 103
KiloHecto-
100 = 102
Deca- or (deka-)
10 = 101
Basic
Multiples
unit
Deci-
0,1 = 10–1
Centi-
0,01 = 10–2
Milli-
0,001 = 10–3
5
Submultiples
WORKING ON MATHS IN ENGLISH
Isabel Leo de Blas
1. LENGTH Measurements of 1 dimension
How long is your pencil?
Measure it using a ruler from one end to another.
It is about 12 cm long.
Length is a measure of how long or wide something is.
For example: the bed is 1,90 m long and 80 cm wide.
What’s the perimeter of the bed? We have to add twice the length plus twice the width:
Length 1,90 x 2 = 3,80 m
Width 80 x 2 = 160 cm
To add length plus width we must change the amounts to the same units: m or cm
3,80 m = 380 cm + 160 cm = 540 cm or 160 cm = 1,60 m + 3,80 = 5,40 m
The basic unit of length is the metre. Multiples and submultiples are:
Kilometre
Hectometre Decametre metre
decimetre
1km=
1000m
1 hm =
100m
1dm=0,1m 1cm=
0,01m
1 dam=
10m
MultIples
centimetre millimetre
1mm=
0,001m
S u b m u l t i p l e s
How many dm, cm and mm are in one metre? 1 m = 10 dm, 100 dm and 1000 mm
Exercise:
1.Choose the most appropriate unit – km, m, cm, mm – to measure:
a) a pen
b) a stamp c) a building d) the distance from London to Oxford e) an eraser
2. Choose the most reasonable measurement:
1. Width of your hand
a) 95 mm
2. Height of an adult
a) 163 mm
3. Length of a pair of scissors
b) 9,5 dm
c) 95 cm
b) 1.63 m
a) 20 cm
c) 1630 cm
b) 2000 mm
1.2 CONVERTION OF METRIC UNITS
Metric system is based on multiples of ten.
To change from one unit to another, we must multiply or divide by ten.
6
c) 2 m
WORKING ON MATHS IN ENGLISH
Isabel Leo de Blas
To change LARGER UNITS TO SMALLER UNITS, multiply by 10 for every place
moved to the right.
To change SMALLER UNITS TO LARGER UNITS, divide by 10 for every place moved
to the left.
For example change 50 cm to mm. 50 x 10 (1 place to the right) = 500 mm.
cm (larger)mm (smaller)
700dm to m 70 : 100 (2 places to the left) = 0,7 m
dm (smaller) m (larger)
Exercise:
Complete: a) 1,2 km =_______m
d) 0,5 dm= _______mm
b) 4 m = _____ cm
e) 2 dam = _____km
c) 25 cm = ______m
f) 1550 mm = _____________hm
1.3 PRACTICES of Length
EXERCISE 1 Drawing dictation (materials needed: a ruler)
To the whole class: ask them to draw lines or figures using rulers. Give them five minutes
Example: A)draw a line of 4,5 cm
D) Draw a tree of 40 mm tall
B) Draw a line of 30mm
C) draw a line of 1,5dm
E) Draw an envelope of 5cm of length and 35mm width
Correct in class checking in groups or at the blackboard.
GAME: Students propose similar dictations in groups or to the whole class as a BINGO.
EXERCISES 2 How tall are you? (materials needed: ruler and tape measure)
Divide the class in groups of 4 or 5 students. Who is the tallest of the group? Who is the
smallest of the group? Use a tape measure and show your answers with a drawing.
In my group the tallest is David. He is 1,56 m tall and the shortest is Lucas. He is
1,35 m tall.
Lucas
David
1,56
Express
m
the
tall
measurements in dm, cm, mm.
7
1,35 m tall
WORKING ON MATHS IN ENGLISH
Isabel Leo de Blas
EXERCISE 3 How long are objects in class? (materials needed: ruler and tape measure)
Complete this table. In groups they have to measure these objects and compare the results
with other groups (give them 10 minutes maximum).
