Thursday, July 16, 2015

July 17 on Jumping

Plyo Soft Box comes in three sizes and colours. It claims that you can make seven different heights when these are placed properly.

If it comes in one size, you can make only one possible height. Two sizes, three possible heights. Three sizes, seven heights.

Thursday, July 9, 2015

July 8 on Flowers

Each of these requires 2500 flowers and it is changed once a week. There are four of these in the hotel for the entire month of June and July. 

How many flowers are needed?

July 7 on Coating

This whatever-you-call-it is an apple coated with chocolate coated with M&Ms 

How many M&Ms are needed for each of this?

July 6 on Venetian

Three 45-ml bottles of soap, shampoo and conditioner are supplied to each room each day. How much of each is used by The Venetian each month?

What's the missing information?

Monday, July 6, 2015

Thursday, June 25, 2015

June 25 on Nasi Lemak

In Singapore and Malaysia, a common breakfast food is nasi lemak - rice cooked with coconut milk (not healthy at all) and served with simple condiments and curry (Malaysia) or chili paste aka sambal (Singapore).

Killiney has been in business since 1919 starting off as the ubiquitous kopi tiam.

The pack of nasi lemak i had with kopi o is 100% organic - not a single synthetic material is used. Banana leaf is used to pack the rice, giving it a nice aroma as well. Had I used my fingers to eat it as it is done traditionally, you can see how we used to be green without having to say we were green.

A 2 unit x 2.5 unit rectangular sheet of banana leaf folds into a rectangular pyramid with a 1 unit x .75 unit base and .75 unit height. The unit is the length of iPhone 6. 

How much rice is packed into this package?

Friday, June 12, 2015

June 11 on Subway

12" Turkey Sub costs $6.75 and with taxes the customers has to pay $7.24.

He pays $8 and does not collect the change which the cashier keeps as tips.

(a) Calculate the tax rate in this city.
(b) If a tip of 10% is customary, did the customer tip above or below that?
(c) How many Turkey Sub can one buy with two $20 bills?

Sunday, May 31, 2015

June 3 on Donuts

Donuts costs P42 each. Half a dozen cost P252. A dozen cost 380 and two dozens cost 595.

Describe strategies that allow us to estimate the cost per donut easily.

Thursday, May 28, 2015

June 2 on Cafe

Marcus buys 3 cups of hot beverages and they cost $5.10 .

All the beverages are different.

What hot beverages did he buy? How many possible answers are there?

Other than guess and check, students can use reasoning to solve this problem. They are required to use their knowledge about number properties to help them reason.

May 31 on Reservoirs

Soil samples will be taken from reservoir beds, at 0.9m, 1.9m, 2.9m below the bed, and if possible, at every 3m, up to a depth of about 30m | Straits Times

June 1 on Torch Bearers

Charles is 83 years old. Jesy turns 9 years old on the day of the parade. 

They are the oldest and youngest torch bearers at SEA Games Torch Parade.

How much older is Charles than Jesy?

May 30 on Big Numbers

Big numbers are not so common.

But in today's newspaper, I come across several. Parents can use the newspaper as a source of guiding their children in learning mathematics.

In 1974, anthropologists in Ethiopia found the astonishing fossilised remains of a human-like creature who last walked the planet some 3.2 million years ago. | Straits Times

The above can lead to an understanding of the magnitude of the million. The fact that this year is just 2015 years after the birth of Christ makes 3.2 million years ago seems like several lifetime (literally!!) away.

Did you know that Singapore does quite a bit of business in exporting ornamental fish?

Value of Ornamental Fish Exported
2008 USD69 million
2009 USD60 million
2012 USD62 million
2013 USD56 million

Parents can use this with upper primary children to calculate percentage change. Or learn the use of line graphs to make predictions.

Wednesday, May 27, 2015

May 29 on Drinks

For every banana used, how many of each fruit are needed?

For example, we would need 6 fourths mangoes. That's 1.5 mangoes - so we need 2 mangoes and have half left over. 

May 28 on Market Place

Tomatoes are sold at 12 cents per 100g.

