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Speed and Rate Problems

October 6, 2009 by Leave a Comment

song chart memes

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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Singapore Math – Old School

August 17, 2009 by Leave a Comment

old_school
Old School claims to be Singapore’s #1 Primary School site. From the site:

Old School aims to be the premier resource for FREE educational material from Singapore, especially Singapore Math and Singapore Science. We have a large database of test questions and assessments and are always adding new content.

Currently, they offer test papers as well as the ability to take tests online in English, Mathematics and Science. Registering on the site allows you to track your progress on the online tests (usually the “A” part of each). Best of all, you can search the questions by topic and select questions with either a multiple choice or free-response format.

As an example, the Primary Four 2009 Mathematics page offers:

  • 3  Continual Assessment 1 tests
  • 4  Mid-Year Examination tests
  • 3  Continual Assessment 2 tests
  • 4 End Year Examination tests

That include the following topics (with the percentage of questions):

  • Angles (7%)
  • Area and Perimeter (8%)
  • Decimals (4%)
  • Factors and Multiples (6%)
  • Four Operations (22%)
  • Fractions (18%)
  • Geometry (2%)
  • Graphs (2%)
  • Measurement (7%)
  • Non-Standard Questions (6%)
  • Perpendicular and Parallel Lines (4%)

The majority of mathematics papers are a 2 out of 4 on the site’s scale of difficulty. There were some assessments with a difficulty rating of 1.

Here’s a problem from the 2009 Primary Four End Year Assessment for your enjoyment:

Fill in the missing number.

108 x 99 = 110 x 99 + 10 x 99 – ( ? ) x 99
  1. 8
  2. 2
  3. 12
  4. 228
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Intermediate Word Problem

August 15, 2009 by Leave a Comment

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.

Enjoy!

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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Comparing Singapore Math Materials: Workbooks

June 30, 2009 by 2 Comments

In Part 1 and 2,  I shared examples from the Teacher’s Guides and Textbooks from four sets of materials used in Singapore and the United States. The materials are all from the third grade level:

  1. Primary Mathematics U.S. Edition (2003)  from SingaporeMath.com
  2. Primary Mathematics Standards Edition (2008)  from SingaporeMath.com
  3. My Pals Are Here Maths (2007) obtained in Singapore from Marshall Cavendish
  4. Shaping Maths (2007) obtained in Singapore from Marshall Cavendish

Following are the practice pages from each workbook that correspond with the lesson on addition within 10,000 that introduces regrouping in the hundreds. As before, each thumbnail links to a full-sized file. Once again, there are minimal differences between the U.S. and Standards editions of Primary Mathematics.  Problem #1 changes pictures from towels hanging on a clothesline to boats. Problem #2 has one small change. The equation for  letter B changes from  4107 + 5 to 4105 + 5. Finally, on problem #4, “Weihua” becomes “Will” U.S. Edition Workbook 3A: USp25USp26USp27 Standards Edition Workbook 3A: STp48STp49STp50 The My Pals Are Here Workbook is perforated and 3 hole punched. Perforated pages would be a great change to make to the Primary Mathematics workbooks! Neither My Pals Are Here nor Shaping Maths have any word problems tied to this practice lesson, in fact, there are very few word problems in the books at all. My Pals Are Here Workbook 3A Part 1: MPAHp29 MPAHp30 Shaping Maths Activity Book 3A part 1: SMp31 SMp32 Were you expecting less practice in the materials from Singapore?

Parts in the series:

Part 1 – Teacher’s Guides

Part 2 – Textbooks

Part 3 – Workbooks

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Creative Thinking Problems

June 22, 2009 by 9 Comments

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:
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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