OBJECT
Window
Length
In
In
In
Width
In
In
In
m
dam
cm
mm
m
dam
cm
mm
1,20m
0,120dam
120cm
1200mm
1m
0,1dam
100cm
1000
mm
Door
Ruler
Math book
Classroom
Sharpener
EXERCISE 4 How long is your body? (materials needed: ruler and tape measure)
Estimate and measure parts of your body. One student helps others to measure different
parts of the body. First estimate and then check in real measurements units. Show your
results on a table to compare.
The
circumference
of your head
The length of Distance
your arm
from
your
knee to your
ankle
The width The width
of
your of
your
thumb
wrist
nail
Student
Estima
ting
Estimat
Real
Real
Estimat
ing
Real
Estim
ating
Re
al
Estim
ating
Real
65cm
50cm
47,2
cm
2cm
18
mm
12cm
15cm
ing
Mati
50cm
61cm
70cm
Eva
Marina
Charles
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WORKING ON MATHS IN ENGLISH
Isabel Leo de Blas
2. MASS
How fat are you? I am 45 kg fat. How much does your schoolbag weigh?
My schoolbag weighs 12 kg.
Health advice: Do not carry on more than 10% of your body weight.
10% of 45 kg = 4,5 kg Since, 12 – 4,5 = 7,5 kg of overcharge. That’s not good for your
back, so you could carry your books on a trolley.
Investigate how heavy an elephant, an ant, a cow…are.
What units of mass do we use to express their weight? Tons, kilograms, grams
Mass is a measurement of how heavy something is.
The basic unit of mass in the metric system is gram (g).
Metric units of mass are related to each other in the same way that place-value positions
within the decimal system of numeration are related.
Units of mass. Multiples and submultiples are:
Kilogram
Hectogram Decagram
1kg=
1000g
1 hg =
100g
gram
1 dag =
10g
decigram
centigram
milligram
1dg = 0,1g
1cg =
0,01g
1mg=
0,001g
Multiples
S u b m u l t i p l e s
To measure mass we can use scales (metric balance).
Examples: - A dictionary has a mass of about 1 kg
- A paper clip has a mass of about 1 g
- A grain of salt has a mass of about 1 mg
- The mass of heavy things is expressed in tons (t)
1 ton = 1000 kg
We use also “quintal” (q) for 100 kg. Search on Internet other units of mass in Spain: like
arroba, fanega…
Exercise: Choose one of these units (g, mg, kg, t) to express the mass of:
a) a bag of potatoes
b) a box of cereal c) a feather d) a hamster e) a lorry
To convert one unit to another proceed as in length: count the number of places and
multiply or divide by powers of 10.
Example: 150g to kg there are 3 places to the left, so divide by 1000 150:1000= 0,150kg
150g to mg there are 3 places to the right, so multiply by 1000
9
150 x 1000 = 150 000 mg
WORKING ON MATHS IN ENGLISH
Isabel Leo de Blas
Exercise: compare, write <, =, or > a) 754 kg _____754 000g
c) 280 000 mg____ 28 g
d) 1845hg ____18,45 kg
b)876 hg____8.96 kg
e) 0,0001 g ____10 mg
Propose similar exercises to your teams and correct them together.
Complete this converting unit table:
0,854 kg
kg
hg
dag
g
dg
cg
mg
0,854
8,54
85,4
854
8540
85400
854000
324,54 g
910 dag
2t
2.1 PRACTICES of Mass
EXERCISE 1 Body mass index (materials needed: bathroom scales and tape measure)
To calculate the body mass index we use this formula:
weight
height 2
Use a bathroom scale to measure your weight and a tape measure to measure your height,
then divide the weight by the square of your height.
47
47
=
= 20,346 20,35
2
1,52
2,31
Paula weight 47 kg
Height 1,52 m
to know more visit:
http://www.nhlbisupport.com/bmi/bmi-m.htm
EXERCISE 2 How heavy is…? (materials needed: scales)
Divide the class in groups and ask students to measure the weight of school materials and
their lunch. They have to choose 5 items and then change them to different mass units.
