Simple explanations of important techniques to help you through your SATS exams. http://www.satsguide.co.uk Finding information in texts is something you have to do every day, for example when you read a book, use a timetable or research on the internet. You will almost certainly have been practising finding information in a variety of school subjects for as long as you can remember. In the SATs, questions which ask you to pick out facts or details can be a quick way of picking up several vital marks, so it's important that you do them well. Here's a reminder of how to go about finding information: Firstly, read the text really carefully, at least once. Next, read the question a couple of times to make sure you understand exactly what it's asking you. Lots of people lose marks by half-reading the question and doing what THEY think it says, not what's actually on the page! Use you skimming and scanning skills to home in on the information, and write it down. http://www.satsguide.co.uk/mod-how_to-21-41.htm Magnetism - A magnet will pull some metals towards itself. - Most metals are not attracted (not pulled) to magnets. - The metals that are attracted to magnets are iron, nickel and cobalt. These metals are called magnetic. - Steel is a mixture of metals. Steel is magnetic because it contains iron. - All magnets have two poles. - Two magnets with unlike poles facing will attract (pull towards) each other. - Two magnets with like poles facing will repel (push away) each other. - The pull of a magnet can be measured with a newton meter. http://www.satsguide.co.uk/mod-how_to-18-26.htm Physical Processes: Sound Loudness - A vibrating object can make a quiet sound or a loud sound. - To make a louder sound from a drum, hit the skin harder. - To make a louder sound from a string, pluck it with a greater force. Pitch - A vibrating object can be made to change pitch. - If the length of a vibrating string is shortened then the pitch will rise (it will have a higher pitch). - If the tension (amount it is stretched) in a vibrating drum skin is less, then the pitch will fall (it will have a lower pitch). Materials and sound - If there is a material such as gas, liquid or solid next to the vibrating object, the sound can travel. - The sound travels through a material. The sound makes the material vibrate. - Sound can travel very well in some solids, such as metal pipe, because the vibrations travel easily. - We generally hear sounds because the air is carrying vibrations from objects to our ears. - If there is no material between an object and our ears we cannot hear any sound. http://www.satsguide.co.uk/mod-how_to-19-30.htm Accuracy If we weigh each plum individually, we may get a range of weights between 36.25g and 44.68g. It may not be necessary to be this accurate in an answer: to say that the plums range in weight from 36g to 45g may be good enough. We often have to judge the level of accuracy we need to give to our answers, estimated or final, according to the situation the question addresses: - Population figures are given to the nearest thousand. - Drug doses are given to the nearest whole mg. - Athletic times are given to the nearest hundredth of a second - Distances are given to the nearest mile or kilometre. http://www.satsguide.co.uk/mod-how_to-4-12.htm Classification Classifying means arranging animals or plants in groups. Scientists use similarities and differences to put living things into groups. The two really big groups are called animals and plants. Animals are divided into two groups: Vertebrates have a spine or backbone. Invertebrates do not have a backbone. Vertebrates are divided into five groups: 1. Mammals 2. Birds 3. Amphibians 4. Fish 5. Reptiles Animals in each group share similarities: all mammals feed their babies on milk, for example. Invertebrates are divided into seven groups. But don't worry - you don't need to know all their names. The biggest group of invertebrates is the arthropods. This includes insects and spiders. Plants are divided into two groups, flowering plants and non-flowering plants. Flowering plants all have flowers, but they can be very different from each other. Non-flowering plants do not have flowers, but again they can be very different from each other. Scientists often use keys to identify the group an animal or plant belongs in. A key is a series of questions. The answers help to identify the animal or plant. The best way to understand this is to try one yourself. Follow these steps. 1. Look at the pictures. 2. Take one animal at a time. 3. Start with the first question, and answer it for that animal only. 4. Follow the line from each answer http://www.satsguide.co.uk/mod-how_to-13-33.htm Sources and reflectors of light - A source makes its own light. - The sun and other stars, very hot metal and fires are sources of light. - The moon is not a source of light. It reflects light from the sun. - Planets do not make their own light. They reflect light from the sun. - When driving at night 'cat's eyes' on the road reflect light from the car's headlamps. - A reflector of light such as a mirror will not be seen in a completely dark room. Seeing a light source - We see a light source when light from the source enters our eyes. - Danger! You must never look directly at the sun. The amount of light travelling from it will damage your eyes very quickly. - Fireflies and glow-worms make their own light to attract mates. Shadows - Light can travel through some transparent materials so that you can see clearly the light source. - Light can travel through some translucent materials, but the light source will not be seen clearly. - Light cannot travel through opaque materials. The light is blocked. - A shadow is formed where light is blocked. - If an object is moved closer to a light source the shadow gets bigger. http://www.satsguide.co.uk/mod-how_to-9-29.htm Steps: 1. Use the straight edge of the protractor to draw a straight line. This line will form one side of your angle. 2. Find the center hole on the straight edge of the protractor. 3. Place the hole over one end point of the line you have drawn. 4. Line up the zero on the straight edge of the protractor with the line. 5. Make a mark at the number on the curved edge of the protractor that corresponds to the desired measure of your angle. For example, mark at 90 for a 90-degree angle. 