Christmas Special. Answers. Rudolf and Santa. A Child is Born. The Elves Workshop. Christmas in Colour

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1 Page Answers Christmas in Colour Rudolf and Santa Prime numbers Square numbers Multiples of 3 Even numbers No numbers Multiples of 5 Red Dark Brown Pale brown Blue White. Green A Child is Born Prime numbers Multiples of 5 Multiples of 7 Multiples of 3 Multiples of Square numbers The letter B No number or letter Pale brown Purple Green Red Dark blue Pink Black White The Elves Workshop Triangular numbers Square numbers Prime numbers Cube numbers Multiples of 3 Multiples of 7 Other numbers Dark brown Blue Yellow Green Pale brown Red Pink

2 Page Answers Thin ice Route A This can be discovered by using compasses to find where the appropriate distance touches crossing grid lines. But pupils with more knowledge should use Pythagoras. All legs are one side of a right angle triangle. For any leg of the journey there is only one right angle triangle which has a side of the appropriate length. Example: Leg The only way to get a line 9.cm long which ends on crossing grid lines and without going onto thin ice is to go 7 across and 6 up. Using pythagoras = 85 = = 9. to d.p. Of course 9 + = 85 as well but combinations of 9 and bring you to thin ice or off the paper! Route A = = 34.4km Route B This requires very accurate drawing of the route onto the map with a protractor. Remember, a line must finish on crossing grid lines. Route B = = 37.8km Christmas Logo Puzzles Christmas Tree Company Logo , 4,, 4 Rudolf dashes off!,,,,,, 5, 6, 0,,, 7, 4,,,,,,,,, 4,, 3,,

3 Page 0 Answers Home Start Scale cm : km

4 Page 9 Answers Santa s Dilemma Best route: C, A, L, D, F, J, B, H, E, G, E, C, K, C = 5 strides Best route without back-tracking: C, K, A, L, D, F, J, B, H, G, E, C = 55 strides Santa s Journey Santa chooses the Midi sleigh. Best route: 4 Ways (0650), Archways (0740), South Bridge (0830), Old Ferry (090/090), Old Man s Arch (0935), High House (035), Castle (50) Santa s Elves Rudi Beanz Godfrey Yolande Hat Green Yellow Red Blue Food Mince pie Choc log Chr. pud Turkey Present Trainers Tools Bike TV Village calculations a Area = x 5 = 55 m a Area = 0 x 4.5 = 45 m b Area = x 5 = 55 m b Area = 0 x 4.5 = 45 m c Area = = 0 m c Area = = 90 m d Volume = ( x 5 x 6) + ( x 5 x ) d Vol = (45 x 4) = (4.5 x 0 x ) = 385 m 3 = 5 m 3a Area = 6 x 4.5 = 7 m b Area = 8.5 x 4.5 = 38.5 m c Area = 5 x 3 = 5 m d Area = 3 x 3 = 9 m e Area = 89.5 m f Volume main building = (4.5 x 8.5 x 4) - (.5 x.5 x 4.5) + (4.5 x 8.5 x )= 63.5 m 3 Volume lean-to = x 3 x 5 = 4.5 m 3 Volume extension = (3 x 3 x 3) + (3 x.3 x 3) = 3.85 m 3 Total Volume = 37.5m 3 4a Area Nave = x 5 = 55 m b Area Tower = 5 x 5 = 5 m c Area Porch = x 3 = 6 m d Total Area = 86 m e Volume = Nave + Nave roof + Tower + Spire + Porch + Porch roof = (55 x 6) + ( x 5 x ) + (5 x 0) + (5 x 7.6) + ( x 3 x 4) + ( x 3 x.3) 3 = = 76. m 3

5 Page 8 Santa s Dilemma Santa lands in his sleigh at the church. From the church he must visit each house. He is late and in a hurry. Santa s mathematician has worked out the shortest route to take so that he goes to all the houses and then back to the church. The distances are measured in Santa s giant strides. Can you find the shortest route? F 5 J L 4 7 D A 6 3 B 3 C 4 5 K 4 7 E H 0 G 8