Item
g
kg
Math book
School bag
Sandwich
Biscuits
10
mg
hg
WORKING ON MATHS IN ENGLISH
Isabel Leo de Blas
EXERCISE 3 Searching food data and nutritional facts
Ask students to bring labels from food products
.
They have to write down:
a) The weight of the product
b) All the data about nutritional information
For example: - a bottle of jam weighs 335 g and contains 35 g of fruit per 100 g of product.
How much fruit is in total? 35% of 335 =
35x335
35
= 117,25 g of fruit
of 335 =
100
100
- An envelope of soup weighs 51 g and contains 56% of vegetables.
How many grams of vegetables does it contain? 56% of 51g =
56
56x51
= 28,56 g
of 51 =
100
100
Energetic value per 100 g: 309 kcal Proteins: 8,5 g Carbohydrates 58,8 g Fat 0,5 g
Propose them to make a table to compare nutritional facts per 100 g of 3 products:
Per 100 g
Mash potatoes
Calories
Proteins
Carbohydrates
Fats
66kcal
1,9g
12,4g
1,0g
Bottle of asparagus
Can of tuna fish
Calculate each value for a regular portion of 200 g
EXERCISE 4 Ingredients
Bring to the class some cooking recipes. Reading the ingredients, we do a dictation and
then in groups they have to convert the measurements to grams and invent a cooking recipe
with those ingredients for four people and the portion to each one.
For example: Ingredients needed: half a quarter kilo of cheese, 200g of ham and half kilo
of tomatoes:
200 g ham
1
1 2
÷ cheese =
= 125 g
8
4
1
kg tomatoes = 500 g
2
EXERCISE 5 How
Total: 200 + 125 + 500= 825 g
We can prepare a salad for four.
825 : 4 = 206,25 g to each one
heavy is an earring?
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WORKING ON MATHS IN ENGLISH
Isabel Leo de Blas
Practise to measure little things as jewellery or very light things like a feather, medicines,
spices… with a special scale: precision balance or scale.
3. CAPACITY
It’s the amount of liquid a container can hold. (Also volume)
We should drink 2 litres of water per day. If we have glasses of
ml. How many glasses will we fill?
2 litres = 2000 ml
200
2000 : 200 = 10 glasses of water.
To measure how much a container can hold we use the units of capacity:
Example: a carton holds 1 litre of milk: it has the capacity of 1 litre.
The litre is the basic unit of capacity in the metric system. It represents
what a cube of 1 dm of side can hold. So 1 dm3= 1 L
Units of capacity. Multiples and submultiples are:
Kilolitre
Hectolitre
Decalitre
1kL=
1000L
1 hL =
100L
1 daL=
10L
Litre
L
Multiples
decilitre
1dL
0,1L
centilitre
= 1cL =
0,01L
millilitre
1mL=
0,001L
S u b m u l t i p l e s
Example: The water in a swimming pool is measured in kilolitres.
A tall thermos holds about 1 L.
20 drops of water equals 1 mL
To measure capacity we can use a measuring cylinder or a beaker.
Give more examples of measurements of capacity.
To convert one unit to another: count the number of places and multiply or divide by
powers of 10.
Covert 2 L to KL = 3 places to the left Divide by 10 raised to 3 2 : 103 = 0,002 kL
Example 5L = 0,005kL = 0,05 hL = 0,5 daL = 50 dL = 500cL = 5000 mL
Exercise:
1. Convert these units: a) 8,2 kL to L
b) 65,4 mL to L
c) 45 daL to mL
2. Express in litres the following measurements:
a) 3 daL, 6 L and 2 dL
b) 7hL, 2 L and 8 mL
12
c) 3 kL, 20cL and 300 mL
WORKING ON MATHS IN ENGLISH
Isabel Leo de Blas
2.1 PRACTICES of Capacity
EXERCISE 1 Finding the volume of irregularly shaped object. Displacement
method. Investigate how Archimedes discovered this method.
