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TRANSITION BOOKLET NUMERACY Welcome to St Wilfrid’s! Why is it important? Mathematics is a very important subject to study because it is useful for many other subjects as well as being fun. We want you to continue to practice your mathematics over the summer so that you remember the skills you have already learnt. This will help you to be ready at the start of Y7 to make good progress developing your fluency in mathematics, working with increasingly complex topics and problems. Every week during the summer holidays, you will be expected to complete a section of your Mathematics booklet. The purpose of this booklet is to: What do I have to do? • Show what you can already do • Help you to feel confident about your mathematical skills and ready to learn in Y7. • Help you to develop your interest and enjoyment in answering sums and solving puzzles. You should ask someone at home to help you with this booklet and to check your work! 2 Coordinates in all 4 quadrants Task Use the coordinates to find the hidden message. (-3, 5) (2, -5) (0, 4) W H (-3, 5) (1, -3) (-5, 1) Y (4, 0) (2, -5) (3, 3) (1, 5) (1, -3) (4, 0) (2, -5) (-5, 1) (-4, 3) (4, 3) (4, 3) (-3, 0) (-5, 1) (1, -3) (-2, -2) ? (-4, 3) (3, 3) (-4, -4) (1, -3) (-3, -5) (-5, 1) ((3, 3) (-2, 4) (4, 0) (2, -5) (1, -3) (-2, -2) (4, 0) (4, 3) (4, 3) (1, 5) (1, -3) (4, -4) (0, 4) (-5, 4) (4, 5) (4, 3) (-4, 3) (2, -1) (3, 3) (1, 5) (-5, 1)!! 3 Money Problems 1 A packet of biscuits costs 56p. A bottle of cola costs £1.14. Emma buys 4 packets of biscuits and one bottle of cola. She pays with a £10 note. How much change should she get? 2 Two ice creams and one cola costs £3.80. One ice cream and one cola costs £2.40. How much does: a) one ice cream cost? b) one cola cost? 3 Lorenzo makes pizzas. One day he makes 24 pizzas. He charges £3.70 for each pizza. Work out the total he charges for all 24 pizzas. 4 Guissepe charges £3 for delivering pizzas. The total cost of some pizzas including delivery is £114. How many pizzas did Guiseppe deliver? 4 Party Pooper To come to the party you must first crack the code. Where and when is the party? P A W T C O D A E N Y R O H U M N Y V E M T L E O E O A T S O Y L T Y T M E C A T I O R R O M Y P L E F F A O F T F E L M Y O I L I H A V E O O T E D O C E H T C U C A N C R A C K Y L N O N A C U O Y 5 Shading Fractions What fraction? Write what fraction is shaded. The first one is done for you. a) b) 1 __ 4 Colour the fraction True or False? Shade in the fraction of each shape given. The first one is done for you. Circle the correct answer. a) 3 __ 4 b) 5 __ 8 a) Half of the shape is shaded: TRUE FALSE b) 1/4 of the shape is shaded c) c) 5 __ 6 TRUE d) d) 1 __ 2 c) It is impossible to shade 3/6 of the shape below: TRUE e) f) g) 6 e) 4 __ 6 FALSE FALSE Venn Diagrams (1) Task Add the objects from the list below into the correct place on the Venn Diagram. (Some examples have been added in for you) Koala Bear Helicopter Kite Bat Cat Guinea Pig Eagle Bee Aeroplane Hot Air Balloon Flying Squirrel Caterpillar Rocket Zebra Fly Animals Lion Things that fly Wasp Boomerang 7 Symmetry How many different symmetrical butterflies can year 7 create? Task Draw the other half then colour a symmetrical pattern. Line of symmetry 8 Introducing Algebra Task 1 Find the value of the letter in the following sentences. Here is an example of what to do: e.g. There are k days in October. k = 31 1) u players in a football team. u= 2) The h Days of Christmas (song). h= 3) p centimetres in a metre. p= 4) g aces in a pack of cards. g= 5) k legs on a dog. k= 6) Donald Duck has d nephews. d= 7) A right angle is w degrees. w= 8) e millimetres in a centimetre. e= 9) Henry the 8th had m wives. 