6. Use the straight edge of the protractor to connect the mark to the end point of the first line, forming an angle. http://www.satsguide.co.uk/mod-how_to-22-50.htm Construction steps Draw a circle. Without changing the compass opening, pick a point on the circle as a new center and draw another circle with the same radius. Pick one of the two points where the circles intersect. Connect the two centers and your chosen intersection point with line segments. You have just constructed an equilateral triangle. http://www.satsguide.co.uk/mod-how_to-22-47.htm When rounding off numbers, we can take the number of places after the decimal, or look at the whole number. e.g. if we work out the square root of 5 on a calculator, we get the answer 2.2360679774…. To work with a number having this number of decimal places is very long-winded, so we can round the number up or down according to the level of accuracy we need. To round off 2.2360679774 to 3 decimal places, we look at the 4th digit after the decimal point: 2.2360679774 this is less than 5, so the answer is 2.236 If we round off 2.2360679774 to 2 decimal places, the answer is 2.24, as the 3rd number after the decimal point is greater than 5. Note: Round 0.00321 to 2 decimal places: The 3rd number after the decimal point is less than 5, so the answer is 0.00. We need the two places of decimals in the answer. http://www.satsguide.co.uk/mod-how_to-4-14.htm Expressions An expression is a mathematical statement that may use numbers, variables, or both. Example: The following are examples of expressions: 2 x 3 + 7 2 × y + 5 2 + 6 × (4 - 2) z + 3 × (8 - z) Example: Roland weighs 70 kilograms, and Mark weighs k kilograms. Write an expression for their combined weight. The combined weight in kilograms of these two people is the sum of their weights, which is 70 + k. Example: A car travels down the freeway at 55 kilometers per hour. Write an expression for the distance the car will have traveled after h hours. Distance equals rate times time, so the distance traveled is equal to 55 × h.. Example: There are 2000 liters of water in a swimming pool. Water is filling the pool at the rate of 100 liters per minute. Write an expression for the amount of water, in liters, in the swimming pool after m minutes. The amount of water added to the pool after m minutes will be 100 liters per minute times m, or 100 × m. Since we started with 2000 liters of water in the pool, we add this to the amount of water added to the pool to get the expression 100 × m + 2000. To evaluate an expression at some number means we replace a variable in an expression with the number, and simplify the expression. Example: Evaluate the expression 4 × z + 12 when z = 15. We replace each occurrence of z with the number 15, and simplify using the usual rules: parentheses first, then exponents, multiplication and division, then addition and subtraction. 4 × z + 12 becomes 4 × 15 + 12 = 60 + 12 = 72 Example: Evaluate the expression (1 + z) × 2 + 12 ÷ 3 - z when z = 4. We replace each occurrence of z with the number 4, and simplify using the usual rules: parentheses first, then exponents, multiplication and division, then addition and subtraction. (1 + z) × 2 + 12 ÷ 3 - z becomes (1 + 4) × 2 + 12 ÷ 3 - 4 = 5 × 2 + 12 ÷ 3 - 4 = 10 + 4 - 4 = 10. http://www.satsguide.co.uk/mod-how_to-2-4.htm Fractions This section is designed to help you understand "fractions" and to lead you through a number of calculations involving fractions. Hopefully much of what follows is familiar to you. A fraction is a part or subdivision of the whole and is written in the form x/y where x is the numerator and y is the denominator. In proper fractions the numerator is smaller than the denominator whereas in improper fractions the reverse is true. Hence, 1/2, 1/4 and 2/5 are all proper fractions whereas 5/3, 9/2 and 7/3 are all improper fractions. In proper fractions the value represented is always less than 1 but for improper fractions the value represented is always greater than 1. Conversion of fractions We can convert fractions into other fractions by multiplication or division. For example, if we wanted to express 1/5 in terms of "tenths" we simply need to multiply the 5 by 2 to give us "10" as the denominator and also multiply the numerator by the same amount. Hence; 1/5 = 2/10 = 5/25 = 10/50 and so on. We can complete the reverse procedure by division, hence; 25/75 = 5/15 = 1/3 (In this case we have divided both numerator and denominator by 5 each time). These fractions are called equivalent fractions. Check-point #1 Express the following fractions as indicated; 1/6 as x / 18 To convert 6 to 18 we must multiply by 3 so we multiply both numerator and denominator by 3, 1/6 = 3/18 You try: 1/3 as x/9 1/5 as x/30 1/9 as x/36 Answers It is normal practice to express fraction as their "lowest forms", in other words with the smallest denominator whilst leaving the numerator as a whole number. So we would express 3/9 as 1/3, 36/48 as 3/4 and 12/ 24 as 1/2. Addition/Subtraction of Fractions To add or subtract fractions we must first convert them so they have a common denominator. So to add 1/5 and 1/15 together we convert the 5 to 15; (1/5 + 1/15) = (3/15 +1/15) = 4/15 Subtract 1/9 from 1/3 (1/3 – 1/9) = (3/9 – 1/9) = 2/9 Multiplying and Dividing Fractions To multiply fractions we simply multiply the numerators and denominators as required. Hence 1/5 x 2/6 = 2/30 or 1/15 (= 1 x 2 / 5 x 6) But what happens if we have mixed numbers? How can we multiply 1 ½ x 2 ¾ ? For this calculation we must first convert the numbers into improper fractions; 1 ½ = 3/2 2 ¾ = 11/4 So 1 ½ x 2 ¾ = 3/2 x 11/4 = 33/8 We can now cancel down this improper fraction to give 4 1/8 Check-point #2 Complete the following calculations; 2/3 x 4/5 = (2x4)/(3x5) = 8/15 You try: 2/3 x 7/15 5/8 x 4/5 1 1/3 x 3 1/6 Answers Division of fractions is little more involved. To divide fractions we invert (turn upside down) the fraction we wish to divide by and change the division into a multiplication. An example is probably the best way to explain this. So let’s do the division 1/5 ¸ 2/9 First invert 2/9 to give 9/2 Change the division sign to multiplication 1/5 x 9/2 = 9/10 and that’s our answer! This might seem a little odd but if we take a more obvious example of how this might work. Suppose we have 3 ½ cakes and want to cut them up into quarters, the calculation would be; 3 ½ ¸ ¼ Following the rules above we invert the ¼ to give us 4/1 and change the division sign to a multiplication sign; 3 ½ x 4/1 Now convert the 3 ½ to an improper fraction (7/2) 7/2 x 4/1 = 28/2 Simplify; 28/2 = 14/1 = 14 So 3 ½ cakes will give us 14 quarters. http://www.satsguide.co.uk/mod-how_to-4-20.htm 16 grams = 1 ounce 16 ounces = 1 pound 7 pounds = 1 clove 14 pounds = 1 stone 28 pounds = 1 tod 112 pounds = 1 hundredweight 364 pounds = 1 sack 2240 pounds = 1 ton 2 stones = 1 quarter 4 quarters = 1 hundredweight 20 hundredweight = 1 ton http://www.satsguide.co.uk/mod-how_to-6-17.htm Imperial units We mainly use metric measures, but there are some older units called imperial units that we sometimes use. For example, road signs always give distances in miles rather than kilometres Here are the rough approximations between metric and imperial units for lengths, weights and capacities: 12 inches = 1 foot 16 ounces = 1 pound 8 pints = 1 gallon 2½ cm = 1 inch 25g = 1 ounce 1 litre = 1¾ pints 30 cm = 1 foot 2¼ pounds = 1kg 4½ litres = 1 gallon The area is the amount of surface a 2D shape covers. To work out the area of a shape, multiply its length by its breadth. The units we use to measure an area include square centimetres (cm²), square metres (m²) and square kilometres (km²). It is more difficult to measure the area of irregular shapes. Look at the shape: (picture) To measure its area: - Count the squares that are wholly within the shape. 