# Side Totals How many sides altogether are there on 80 triangles and 15 squares?

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1 Make it Simpler Side Totals How many sides altogether are there on 80 triangles and 15 squares? Houses in My Street If the houses in your street are numbered from 1 to 150, how many houses will have the digit eight as part of the number? The Group Project If it takes 15 children ten hours to complete half of a group project, how long will it take four children to complete the other half? Board Game Grid A game uses a board with a 6 x 6 square grid. How many squares of all sizes are on the board? Gift Exchange At Christmas, six friends decide to give each other presents? How many presents are given altogether? Beach Hop A group of children are playing on the beach. They are hopping and jumping along the beach. Each child does three hops followed by one jump. From a standing start, how many footprints in the sand would there be for each child after 3 jumps? 10 jumps? 20 jumps? The School Reunion At a school reunion, all of the 12 people present give their address to every other person there. How many addresses will be given out? Departing Trains At exactly the same time, two trains depart in opposite directions from the station. One train is moving at a speed of 56 kilometres per hour, while the other is moving at a speed of 64 kilometres per hour. After three hours how far apart will they be?

2 Marco s Fence Marco is making a fence out of match sticks for his toy farm. The fence is made up of a series of square sections. How many matches will Marco need to make a fence five sections long? How many matches will he need for 8 sections? 20 sections? 30 sections? Board Game Design James and Ling are making up a board game. The board for their game is three squares by three squares in size. What is the total number of squares you can find on their game board? If they increased the size of the board to four squares by four squares, what would be the total number of squares on the board? What if they increased the board to five by five squares? Diagonal Drawings How many diagonals can be drawn from one corner of the following regular two dimensional shapes a square a pentagon a hexagon a heptagon a octagon; a regular flat shape with 50 sides; 80 sides; or 100 sides? The Race A snail and an ant are moving slowly crossing the playground. For every ten metres the ant travels, the snail travels one metre. By how far will the ant be ahead of the snail over a distance of 10 metres? 100 metres? 200 metres? Handshakes Galore How many handshakes will take place if 11 people all shake hands with one another? How Many Fours? If nine fours are all multiplied together (for example, 4 x 4 x 4 x 4...) what is the remainder when the answer is divided by six?

3 The Tennis Tournament Twelve people are playing in a Tennis Competition. Each person must play one game against each other person. How many games are played altogether? Playground Grids On the playground is painted a grid of six squares by six squares. The teacher has asked her class to place blue markers in all of the 1 x 1 squares, red markers in the 2 x 2 squares, green markers in the 3 x 3 squares, purple in the 4 x 4 squares, orange in the 5 x 5 squares and yellow markers in the 6 x 6 squares. How many markers of each colour will the class need? How many markers will they use altogether? The New Year s Eve Bash Mary and her family are holding a street party for New Year s Eve. They are going to make one long banquet table down the middle of the street by joining together square tables that seat four people. How many square tables will Mary need if ten people come to the party? How many square tables will she need for 30 people? 50 people? 100 people? Team Leaders A Basketball Team of five players must choose a Captain and a Vice Captain. How many different combinations are possible? How many combinations are possible for a football team of 12 players? Tricky Calculations Calculate the sum of every odd number between one and 99, (for example, ) Restaurant Arrangements At a restaurant there are 40 square tables and each can seat four people. When two tables are joined together they can seat six. When three tables are joined together they can seat eight. The following parties have made bookings at the restaurant Thursday a party of 64; Friday a group of 98 and Saturday a group of 120. How can the restaurant organise the tables to fit each of the parties in easily? Note The restaurant is quite small and the largest group of tables it can fit is one that seats ten people.