Sweet potatoes are sold at 35 cents per 100g.

Oranges cost $4.50 for 5.

Cucumbers 60 cents each or $1 for two.

May 23 on Sea Creatures

Lugworms are rarely seen but they leave these on beaches at lowtide. You have to dig them out if you are curious or if you want to use them as a bait.

What measurements are needed to find the volume of this coil structure created by the lugworm. 

Thursday, May 21, 2015

May 19 on Transportation

Heathrow Express left Paddington at 0941 and arrived at the airport at 0955. Even with 13 minutes walking time to the check-in counters I was early for my 1030 checkin. What is the latest Heathrow Express I could take to be not late for my 1030 checkin? 

By 1020 I was through security screening. But it is another 15-minute walk to the gate. Boarding is at 1130. What is the latest time my Heathrow Express should leave Paddington for me to be at the boarding gate at 1130.

Sunday, May 17, 2015

May 18 on Markets

How much does 4lbs of tomatoes cost?

Note to Parents | The ability to compute on paper is less important than the ability to use mental strategies such as doubling to arrive at an answer. Or the ability to tell how much change is expected if one pays £5. 

Also how many tomatoes make a pound, approximately? 

Saturday, May 16, 2015

May 17 on Flights

The number of flights taking off from Sunavarbhumi Airport are as follows 0800-0859 14 flights
0900-0959 19 flights
1000-1059 19 flights
1100-1159 16 flightA

On average, how many flights depart from Sunavarbhumi Airport per hour? 

What if the data is  

0800-0859 14 flights
0900-0959 19 flights
1100-1159 19 flights

Does the answer change? 

May 16 on Trains

The Heathrow Express is the best way to and from the airport. It costs £21.59 one-way except on Saturday when it costs only £10 one-way. 

You can also buy a two-way ticket. 

How much should a two-way ticket cost so that it is never more expensive to use it? 

Thinking versus computation - it is important to engage your child in conversation about how much a two-way ticket might cost. Should it be twice of £21.90 (mentally, 20p less than £44)? It is usually cheaper than that to encourage passengers to buy two-way tickets. 

The key to help your child is to have conversation and discussion. You are not helping very much by simply putting a stack of worksheets in front of the kid. 

Sunday, May 10, 2015

May 10 on Signs

The ability to see basic shapes in composite shape is a fundamental ability called visualization. 

L can be seen as made up of two rectangles. How about N and K?

Saturday, May 2, 2015

May 2 on Penang Street Food

The regular plate cost RM2.80 and the premium plate, fried with duck eggs, cost RM3.50. In 15 minutes, the hawker sold RM32.90. Is that possible?

Note for Parents
Students who are strong in maths have good number sense. They can reason if 2.80m + 3.50n = 32.90 is possible.

Some may reason that since 2.80 + 3.50 = 6.30, there is some chance of getting the 0.90 in 32.90. So is it possible?

Also students with good measurement sense can tell if it is reasonable to prepare 10 plates of the dish in 15 minutes is reasonable. You need knowledge of context in this case. This is also an example of linking mathematics to everyday situations.

Photo | Street Food in Penang  

Wednesday, April 29, 2015

April 29 on Earthquake

Rushi was rescued after being trapped for 82 hours in the recent earthquake in Nepal.

How many days is 82 hours?

Notes for Parents | Encourage mental strategies. Instead of doing long division for 82 / 24, get students to think of 82 as 48 and 34 and 34 as 24 and 10. From there it is easy to see that 82 hours is 3 days and 10 hours. 

When practicing computations, make sure they acquire number sense. What I described is one way to develop number sense.

Monday, April 27, 2015

April 28 on Airbus

Singapore Airlines A380 at LHR.

Since 2000, the A380 has won just 317 orders, less than a third of the 1,200 Airbus projected in its first 20 years.

Why is 317 less than a third of 1200?

Notes for Parents
Can your 11-year olds do mental arithmetic such as a third of 1,200?

Challenge your child to explain if Airbus is expected to meet its sales projection for the first 20 years.

