Example 12
Example 12
Example 12
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themselves or by the teachers in the project learning activities.
The teacher first chooses an authentic problem which most students are concerned.
Quite often, students complain about the taste, quality and quantity of the lunch boxes provided by the school lunch box provider. However, the nutritional values of the lunch boxes are also important to the health of teenage students. The teacher asks students to conduct a project on designing a healthy diet menu for the lunch box supplier to help students understand the importance of healthy diet.
Starting with the enquiry questions, plenty of learning opportunities can be provided for the students to construct, integrate and apply knowledge and skills from the three KLAs. Students can use IT skills to search for information from the Internet about food and diet, including the functions of various food substances, nutritional values, recommended daily intake, etc. Students can apply mathematical skills to calculate and analyse the nutritional values of different types of food. Students could collect data about the food preference of their fellow students, and prepare food samples for tasting. After proper analysis, student can submit the healthy diet menu to the school lunch box provider for reference.
During the progress of the project, teachers can provide proper guidance and feedback, resources and assistance to their students when needed.
This example mainly involves the following generic skills:
1. Collaboration Skills
Share responsibilities and understand the role of each member in the project
Agree on suitable strategies for carrying out the project through discussion
2. Creativity
Under the constraints in the aspects of nutrition and proportion of ingredients, students design their healthy diet menu.
3. Problem solving Skills
Identify the problems associated with the project
Make use of data collected to design the menu
Example 13
Example 13 Mathematics Magic
Key Stage: 3
Strand: Number and Algebra Learning Units: Algebraic Expressions
Laws of Integral Indices
Objectives: To apply algebraic language and concepts of place value to explore the principles behind some number games
Prerequisite Knowledge: (i) Representing word phrases by algebraic expressions (ii) Representing a number in the sum of products of each
digit and place value of the corresponding place
Description of the Activity:
1. The teacher helps students form groups for the project work. Since the complexity of the project is not great, the group size could be less than four.
2. The teacher shows an example of “mathematics magic”, such as an age guessing game, and explains to students the topic of the project.
An example of a simple game:
(a) Choose a two digit number.
(b) Add 6 to it and multiple the sum by 2.
(c) Do something “reverse”, that is, subtract 6 from the product in (b) and divide the result by 2.
(d) Subtract the original two-digit number from the result of (c).
(e) I know what you get. It is 3.
An example of a more complicated “magic”:
(a) You are asked by the “mathematics magician” to use the format yyyymm to form two numbers, one from the present year and month and one from your year and month of birth, and then subtract the second number from the first.
(b) Then you find the difference between the result of (a) and the number formed
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by reversing the digits of it, e.g. if the result of (a) is 12345, then calculate 54321 12345, the larger one minus the smaller one.
(c) You choose a digit from the result of (b) to delete and tell the magician the sum of the remaining digits.
(d) Although the magician does not know your year and month of birth, he can tell the digit that you choose to delete.
(Reference: http://www.guokr.com “數學魔術：瑪雅人告訴你哪個數字被偷了” ) 3. Students are required to
(i) search for some “mathematics magic” or number guessing games, from books or the Internet, butt the principles behind is not provided;
(ii) investigate the principles of the games or magic;
(iii) make comparisons between different games or magic; and (iv) design their own mathematics magic.
4. The teacher should keep track of the progress of each group and provide guidance/assistance whenever necessary.
5. Students are required to write a brief report and present their findings to their classmates.
Notes for Teachers:
1. According to students’ abilities, the teacher could choose to give further explanations to the examples provided to students. For example, for the first game mentioned above, the teacher could demonstrate the use of algebraic language to represent the process:
3 2
) 6 2 ( 2 ] 6 2 ) 6
[(x x x x
2. There are different types of number games for the project, for example, Guessing numbers or dates
http://www.cut-the-knot.org (search for “a matter of age”) Using binary numbers
https://scratch.mit.edu (search for “生日密碼與數學魔術”)
Example 13
3. Below are some suggested criteria for assessing students’ performance in the project:
Criteria Description of the Criteria
Understanding the theme of the project
Do students demonstrate a thorough understanding of the topic of the project?
Do students know how to carry out the project and what information they are expected to collect?
Use of strategies and methods
Do students use algebraic expressions to investigate the principles of the games/magic?
Do students adopt feasible strategies to investigate the principles of the games/magic? Are variables set systematically?
Accuracy Are the algebraic expressions formulated correctly?
Are the algebraic manipulations carried out correctly?
Can the principles suggested fully explain the games/magic?
Creativity Can the groups design their own game/magic?
Presentation and communication
Can students present their exploration process in a systematic and logical way?
Is the report clear and concise, and can it match the theme?
Collaboration Is the division of duties among students in the group appropriate?
Is there good collaboration among members?
The criteria suggested are by no way exhaustive and each criterion above may have different weightings.
4. Each group, after completing the project, is invited to present their findings to their classmates. Groups that have designed a game can play the game with their classmates during their presentation. Time for each group to respond to questions raised by classmates and the teacher should also be reserved.
5. It should be emphasised that the process of the project is considered to be more important than the corresponding results/findings in this project. Encouragement should be rendered to the group members who participate in the project but end up with unsatisfactory/incorrect results.
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6. Students should be discouraged from spending too much time on the art design of the report. The teacher should make it clear that sophisticated computer art-work in the report is not necessary. In addition, the teacher should give students suggestions on the time schedule and indicate the deadline for the completion of their project work.
7. Students should be given sufficient time to complete the project.
This example mainly involves the following generic skills:
1. Collaboration Skills
Share responsibilities and understand the role of each member in the project
Select suitable strategies for investigating the principles of the games through discussion and by considering supporting reasons
2. Communication Skills
Discuss and exchange ideas openly with other members
Put forward ideas in a systematic and logical way during discussion
Prepare a concise and relevant report after the completion of the project
Respond to questions raised by the teacher and classmates during an oral presentation
3. Critical Thinking and Problem Solving Skills
Identify the main task of the project
Make use of appropriate knowledge and skills to find out the principles of the games
Example 14