UNIT 7 MEASUREMENTS 1 ST LEVEL

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1 UNIT 7 MEASUREMENTS 1 ST LEVEL 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

2 Webs for more practice: - Facts and worksheets - latestyle=maths TEST - games - Theory - units of measure - 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 2

3 UNIT 7 MEASUREMENTS 1 ST 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. 3

4 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 2. Length of a shoe 3. Mass of a stamp 4. Length of a swimming pool 5. Temperature of the fire 6. Capacity of a cup 7. Mass of a concert piano 8. Temperature of the hot 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) C h) 50 0 C 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: 4

5 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 m 3 SURFACE square metre m 2 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: Kilo = 10 3 Hecto- 100 = 10 2 Deca- or (deka-) 10 = 10 1 Multiples Basic unit Deci- 0,1 = 10 1 Centi- 0,01 = 10 2 Submultiples Milli- 0,001 =

6 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 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 centimetre millimetre 1km= 1000m 1 hm = 100m 1 dam= 10m 1dm=0,1m 1cm= 0,01m 1mm= 0,001m M u l t I p l e s 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 b) 9,5 dm c) 95 cm 2. Height of an adult a) 163 mm b) 1.63 m c) 1630 cm 3. Length of a pair of scissors a) 20 cm b) 2000 mm c) 2 m 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

7 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) Exercise: 700dm to m 70 : 100 (2 places to the left) = 0,7 m dm (smaller) m (larger) Complete: a) 1,2 km = m b) 4 m = cm c) 25 cm = m d) 0,5 dm= mm e) 2 dam = km 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 B) Draw a line of 30mm C) draw a line of 1,5dm D) Draw a tree of 40 mm tall 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 1,35 m tall David 1,56 m tall Express the measurements in dm, cm, mm. 7

8 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). Length In In In Width In In In OBJECT m dam cm mm m dam cm mm Window 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 The length of Distance The width The width circumference your arm from your of your of your of your head knee to your thumb wrist ankle nail Student Estima ting Real Estimat ing Real Estimat ing Real Estim ating Re al Estim ating Real Mati 50cm 61cm 70cm 65cm 50cm 47,2 cm 2cm 18 mm 12cm 15cm Eva Marina Charles 8

9 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 gram decigram centigram milligram 1kg= 1000g 1 hg = 100g 1 dag = 10g 1dg = 0,1g 1cg = 0,01g 1mg= 0,001g M u l t i p l e s 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= 0,150kg 150g to mg there are 3 places to the right, so multiply by x 1000 = mg 9

10 Exercise: compare, write <, =, or > a) 754 kg g b)876 hg 8.96 kg c) mg 28 g d) 1845hg 18,45 kg e) 0,0001 g 10 mg Propose similar exercises to your teams and correct them together. Complete this converting unit table: kg hg dag g dg cg mg 0,854 kg 0,854 8,54 85, ,54 g 910 dag 2 t 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. Paula weight 47 kg Height 1,52 m 47 1,52 = 47 = 20,346 20,35 2 2,31 to know more visit: 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 mg hg Math book School bag Sandwich Biscuits 10

11 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 = 35 35x335 of 335 = = 117,25 g of fruit 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 of 51 = = 28,56 g 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 Calories Proteins Carbohydrates Fats Mash potatoes 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 Total: = 825 g cheese = 1 = 125 g We can prepare a salad for four. 8 1 kg tomatoes = 500 g 825 : 4 = 206,25 g to each one 2 EXERCISE 5 How heavy is an earring? 11

12 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 200 ml. How many glasses will we fill? 2 litres = 2000 ml 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 dm 3 = 1 L Units of capacity. Multiples and submultiples are: Kilolitre Hectolitre Decalitre Litre decilitre centilitre millilitre 1kL= 1000L 1 hl = 100L 1 dal= 10L L 1dL = 0,1L 1cL = 0,01L 1mL= 0,001L M u l t i p l e s 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 : 10 3 = 0,002 kl Exercise: Example 5L = 0,005kL = 0,05 hl = 0,5 dal = 50 dl = 500cL = 5000 ml 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 c) 3 kl, 20cL and 300 ml 12

13 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 = 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? 5. The recipe for a cocktail says: 1 1 of orange juice, 8 10 of lemon juice, 2 of pineapple 3 juice and the rest of water. If I want to prepare 1 litre, how much of each juice will I use? Solve them in groups and invent similar ones to your class group. 13

