Mathematics Examination 563-212 Secondary Cycle One Year One June 2008 Student Booklet 1 Competency 2 Situations No calculator allowed Time: minutes Name : Group : June 2008
The following criteria will be used to evaluate your level of competency development in the different situations presented in this booklet. Evaluation Criteria Uses Mathematical Reasoning Cr3 - Proper application of mathematical reasoning suited to the situation Cr2 - Correct use of the concepts and processes appropriate to the situation Cr4 - Proper organization of the steps in an appropriate procedure Cr5 - Correct justification of the steps in an appropriate procedure Cr1 - Formulation of a conjecture appropriate to the situation Instructions 1. Fill in all the required information in the spaces provided in this booklet. 2. There are 8 questions in this booklet. For each question, you must demonstrate your reasoning to justify your answer. The steps in your procedure must be organized and clearly presented. 3. You are permitted to use graph paper, a ruler, a compass, a set square and a protractor. You may not use a calculator. 4. You may refer to the memory aid you prepared on your own before the examination. The memory aid consists of one letter-sized sheet of paper (8½ 11). Both sides of the sheet may be used. Any mechanical reproduction of this memory aid is forbidden. All other reference materials are forbidden. Note: Figures are not necessarily drawn to scale. Secondary Cycle One Year One 563-212 Booklet 1 Page 1
1. Abandoned Chocolate Bars Charlie left some Fair Trade chocolate bars in an empty classroom. Larry, Moe, and Curly found them later that day. Larry sorted them into 3 equal piles, and took one of the piles. Moe sorted the remainder into 4 equal piles and took one of the piles. Then Curly took half of the remaining chocolate bars. When Charlie returned, there were only 9 chocolate bars where he had left them! Moe and Curly wondered how many chocolate bars there were to begin with. Moe thought there were 48 chocolate bars. Curly thought there had been 36 chocolate bars. Who is correct? Justify your answer. Work out your solution here. I think that! Moe! Curly is correct, because: Secondary Cycle One Year One 563-212 Booklet 1 Page 2
2. In Pursuit of Chocolate Coco and Lottie will go anywhere in their pursuit of good sources of cocoa beans for their fair trade chocolate enterprise. They were given instructions on how to find the Chocolatté cooperative in Costa Rica. They started out hiking along a riverbed that was 29 metres above sea level. They climbed 65 metres higher, then descended down a very steep slope into a valley 110 metres below. After following the valley path, they climbed up a height of 22 metres to the cocoa trees. What was the elevation of the cocoa trees? Show how you found your answer, and be sure to express it as a positive or negative number. Work out your solution here. The elevation of the cocoa trees was metres. Cocoa trees grow best in the shade of other trees. When very young, they require deep shade. As they mature, they require more filtered sunlight. Farmers plant a shade umbrella of taller trees to shelter their cocoa trees. Shade-grown cocoa trees can produce fruit for 75 to 100 years or more. Secondary Cycle One Year One 563-212 Booklet 1 Page 3
3. Are You Smarter than a Seventh Grader? Julius was a contestant on the brand new TV show Are you Smarter than a Seventh Grader? He was given the statements 7 3 = 343 and 7 0 = 1 and asked to explain whether they were true or false. He had no idea! You, the Grade 7 math consultant, were asked to tell him the correct answer and explain the reasoning behind it. What explanation would you give to Julius? You tell Julius:! Yes, it is true that 7 3 = 343 and 7 0 = 1! It is true that 7 3 = 343, but 7 0 = 1 is not true; in fact 7 0 =! It is true that 7 0 = 1, but 7 3 = 343 is not true; in fact 7 3 =! No, it is not true that 7 3 = 343 and it is not true that 7 0 = 1. In fact 7 0 = and 7 3 = Show or explain how you found your answer. The melting point of cocoa butter is just below the human body temperature, explaining why it literally melts in your mouth. Secondary Cycle One Year One 563-212 Booklet 1 Page 4