Saturday, April 25, 2015

April 24 on Food

I paid £8.45 for three food items. Is that possible?

Notes for Parents
Is that possible opens up a child's thinking.

It is fine for children to learn computation but make sure that's not all they learn.

Can your child say that one if the food item must be burgers? That's having number sense.

If a child can compute flawlessly and no able to make deductions like that then he or she had procedural understanding but not number sense. This often happens when parents and teachers overemphasize drills and computations. The mind becomes desensitized. 

Saturday, April 18, 2015

April 16 on Naked Juice

This is my favourite drink because it's yummy and its bottles have cool information I can use to challenge more able students.

What is the fewest number of bottles that can be obtained by using whole number of each of peach, orange, mango and apples?

In preparing two bottles, a peach and an orange are needed but only a third of a mango is used and half an apple got left over. So the number of fruits used are not all whole numbers. 

Notes to Parents 
If your child is advanced, refrain from accelerating him or her. In other words, it is less fruitful to move on to learn to multiply two-digit numbers if the child gets his times table easily than to have enrichment opportunities.

The above task is an enrichment task for advanced learners.

April 15 on Tomatoes

Tomatoes cost $1.98 per pound. 
How much does 4 lbs cost? | Grade 3 onwards 
How much does 2.5 lbs cost? | Grade 5 onwards

Notes for Parents
Encourage your child to do more mental strategies. Reciting times tables is not doing mental math. 

Hopefully your Grade 3 child will be able to say that it's almost $8 for 4 lbs. Even better if he can say it's 8 cents less than $8. If your child is advanced she should be using clever mental strategies all the time.

Grade 5 children should be able to handle 2.5 lbs. They should be able to say half a pound cost half a dollar plus half of 98 cents. Even better if he can give the final amount as 99 cents for half a pound and 2 cents less than $4 or $3.98 for the 2 lbs. $3.98 + 99 cents = $4 + 97 cents.

Encourage mental strategies in computations of friendly numbers. Use a calculator otherwise. There is no room for tedious computation by hand.

Sunday, April 12, 2015

April 9 on Cups and Saucers

This tray to place cups and saucers holds seven rows of cups and a row of saucers. Its width is about 5 cups wide or 3 saucers wide. With the cups stacks two cups high and the saucers  ten saucers high, what is the greatest number of cups and saucers it can hold? Comment on your answer. 

April 11 on Gym Lockers

The lockers are numbered consecutively and are in a rectangular arrangement. 

075 and 081 are next to each other. 

How many lockers are there from top to bottom?

April 10 on Buddha

At 39.5 cm, this piece of art is exquisite. But it is not in any museum. It was impounded by a Samut Prakan police station and is now sitting in some storage place in another province. I wonder what's the story.

There are five rows of smaller Buddhas forming the base. 11 statues on the lowest base and one fewer in each successive steps. 

How many smaller Buddhas make up the base? 

What if the height of the entire work is doubled by keeping the height of the largest Buddha and increasing the height of the base - how many small Buddha statues are needed on the lowest step? 

April 8 on Pathlight Mall

Pathlight Mall sells cool stuff. These notebooks (SGDx.90) and coasters (SGDxx.90) are based on the art work of a student, Jun Yi, who draws cute animals in groups, interacting.

I bought 2 sets of coasters and 5 notebooks as gifts. I paid a total of SGD87.30

Is it possible to figure out the unit price for each item? 

Monday, April 6, 2015

April 7 on Wings

Mr Tan wants to get two drumlets for each of the 37 children in his Primary 3 class as a treat for achieving 15 'clever days' in a month. What is the least amount of money he needs to spend on the drumlets?

In Singapore, prices are inclusive of 7% GST.

Tuesday, March 31, 2015

March 31 on Apples

How many such plates can be prepared using 45 green apples and 45 red apples?

Which of these is correct?
45 divided by 4 = 11 remainder 1
45 divided by 5 = 9
90 divided by 9 = 10

Sunday, March 29, 2015

March 30 on Public Housing

Calculate the percentage increase in the number of public flats since 1959.

