Mathematics Examination — 563-212

Secondary Cycle One Year One June 2008

Student Booklet 1

Competency 2 Situations

No calculator allowed

Name : Group :

June 2008

Time: __ minutes

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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.

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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: ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________

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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.

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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 73 = 343 and 70 = 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 73 = 343 and 70 = 1

! It is true that 73 = 343, but 70 = 1 is not true; in fact 70 = ________

! It is true that 70 = 1, but 73 = 343 is not true; in fact 73 = ________

! No, it is not true that 73 = 343 and it is not true that 70 = 1.

In fact 70 = ________ and 73 = ________

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.

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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 cm2.

A rectangle: its area is 6 cm2.

A trapezoid: its bases are 5 and 3 cm and height is 2 cm.

A parallelogram: it has an area of 8 cm2.

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.

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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 cm2, 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.

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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 B

C E

D

F

G

H

I

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

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

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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.

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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: 41 cup,

31 cup and

32 cup

and two measuring spoons: 81 tsp and

41 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 43 cup flour

2 cups sugar

43 cup cocoa

1 21 tsp baking soda

2 tsp vanilla

2 eggs

1 cup milk

21 cup oil

43 tsp baking powder

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.