6 Page 7 Christmas Logo Puzzles Shade in the correct squares to create a logo Example: this H logo is completed. H Logo 4 4, 3,, The numbers to the right of the grid show you how many squares to shade in. The and the by the top row show that there is a block of to the left of a block of one. The numbers below the grid also show you how many squares to shade in the column above. So in column one you have square shaded above another square shaded. There must be at least one square space between shaded squares. Try this simple one. You are given one square to help you start. Take your time. Do not guess. Be sure before you shade a square. Now try the Christmas Tree Company Logo , 4,, 4 Christmas Tree 6 4 3,,,,,,,,,, 4 3, 3 If you really want a challenge try Rudolf dashes off Rudolf dashes off ,,,, , 4,,,,,,,,,

7 Santa s Journey Santa s Castle Page 6 North Bridge Motorway A Road B Road Cone Top Ferry kg Ice House 60 Pinnacle Tower 60 Windmill Stop Temple House Midwinter Tower Church Ferry 60 Clock Tower 75 Start Fourways South Bridge Mill Ferry kg Archways Square Tower High Arch Old Ferry Pottery Ferry 75 Old Man s Arch High House Sailor s Rest Pinnacle Education

8 Page 5 Santa s Journey Puzzle Santa has finished his deliveries for another year. It is time to go home. It is 6 a.m. and he wants to get home by noon in time for his Christmas dinner. But can he make it in time? Look at the map. He has a choice of routes. He also has a choice of sleighs: The Mini which weighs 500 kg and has a top speed of 75 kph The Midi which weighs 750 kg and has a top speed of 90 kph The Maxi which weighs 000 kg and has a top speed of 00 kph There are some problems though: The bridges over the rivers have weight restrictions. See map. The way to avoid bridges is to cross the rivers by ferry. Cone Top ferries start at 0800 and leave every 5 minutes after that. Crossing times: to Ice House - 4 min... to Temple House - 60 min. Mill Ferry starts at 065 and leaves every one hour after that. Crossing time - 50 min. Church Ferry starts at 085 and leaves every one hour after that. Crossing time - 5 min. Old Ferry starts at 0800 and leaves every 0 minutes after that. Crossing time - 5 min. Pottery Ferry starts at 0745 and leaves every one hour after that. Crossing time - 30 min. Each road section is either 60 km, 75 km or 90 km long and this is shown on the map. As you can see Santa starts at the bottom left hand corner of the map. Motorways (blue) have no speed limit. A roads (red) have a speed limit of 90 kph. B roads (orange) have a speed limit of 60 kph.

9 Page 4 Santa s Elves Santa has 4 elves called Rudi, Beanz, Godfrey and Yolande. Each elf wears a different coloured hat: red, blue, green, yellow. Each has a favourite food. Each has been promised the ideal Christmas gift by Santa, because he has worked so hard throughout the year. The initial of the elf s name is always different from the initial of his hat colour. Godfrey is vegetarian, will not watch TV and never wears yellow. The elf who wants a tool kit for Christmas does not like mince pies. The elf who wears green loves mince pies. Rudi wants a pair of trainers for Christmas, but he never wears blue. A red hat is worn by the elf who wants a bike for Christmas. Yolande is allergic to chocolate. Beanz wants a tool kit for Christmas and he wears a yellow hat. One elf loves roast turkey and wears a blue hat. Christmas pudding is the favourite Christmas food of the elf who wears a red hat. One elf really wants his own TV for Christmas. Chocolate log is the treat that one elf most looks forward to at Christmas. Which elf wears which colour hat? Who likes what food and who gets which Christmas present?