Friday, March 27, 2015

March 27 on Politics

Lee Kuan Yew had just passed away and the country is in mourning and there news is filled with the life of the great leader.

"The People's Action Party had just swept the 1959 Legislative Assembly General Election, winning 43 out of 51 seats. It was the first time the PAP, which up till then was an opposition party, had come to power." | Source Straits Times

How many percent of the seats was won by PAP in 1959 General Election? Explain how the caluxlation can be done easily without the use of a calculator.

Thursday, March 26, 2015

March 26 on Queue

How many persons are in front of you for you to have to stand in line for eight hours to pay your last respects?

Wednesday, March 25, 2015

March 25 on Exercise

Mr Lee Kuan Yew liked to exercise. Some politician got slammed for dedication his exercise to Mr Lee Kuan Yew. Here is one on exercise.

Ben has an hour of exercise with his trainer. He has to complete ten exercises. Each exercise is to be done three repetitions, each time takes 1.5 minutes including rest time. Can he complete all these in an hour? What is the latest time he needs to arrive to finish all these exercises by 7 p.m.?

Sunday, March 22, 2015

March 23 on Lee Kuan Yew

Remembering Lee Kuan Yew.

(1) How old was he when he passed away?

(2) Looking at the line graph, what can you say about GDP per person for Singapore since 1960?

Thursday, March 19, 2015

March 20 on Private Club

In Singapore, the ubiquitous hawker centres exist alongside very atas members-only establishments clubs where "a vote at a special general meeting on Monday came out 206 to 95 in favour of counting a member's nationality at the time of joining". 

The maths Is mind-boggling, so are the concerns of the members. You see, in this club "only 51% can be of any one nationality" (they got use only correctly here anot? Standard English - Is only used correctly here?). Then they discovered that, what a surprise, 55.5% of the members are Singaporeans (duh, the club is in Singapore!). That breached a cardinal rule. After much investigation, the mystery was resolved. 292 members were not Singaporeans when they joined but later took up citizenship. With the result of the voting on Monday, these 292 members "went back to retaining their original citizenship at the club" (lol) "This move brings the number of Singaporean members down to 48%, meaning there is now space for 112 more - from a waiting list of 1,301 Singaporeans - to sign up" (lol). Told you it is one-boggling. And parents complain we give problem like 'Ali has four-fifths as much money as Sam in school.' You find more complex stuff on Straits Times. Maths Problem | How many members does this club have?

Oh! By the way the club increased its entrance fee from $35,000 to $50,000 for new members. This gave the club  a $5.6 million windfall. Maths Problem | How many suckers, I mean new members, paid the new fee?

Sorry ah if you are a member and think I am making fun of you. I am.   

Those who can, join the club. Those who can't, make up maths problems about it. 

March 19

Tuesday, March 17, 2015

March 18 on Bread

How much does it cost to buy (a) 24 (b) 25 and (c) 26 pieces?

Note for Parents | Practice is not doing repetitive exercises. Practice is to solve one problem and its variations. The three tasks are not repetitive but get students to think about different aspects of the problem. 

Monday, March 16, 2015

March 17 on Private Property

These are actually public housing in Singapore - the ubiquitous HDB flats which the majority of Singapore residents live in. 
There were 382 apartments sold in January, a modest 2% gain over January's figure. 

How many apartments were sold in January? (Basic)

The figure 2% has been rounded to the nearest 1%. Find the possible number of apartments sold in January. (Advanced)

Another source of word problems in the real-world context is the mass media. I adapted a sentence from Straits Times (17/3/2015 p.1) for the word problem above. 

Sunday, March 15, 2015

March 16 on Private Schools

In few places around the world are public schools preferred to private schools even among affluent families. Singapore is one of them. 
In 2013 SIM's enrollment hit a high of 23,000, with 20,000 locals. Last year, the number fell to 21,500, with 18,000 locals. 
What is the percentage decrease of local students in SIM? Can the decrease be expressed as a fraction? State a unit feaction that can be used as a good estimate for the percentage decrease.

The reason is because there are now more places in the public universities. SIM is a private school.