14 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 m 3 Units of volume. Multiples and submultiples are: Cubic Kilometre 1km 3 = m 3 Cubic Hectometre 1 hm 3 = m 3 Cubic Decametre 1 dam 3 = 1000 m 3 Cubic metre m 3 Cubic decimetre 1dm 3 = 0,001m 3 Cubic centimetre 1cm 3 = 0, m 3 Cubic millimetre 1mm 3 = 0, m 3 M u l t i p l e s 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 hm 3 to m 3, 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 hm 3 to m 3 we should multiply by = 2 x = m 3. Example: An object has a volume of 245 cm 3, how many dm 3? and mm 3? Exercise: 245 : 1000 = 0,245 dm x 1000 = mm 3 Express in m 3 the following volume: a) 0,4 hm 3 b) 0,0032 dm 3 c) 24 dm 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 dm 3 = 1L of water = 1 kg Exercise: How many litres are in 3 m 3? 1 st we convert m 3 to dm 3 3 x 1000 = 3000 dm 3 = 3000 L Solved problem: A child wants to fill a 500 cm 3 bucket. How many litres of water does he need to fill it? 500cm 3 dm 3 1 place to the left, so divide by 1000 = 0,500 dm 3 = 0,5 L what is half a litre or 500 ml 14

15 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 m 2 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 m 2 Units of surface: Multiples and submultiples are: Square Square Square Square Square Square Square Kilometre Hectometre Decametre metre decimetre centimetre millimetre 1km 2 = m 2 1 hm 2 = dam 2 = 100 m 2 m 2 1dm 2 = 0,001m 2 1cm 2 = 0, m 2 1mm 2 = 0, m 2 m 2 M u l t i p l e s 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 hm 2 to m 2, 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 hm 2 to m 2 we should multiply by = 2 x = m 2. Example: A table is 120 cm long and 70 cm wide. Its area is 120 x 70 = 8400 cm 2 = 8400 : = 0,84 m 2 Other units for large surfaces: area 1(a) = 100 m 2 Área and hectárea en español. y fanega? And hectare 1(ha) = 1hm 2 =100 areas = m 2 Exercises: 1. What unit of surface will you use to measure: cm 2, mm 2, km 2, m 2, dm 2? a) Your room floor b) a paper area c) The surface of a country 2. Complete the table: Km 2 hm 2 dam 2 m 2 dm 2 cm 2 mm ,

16 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). OBJECT Length Width AREA AREA in m 2 Door 2 m 70cm 200 x 70 = 14000:100 00= cm 2 1,4 m 2 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 m 2 will I need? EXERCISE 3 Surfaces of places Find out the surface of different countries or towns; express it in m 2 and compare. Example: Spain has a surface of 506,990 km 2, is it bigger than France? If we have 30% of forest surface, How many hectares are there? 30% of 506,990 = 152,097 km 2 = 152,097 x 100 = 15209,7 ha 16

17 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 km 2 area. This is called population density: inhabitants For example, Hervás has a surface of 60 km 2 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 A screen of 12 inches 3 TEASPOONS 1 TABLESPOON 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? 17

18 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. 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. They settle in different degrees the freezing point of water and the boiling point of water. CELSIUS O C FAHRENHEIT O F Freezing point of water Boiling point of water Normal Body temperature 0 o C 32 o F C 212 o F 37 o C 98,6 o F To convert o F to o C ( o F 32) 5 9 = Example 78o F (78 32) 5 9 = 25,5 o C Twenty-five point five degrees Celsius or Centigrade To convert o C to o F o C = Eighty-nine point 6 degrees Fahrenheit Example 32 o C 32 x = 89,6 o F Why the fraction 5/9 and 9/5? The difference between the freezing point and the boiling point in Fahrenheit is = 180, in Celsius is = 100. The proportion is o C to o F = = if we reduce it. And o F to o C = = Converting practices and reading temperatures: 18

19 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) = = 48 o F (48 32) 5/9 = 8,8 o C 1. The pool water temperature at 9 a.m. was 62 o F, 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 o C b) Inside a freezer it is 10 o C 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 70 o C Exercise 3: Choose a reasonable temperature for: 1) The temperature of your classroom in a warm day: a) 68 o F b) 80 o F c) 45 o F 2) The temperature of a dish of ice cream: a) 31 o F b) 0 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 Yesterday the temperature in Oxford was 7 o C, Today the temperature will be 10 o C and Tomorrow it will be 8 o C Celsius degrees and Fahrenheit degree: In degrees Fahrenheit: Yesterday was 44,6 o F, today 50 o F and tomorrow it will be 46,4 o F 19

20 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 dm 3 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. Marina bought the following groceries: 1 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? 20

21 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. 21

22 - 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 please. - Here you are 20 - Thanks, 7.10 is your change. - Thanks, Can I have an invoice, please? - Yes, of course. Here you are is the base plus 4% VAT =0.50. Final price 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 m 2 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. 22