4. The C Bar CANADIAN CHOCOLATIERS CORPORATION held a competition to design a logo for their new chocolate bar, the C Bar. The winning design is in the shape of a C and is made up of various geometric shapes, listed below, and shown in the diagram at right. Two isosceles triangles: each has a height of 2 cm and an area of 2 cm 2. A rectangle: its area is 6 cm 2. A trapezoid: its bases are 5 and 3 cm and height is 2 cm. A parallelogram: it has an area of 8 cm 2. Construct the logo in the space below, using your geometry instruments. Construction of the C Bar Logo. Giri Choco" is a Japanese custom which means "Duty Chocolate". It calls for employees to give chocolates to their managers as a token of loyalty. Secondary Cycle One Year One 563-212 Booklet 1 Page 5
5. Chocolate Business Amelia and Ted decided they wanted to try making chocolate to sell at their bake sale. They know the standard chocolate bar has a surface area of 48 cm 2, so they decided to keep this area. However, they would like to investigate possible ways of presenting the same area, with different geometric shapes (examples: rectangle, triangle, trapezoid, parallelogram). Use the grid below to draw at least 3 different shaped chocolate bars they could make. Be sure to label the dimensions on each bar. Show your work. The largest chocolate bar ever manufactured weighed 2284 kg and was exhibited in Turin, Italy in March 2000. Secondary Cycle One Year One 563-212 Booklet 1 Page 6
6. Fractions of a Bar The Melt-In-Your-Mouth Chocolate Factory is ready to sell a new bar creation. It is a square chocolate bar made up of a mixture of chocolates. The diagram below shows the chocolate bar sections, with the letters indicating the different types of chocolate as shown in the legend. Each chocolate section is in the shape of a rectangle, square, or triangle, except for piece F. A F B G C D H I E Legend A = milk chocolate B = dark chocolate (Brazilian) C = non-chocolate D = almond mixture E = dark chocolate (Ecuadorian) F= chocolate-covered caramel G = white chocolate H = semi-sweet chocolate I = bitter chocolate The Melt-In-Your-Mouth Chocolate Factory wants to put the amount, in fractions, of each type of chocolate on the outside of the wrapper. What fraction of the WHOLE BAR is each of the pieces listed in the table below? Write the fraction in the table. Bar Piece Fraction Bar Piece Fraction A G F H What fraction of the bar is the almond mixture? Explain, using words or diagrams or calculations, the strategy that you used. Explanation: Fractions of a Bar Almond Mixture Secondary Cycle One Year One 563-212 Booklet 1 Page 7
7. Tell Your Friends You are asked by the school committee to come up with an idea to advertise the sale of fair trade chocolate. You decide to start a chain letter, so you write about the chocolate sale to your 3 best friends. You ask each of them to send a copy of your letter to three other friends, who will each send it to three of their friends, and so on and so on and so on. How many students IN TOTAL will have received a letter at the fifth day of the chain if your 3 friends represent the first day of the chain? Show how you arrived at your answer. At the fifth day of the chain students will have received a letter. Explain, using words, numbers or diagrams, how you could find the number of letters that will be sent on the tenth day of the chain. On the tenth day of the chain, letters will be sent. In 1907, Milk Chocolate Hershey's Kisses were introduced. They are one of the most successful chocolates and Hershey produces approximately 20-25 million per day in a variety of flavours. Secondary Cycle One Year One 563-212 Booklet 1 Page 8
8. Yummy Chocolate Cake Sarah wants to use the chocolate cake recipe below for her son s birthday party. She is going to double the recipe to have enough cake. She can find only three measuring cups: 4 1 cup, 3 1 cup and 3 2 cup and two measuring spoons: 8 1 tsp and 4 1 tsp. Clearly show how to use these measuring cups and spoons to obtain the required quantities of each ingredient. Yummy Chocolate Cake Recipe Ingredient Doubled Recipe How To Measure 1 4 3 cup flour 2 cups sugar 3 cup cocoa 4 1 2 1 tsp baking soda 2 tsp vanilla 2 eggs 1 cup milk 1 cup oil 2 3 tsp baking powder 4 1 cup boiling water Mix all the ingredients except the boiling water. Stir in the boiling water. Pour into a greased and floured pan. Bake at 350 for 35 minutes. Secondary Cycle One Year One 563-212 Booklet 1 Page 9