# Singapore Math Age Problems for Younger Students

Age problems have often been the bȇte noire for generations of students, even among those who are considered above-average in school math. Like trains, speed, and algebra word problems in elementary math, these before-and-after word problems have instilled fear and anxiety among both mathophobic school teachers and parents, who find themselves helpless or clueless in guiding their students and children to solve these non-routine questions.

Traditionally, these age problems used to be set in elementary and middle schools—grades 5–10— but a decade ago, at least in Singapore, they started to appear in a few assessment (or supplementary) math books meant for grades 1–2 students, then slowly infiltrating their way in school mid- and final-year exam papers. They tend to appear in Sections B and C of school semestral assessment papers—these last two parts of a Singapore’s school math paper are made up of questions that are often used to discriminate the average from the better math students.

## From Algebra to Model

Many of these age problems, especially when set in grades 7–10, and which traditionally use an algebraic approach to solving them, can now be posed in lower grades, thanks to problem-solving strategies like the Singapore model method or the Stack method. These visualization methods of solution do away with the abstract (or analytic) methods of solution not formally taught in lower grades, by offering younger students the opportunity to solve these age problems in an intuitive or a creative way.

## From Routine to Non-routine

Like most non-routine or challenging word problems, with the right mix of questions tailor-made for students of mixed abilities and with sufficient practice, these questions soon become routine, What at first appears challenging (or frightening?) becomes in the end routine (or even boring?); however, being able to solve these non-routine questions does indirectly help raise the self-esteem and confidence of many local average math students.

Most current assessment math titles contain at most four or five of these age-related questions, often offering only one method of solution; few go broad or deep enough to enable students to practice the different types of thinking skills (or problem-solving strategies) needed to solve a wide range of these age problems. Unless students are exposed to an arsenal of these non-routine questions, most are unlikely to feel confident that they’ve mastered these brain-unfriendly word problems.

To meet the mathematical needs and wants of students, teachers, and parents, who wish to enhance their mathematical problem-solving skills, here are two Singapore math ebooks that focus on these age-related word problems: one for grades 1–3 and one for grades 3–6 students, with both titles offering more than one method of solution to solving many of these word problems.

## A Sample of Grades 1–3 Singapore Math Age Questions

Here are some questions taken from the grades 1–2 problem-solving ebook. Can you solve them in more than one way?—No algebra allowed!

Four years ago, Amy was 8 years old, and her sister was 13 years old. How old will her sister be when Amy is 18 years old?

Ian is 5 years old. His mother is 23 years old. In how many years’ time will his mother be 3 times as old as Ian?

Beth will be 7 years younger than her brother in 5 years’ time. Beth is 12 years old. How old is her brother?

My grandfather is 61 years old. My father is 25 years old. I am 5 years old. In how many years’ time will the sum of our ages be 100?

Mr. Jones is 12 years younger than Mr. Jack. The sum of their ages is 68. How old is Mr. Jack?

Aaron is 11 years old. His dad is 47 years old. How many years ago was his dad five times as old as him?

Valerie is 11 years old. When she asked her mum about her age, her mum replied, “When you reach my age, I’ll be 67 years old.” How old is the mother now?

Below is the ebook cover of the grades 1–2 problem-solving title that explores more on these age problems, by providing a number of problem-solving strategies and heuristics to solving them, with a focus on the Singapore model (or bar) method.

A value-for-money Singapore math Kindle ebook that may give your child an unfair advantage!—Ideal to be read on iPad and Android tablets, using the free Kindle Reading App. http://tinyurl.com/m25kfku

## A Sample of Grades 3–6 Singapore Math Age Questions

Here are some age-related questions extracted from for the grades 3–6 problem-solving ebook. Try to solve these word problems in as many non-algebraic ways as possible—e.g., using bar and stack methods, and Sakamoto method.

Probably the best value-for-money ebook on Singapore math, focusing on age problems, you could find in the market! Coming SOON on Amazon.com!

This year Robert’s age is between 30 and 60 years old and is a multiple of 6. Next year, his age will be a multiple of 7. How old is he now?

The total age of a father and his two sons is 54. Twelve years later, the age of the father is 4/5 the total age of his sons. How old is the father now?

Five years ago, Mr. Smith was 6 times as old as his son. In 3 years’ time, he will be 4 times as old as his son. How old is Mr. Smith now?

Mrs. Tan is 4 times as old as her son. In 20 years, she will be twice as old as her son. How old is Mrs. Tan now?

