Speed and Rate Problems

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Rate problems provide some of the biggest challenges to students and adults. These come from Problem-Solving Processes in Mathematics -6 B by Fabian Ng.

  1. At 10:15 am, a car left Town X for Town Y at an average speed of 86 km/h, while a truck left Town Y for Town X at an average speed of 74 km/h. At 3:15 pm, the two vehicles were 12 km apart. How far apart were the two towns?
  2. At 10:30 am, a cyclist started traveling on a road at an average speed of 60 km/h. At 2:30 pm, a motorist started from the same place, traveling on the same road. If the motorist took 4 hours to catch up with the cyclist, find his average speed.
  3. The distance from Town P to Town Q was 312 km. Winston started from Town P at an average speed of 76 km/h. He maintained this speed for 2 hours before increasing it by 4 km/ for the rest of the journey to Town Q.
  4. a. how long did he take to complete the whole journey?
    b. What was his average speed from Town P to Town Q?

Can you draw a model or diagram to illustrate each of these problems?

(Answers next week!)

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Intermediate Word Problem

Published in Singapore, Challenging Problems in Mathematics for Primary Schools: Intermediate by Dr. Y.H. Leong is a series specially written to provide enrichment activities for students.  The intermediate edition is designed for Primary 4 & 5 students.


A farmer planted 22 rambutan trees in a straight row. The trees were spaced out equally. If the distance between the 3rd tree and the 10th tree was 42m, find the distance between the 2nd tree and the 22nd tree.

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Creative Thinking Problems

I had coffee with another fan of Singapore Math this week and he loaned me some supplemental materials from his travels to Popular Books in Singapore. These two problems come from Accelerated Learning Primary Mathematics 3 by Ching Kheng Huat published in 1999.

The front page states:

In this book, “Accelerated Learning” fosters in pupils the ability to learn faster, to remember more and to think creatively.

The Ministry of Education has initiated IT in education for pupils. To make time for IT, pupils need to learn faster to cover the syllabus. And this requires ACCELERATED LEARNING – a new dimension in pedagogical skills. MOE has also emphasized the need to develop CREATIVE THINKING, which we have incorporated in this book.

The book has seven pages of “Infographic  Images” at the beginning (visual dictionary of terms), then practice pages for 12 units. Each unit of six to seven pages has:

  1. two worked examples
  2. multiple choice practice
  3. short answer practice
  4. problem sums practice
  5. creative thinking problem (one or two)

Here are the Creative Thinking problems from the unit on fractions:

And a Creative Thinking problem from the unit on time:

It takes 4 h 15 min to repair 3 computer. Repairing a radio takes 47 minutes less that the time needed to repair a computer. If a worker works 9 hours a day, he needs to complete repairing 10 items that can include both computers and radios. How many computers can he repair if he needs to repair as many computers as possible?

Do you feel that these problems will help students “develop creative thinking” ?

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Math Problem Comparison

Teachers often ask, “What’s the difference between (the textbook I’m using now) and Singapore Math textbooks?” While there are many answers, I’d like to direct you to a resource that has been pointing out some differences  for over a year.

Once a week, Lefty (as in left-brained) over at Out In Left Field posts assignment comparisons between either a traditional math program or Singapore Math and various reform math textbooks.

From the original post:

Math problems of the week: Reform Math vs. other math

We’ll pair up a specific assignment drawn from this set with a specific assignment drawn either from a traditional series like McGraw-Hill, or from the foreign series most popular in America: Singapore Math.
I’ll try to pick assignments that take place at approximately the same point in the school year.  For example, I might choose two assignments from the first few weeks of first grade, or from the last few weeks of second grade, or from approximately 2/3 of the way into third grade.

At the end of many posts are some thought provoking Extra Credit questions. Some examples:

  • Which problem set involves more rote repetition of a given algorithm?
  • Which problem set is more accessible to children with language impairments?
  • Discuss how the two problem sets reflect the cultural and political differences between American and Singaporean societies.

Although many of the sample problems come from Singapore Math, there are also comparisons to traditional math books from the 1920s.


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Grade 6 Word Problem Solutions

Earlier this month, I posted the following problem from a Nanyang Primary School 2007 Preliminary Examination I found at MissKoh.com:

A mixture, weighing 100 kg is made up of 2 chemicals A and B in the ratio of 7:3. When some volume of Chemical A evaporates, the content of Chemical A is reduced to 60% of the new mixture. What is the mass of the mixture now?

I thought I’d share how my son worked the problem:

chemical wp

He knew that if he multiplied 40% x 2.5, he’d get 100% so:

2.5 x 30 kg = 2.5 x 40%

75kg = 100%

I used a different drawing for “after” :

chem after

How did you solve the problem?

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