1. Pour water into a beaker. Read the water level. 50 mL
2. Drop a stone into the water. Read the new water level. 65mL
3. Subtract 65 – 50 = 15 mL is the volume of the stone.
EXERCISE 2 Liquid products
Bring to the class labels of different liquid products, for example: empty bottles of
medicines, cleaning products, cans of drinks, cartons of milk or juice, yogurt…
How much liquid can they hold? Express it in different units and show on a table.
Item
L
kL
mL
cL
A bottle of bleach
A bottle of shampoo
A can of coke
A brick of juice
EXERCISE 3 Problems in daily life.
1. I have 36 containers of 15 L of olive oil to sell to the market.
2
are full and I pour the
3
rest in bottles of 1 L to s. How many bottles of 1 L will I have?
2. How many glasses of 330 mL do we need to fill a bottle of 2 L?
3. From one orange I get 5 cL of juice. How many oranges will I need for
one litre of juice?
4. For a party I bought 5 cans of 33 cL of coke, 2 bottles of 2 litres of lemonade and 10
cartons of 125 mL of juice. How much liquid did I buy?
1
1
2
of orange juice,
of lemon juice, of pineapple
8
10
3
juice and the rest of water. If I want to prepare 1 litre, how much of each juice will I use?
5. The recipe for a cocktail says:
Solve them in groups and invent similar ones to your class group.
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WORKING ON MATHS IN ENGLISH
Isabel Leo de Blas
4. VOLUME Measurements of 3 dimensions 10 X 10 X 10 = 1000
In a 3 D shape or solid shape, the volume is how much space
something occupies. We use a cube as a measurement unit.
The basic unit of volume in the metric system is the cube metre, and it is the space
that takes a cube of 1 m of side: 1 m3
Units of volume. Multiples and submultiples are:
Cubic
Cubic
Kilometre Hectometre
1km3=
1 hm3 =
1000 000 1000 000
000 m3
m3
Cubic
Decametre
1 dam3=
1000 m3
Cubic
Cubic Cubic
decimetre
centimetre
metre
m
3
1dm3 = 1cm3 = 0,000
0,001m3
001 m3
Multiples
Cubic
millimetre
1mm3=
0,0000
000
001m3
S u b m u l t i p l e s
To convert units of volume we multiply or divide by 1000 for each place it depends on if
we move to the right or to the left. For example to change 2 hm3 to m3, as we change from
a greater to a lowest we multiply by 1000 as many times as places. Since we move 2 places
to the right from hm3 to m3 we should multiply by 1000 000 = 2 x 1000 000 = 2000 000
m3.
Example: An object has a volume of 245 cm3, how many dm3 ? and mm3?
245 : 1000 = 0,245 dm3
245 x 1000 = 245 000 mm3
Exercise:
Express in m3 the following volume: a) 0,4 hm3
b) 0,0032 dm3 c) 24 dm3
4.1 RELATING METRIC UNITS
Metric units of volume, capacity and mass are related to one another in this way:
A cube of 1 dm of side holds 1 litre of water and has a mass of 1 kg (Only for water o
similar liquids density, for example not for honey)
1 dm3 = 1L of water = 1 kg
Exercise: How many litres are in 3 m3?
1st we convert m3 to dm3 3 x 1000 = 3000 dm3 = 3000 L
Solved problem: A child wants to fill a 500 cm3 bucket. How many litres of water does he
need to fill it?
500cm3 dm3 1 place to the left, so divide by 1000 = 0,500 dm3 = 0,5 L what is half a
litre or 500 mL
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WORKING ON MATHS IN ENGLISH
Isabel Leo de Blas
5. AREA Measurements of 2 dimensions 10 X 10 = 100
In a flat shape is the space inside the lines.
What’s the measure of your blackboard?
