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Mathematics Examination — 563-212
Secondary Cycle One Year OneJune 2008
Student Booklet 1
Competency 2 SituationsNo calculator allowed
Name : Group :
June 2008
Time: __ minutes
The following criteria will be used to evaluate your level of competency
development in the different situations presented in this booklet.
Evaluation CriteriaUses 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.
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.
Work out your solution here.
The elevation of the cocoa trees was _____________ metres.
Secondary Cycle One Year One – 563-212 Booklet 1 Page 3
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.
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.
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.
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 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.
Construction of the C Bar Logo.
Secondary Cycle One Year One – 563-212 Booklet 1 Page 5
“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.
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).
Show your work.
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.
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.
Bar Piece Fraction Bar
Piece Fraction
A G
F H
Explanation:
Secondary Cycle One Year One – 563-212 Booklet 1 Page 7
LegendA = milk chocolateB = dark chocolate (Brazilian)C = non-chocolateD = almond mixtureE = dark chocolate (Ecuadorian)F= chocolate-covered caramelG = white chocolateH = semi-sweet chocolateI = bitter chocolate
Fractions of a Bar
AlmondMixture
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.
Show how you arrived at your answer.
At the fifth day of the chain ______________ students will have received a letter.
On the tenth day of the chain, _______________ letters will be sent.
Secondary Cycle One Year One – 563-212 Booklet 1 Page 8
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.
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: cup, cup and cup
and two measuring spoons: tsp and tsp.
Yummy Chocolate Cake
Recipe Ingredient Doubled Recipe How To Measure
1 cup flour
2 cups sugar
cup cocoa
1 tsp baking soda
2 tsp vanilla
2 eggs
1 cup milk
cup oil
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.
Secondary Cycle One Year One – 563-212 Booklet 1 Page 9