1, 2 - Squares that are half or more in the shape count as whole ones. 3, 4, 5, 6, 7, 8, 9, 10 - Don't count squares that are less than half in the shape. - So the area is approximately 10cm² http://www.satsguide.co.uk/mod-how_to-6-23.htm Lengths 1 nail = 2¼ inches 4 inches = 1 hand 12 inches = 1 foot 3 foot = 1 yard 5.5 yards = 1 rod 6 foot = 1 fathom 22 yards = 1 chain 100 links = 1 chain 10 chains = 1 furlong 8 furlongs = 1 statute mile 6080 foot = 1 nautical mile http://www.satsguide.co.uk/mod-how_to-6-18.htm Measures Length Weight Capacity You need to know these units: millimetre (mm) gram (g) millilitre (ml) centimetre (cm) kilogram (kg) decilitre (dl) metre (m) tonne centilitre (cl) kilometre (km) litre (l) You need to know these equivalent measures: 1cm = 10mm 1m = 100cm 1m = 1000mm 1km = 1000m 1kg = 1000g 1 tonne = 1000kg 1dl = 10ml 1cl = 100ml 1l = 1000ml = 100dl = 10cl Try to remember: deci = tenth part centi = hundredth part milli = thousandth part kilo = 1000 times the unit http://www.satsguide.co.uk/mod-how_to-6-22.htm Operators and BODMAS Operators are processes which can be performed on numbers, e.g. +. - , x, ÷, raising to a power by the use of indices. When we are confronted with a long calculation, the order in which we use the operators is important: 16 ÷ 4 x 2 could be 16 ÷ 4 = 4, x 2 = 8 or 16 ÷ 4 x 2, (which equals 8, ) = 2 To make sense of this, we can use brackets, or take the operations in the correct order. The first answer takes each operation in the correct order, (divide before multiply) If we require the second answer, we must put brackets round the operation we wish to do first: 16 ÷ (4 x 2) BODMAS is the memnonic which helps us remember the order of operations: B is for brackets O is for "over", or finding a fraction, or using indices D is for divide M is for multiply A is for additon S is for subtraction. e.g. Find the value of a in the equation a =5(6 + 3) 10 a = (5 x 9) ÷ 10 a = 45 ÷ 10 a = 4.5 http://www.satsguide.co.uk/mod-how_to-4-10.htm We sometimes have to deal with very large or very small numbers. These are often approximations of real quantities which cannot be measured accurately. e.g. The planet Pluto is, on average, 3,500,000,000 miles from the earth To work with a number which has lots of 0s is difficult and prone to error We therefore use standard notation to reduce the figures to a workable form. We do this by writing the number multiplied by powers of 10. 101 = 10 x 1 = 10 102 = 10 x 10 = 100 103 = 10 x 10 x 10 = 1000 etc. Similarly, 10-1 = 1/10 10-2 = 1/100 10-3 = 1/1000 A very large number like the one above is usually written in the form of a number between 1 and 10 multiplied by 10x e.g. 3,500,000,000 = 3.5 x 109 0.000 000 000 023 = 2.3 x 10-14 Simply count the number of places the decimal point has to be moved in either direction. Operations on numbers in Standard Form Obviously multiplying, adding or dividing very large or very small numbers is liable error: 32, 000,000,000 x 2,000,000 = 64,000,000,000,000,000 ; counting the "0"s takes longer than writing them! We can perform operations on numbers in standard form: e.g. multiply 5.6 x 104 by 5.1 x 105 5.6 x 5.1 = 28.56 104 x 105 = 109 (Add the indices when multiplying) N. B. 28.56 x 109 is not incorrect, but is usually written 2.8 x 1010 Divide 2.1 x 106 by 7 x 103 2.1 x 106 = 0.3 x 103 = 0.3 x 102 7 x 103 Add 7 x 104 to 5 x 104 (7 + 5) = 12, x 104 = 1.2 x 105 Note: you do not add the indices when you are adding, only when multiplying. It is probably easier to understand why if we write out the whole sum 70,000 50,000 120,000 Add 5 x 105 and 6 x 106 To do this we have to write both numbers in the same power of 10: 6 x 106 is the same as 0.6 x 105 (5 + 0.6) = 5.6 x 105 http://www.satsguide.co.uk/mod-how_to-4-16.htm When looking at significant figures, the numbers are counted from the left The abbreviation s.f. can be used. e.g.Write the number 2.2360679774 to 3 significant figures: 2.2360679774: the 4th number is 6, which is greater than 5. The answer is therefore 2.24 Round 2.2360679774 to 4 s.f: 2.2360679774; the 5th number is less than 5, therefore the answer is 2.236 e.g. Round 1890 to 2 s.f: 1890: the 3rd number is greater than 5, Therefore the answer is 1900. The first 2 figures are significant, the last two keep the magnitude of the number. http://www.satsguide.co.uk/mod-how_to-4-15.htm The temperture at which volumes etc. are defined in the Imperial system is 62°F To convert a Fahrenheit temperature to centigrade, do the following: a) Subtract 32 b) Multiply by 5 c) Divide by 9 Try it with 66°F - you should get 19°C. To convert C to F, just do it the other way round! http://www.satsguide.co.uk/mod-how_to-6-19.htm The continuous present The tense of a verb tells us when the action was done. The action can be done in the past, present or future. When do I use the present tense? There are two types of present tense - 2. Present continuous Use the present continuous form of a verb when: The action isn't a single action, it is an action that carries on. It is good for describing what people are doing at a particular moment. e.g. I am kicking the ball. He is walking the dog. The present continuous is made by having am, is or are + the verb + 'ing'. I am working hard you we they are working hard he she it is working hard NOTE! Sometimes you can use the present continuous to talk about the future. e.g. I am going on holiday on Friday. http://www.satsguide.co.uk/mod-how_to-12-6.htm The simple present The tense of a verb tells us when the action was done. The action can be done in the past, present or future. When do I use the present tense? There are two types of present tense - 1. Present simple Use the present simple form of a verb when The action takes place now. e.g. I want you to help me now. The action is something that happens regularly. e.g. I walk the dog