4 Flooded Farms A group of people has been stranded on a farm by floods. There are 40 people on the farm and they have enough food to last for 12 days. Three days later eight more people struggle to reach them from a neighbouring farm. How long will the rest of the food last now that there are eight extra people to feed? The Amazing Race In a running race there are five runners competing. How many possible combinations for first, second and third are there? How many combinations are possible if there are ten runners? Rise to the Top A frog fell into a hole 8 metres deep. Every day the frog was able to climb 3 metres up the side of the hole. Every night he slid back 2 metres. How many days did it take the frog to climb out of the hole? The Historical Copier The first automated photocopier was invented in This machine took 9 seconds to copy 1 page. Ken needs to make 345 copies of a memo and 258 copies of a flyer. How long would it take him to copy all those pages on the 1959 machine? Author James James began writing a book. At the end of the first week, he'd written 10 pages. By the end of the second week, he'd written 6 more pages, for a total of 16 pages. At the end of the third week, he had a total of 23 pages and by the end of the fourth week he had 31 pages completed in his book. If he continues writing at this same rate, how many pages will his book have at the end of the seventh week? The Exercise Group Mary's five friends began an exercise group. They decided to walk along a trail each day. On the first day, they walked 2/3 of the trail. On the second day, they walked 3/5 of the trail. On the third day, they walked 4/7 and on the fourth day 5/9 of the trail. If this pattern continues, how far will Mary and her friends walk on the tenth day? Fruit Sales Josh buys a five kilo watermelon for \$0.49 per kilo and two kilos of grapes for \$1.29 per kilo. Sabrina buys an eight kilo watermelon for \$0.29 per kilo and three kilos of grapes for \$0.99 per kilo. Who spends the most money and by how much?

6 Door Wreaths Mrs Wilson has enough ribbon to decorate 24 door wreaths. For 24 pieces of ribbon, how many cuts will she have to make? The Tennis Match 8 boys and 8 girls are in a Tennis Tournament. Each boy plays each girl once. How many games are played? The Nut Bag In a bag of mixed nuts, there is one Brazil nut for every 3 cashews. If there are 48 cashews, how many Brazil nuts will there be? The Apprentice A group of S4 students have applied to be apprentice bricklayers. The foreman asks the students to look at the small brick pyramid he is building and work out how many bricks are needed to build it. That s easy, says Usman. It is 4 steps high and the total number of bricks required is 16. Excellent. But this is just a model. We will have to work out how many bricks are needed for larger walls, replies the foreman. How many bricks are required for a 10 step pyramid? I m stuck. Can t we make it easier? says Usman. Ladders Ismael is painting the walls and ceilings in a house and is using a ladder to help. The ladder has ten rungs. Ismael can step up either one or two rungs at a time. He cannot step up more than two rungs at a time because he knows this would be dangerous. To stand on the second rung he could go up taking one at a time, (ie; 1, 1) or go up taking two at a time, (ie; 2) So there are two different ways for Ismael to go up to the second rung. Ismael wants to stand on the tenth rung to paint the ceiling. How many different ways can he climb to the tenth rung? The Chess Game Joe and Tilak are playing chess when Joe suggests that they count the number of squares on the chessboard. Easy, says Tilak. There can only possibly be 64. Definitely not. There are more than 100, replies Joe. Find how many squares there are on a chessboard. The squares can be of 1 by 1 or 2 by 2, etc.

7 Dominoes Kurt, Ali and Mary enjoy playing dominoes and decide that it would be fun if all the class could play the same game of dominoes at the same time. Ali suggests that each person in the class must have at least 2 dominoes to make the game fair. Mary insists that they would not have enough dominoes for the class of 28 students to have at least two each. John says that they will have to make a special set of dominoes and that this new set of dominoes should be numbered 0 to 9. Problem Would a set of dominoes numbered zero to nine be sufficient to allow 28 pupils two dominoes each? Mixed Marriages Anna and Hazim are discussing star signs and decide that marriages should not take place between people of the same star signs marriages should not take place between people who have star signs that are next to each other in the calendar all other combinations of star signs would make suitable marriages How many different combinations of star signs would make a suitable marriage? Write down as many star signs as you know. Which marriages would be suitable? Remember that marriages of people with the same star sign and marriages of adjacent star signs are not suitable. Cancer and Leo Scorpio and Libra Leo and Pisces Leo and Leo Sagittarius and Leo What strategies could you use to find how many combinations of the 12 star signs would make a suitable marriage? Find a formula to calculate the number of suitable marriages and use it to calculate the number of suitable marriages if there were 100 different star signs. Drinks Louisa plans to serve fruit juice to her guests at lunch. Louisa, 1 of her friends, and her 2 parents will all have juice. Each juice glass holds 100 millilitres. If each person will have a full glass of juice, how many cups of juice will Louisa need?

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