10 Page 3 Model Village : House

11 Page Model Village : Inn, Lean-to Extension Cut out Cut out Inn insert

12 Page Model Village : Church Porch and Spire, Inn Extension

13 Page 0 Model Village : Church Nave

14 Page 9 Model Village : Church Tower

15 Page 8 Model Village : Terrace of Cottages

16 Page 7 Model Village The models are best made from card. Photocopy the nets onto card. Score along the fold lines and cut out the models. Uhu glue works better than Pritt-Stick. Calculations You can get the real dimensions of the buildings by using the scale of the models, cm : m. The House a Calculate the ground floor area of the house in m. b What is the area of the first floor of the house? c Find the total floor area of the house. d Calculate the total volume of the house, including the roof space in m 3.. The Terrace of Cottages a Calculate the ground floor area of the terrace in m. b What is the area of the first floor of the terrace? c Find the total floor area of the terrace. d Calculate the total volume of the terrace, including the roof space in m The Inn a b c d e f Calculate the ground floor area of the main building of the inn. Remember to subtract the area of the cut out. Calculate the floor area of the first floor, which does not lose floor space because of the cut out. Calculate the floor area of the lean-to extension, one storey only. Calculate the floor area of the other extension, one storey only. Find the total floor area of the inn buildings. Calculate the total volume of all the inn buildings. 4. The Church a b c d e Calculate the floor area of the nave of the church. Calculate the floor area of the tower of the church. Calculate the floor area of the church porch. Calculate the total floor area of the church. Calculate the total volume of the church including the spire.

17 Page 6 Eleves Workshop My own design

18 Page 5 A Child is Born B B 9 B B

19 Page 4 Santa and Rudolf

20 Page 3 Christmas in Colour Each shape in these pictures has a number. Colour the shapes like this: Some small areas have no number but need a colour. Use your judgement. Rudolf and Santa Prime numbers Square numbers Multiples of 3 Even numbers No numbers Multiples of 5 Red Dark Brown Pale brown Blue White. Green A Child is Born Prime numbers Multiples of 5 Multiples of 7 Multiples of 3 Multiples of Square numbers The letter B No number or letter Pale brown Purple Green Red Dark blue Pink Black White The Elves Workshop Triangular numbers Square numbers Prime numbers Cube numbers Multiples of 3 Multiples of 7 Other numbers Dark brown Blue Yellow Green Pale brown Red Pink

21 Page Puzzle Santa desperately needs help! He is on the last stage of his journey home. Global warming is causing the polar ice cap to melt in places. Santa has been given a map by his cartographer gnomes so that he can avoid the areas of thin ice. There are two possible routes that he can take and the gnomes have provided information for both. Unfortunately, when they ed this information to Santa, some of the data got lost in cyberspace. Modern technology!! On route A Santa has the distance of each leg of the route, but not the compass bearing. On route B he has the bearing but not the distance. As you may imagine Santa is tired and pretty fed up with this situation. Can you help him sort out the two routes? Can you also tell him which of the two routes is the shorter one? Some further helpful information We know that: Each stage point is on a whole number grid reference. All legs of the route are straight lines of less than 0km. Routes never cross thin ice ares. Route A Route B S - 9. km to d.p. S km to d.p km to d.p km to d.p Home 8.0 km to d.p. 4 - Home 058 0

22 Page Map Home Start Scale cm : km

23 Contents This pack should contain: Map Puzzle 3 Christmas in Colour 4 Santa and Rudolf 5 A Child is Born 6 Elves Workshop 7 Model Village 8 Model Village : Terrace of Cottages 9 Model Village : Church Tower 0 Model Village : Church Nave Model Village : Church Porch and Spire, Inn Extension Model Village : Inn, Lean-to Extension 3 Model Village : House 4 Santa s Elves 5 Santa s Journey Puzzle 6 Santa s Journey Map 7 Christmas Logo Puzzles 8 Santa s Dilemma 9 Answers 0 Answers Answers Cut-out Characters for Model Village in colour.