06 Tutorial 1.1 & 1.2 (Problem Solving)

TUTORIAL 1 - PROBLEM SOLVING

Work in groups of two or three

Tutorial 1.1

Dayang Norhafizah Abang Shamat (PISMP Pemulihan Januari 2009)...

Question 1: The King’s Elephant Problem.

Once upon a time the King of Siam asked his warriors to measure the weight of an elephant. However the weight of the elephant was too heavy to be measured by the biggest weighing machine available. Your task is to help the warriors to solve the problem.

Question 2 : Abu Nawas’ Problem.

In one of the stories in ‘One Thousand and One Night’, Abu Nawas would only allow any traveller to fetch water from the only well in the desert after solving the following problem:

The travellers were given a 3-litre container and a 5-litre container. They have to measure exactly four and seven litres of water using the above containers. You are required to help the travellers solve the problem.

Tutorial 1.1

1: King’s elephant problem.

• Put the elephant into a boat

• Mark the water levels on its hull

• Remove the elephant (the boat will rise in the water)

• Place blocks of brick (ten kg each) on the boat until the water level rise again to the

marked line.

• Calculate the number of blocks used and the total weight is equal to the weight of the

elephant

2 : The Abu Nawas’ Problem

• Fill the bigger container with water

• Use it to fill the smaller container

• Now, you have exactly 2 liters in the bigger container

• Empty the smaller container

• Pour the 2 liters into the smaller container

• Refill in the bigger container using the water supply

• Pour the water into the smaller container that contains the 2 liters

• The remaining water in the bigger container is exactly 4 liters



Tutorial 1.2 : Creative Problem Solving.

Identify the strategy that you used to solve the problems in Tutorial 1 Create another problem that can be solved using different strategy/strategies. Group Presentation

TUTORIAL 2.1

In groups of 2 -3, discuss:

What is Numeracy?

Relate Numeracy to National Mathematics Curriculum.

As a teacher, how can you help your students to acquire this proficiency?

Present results of your group’s discussion to the whole class.

TUTORIAL 2.2

Physical manipulative materials such as counters are commonly used to promote the learning of computation among primary school children. In recent years, the advancement in computer technology has resulted in the creation of virtual manipulative material that can be seen and manipulated on a computer screen.

Compare and contrast the effectiveness of using virtual manipulative materials and physical manipulative materials in the teaching and learning computation among primary school children.

Identify appropriate and inappropriate uses of calculator and computer in the teaching of computation among primary school children.

TUTORIAL 2.3

In groups of 2 – 3, discuss:

Why and when do we need rough estimation?

What are the advantages and disadvantages of applying estimation in real life?


Tutorial 3.1

1. Discuss and identify all measurable properties of the following objects:

a) a bulletin board

b) a table

c) an extension cord

d) a bowl

2. Suggest a suitable standard unit for each of the following measurements:

o the distance between Kuala Lumpur and Bangkok

o the height of a front gate

o the amount of annual rainfall of a place

o the amount of water in a dam

o the amount of petrol to fill the tank of a car

o the mass of a piece of A4 paper

o the height of Mount Kinabalu

Justify each of your choices of measurement units.

3. Identify some examples of non-standard units of measurement that are commonly used in any local community in Malaysia.

4. Explore the following two problems:

o Do all shapes with fixed area have the same perimeter?

o Do all shapes with fixed perimeter have the same area?

Tutorial 3,2

1. What is the relationship between gram and litre?

2. What are the advantages of the metric units of measurement?

3. Given that 1 mile = 1.6 km. Use a calculator to verify that a hectare is about 2.5 acres. Show all the steps in your calculation.

4. Cullianan diamond, the largest diamond found in 1906 at the Premier Mine in S Africa, weighed 3106 carats. Estimate the weight of Cullianan diamond in pounds


(Given that: 1carat =200mg, 2.2kg = 1 lb)

Tutorial 4.1

In small groups, discuss on the following:

Words, vocabulary, and language used to describe 2-D shapes and 3-D solids.

Similarities and differences between

(a) cube, cuboid, cylinder and prism;(b) prism and pyramid;(c) pyramid and cone.

The relationships between

(a) cube and cuboid;(b) cylinder and prism

Definition of polygon and classifications of polygons according to number of sides.

Properties of n-sided polygons for .

Tutorial 4.2

Paper-folding activities

Construct the following 2-D shapes by folding an A-4 paper:

a scalene triangle an isosceles triangle an equilateral triangle a rectangle a square a kite a rhombus a parallelogram a trapezium a regular pentagon a regular hexagon


Tutorial 4.3Area & Perimeter of 2-D Shapes

This is a unit square tile.The length of each side of this tile is 1 unit.

The area of this tile is 1 unit2.

Task A: Below are ALL the possible shapes constructed by joining 4 unit square tiles.

What is the area of each of these shapes?What is the perimeter of each of these shapes?Which shape has the minimum perimeter?

Task B: Construct all the possible shapes by joining 9 unit square tiles.

What can you say about the area of all the shapes?Which shape has the minimum perimeter?

Make a conjecture about the shape with minimum perimeter.

Task C: Test your conjecture with shapes constructed by joining

16 unit square tiles 8 unit square tiles 5 unit square tiles


1 unit

1 unit

25 unit square tiles 10 unit square tiles 11 unit square tiles

Base on your investigation in Tasks A, B and C, make a conclusion on the shape with minimum perimeter constructed by joining unit square tiles.


Tutorial 5.1

1. When flipping a coin, there are only two possible outcomes: a “heads” or a “tails”. So, we say that the probability of getting a “heads” is one out of two, that is ½ . When you sit for the examination at the end of this semester, there are also only two possible outcomes: you “pass” or you “fail”. So, is it right to say that the probability of you passing the examination is also ½ ? If yes, why? If no, why not?

2. A person in a small foreign town applies for a marriage permit at age 18. To obtain the permit, the person is handed six strings, as shown in Figure (a). On one side (top or bottom) the ends are picked randomly, two at a time, and tied, forming three separate knots. The same procedure is then repeated for the other set of string ends, forming three more knots, as in Figure (b). If the strings form one closed ring, as in Figure (c), the person obtains the permit.

(a) Do you think the probability of the person getting the marriage permit is higher or lower that the probability of not getting the permit?

(b) Carry out an experiment to check your guess in (a).(c) Determine the theoretical probability that the marriage permit will

be obtained on the first try.

Source: Billstein, R., Libeskind, S. & Lott, J. W. (1990). A problem-solving approach to mathematics for elementary school teachers. 4th ed. Redwood City, CA:Benjamin/Cummings.p. 402.


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06 Tutorial 1.1 & 1.2 (Problem Solving)