Train your brain with these problem-solving puzzles
-
Fun with mathematics: Question 1
Test your children’s problem-solving skills – and your own – with this new weekly series of maths questions presented by Marshall Cavendish Education.
The series will feature a new question each week. The worked solution for that question will be published online at http://str.sg/4eEy on the same day, and in print the following week.
To start off the series, we have provided one question and its solution, as well as a second question to keep your brain juices flowing.
The questions are targeted at students in upper primary, and the worked solutions have been given by Assistant Professor Dr Lee Ngan Hoe, Assistant Head (Mathematics Education – Teaching) of the Mathematics & Mathematics Education Academic Group from the National Institute of Education (NIE) at Nanyang Technological University (NTU). Dr Lee is also the co-author of Shaping Maths and Maths Works!
ADVICE FOR STUDENTS
1. Try to understand the question first. What is the problem about? What information has been given? What does it mean? What are you supposed to find?
What happens to a number when its decimal point is shifted to the right by one place? What does it mean to say “the difference between the original number and this new number is 7.29”?
2. Work out a plan to solve the problem. What could you try to do?
How could you represent the information? Are there relationships among the pieces of information contained in the problem?
3. Try to make sense of the answer. How comfortable are you with your answer? Is there a way to check it? What have you learnt from solving this problem?
OVERALL ADVICE
Be systematic when solving an unfamiliar problem. Do not focus too much on whether you can get the answer.
Try to understand the problem and draw on your mathematics knowledge to make sense of it. It is helpful to represent a problem in diagrams to look for relationships.
Avoid being too quick to accept an answer to a problem. Try to see if the answer makes sense and find a way to check your answer.
ADVICE FOR PARENTS
1. Be a partner along this problem-solving journey. For some children, solving such unfamiliar problems may be a rather challenging experience and it is reassuring to have a loved one on the journey. Do not be too anxious to lead as that may block the child's view. Encourage the child and give him or her a helpful tug along the way.
2. Discourage the child from making pre-emptive judgements on whether he or she can solve the problem. Encourage him or her to make sense of the problem instead. Ask the child questions about the context of the problem to help him or her understand it. Act out how you would attempt to solve the problem. Sometimes your experience is the best teacher for the child.
3. Help the child activate the necessary maths knowledge and skills to solve the problem. Encourage the child to look for familiar words in the problem context which might trigger the necessary skills. It would also serve the child well to continuously revisit his or her mathematical knowledge and skills Maths skills needed for this problem include decimals and place values, multiplying numbers with decimals by 10, and dividing numbers with decimals by a single-digit number.
4. Children may be hasty in accepting an answer, especially if the journey has been challenging. Encourage children to check the steps in their work and also to make sense of their final answer.
Brought to you by Marshall Cavendish Education
-
Algebra version of solution :
10x - x = 7.29, hence x = 0.81
-
QUESTION 2
Leonard took four Mathematics tests. The average score of the four tests was 86. His lowest score was 17 marks lower than his highest score. His lowest score was no less than 75. Which of the following cannot be his scores for the other two tests?
1. 85, 90
2. 83, 92
3. 84, 89
4. 88, 91SOLUTION TO QUESTION 2
Consider Option 1:
Total score of the other two tests = 85 + 90 = 175
So, total score of the highest and lowest tests = 344 - 175 = 169
Therefore the lowest score = (169 - 17) / 2 = 76 (which is greater than 75)
This, the total scores in Option 1 are possible.Next, consider Option 2:
Total score of the other 2 tests = 83 + 92 = 175
This is the same as that for Option 1.
Thus the test scores in Option 2 are possible.Let’s consider Option 3:
Total score of the other 2 tests = 84 + 89 = 173
So, the total score of the highest and lowers tests = 344 - 173 = 171
Therefore the lowest score = (171 - 17) / 2 = 77 (which is greater than 75)
Thus the test scores in Option 3 are also possible.By elimination, the test scores in Option 4 cannot be his scores for the other two tests.
-
Fun with Mathematics: Question 3
-
Bits, Bytes, And Smaller Chunks Of Information Is Retained better By The Human Mind! : http://robertgsolomon.com/bits-bytes-and-smaller-chunks-of-information-is-retained-better-by-the-human-mind
How to Calculate The Perimeter Of A Rectangle : http://www.wehows.com/app/review/how-to-calculate-the-perimeter-of-a-rectangle
-
Fun with Mathematics: Question 4
QUESTION 4
Ken buys some mangoes. If he packs them equally into bags of 40, he will have seven mangoes left. If he packs them equally into five bags, he will need to buy more mangoes. What is the smallest number of mangoes he needs to buy?
SOLUTION TO QUESTION 4
If the mangoes are packed equally into bags of 40, the total number of mangoes in all the bags must be a multiple of 40.
Since 40 = 4 x 10, the total number of mangoes in all the bags must be a multiple of 10. In other words, the digit in the ones place for the total number of mangoes in all the bags must be 0.
We also know that if Ken packs the mangoes equally into bags of 40, he will have seven mangoes left. Thus, the digit in the ones place for the total number of mangoes Ken has is seven.
For Ken to pack his mangoes equally into five bags, the number of mangoes he eventually has must be a multiple of five. So the digit in the ones place must be 0 or 5.
Since the digit in the ones place for the number of mangoes Ken now has is 7, the smallest number of mangoes he needs to buy is three, to make the digit in the ones place to be a 0 or 5.
ADVICE FOR STUDENTS
1. Try to understand the problem first. What is the problem about? What information is given to you and how does it help you to better make sense of the problem?
What does it mean to say that if Ken packs the mangoes “equally into bags of 40, he will have seven mangoes left”? What else do you know based on this information?
What does it mean that Ken “packs them equally into five bags”? What else do you know about the new number of mangoes Ken has?
What are you supposed to find? What is meant by the “smallest number” of mangoes he needs to buy?2. Work out a plan to solve the problem. Do you have enough information to know the number of mangoes that Ken originally had? If not, what do you think this number may look like? Is there a pattern that all the possible numbers must follow?
How about the final number of mangoes Ken has? Can you tell what this number may look like?
3. Try to make sense of the answer. Is there a way to check it? What have you learnt from solving this problem?
Can you create a similar problem for others to solve? This would help you better understand such problems and develop more effective strategies to handle them.