To find it out we measure the area (green part) using surface units. We have to measure 2
dimensions:
Length and width and multiply them: 2m long x 1,20 m wide = 2,40 m2
The basic unit of surface in the metric system is the squared metre, and it is the area
of a square of 1 m of side: 1 m2
Units of surface: Multiples and submultiples are:
Square
Square
Square
Kilometre Hectometre Decametre
1km2=
1 hm2 =
1000 000
10 000
m2
Square
metre
1 dam2=
100 m2
Square
Square
Square
decimetre
centimetre
millimetre
1dm2 = 1cm2 =
0,001m2
0,000 01 m2
m2
1mm2=
0,0000
001m2
m2
Multiples
S u b m u l t i p l e s
To convert units of surface we multiply or divide by 100 for each place it depends on if we
move to the right or to the left. For example to change 2 hm2 to m2, as we change from a
greater to a lowest we multiply by 100 as many times as places. Since we move 2 places to
the right from hm2 to m2 we should multiply by 10 000 = 2 x 10 000 = 20 000 m2.
Example: A table is 120 cm long and 70 cm wide.
Its area is 120 x 70 = 8400 cm2 = 8400 : 100 00= 0,84 m2
Área and hectárea
en español. ¿y
fanega?
Other units for large surfaces: area 1(a) = 100 m2
And hectare 1(ha) = 1hm2 =100 areas = 10 000m2
Exercises:
1. What unit of surface will you use to measure: cm2, mm2, km2, m2, dm2?
a) Your room floor
2. Complete the table:
b) a paper area
Km2
c) The surface of a country
hm2
dam2
m2
7
5
0,0025
15
dm2
cm2
70000
mm2
WORKING ON MATHS IN ENGLISH
Isabel Leo de Blas
2.1 PRACTICES of surface
EXERCISE 1 Area of objects (materials needed: ruler and tape measure)
Complete this table. In groups they have to measure length and width of these objects to
find the area. Remember to use the same units to operate. Compare the results with other
groups (give them 10 minutes maximum).
AREA in m2
Length
Width
AREA
2m
70cm
200 x 70 = 14000:100 00=
14000 cm2
1,4 m2
OBJECT
Door
Window
Ruler
Math book
Classroom
Paper sheet
EXERCISE 2
Space at home.
Measure at home the area of your bedroom and other rooms from your house. Then
prepare problems to show to your group or class.
For example: My bedroom is 230 cm wide and 4,5 m long. If I want to covert the floor
with a blue carpet, how many m2 will I need?
EXERCISE 3 Surfaces of places
Find out the surface of different countries or towns; express it in m2 and compare.
Example: Spain has a surface of 506,990 km2, is it bigger than France?
If we have 30% of forest surface, How many hectares are there?
30% of 506,990 = 152,097 km2 = 152,097 x 100 = 15209,7 ha
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WORKING ON MATHS IN ENGLISH
Isabel Leo de Blas
EXERCISE 4 Population density
To find out if one place is sparsely or densely populated we divide the number of
inhabitants by the area of the place in km2. This is called population density:
area
inhabitan ts
For example, Hervás has a surface of 60 km2 and 4062 inhabitants, so its density is
4062
= 68 person / km2
60
Ask students to find out the density of their town and compare them.
II. IMPERIAL UNITS
In United Kingdom and U.S.A. they use different system of measurements. It is called the
imperial system and they use imperial units. (Sometimes it is different the value of a unit in
UK and in USA)
LENGTH
MASS
CAPACITY
1 MILE 1,6 km
1 POUND (lb) 550 g
1 PINT (pt) litre
1 FOOT 30 cm
1 OUNCE (oz) 30 g
1 GALLON 5 litres (4
litres in USA)
1 YARD 90 cm
1 pound of strawberries
1 CUP litre
1 INCH 2, 5 cm
1 QUART (qt) 1 litre
3 TEASPOONS 1 TABLESPOON
A screen of
12 inches
Exercises
1. The supermarket sells apples for £1.50 per kg. The next shop sells
apples for 58 p per pound. Which is the cheapest?
