Are You Smarter than a 3rd-6th Grader?

Recently, I stumbled on an old blog post featuring Singapore Math problems, and it brought back memories.

Back when my children were young, the original Primary Math series from Singapore was one of my favorite math curricula. I tweaked our school program constantly, so none of my kids had the same education, but three of them spent a good part of their elementary years in those books.

And I followed the Math in Singapore 2007 blog for its single season of publication. The blog has gone the way of many others, preserved only in the Internet Archive.

In the post I re-discovered, Patsy Wang-Iverson was reporting on a week-long seminar organized by Celine Koh, who offered the following problems (adapted from school exams and study books) for teacher discussion.

How many can you solve?

The Puzzles

Grade 3

A mechanic fixed 12 wheels to 5 bicycles and tricycles.

How many of them were bicycles and how many were tricycles?

Grade 3/4

Mrs. Tan is 31 years old and her daughter is 13 years old.

How many years ago was Mrs. Tan 3 times as old as her daughter?

Grade 4/5

Jane used 880g of a packet of sugar to bake a cake and 1/10 of the remaining sugar to make jelly.

She then had 3/7 of the packet of sugar left.

How much sugar was in the packet at first?

Grade 5/6

Tim and Sally each have some money.

If Tim spends $80 per day and Sally spends $40 per day, Tim will have $500 left when Sally has spent all her money.

If Tim spends $40 per day and Sally spends $80 per day, Tim will have $1100 left when Sally has spent all her money.

Find the amount of money Sally has.

Grade 5/6

Four toy cars cost as much as 3 dolls.

Five toy cars cost $3.50 more than 2 dolls.

Clare spent $14 on equal number of toy cars and dolls. How many toy cars did she buy?

Grade 5/6

John has a tank of fish.

The number of guppies is 25% of the total number of fish in the tank.

He buys as many guppies as he had.

Find the percentage of the angel fish now in the tank.

Grade 5/6

A jar contained some chocolates and sweets.

At first, the number of chocolates was 60% of the sweets.

After adding in another 10 chocolates and 10 sweets, the number of chocolates becomes 80% of the number of sweets.

How many sweets were there at first?

Grade 5/6

Class A and Class B have the same number of pupils.

The ratio of the number of boys in Class A to the number of boys in Class B is 3:2.

The ratio of the number of girls in Class A to the number of girls in Class B is 3:5.

Find the ratio of the number of boys to the number of girls in Class A.

Grade 6

The number of 20-cent coins to the number of 50-cent coins in a box was 3:2.

Lyn took out four 50-cent coins and replaced them with 20-cent coins of the same value.

After that the ratio of the number of 20-cent coins to the number of 50-cent coins became 7:2.

How much money was there in the box?

Grade 6

There are two bags of stones labelled A and B.

In Bag A, there are 350 black stones and 500 white stones.

In Bag B, there are 400 black stones and 100 white stones.

How many black and how many white stones should be transferred from Bag B to bag A so that 50% of the stones in Bag A and 75% of those in Bag B are black?

The Answers

The cool thing about math is that you really don’t need an answer key. Just put your numbers back into the original problem to check whether they make sense.

I’m a Bit Rusty

I did fine on the first two problems, but I stumbled a bit on the 4/5th-grade “How much sugar…” problem. Got it in the end, but it took some thought.

Tim and Sally threw me for a bit, because I made an arithmetic mistake in checking my first answer. So then I did the problem again with a different approach, only to get the same “wrong” answer. So I went back, found my misstep, and everything checked out.

Then the toy cars were tricky, but manageable. When I checked my answer, I saw a different approach that would been much easier.

After that, the guppies felt like a walk in the park. (Or, maybe, a swim in the kiddie pool?)

I misread the problem with the chocolate and sweets at first — I think of chocolates as a sub-category of sweets, but in this problem they are totally different. (Perhaps “sweets” are what I would call “hard candy”?)

Finally, I resorted to algebra for three of the last four questions.

Since algebra isn’t allowed, I guess that makes me smarter than a 4th grader, but only about mid-way through 5th grade?