Posted on : 2011-08-10

The word ‘heuristic’ is taken directly from the Greek verb, *heuriskein* which means ‘to discover’. In Mathematics, there are usually different ways to go about solving problem sums. These ways or methods are known as heuristics.

**Three: Going through the process**

Example:The figure is made of 17 sticks. Move 4 sticks to form 8 squares.
Solution: |

· Pupils can apply the ‘work backwards’ method when given a problem that provides the final result and that requires them to find the initial quantit

There were some chocolates in a basket. Michael and three of his friends took 8 chocolates each. 25 chocolates were given to Shirley. There were then 11 chocolates left in the basket. How many chocolates were there in the basket at first?
Using the ‘work backwards’ method, first find the number of chocolates taken away by Michael and his three friends. 4 × 8 = 32 chocolates Then, find the total number of chocolates taken away from the basket. 32 + 25 = 57 chocolates Number of chocolates in the basket at first =
57 + 11 = 68 chocolates |

Example:
Jacky had $56 more than Jill. When he spent $108, Jill had thrice as much as what he had left. How much did Jacky have at first? Solution: 2 units → $108 - $56 = $52
1 unit → $52 ÷ 2 = $26
$26 + $108 = $134 Jacky had $134 at first. |

**Four: Changing the problem**

· By restating a problem in another way, pupils can view the problem in another perspective.

Example:
Find the sum of 10 + 12 + 14 + … + 146 + 148 + 150.
There are 75 numbers in the sum 2 + 4 + 6 + … + 146 + 148 + 150. There are 4 numbers in the sum 2 + 4 + 6 + 8. 75 – 4 = 71 Hence, there are 71 numbers in the sum 10 + 12 + 14 + … + 146 + 148 + 150.
There are 35 pairs of 160 and a ‘80’. 10 + 12 + 14 + … + 146 + 148 + 150 = 35 × 160 + 80 =5680 |

· When facing a complex problem, pupils can split the problem into smaller parts and start by solving the simpler parts. After doing so, the problem is simplified and solving the problem is much easier.

*Written by Gui Yan Tong*

Check out the series "Use of Heuristics in Problem Solving" by EPH and have more practice on the different types of heuristics |

**Extra!**

**For more pointers on Model Drawing and Guess and Check, check out these related articles at the Popular Community:**

Posted on : 2011-08-10

The word ‘heuristic’ is taken directly from the Greek verb, *heuriskein* which means ‘to discover’. In Mathematics, there are usually different ways to go about solving problem sums. These ways or methods are known as heuristics.

Heuristics can be divided into 4 main types, which will be covered in this 2-part article.

**One: Giving a representation**

· Pupils can transform word problems into pictorial representations and represent information with a diagram/model. This skill helps pupils to understand the question better when they see the visual representation of the word problems.

· A systematic list should be made for word problems that require pupils to identify patterns such as repeated numbers or a series of events that repeat. This skill helps pupils in identifying patterns easily as the list organises all possible answers systematically.

Example:Michele saved $150 on the first month. On the second month, she saved $60 more than the first month.
On the third month, she saved $70 more than the second month. On the fourth month, she saved $55 more than the third month. How much did she save in four months?
Making a list: 1st month → $150 2nd month → $150 + $60 = $210 3rd month → $210 + $70 = $280 4th month → $280 + $55 = $335 Total amount saved =
$150 + $210 + $280 + $335
= She saved |

**Two: Making a calculated guess**

Example:
Jenny has a total of 7 dogs and parrots. The animals have 20 legs altogether.
How many dogs does she have?
Using the ‘guess and check’ method,
She has
3 dogs. |

· The ‘look for patterns’ method is usually used by pupils when they have to identify a certain pattern in a number sequence.

Example:
Solution: Making a list of possibilities:
12 - 4 + 5 = 13
11 - 9 + 16 = 18
16 - 12 + 3 = 7
The value of X is
7. |

*Written by Gui Yan Tong*

Check out the series "Use of Heuristics in Problem Solving" by EPH and have more practice on the different types of heuristics |

**Extra!**

**For more pointers on Model Drawing and Guess and Check, check out these related articles at the Popular Community:**

Posted on : 2011-04-08

**Pictures speak a thousand words**

**The key here is to read the story and interact with the child.**

**Interaction involves leading the child to describe the picture using a few complete sentences. In addition, parents can also motivate their child to verbalise their thoughts after reading the story.**

**Incorporating into interests**

**Parents should try to link their children’s key interests and hobbies together with language learning to encourage effective learning.**

**Making it relevant**

**Parents can also try to incorporate Chinese in their children’s daily lives**. Besides encouraging them to watch Chinese television programmes and cartoons, they can also conduct some daily conversations in the language and even teach them some popular songs as well. Parents can also encourage their children to communicate in the language with their neighbours or with shop owners and other people in the neighbourhood.