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WORKING ON MATHS IN ENGLISH
Isabel Leo de Blas
2. On this signpost, the distance to Madrid is given as 9 miles. Show the distance in km.
Madrid 9
Airport Invent similar problems to your class and check the results.
http://www.math-drills.com/measurement.shtml Metric- imperial conversion exercises.
III. MEASURING TEMPERATURE
We have three scales to measure temperature: CELSIUS, FAHRENHEIT AND
KELVIN.
Celsius is used In Spain and many countries in Europe and Fahrenheit is used in U.S.A.
http://www.bbc.co.uk/skillswise
They settle in different degrees the freezing point of water and the boiling point of water.
CELSIUS
O
C
FAHRENHEIT
Freezing point of
water
0 oC
32 o F
Boiling point of
water
100 0 C
212 o F
Normal Body
temperature
37 o C
98,6 o F
O
F
5
5
= Example 78oF (78 – 32) = 25,5 o C
9
9
Twenty-five point five degrees Celsius or Centigrade
To convert o F to o C (oF – 32)
9
9
+ 32 = Example 32 o C 32 x +32 = 89,6 o F
5
5
Eighty-nine point 6 degrees Fahrenheit
To convert o C to o F o
C
Why the fraction 5/9 and 9/5? The difference between the freezing point and the boiling
point in Fahrenheit is 212 – 32 = 180, in Celsius is 100 – 0 = 100. The proportion is
o
C to o F =
180 9
=
+ 32 if we reduce it.
100 5
And o F to o C =
100 5
= – 32
180 9
Converting practices and reading temperatures: http://www.mathdrills.com/measurement.shtml
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WORKING ON MATHS IN ENGLISH
Isabel Leo de Blas
Solve these problems and convert the degrees to Celsius. Invent similar ones for the class.
Example: At 11 a.m. the temperature outside is 35 o F, and at 11 p.m. is – 13 o F. By how
many degrees has the temperature fallen?
35 – (–13) = 35 + 13 = 48 o F (48 –32) 5/9 = 8,8 o C
1. The pool water temperature at 9 a.m. was 62 oF, but by 6 p.m. the temperature was 70
o
F, How much has the temperature risen?
2. When Susan was sick, the temperature was 38,8 o C. After she recovered, her
temperature was 36,5 o C. How much has her temperature dropped?
Exercise 2: Write “R” if the statement is reasonable and “U” if it is unreasonable:
a) Your body temperature when you are well is about 37 oC ______
b) Inside a freezer it is 10 oC _______
c) The skating lake is frozen when the temperature is – 5 o C _____
d) You need a coat in 25 o C ______
e) When you boil potatoes the water is about 70o C ______
Exercise 3: Choose a reasonable temperature for:
1) The temperature of your classroom in a warm day: a) 68 o F
2) The temperature of a dish of ice cream: a) 31 o F
b) 80 o F
b) 0 o F
c) 45 o F
c) –10 o F
PRACTICE 1 Weather report
Bring newspapers or documents where the students can read the weather report and
temperatures.
In groups they choose a country or area and they should convert the temperature in degrees
Fahrenheit. Then they will write and read aloud a report about the temperatures from
yesterday to tomorrow in
Celsius degrees and
Yesterday the temperature in
In degrees Fahrenheit:
Fahrenheit
Oxford was 7oC, Today the
Yesterday
was 44,6oF,
degree:
o
o
temperature will be 10 C and
Tomorrow it will be 8 oC
today 50 F and tomorrow
it will be 46,4 oF
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WORKING ON MATHS IN ENGLISH
Isabel Leo de Blas
IV TEST THE METRIC SYSTEM
FILL IN THE BLANKS
1. The basic metric unit of measure for weight is the _____________________.
2. A millimeter is _________________ metres.
3. The metric measure most closely related to a quart is __________________.
4. If an inch is 2,5 cm, then 10 inches is about ___________________.
5. If a dosage of a medicine prescription is 20 mg, then that amount is ______________
than a gram.