10) A spider has r legs. Task 2 m= r= Every letter below represents a number. In each case, write down what each letter is worth. e.g. m+4=9 m=5 1) a + 3 = 12 a= 2) 25 – w = 11 w= 3) r x 3 = 15 r= 4) 32 ÷ f = 4 f= 5) g÷3=7 g= 6) 12 = d – 5 d= 7) 2 x j = 26 j= 8) y + 56 = 142 y= 9) 17 = 5 + c c= 10) g÷5=9 g= 9 Short Division Can you crack the code? A B C D E F G H I J K L M 45 39 124 84 12 46 78 157 97 61 80 184 13 N O P Q R S T U V W X Y Z 47 56 44 91 37 27 43 21 88 23 99 63 66 12 4 Example: 496 ÷ 4 = 4 4 9 16 e.g. 496 ÷ 4 108 ÷ 4 225 ÷ 5 291 ÷ 3 235 ÷ 5 301 ÷ 7 184 ÷ 8 485 ÷ 5 368 ÷ 2 138 ÷ 3 222 ÷ 6 582 ÷ 6 756 ÷ 9 189 ÷ 7 10 124 C Venn Diagrams (2) Task Place all the integers (whole numbers) in the set of numbers 1 to 30 (inclusive) in the correct place in this Venn diagram. Multiples of 2 Questions Multiples of 3 Answer these in full sentences: 1) What factors do the numbers in the intersection of the circles have in common? 2) Which numbers are multiples of 2 and multiples of 3? 3) Which numbers are multiples of 2 or multiples of 3? 4) How could you describe the numbers that are not inside the circles? 11 Venn Diagrams (3) Task 1 Create your own Venn diagram - what could you label the third circle? Using the same set of numbers (1-30) complete this diagram with your new label. Multiples of 2 Multiples of 3 Multiples of Task 2 Think of a question you could ask about your new diagram. My question is... 12 Pet Rabbits Three pet rabbits cost £19.70. The second rabbit cost £2 more than the first. The third rabbit cost 80p less than the second. What was the cost of each rabbit? Working out... 1st Rabbit cost: 2nd Rabbit cost: 3rd Rabbit cost: Fill in the Gaps 3 2 3 + 4 - 6 1 6 8 2 5 1 6 0 8 - 5 9 6 1 9 2 1 8 7 + 8 7 - 6 3 5 6 5 + 13 Long Multiplication Section A (2 digit by 2 digit) 1 5 4 x 1 2 2 3 4 x 4 8 2 8 6 x 1 7 3 1 2 x 1 9 3 9 8 x 7 4 6 3 x 6 7 EXAMPLE: 37 x 24 37 x 24 148 2 740 1 888 Task Now try the three questions in the grid! Section B (3 digit by 2 digit) EXAMPLE: 476 x 29 476 x 29 4284 2 5 9520 1 1 13804 Task Now try the three questions in the grid! 14 1 2 5 7 Ordering Decimals EXAMPLE - Put these decimal numbers in order of size. Start with the smallest. 3.4 3.5 3.26 5.4 Write the numbers in columns (Three of them have the same number of units!) U T 3 4 3 5 3 2 5 4 H 6 Look at the digits in the Units (U) column first, then look at the tenths (T). Then look at the hundredths (H) if you need to. The Correct Order Is: Smallest 3.26 3.4 3.5 5.4 Biggest Now try these: 1. 3.45, 3.52, 3.4, 3.58, 3.49 Smallest 2. Biggest 1.4, 1.06, 1.7, 1.57, 2.56 Smallest 3. Biggest 5.7, 5.88, 5.63, 5.08, 5.725 Smallest Challenge: Smallest Biggest 3.5, 0.035, 0.35, 0.0305, 0.305, Biggest 15 The Values of Shapes TOTAL = 54 Working out: To find the value of 1 heart: 54 ÷ 3 = 18 1 heart and 2 suns add up to 32. 