everyday. You are describing things that are generally true. e.g. Train travel is expensive. NOTE! When it is 'he', 'she' or 'it' doing the action, remember to add 's', 'es' or change the 'y' to 'ies'. e.g. I like football, we like football, he likes football. I always try hard, we always try hard, she always tries hard. I watch a lot of films, we watch a lot of films, he watches a lot of films. I seem OK, we seem OK, it seems OK. http://www.satsguide.co.uk/mod-how_to-12-5.htm Time You need to know these equivalent times: 1 minute = 60 seconds 1 hour = 60 minutes 1 day = 24 hours 1 week = 7 days 1 fortnight = 14 days 1 year = 12 months = 52 weeks = 365 days leap year = 366 days Many timetables and digital watches use the 24-hour clock time. Use this scale to change between 12-hour and 24-hour time. 6.15 am 0615 6.15 pm 1815 Remember: am is morning time (it comes from the Latin ante meridian, meaning 'before midday'). pm is afternoon and evening time (it comes from the Latin post meridian, meaning 'after midday'). The 24-hour clock always uses 4 digits Here is a way to remember how many days there are in each month. All the 'knuckle' months have 31 days. February has 28 days (29 in a leap year). April, June, September and November have 30 days. http://www.satsguide.co.uk/mod-how_to-6-21.htm Growth - G - Giraffes To grow is to increase in size. Growth is the process of growing Baby animals get bigger and become adults Seedling plants become mature larger plants Reproduction - R - Ride Animals and plants make new animals and plants that are like their parents Movement - M - My Animals move in lots of different ways Plants can move their leaves to absorb the sunlight Nutrition - N - New Plants make their own food from simple raw materials Animals don't make their own food. They eat plants or other animals Sensitivity - S - Skateboard Animals and plants are aware of how their surroundings change and respond to them REMEMBER... being able to do all of these is what makes things living organisms http://www.satsguide.co.uk/mod-how_to-13-32.htm ANIMALS CANNOT MAKE THEIR OWN FOOD AND SO THEY HAVE TO - EAT PLANTS AND OTHER ANIMALS. A FOOD CHAIN SHOWS HOW PLANTS ARE EATEN BY ANIMALS AND ANIMALS ARE EATEN BY OTHER ANIMALS. A FOOD CHAIN ALWAYS STARTS WITH A PLANT. http://www.satsguide.co.uk/mod-how_to-16-36.htm All animals grow and reproduce Animals grow at different rates during their lives There is a lot of variation - children of the same age vary in size These are main stages in the life cycle of humans and other animals http://www.satsguide.co.uk/mod-how_to-13-35.htm When the weather is warm, water in lakes, rivers and the sea evaporates - it turns into vapour and rises into the air. In the air, the vapour cools down again and turns into small drops of water. This is called condensation. The drops make clouds. As the drops get bigger, they fall back down to the earth. This is called precipitation. On earth, the water runs into rivers, and back into the sea. Trees and plants use water in the soil. The water moves from the roots into the leaves. Somes of it evaporates into the air. This is called transpiration. http://www.satsguide.co.uk/mod-how_to-10-37.htm What are solids, liquids and gases made of? To help explain the differences between solids, liquids and gases we need to look closely at what they are made of. Scientists have found that all materials are made of very, very tiny particles. These particles are so small that we can’t see them with our eyes or even a microscope. We can explain why solids, liquids and gases are different from one another using ideas about particles: how near they are to each other - when particles are close together they attract each other. This affects the behaviour of solids, liquids and gases. the way that they move - when we heat a material, its particles move faster or more vigorously. Picture 1.5 Animation of a solid, a liquid and a gas. In the real thing, there would be billions of particles. A solid In a solid the particles fit very closely together. They are constantly vibrating and twisting. But they do not move past their neighbouring particles. Because the particles are close together: they attract their neighbours - this is why solids tend to keep their own shape and to stay where they are put solids are very difficult to compress - the gaps between particles are already very small. Liquids In a liquid the particles are still close together but a little further apart than in a solid. The particles can move around and mix with other particles. Therefore, liquids can change shape to match their container. There is still very little space between particles, so liquids are also difficult to compress. Gases In gases the particles are much further apart than in solids or liquids. There is a lot of space in between the particles and they are constantly moving about. The particles collide with other particles and with the walls of the container. Because the particles are moving about, a gas will fill any container that it is put into. Because there is space between the particles, they can be squashed into a smaller volume when the gas is compressed. http://www.satsguide.co.uk/mod-how_to-8-38.htm A sector is the part of a circle between two radii. Draw a circle using a compass. Then mark a sector Then join the ned points of a sector with a straight line http://www.satsguide.co.uk/mod-how_to-22-45.htm Probably the most frequent means of drawing a right triangle is when the length of the sides of the right triangle have been calculated, and those dimensions are used to lay out the triangle. For instance, you know a 45° right triangle with a leg length of 4" is needed. You also know that the legs of a 45° right triangle are perpendicular and are equal in length. This knowledge is used in drawing that triangle. First: Use a framing square or a compass to draw perpendicular lines. Second: Set the dimension of your compass for 4" and mark both lines from the vertex of the 90° angle. Third: Connect the points and you will have drawn a 45° right triangle. http://www.satsguide.co.uk/mod-how_to-22-46.htm Counting on Counting on is a good method for subtracting numbers mentally. To find the difference between 37 and 63... Picture a blank number line in your head with 37 at one end and 63 at the other. Count on from 37 to 40 and keep that 3 in your head. Now count on from 40 to 63, which is 23 Add the 3 to 23 to make 26 Adding by rounding To add 9 to another number, add 10 and then subtract 1 36 + 9 = 36 + 10 - 1 = 45 To add 8 to another number, add 10 and then subtract 2 45 + 8 = 45 + 10 - 2 =53 To add 19 to another number, add 20 and then subtract 1 48 + 19 = 48 + 20 - 1 = 