Thus, through the use of these methods, children will be more exposed to the Chinese language and will gradually grow to become competent users of the language.

*Written by Eric Pang*

Posted on : 2011-08-10

In linguistics, grammar refers to the rules of the language.** **When we learn about grammar in the English language, we learn about the set of rules which governs how a sentence or phrase is composed. Besides building up a good vocabulary, the key to speaking and writing good English lies in your ability to first understand how a sentence is formed and how it can be used.

More often than not, your child will find the process of learning grammar tedious and boring. Seeing as how children are still too young to understand the importance of grammar, trying to force them to memorise a seemingly endless set of rules will be a tiresome chore.

Here are some ways in which you can make learning grammar fun and interactive for your child.

1. Provide examples that they can relate to. Instead of textbook examples, try engaging their attention by talking about a real-life example. An example about your child’s recent trip to the zoo or aquarium will more likely capture their attention and interest.

2. Use humorous examples. You may have noticed that children find it much easier to remember situations or examples which they find funny. This also changes their mindset that learning grammar is boring and mundane.

3. Read widely and wisely. Select books which are informative and entertaining as your child will be more inclined to read them.

You can also purchase books on grammar to give your child adequate practice. Try searching for books with more illustrations, stories and examples which your child will be able to relate to.

*Written by Michelle Lim*

You may want to look at the series Fun with Grammar by EPH where grammar components are skilfully weaved into the storyline and multiple illustrations are provided. |

**Extra!**

**What are some common grammar mistakes to watch out for? Find out in this related article at the Popular EduCommunity:**

Posted on : 2011-04-08

**Open-ended Questions**

- For open-ended questions, circle the keywords in each question to help you to focus on what is being asked. It is important that you understand the question.

Example:
To answer such a question, first, identify the keywords. The keywords are ‘photosynthesis’ and ‘products’. When you see ‘photosynthesis’, you should recall what this word means. Photosynthesis is a process whereby plants make food in the presence of sunlight. The question is asking about the products of photosynthesis. This means that you have to provide more than one answer to the question. Recall that food (sugar) is made in plants and oxygen is given out during photosynthesis to replenish the air. Hence, the answers are sugarand oxygen. |

- Note the question terms used in the question. This will help you understand what answer is required of you in order to score full marks for that particular question.

For (a), the question term used is ‘Explain’. ‘Explain’ means that you have to give reasons for the observation stated. The observation is that object X does not move. Object X does not move because it is neither a magnet nor an object made of magnetic material. If object X is a magnet or a magnetic material, it will either be attracted to or be repelled by the magnet. Thus, the correct answer is ‘Object X is made of a non-magnetic material, hence it is not affected by the magnet.’ For (b), the question term used is ‘State’. State means that you only need to write short answers, meaning a few words or short phrases. Since object Y moves away from the magnet, object Y is also a magnet. Magnets are made of or can be made by one of the four types of magnetic materials. Hence, the answer for (b) is ‘Iron, steel, nickel or cobalt’. |

- It is always good to be concise in your answer. Using the correct keywords in your answer will help you score the marks allocated.

Example:
For (b), the question is asking for a reason. As mentioned earlier, air does not have a fixed volume and a fixed shape. We can only see the shape of the air changing when it is being transferred from one container to another of a different shape. Hence, we cannot write ‘Air does not have a fixed shape’ as the answer. Air does not have a fixed volume, hence its volume changes from 50 cm^{3} to 30 cm^{3}. Writing ‘Air does not have a fixed volume’ as the answer is not wrong, but there is a better word to use for this question. The keywords are ‘can be compressed’ or ‘compressible’. Air does not have a fixed volume and hence it can be compressed. The concise answer to this question would be ‘Air can be compressed’ or ‘Air is compressible’. |

*Written by: Tan Chiang Heng*