32 – 18 = 14 so 14 is the value of 2 suns. 1 sun would be 14 ÷ 2 = 7 = 18 TOTAL =7 = 32 Working out: TOTAL = 39 = TOTAL = = 59 Working out: TOTAL = 2120 16 TOTAL TOTAL = 72 = 240 = = = Adding & Subtracting Fractions Fractions must have the same denominators before you can add or subtract them. EXAMPLES 1 __ + 7 2 __ = 7 3 __ 7 3 __ – 5 1 __ = 5 A denominator is 2 __ 5 Now try these: 1 1 __ + 6 4 __ = 6 __ 2 3 __ – 4 2 __ = 4 __ 4 __ 2 __ = 5 3 __ 5 5 5 __ – 11 __ 2 __ 11 + = 2 __ + 3 3 1 __ = 3 __ Which question gives an answer equal to 1? Challenge a 1 __ + 2 Which of the following has the largest value? 1 __ 8 b 3 __ – 4 3 __ 16 c 3 __ + 16 1 __ 4 Working out: Answer: 17 Compass Points in the Classroom Here is an incomplete classroom plan: JOHN JEAN KARL RICHARD Task Complete the seating plan above using the clues below: 1). Dale is 1 seat North of Richard. 2). Gemma is 1 seat South West of Jean. 3). James is 2 seats East of John. 4). Alex is 2 seats South East of John. 5). Anne is 1 seat South East of Karl. 6). Jim is 3 seats South West of James. 7). Keith is West of Jean and North West of Richard. 8). Ron is South West of John and North West of Karl. 9). Val is 3 seats West of Alex. 10). Martin is North East of Val and North of Anne. 11). Wayne is 1 seat South West of Dale. 12). Rosie looks North East and can see Gemma, Jean and Sally. 13). Beth looks East and sees Keith, Jean and Lynne. 14). Sue is 3 seats North West of Wayne. Task Now your seating plan is complete, use it to answer these questions: If James looks west, which girl can he see? Lynne looks at Anne. Which direction is Lynne facing? Dale looks North West. Who can he see? Sue looks at Gemma. Which direction is Sue facing? Write down the direction and number of seats Karl must go to get to James. 18 Using Times Tables Task Below is part of the 45 times table. Use the table to help you fill in the missing numbers. a) 315 ÷ 7 = 1 x 45 = 45 2 x 45 = 90 b) 135 ÷ 45 = c) 270 ÷ d) 3 x 45 = 135 = 45 4 x 45 = 180 5 x 45 = 225 x 45 = 405 6 x 45 = 270 7 x 45 = 315 e) 495 ÷ 45 = f) 8 x 45 = 360 x 45 = 900 9 x 45 = 405 10 x 45 = 450 g) 450 ÷ 30 = Task Answer the question below and explain your answer. Joe says: “Divide any number by 3. The answer is always an even number.“ Is he correct? Circle the right answer: YES NO Explain how you know: 19 Problem Solving 1 Find the value of each symbol in the grid: £ £ £ $ $ £ € £ $ 2 30 34 30 In rugby 5 points are scored for a ‘try’. Points can also be scored by a ‘conversion’ and a ‘penalty’. In their last game Preston Grasshoppers scored 32 points. They scored 4 tries and 4 penalties, but no conversions. How many points does a penalty score? 3 The game before saw them score 43 points. This was made up with 6 tries, 5 conversion and penalty. How many points does a conversion score? 4 If a team score 2 tries, 2 conversions and 5 penalties... How many points does it score? 20 Famous Five Challenge The famous five have been given 20 sweets as a reward for solving a tricky crime. They have agreed that the oldest of them must receive more than the next oldest, who must receive more than the next oldest, and so on. Task Assuming that each of the five gets at least one sweet, in how many different ways can they share the sweets? Solution: 21