6. If a mile is 1760 yards, then a kilometer is ______________than a mile.
7. A 2 litre bottle of pop water (or gas water) is ___________ dm3
8. If a kg is about 2 pounds, then a 150-pound person weighs about ______________kg.
9. The basic metric unit for length is _______, for mass ________ and for capacity_____.
10. The metric system is a decimal system, and that means that the prefixes are multiples
of _____________.
DAILY LIFE PROBLEMS
The following are some practical problems we could deal with in different situations.
After solving them and checking the answers in groups, the students can propose similar
ones to the class.
1
kg of apples at 1,50 per kg, 2 dozen
2
eggs at 1,25 per dozen, 2 boxes of corn flakes at 3.15 each, 3 cans of soup at 0,79 each and 200 g of cheese at 7,99 per kilo. With her special card she has a 5% discount.
How much change did Marina receive from a 50 bill?
1. Marina bought the following groceries: 1
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WORKING ON MATHS IN ENGLISH
Isabel Leo de Blas
2. We started a fieldtrip at 8:15 a.m. and we returned at 8.30
p.m. How long was the fieldtrip?
3. The speed limit in Spain 120 Km/h in a highway and the
speed limit in Los Angeles in U.S.A is 50 miles per hour. Which
country allows a motorist to drive at a faster speed?
4. In a class of 20 students, each one will need 2 ribbons of 12 cm m to tie the mask
for carnival. At 65 cents per metre, how much will the ribbon cost for the whole class?
5. Alice finished a swimming race in 8 min 12 sec. Tony finished in 7 min 8 sec.
How much faster was Tony tan Alice?
V. PROJECTS: SHOPPING
For working on projects we need to apply the previous arithmetic knowledge and what we
have learned about measurements. Here, we use Maths in real situations where we
integrate our learning.
Divide the class in groups of 4 or 5 students. Each team chooses what kind of products
they want to sell: food, clothes, hardware store, notion store (mercería), books, real
estate…
In the shops they have to:
- Select articles and mark the prices. They could bring real products, drawings, labels or
pictures from magazines.
- Prepare a shopping list
- They have to use instruments to measure the objects: scales, rulers…
- Also they have to know the VAT percentage to increase and a possible offer with a
percentage of discounts.
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WORKING ON MATHS IN ENGLISH
Isabel Leo de Blas
- They have to play roles: shop assistance and customer and learn how to ask and answer in
a usual shopping situation.
- All of them will be customers and shop assistances.
- They have to prepare a shopping list and the vocabulary in use.
- They will include: percentages, fractions, decimals, conversion of units, money and
change…
We can spend half an hour in the week to performance the role-playing choosing 2 shops
per day. Here is an example of role-play conversation:
-
Hello, Can I help you?
-
Yes, please. I would like a quarter of cheese and half of kilo of these lentils?
-
Yes, sure. Anything else?
-
Yes, I would like 100 g of ham
-
Which one? This is very good at 15 kilo and we have this one reduce price if you
take 200 g at 12/kg
-
OK, I will have the especial offer and I will take 200 g of that ham. How much is it?
-
Let’s see: 6 plus 2.50 plus 2.40 in total 12.90 please.
-
Here you are 20
-
Thanks, 7.10 is your change.
-
Thanks, Can I have an invoice, please?
-
Yes, of course. Here you are 12.40 is the base plus 4% VAT =0.50. Final price
12.90
-
Thanks a lot. Good bye
-
Good bye
Variations:
At the Real State: Simulate you want to rent or buy a house. You have to ask about the
surface, the price the discount… The agent must have prepared the publicity: “nice
apartment to rent: 60 m2 with two bedrooms. Close to the city center 700 per month.”
At the travel Agency Prepare a trip to U.S.A. Ask about the weather in ºF and ºC, prepare
your luggage and calculate the volume and weight of the suitcases, organize activities and
budget for a week, convert $ to , ask about the total prices including accommodation, etc.
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