Ten years ago, the ratio of Mark’s age to Tom’s age was 5 : 2. The ratio is now 5 : 3. What will be the ratio in 10 years later?

Regardless of your age, keep mentally young by having fun with these age problems! Indeed, solving them in more than one way every now and then could be an inexpensive prevention from any form of schizophrenia or dementia.

© Yan Kow Cheong, July 24, 2014.

# Are the Days of Singapore Math Textbooks Numbered?

Singapore math textbooks and workbooks are notoriously known to be shy of non-routine questions, which are a necessary but not sufficient step to enhancing the mathematical problem-solving skills of local elementary school students. It’s common knowledge among local teachers, tutors, and parents that a child with an average or above-average IQ studying in a Singapore government school may still flunk her school math paper even after religiously practicing all the questions in her math books. This is because most local school test and exam papers are often set at a standard above the perceived mathematical ability of an average child in Singapore (or maybe even in developed countries like the UK, US, or Australia).

## Thousands of Tutors Are on Standby

Luckily, we’ve enough competent tutors [aka moonlighters] around to help our struggling (but otherwise intellectually normal and healthy) students to solve that problem. Singapore is known as a haven for assessment (or supplementary) books, and math titles inarguably forms an unhealthy percent of them. Until now, most math books from Singapore that are being used overseas are primarily foreign adaptations of local textbooks and workbooks.

In a number of cases, these foreign editions have been adulterated so much to meet the mathematical needs of the students in their respective countries or states, where the Ministries of Education or Heads of Department have nevertheless been bold enough to embrace a foreign curriculum, such as Singapore math, to raise the quantitative skills of their students and teachers, in spite of fierce opposition from stakeholders, colleagues, or parents.

## Go Beyond the Textbooks and Workbooks

Ironically, but not surprisingly, for decades now, the best math books in Singapore tend to be published by small local publishing houses, as compared to the big players which have the financial muscle to invest in the printing of textbooks and workbooks. In fact, this is one key factor how disturbingly small players—often family-owned and ethically challenged businesses—through their value-for-money assessment titles have been able to kick-ass the oft-constipated bigger players, which seem to take ages to publish any submitted manuscripts, and still churn out half-edited published titles.

Thanks to technology, and with new digital channels to distribute their math titles overseas, small local publishers and solopreneurs may eventually benefit more students, teachers, and parents, who have so far been limited (or shortchanged) by a distorted image of what Singapore math is all about—for instance, local students even from non-elite public schools are exposed to more rigorous mathematics, and to more challenging questions, as compared to mathematics contents depicted in Singapore math textbooks and workbooks.

## Will Singapore Math E-Books Be the Solution?

Amazon.com, ClickBank.com, and the like are a God-sent blessing to any local math writers and authors, who wish to share their mathematical knowhow with their fellow math educators overseas. Indeed, the days of traditional publishing of poorly edited and uncreative Singapore math books seem numbered. May creativity and technology triumph over complacency and incompetency. And say NO to editorial ineptitude and unethical practices from both big and small publishers of Singapore math books.

A wallet-friendly Singapore math problem-solving Kindle ebook that may give your child an unfair advantage over his or her peers! http://tinyurl.com/m25kfku

© Yan Kow Cheong, July 3. 2014.

# Mathematical Quickies and Trickies

What are mathematical quickies and trickies? Are they the so-called trick or tricky or IQ questions in mathematics?

mathematical quickie is a problem which may be solved by laborious methods, but which with proper insight may be disposed of quickly. This term was coined by Professor Charles W. Trigg to describe problems that yield almost instantly to a flash of inspiration.

mathematical trickie is a problem whose solution rests on some key word, phrase, or idea rather than on a mathematical routine. Most number riddles would qualify as trickies.

### What Are Mathematical Quickies and Trickies?

● Questions teachers shy away because they are hard to crack if improperly approached. Conventional methods are seldom necessary to solve them; most are rather tackled in a common-sensical and logical approach.

● Questions or variations commonly set in IQ and aptitude tests to trap the unwary. They are what teachers called the “Tricky Questions.”

● Questions that may be solved by a bright 8-year-old child, yet defeat the average mathematics teacher and educated parent.

● Questions that defy intuition, frequently posed in math contests and examination papers to frustrate the rote learner and catch the mathematically challenged.

● Questions whose obvious solution is never the correct one—what offhand appears to be true is false.