67 To add 18 to another number, add 20 and then subtract 2 53 + 18 = 53 + 20 - 2 = 71 To add 0.9 to another number, add 1 and then subtract 0.1 3.7 + 0.9 = 3.7 + 1 - 0.1 = 4.6 To add 0.8 to another number, add 1 and then subtract 0.2 4.5 + 0.8 = 4.5 + 1 - 0.2 = 5.3 Subtracting by rounding To subtract 9 from another number, subtract 10 and then add 1 46 - 9 = 46 - 10 + 1 = 37 To subtract 8 from another number, subtract 10 and then add 2 21 - 8 = 21 - 10 + 2 = 13 To subtract 19 from another number, subtract 20 and then add 1 63 - 19 = 63 - 20 + 1 = 44 To subtract 18 from another number, subtract 20 and then add 2 63 - 18 = 63 - 20 + 2 = 45 To subtract 0.9 from another number, subtract 1 and then add 0.1 8.2 - 0.9 = 8.2 - 1 + 0.1 = 7.3 To subtract 0.8 from another number, subtract 1 and then add 0.2 7.3 - 0.8 = 7.3 - 1 + 0.2 = 6.5 Doubling If you are adding together two numbers that are nearly the same, doubling one of them will help you. 35 + 35 = 70 35 + 36 = 35 + 35 + 1 = 2 x 35 then add 1 = 71 46 + 46 = 92 46 + 47 = 46 + 46 + 1 = 2 x 46 then add 1 = 93 2.7 + 2.7 = 5.4 2.7 + 2.8 = 2.7 + 2.7 + 0.1 = 2 x 2.7 then add 0.1 = 5.5 Inverses Addition and subtraction are inverses (opposites). Subtraction can be checked by adding. 82 - 37 = 45 37 + 45 = 82 Multiplication and division are also inverses. Division can be checked by multiplying. 81 ÷ 3 = 27 27 x 3 = 81 http://www.satsguide.co.uk/mod-how_to-20-24.htm Fractions and decimals You can use your calculator to change fractions to decimals. Divide the top number (the numerator) by the bottom number (the denominator). 1 is the same as 1 ÷ 4. 4 Some fractions do not change exactly into decimals. 2 = 0.2857142... 7 2 = 0.66666666... 3 To round to the nearest tenth (one decimal place), look at the second digit after the decimal point. If it is 5 or more, round up the first digit. So, 2 is 0.3 to one decimal place. 7 To round to the nearest hundredth (two decimal places), look at the third digit after the decimal point. If it is 5 or more, round up the second digit. So, 2 is 0.29 to two decimal places. 7 http://www.satsguide.co.uk/mod-how_to-4-25.htm Looking for a Sensible Answer When we are confronted with a problem it is often helpful to make an estimate of a rough answer to get a feel for the real answer we are seeking. When undertaking experiments or research, it can be useful to have an understanding of the sensible limits of the answer we need. 1.89 x 4.01 is close to 2 x 4, therefore the answer will be about 8 (Accurate answer 7.5789 ) e.g. A pack of ten plums in a Supermarket has a weight of 400g. Each individual plum will therefore weigh approximately 40g. It is unlikely that any plum will weigh exactly 40g, but in any calculation of the average weight of each plum, this will be about right. If any calculation of the weight of any individual plum comes to more than, say, 55g or less than, say 25g. our calculation is likely to be incorrect, as the answer is not sensible in the context of Supermarket plums. A range of 30g difference in weight between the smallest and largest plums in the pack is obviously very large, and not likely in any Supermarket package, so we may need to investigate more closely to get an accurate estimation of the weights. http://www.satsguide.co.uk/mod-how_to-4-11.htm Steps: 1. Find the center hole on the straight edge of the protractor. 2. Place the hole over the vertex, or point, of the angle you wish to measure. 3. Line up the zero on the straight edge of the protractor with one of the sides of the angle. 4. Find the point where the second side of the angle intersects the curved edge of the protractor. 5. Read the number that is written on the protractor at the point of intersection. This is the measure of the angle in degrees. Tips: There are 360 degrees in a circle. A straight line measures 180 degrees. The corner of a square measures 90 degrees. This is called a right angle. Angles that measure fewer than 90 degrees are called acute angles. Those measuring more than 90 degrees are called obtuse angles. http://www.satsguide.co.uk/mod-how_to-22-49.htm If the answer to a calculation gives us an answer which is too accurate to be sensible, we can round the number up or down, according to the level of accuracy we require. e.g. A Local Education Authority has a total of 14 Secondary Schools under its control. There are 13,540 pupils attending those schools. If we find the average number of students per school, the answer does not make sense; 13540 = 967.14285 14 We cannot have .14285 of a pupil! The answer is therefore rounded down to 967 pupils per school. Should one of the schools close, we get an answer of 13540 = 1040.5384 13 This is rounded up to 1041 Rule: Decide what level of accuracy you require. Look at the number after the one you wish to round off to: in the example we rounded the answer to the nearest whole number, or pupil. If that number is 5 or greater, round up. If that number is less than 5, round down. e.g. The population of Ariba Island is 90,563. To the nearest 1,000 this can be written as 91,000 The distance between Glasgow and London is 414 miles. To the nearest 10 miles, this distance is estimated at 410 Darren Scoot broke the men's 100m running record by completing the distance in 9.4567 seconds. To the nearest hundredth of a second, this is recorded as 9.46 http://www.satsguide.co.uk/mod-how_to-4-13.htm Talking about the future The tense of a verb tells us when the action was done. The action can be done in the past, present or future. When do I use the future tense? There are three main ways of talking about the future. You can say: I will work late tomorrow. = future tense I am working late tomorrow. = present continuous tense I am going to work late tomorrow. = 'going to' + verb 1. Future tense This is made by 'will' or 'shall' + the verb, as in the example above 'I will work late tomorrow.' Note that 'will' and 'shall' are often shortened. e.g. Autumn will soon be here. It'll break if you drop it. What will you do? I don't know what I'll do 2. Present continuous You can use the present continuous when you are making plans. It's useful to talk about definite arrangements in the near future, as in the example above 'I am working late tomorrow.' e.g. What time are you leaving tomorrow? I'm leaving at 8 O'clock. I'm going out tomorrow. I'm getting a new car next week. 3. Going to 'Going to' + the verb is also useful to talk about plans. It suggests that something is decided. e.g. What are you going to do this evening? I'm going to watch a film on TV. I think it's going to rain. He's going to play football. http://www.satsguide.co.uk/mod-how_to-12-9.htm Talking about the past (1) The tense of a verb tells us when the action was done. The action can be done in the past, present or future. When do I use the past tense? There are many ways of talking about the past in English, but the two main ones are the simple past and the continuous past. 1. Simple past Use the simple past form of a verb when you are talking about an action that took place at a specific point in the past and that is now finished. e.g. I kicked the ball and scored a goal. I walked the dog yesterday. I went to Florida last year. NOTE! The simple past is formed in different ways for regular and irregular verbs. For regular verbs there is a rule, but irregular verbs just have to be learned! e.g. 