Mathematical Quickies and Trickies will not only enhance your problem-solving skills, but also help you to be more careful in approaching unorthodox mathematics questions.

Once you’re familiar with these trick and tricky questions, the solutions of many of these non-routine questions will make them appear predictable, rather than challenging. What may, at first, appear challenging will, in the end, become routine.

All that you need is a little knowledge of elementary school mathematics, open-mindedness, and persistence to participate in the delights of Quickies and Trickies.

Let’s revisit some old-time mathematical quickies—they’re also some of my favorites.

0. A bottle of wine cost \$10.
The wine was \$9 more than the bottle.
How much did the wine cost?

1. The side of a square is increased by 30%. Find the percentage increase in the area.

2. If 3% of births produce twins. What percentage of the population is a twin: 3%, less than 3%, or more than 3%?

3. In a kilometer race A beats B by 20 meters, and he beats C by 40 meters. By how much could B beat C in a kilometer race?

4. Mrs. Goon’s children are all schooling, and the product of their ages is 45,045. How many children does Mrs. Goon have?

5. If I write all the whole numbers from 1 to 500 in a row, how many digits will there be?

Although there exist thousands of these quickies and trickies in the recreational mathematics literature, many of them require a fairly sophisticated level of mathematics from the problem solver.

To expose both upper primary and lower secondary school (grades 5-8) students to some of these entertaining non-routine questions, and to arouse their interests, Mathematical Quickies and Trickies contains over 300 elementary quickies and trickies, compiled from the fields of arithmetic, geometry, algebra, and recreational mathematics.

Ranging from the simple and trivial to the complex and challenging, most of these problems and solutions should prove accessible to the average primary (or elementary) school student. However, some of these trick and tricky problems may pose a challenge even to the talented or gifted secondary student.

The challenge of mathematical quickies & trickies is not only to solve these mathematical brainteasers, but also to come up with more elegant solutions than the ones provided.

References
Yan, K. C. (2012). Mathematical quickies & trickies. Singapore: MathPlus Publishing.
Yan, K. C. (2012). More mathematical quickies & trickies. Singapore: MathPlus Publishing.

© Yan Kow Cheong, June 7, 2014.

# Trick and Tricky Math Questions

The sequel to the bestselling Mathematical Quickies & Trickies—Suitable for grades 5-8 students

What is the difference between “trick questions” and “tricky questions” in mathematics? Can you spot them to avoid being fooled by them?

Trick Questions

“Trick” questions are difficult because they often conceal or omit information, or because information appears in an unfamiliar setting. Trick questions are set to mislead the unwary — the novice problem solvers.

Trick questions often disguise themselves in the form of riddles and conundrums. Let’s look at two examples of trick questions.

Example 1
Joe cycles from home to school, a distance of 2 kilometers. If he cycles the first kilometer at 5 km/h, how fast will he have to cycle the next kilometer to average 10 km/h?

Example 2
As I was going to Mathland
I met a man with seven wives.
How many in all were going to Mathland?

Did you get 15 km/h as the first answer, and 2803 as the second answer? If yes, welcome to the company of trick-allergic people. Don’t give up so easily. Look at the questions again. Figure out why the two answers are wrong. Resist the temptation to peep at the hints.

Tricky Questions

“Tricky” questions are “fair”; they don’t usually conceal information or depend on some words, which may be misinterpreted. In fact, tricky questions often contain redundant information, which needs to be filtered.

Trickies are problems whose numerical data make the problem meaningless — unrealistic problems. The sensibility of the answers serves as a guide to warn the problem solver that the question may contain redundant or insufficient information. An experienced problem solver will notice the unreality or impossibility of the problem’s specific data.

Here are two “tricky” questions.

Example 3
Write, in algebraic form, the general form of numbers that, when divided by 3, leave a remainder of 5.

Example 4
The perimeter of a right triangle is equal to 3.92 m. Two of its sides are 1.25 m each. Find the third side.

Did you get 3n + 5 and 1.42 m? Or, are you more tricky-sensiive this time? What are the correct answers to these mathematical trickies?

May I direct you to the Mathematical Quickies & Trickies Fan Page for more trick and tricky questions in elementary school mathematics? Or, you may order some titles under the Mathematical Quickies & Trickies series at Amazon.com or download a soft copy from iTunes.

Happy mathematical problem solving!

© Yan Kow Cheong, May 21 2014.

A bestseller in Singapore among grades 4-6 students