'I live in London now, but I lived in France for five years' = regular simple past tense 'I normally go to work by bus, but yesterday I went in the car' = irregular simple past tense http://www.satsguide.co.uk/mod-how_to-12-7.htm Talking about the past (2) The tense of a verb tells us when the action was done. The action can be done in the past, present or future. When do I use the past tense? There are many ways of talking about the past in English, but the two main ones are the simple past and the continuous past. 2. Past continuous Use the past continuous form of a verb when you want to talk about a long action that carried on in the past. The continuous past is often used to describe what people were doing when something else happened. e.g. I was kicking the ball when Dave broke his arm. He was walking the dog when I saw George. The past continuous is made by having was, or were + the verb + 'ing'. I he she it was working hard you we they were working hard http://www.satsguide.co.uk/mod-how_to-12-8.htm Balanced Forces If an object is still the forces are balanced. An upthrust takes place when an object displaces air or a liquid. It is a type of reaction force. if an object floats on water the forces are balanced. The weight of the boat is balanced by the upthrust of the water. If an object such as a cup stands on a table the forces are balanced. The weight of the cup is balanced by a reaction force from the table. You can see balanced forces easily in a tug-of-war when the ribbon is not moving. Unbalanced forces If an object starts to move, speeds up, slows down, stops or changes direction, the forces are unbalanced. http://www.satsguide.co.uk/mod-how_to-18-28.htm Day and night All these effects are caused by the Earth spinning on its axis: The sun appears to move across the sky in the day. The sun rises in the east, is highest in the sky at midday and sets in the west. Shadows are longer in the morning and evening, and shortest at midday. The moon The moon is much smaller than the Earth. We only see one face of the moon. We see phases of the moon because light from the sun reflects off the moon. A solar eclipse is when the moon blocks the sun's light. http://www.satsguide.co.uk/mod-how_to-15-31.htm Gravity An object has a mass, which is the total amount of material it is made of. Mass is not a force and is measured in Kilograms. We measure forces in Newtons using a Force meter (also called a Newton meter). The force that attracts or pulls the earth and an object (such as a person) towards each other is called gravity. The pull on the mass of any object by the planet makes the force that we call weight. Other planets, stars or moons also have gravity. In a diagram we can show gravity or weight by an arrow towards the Earth. Friction When we try to move an object, the force preventing or slowing that movement is called friction. If the object is already moving, the force slowing down the object is called friction, so friction is a push against a moving object. Friction is a contact force between materials. Air resistance is a type of friction between air and another material. Friction can be a useful force because it prevents our shoes slipping on the road when we walk and stops car tyres sliding. Remember! Upthrust is not a type of friction. Upthrust is an upward force found in gases and liquids. It is made by the gas or liquid below, pushing up more than the gas or liquid above. http://www.satsguide.co.uk/mod-how_to-18-27.htm Speed of Light The speed of light is 299,792,458 metres per second. Or approximately 300 million metres per second, or 186 thousand miles per second, or 1 foot per nanosecond. The speed of light, sometimes known as "C" (as in E=MC2), is a constant of the Universe. However you measure it, it really is 299,792,458 metres per second precisely, or about 186,282.4 miles per second. Sometimes the speed of light is approximated as 300 million and is written as 3 x 108. To find out about this way of writing big numbers, see exponential notation http://www.satsguide.co.uk/mod-how_to-9-39.htm Basic Operations. Most calculators today have the following operations, which you need to know how to use: Operation English Equivalent + plus, or addition - minus or subtraction, Note: there is DIFFERENT key to make a positive number into a negative number, perhaps marked (-) or NEG known as "negation" * times, or multiply by / over, divided by, division by ^ raised to the power yx y raised to the power x Sqrt or square root ex "Exponentiate this," raise e to the power x LN Natural Logarithm, take the log of SIN Sine Function SIN-1 Inverse Sine Function, arcsine, or "the angle whose sine is" COS Cosine Function COS-1 Inverse Cosine Function, arccosine, or "the angle whose cosine is" TAN Tangent Function TAN-1 Inverse Tangent Function, arctangent, or "the angle whose tangent is" ( ) Parentheses, "Do this first" Store (STO) Put a number in memory for later use Recall Get the number from memory for immediate use http://www.satsguide.co.uk/mod-how_to-22-51.htm A compass is an instrument used to draw circles or the parts of circles called arcs. It consists of two movable arms hinged together where one arm has a pointed end and the other arm holds a pencil. Note that a compass is also called a pair of compasses. To draw a circle (or arc) with a compass: make sure that the hinge at the top of the compass is tightened so that it does not slip tighten the hold for the pencil so it also does not slip and align the pencil lead with the compass's needle press down the needle and turn the knob at the top of the compass to draw a circle (or arc) Example 2 Use a compass to draw a circle of radius 4 cm. Solution: Step 1: Use a ruler to set the distance from the point of the compass to the pencil's lead at 4 cm. Step 2: Place the point of the compass at the centre of the circle. Step 3: Draw the circle by turning the compass through 360º. Activity 1 1. Use a compass to draw a circle of radius 5 cm. 2. Use a compass to draw a circle of diameter 12 cm. 3a. Use a compass to draw a circle of radius 4.5 cm. 3b. Draw the diameter of the circle; and use a ruler to measure the length of the diameter. 3c. Write an equation to represent the relation between the radius, r, and the diameter, d. 4a. Use a compass to draw a circle of radius 5.5 cm. 4b. Draw a diameter and label it PQ. 4c. Draw a triangle PQR where R is on the semicircle. 4d. Use a protractor to measure the size of angle PRQ. 5a. Use a compass to draw a circle of radius 6.5 cm. 5b. Draw a diameter and label it PQ. 5c. Draw a triangle PQR where R is on the semicircle. 5d. Use a protractor to measure the size of angle PRQ. 6a. Use a compass to draw a circle of radius 7.5 cm. 6b. Draw a diameter and label it PQ. 6c. Draw a triangle PQR where R is on the semicircle. 6d. Use a protractor to measure the size of angle PRQ. 7. Use the results of questions 4, 5 and 6 to complete the following statements: a. The size of the angle on the diameter of a circle with a vertex on the circle is … b. If a triangle is drawn in a semicircle using the diameter as an edge, the angle touching the curved part of the triangle is … http://www.satsguide.co.uk/mod-how_to-22-44.htm Pick an entry or two to review. Find the parts of speech and related words, and look up the abbreviations used. Find several etymologies (word histories) and look up the abbreviations to decipher them. Check the pronunciations of some words you know to become familiar with the conventions used in your dictionary. Then look up a word that you do not know how to pronounce and see whether you can figure it out. Note special features such as quotations or examples of use. These are intended to help you find the exact meaning you're seeking. Try substituting the word in a sentence to test it. Look up abbreviated labels if you need to. These labels can indicate that a word is used in a certain region, for a specific subject, or that it has a special usage such as slang, informal, nonstandard, archaic, obsolete, vulgar and so on. You can use the dictionary to hunt around for synonyms of words. Although it's not as handy as a thesaurus, you will find plenty of related words by doing multiple lookups using the words in definitions. For a print dictionary, read the introductory or front matter of the dictionary. You'll understand the various features and how they're set off using typefaces (bold, italic), numbering, lettering and punctuation. Remember that the dictionary is not an unquestionable authority. It is written by trained professionals reporting on the real use of words and phrases by the general public. http://www.satsguide.co.uk/mod-how_to-21-43.htm A protractor is a tool that allows you to measure an angle or construct an angle of a given measure. Since you can measure angles from either side of the protractor, they have given you two sets of numbers. One set of numbers measures from the left side, the other measures from the right side. The way to figure out which to use is this: Put the bottom marking (where it will say either 0 or 180) on one leg of the angle, such that the other leg of the angle is going through the curved part of the protractor. So now you will know that the angle is one of the two angles it tells you. However, one of the two sets will tell you that the first leg is at 0 degrees; this is the set you want. You can check it because as the two legs get closer together, the angle should get smaller. http://www.satsguide.co.uk/mod-how_to-22-48.htm Apostrophes are a common source of confusion for many writers. They needn't be, though, and this easy-to-follow article will help you to use them properly. Let's start with a very simple explanation of what a noun is. A NOUN is a word that stands for a person or thing. Examples include "dog", "Tim", "love", "house" and "Ireland". SINGULAR NOUNS stand for a single person or thing; forexample, "chair". PLURAL NOUNS stand for several people or things; for example, "chairs". -------------------------------------------------------- Part 1. Using apostrophes to indicate possession -------------------------------------------------------- The most common use of an apostrophe is to indicate possession by a person or thing of some other person or thing. For example: "John's book" or "Europe's history". Using an apostrophe to indicate possession is really quite straight forward, yet it's a frequent source of confusion. There are two separate cases to consider: singular nouns and plural nouns. Singular nouns -------------- When a noun is singular (i.e. it stands for a single person or thing) we show possession by adding apostrophe–s. For example: the girl's book or Japan's recovering economy or the princess's gown or Mauritius's beaches or the cat's whiskers Summary: Singular nouns are made possessive by adding apostrophe–s. Plural nouns -------------- When a noun is plural (i.e. it stands for a several people or things) we show possession by adding s–apostrophe. For example: the CEOs' perks (the perks of two or more CEOs), the players' pride, (the pride of two or more players), the programmers' books, (the books belonging to two or more programmers), the boys' games(the games belonging to two or more boys) Summary: Plural nouns are made possessive by adding s–apostrophe. An exception ------------ As with many rules, there is an exception. This one concerns nouns that form their plural without adding an s. For example: woman/women, person/people, sheep/sheep and child/children. Words like this take apostrophe–s in both their forms. For example: the woman's idea(the idea belonging to one woman), the women's idea (the idea belonging to two or more women, the child's gift(the gift belonging to one child, the children's gift(the gift belonging to two or more children) Summary: Nouns that become plural without using an "s" (e.g. woman/women) are made possessive by adding apostrophe–s to both forms. -------------------------------------------------------- Part 2. Using apostrophes to indicate missing letters -------------------------------------------------------- Another use of the apostrophe is to indicate missing letters in contractions such as "isn't", "doesn't" and "can't". For example: --------------------------- Full form Shortened form --------------------------- can not can't do not don't does not doesn't I will I'll is not isn't it is it's let us let's shall not shan't there is there's you are you're --------------------------- You'll notice that the apostrophe appears in place of the omitted letter or letters. For example, in contracting "is not" to "isn't" the apostrophe replaces the missing "o". But consider contracting "shall not" to "shan't". If we put an apostrophe in place of the missing letters, shouldn't it be written "sha'n't"? After all, we've left out both "l"s and an "o". It's a valid point. Indeed, until a few generations ago, "sha'n't" was a commonly encountered spelling. Today, though, it is rarely if ever seen. That's all there is to it. Practice those simple rules, and you'll be the local expert on apostrophes. http://www.satsguide.co.uk/mod-how_to-21-52.htm Habitats The place where an animal or plant lives is called its habitat. Habitats can be big - a forest - or small - a leaf. Living things are adapted to their habitats. This means that they have special features that help them to survive. Look at the pictures to see how these animals and plants are adapted to their habitats. The African elephant keeps cool by flapping its large ears and using its trunk to spray itself with dust or water. The tufted duck has oiled feathers for waterproofing and webbed feet for swimming. Honeysuckle has flowers that produce nectar to attract insects for pollination. Its berries are brightly coloured for dispersal (birds are attracted by the bright colours, eat the berries and drop the seeds in different places). Marram grass has long roots so it can reach water, and thin leaves so that it doesn't dry up http://www.satsguide.co.uk/mod-how_to-13-34.htm Here is a simple checklist Read the poem Read it again Briefly, what is it about? What happens in each verse? Is it in regular verses or free verse? Does the poem rhyme? Why did the poet make it rhyme or not rhyme in your view? What is the mood of the poem? (e.g. is it humorous, bitter, romantic , unhappy, light-hearted, grieving etc?) Look at the images Which senses do they use? Are there any similes? Are there any metaphors? Try to explain how these images work and what they make you imagine. Look at the sound effects of words Is there any alliteration? Is there any onomatopoeia? Now read the poem again, and decide what the poet is trying to say – what is their message? What is your opinion of the poem? Why do you feel this way about it? http://www.satsguide.co.uk/mod-how_to-21-42.htm I'm convinced, however, that a small number of grammar essentials have the biggest impact on our students' work and it's these we should be concentrating upon. They are (in order of importance): Sentence variety: simple, compound, complex Connectives Paragraph organisation Tense Direct / indirect speech Descriptive detail (modification) Topic sentences Of these the single most important is sentence variety. This is what will most powerfully help your students to make the most improvement in their writing. Your weakest writers will have a shaky hold on sentence structure, sometimes missing out full stops or joining sentences (wrongly) with commas - like this: The play is interesting but it's difficult to know what's always going on, it starts on a battle field then Macbeth sees some witches Your grade 3 writers will probably write in compound sentences (sentences joined by and, but or or), like this: The play is dramatic at the beginning and the first thing we learn is that Macbeth is a successful soldier and how he has killed someone from the "nave to the chops" Your grade 4/5 writer will have learnt the power of sentence variety: Macbeth begins the play as a hero. His aggressive approach to the battle saves his country and begins his obsession with power. Fighting without fear, he shows himself to be completely ruthless. http://www.satsguide.co.uk/mod-how_to-21-40.htm A sentence must have a verb to be a proper sentence. Remember a verb is a doing or being word These are two sentences, the verbs are highlighted in bold. The cow jumped over the moon. I used to be a rhinoceros. The bold phrase is nota sentence because it does not have a verb: I bought a car. For £500. A sentence must also make sense on its own. http://www.satsguide.co.uk/mod-how_to-23-56.htm Speech marks always go at the start of the speech and at the end of the speech: “Come back here, Johnny” said Marcus. E.g. You do not need speech marks for reported speech. E.g. Marcus told Johnny to come back here. You must also use speech marks when quoting. E.g. In line 2, Marcus says to Johnny “come back here”. Remember: Always start speech marks with a capital letter Always end with a full stop, exclamation or question mark (as you would with a normal sentence). “I can’t wait till Christmas!” said Andrew. “Wherefore art thou Romeo?” asked Juliet. “Everyone sit down.” commanded the teacher. http://www.satsguide.co.uk/mod-how_to-23-57.htm The following rules are important in all aspects of English: 1. All sentences MUST start with a capital letter. 2. As well as number 1. all people, places, days and months must begin with a capital letter: Julian woke up on a Monday morning in January and ran to Ireland. 3)All questions NEED question marks. 4)NEVER use more than ONE exclamation mark: NOT: It was absolutely amazing!!!!! The basics are fundemental. DO NOT THROW AWAY EASY MARKS! http://www.satsguide.co.uk/mod-how_to-23-53.htm The most common use of apostrophes is to show ownership: Michael’s cat is black and white. When a group of people ending in‘s’ are owning something, you must add an apostrophe after the‘s’, like so: The teachers’ board pens have dried out. Another important use of apostrophes is for the short forms of words. Here is an important list to learn showing these forms: I’m- I am I’d- I would I’ve- I have We’ll- We will He’s- He is Won’t- Will not Can’t- Can not They’re- They are Who’s- Who is Doesn’t- Does not Here’s- Here is We’re- We are Finally, one of the biggest mistakes in English grammar and punctuation is the meaning and spelling of its and it’s. It’s (as mentioned above) is short for It is or It has: It’s fallen out of the tree. It’s so nice that you two have learnt to get along. Its, on the other hand, is used to show ownership: The grey cat swished its fury tail. http://www.satsguide.co.uk/mod-how_to-23-55.htm If a sentence has more than one point, you may keep those points seperated by using a comma: I asked him to be quite, but he kept on yelling. In this sentence the first point is that "I asked him to be quite" and the second point is that "he kept on yelling". You see- two related points seperated by a single comma. Commas are also used to add extra pieces of information into a sentence thus: John, who was 4ft 2 and had a long beard, spoke softly to the children. Another use for a comma is in lists: I went to the local shop and bought eggs, milk, cheese, bread and coffee. Be sure to use "and" before the last item in the list as shown above. WARNING: Be sure not to add in too many commas! http://www.satsguide.co.uk/mod-how_to-23-54.htm