[S1_20151216] Using a Table to Organise Information for Algebra

Problem

The average monthly salary of  m  male employees and  f  female employees of a company is  $2 000.  If the average monthly salary of the male employees is  $(b + 200), find the average monthly salary of the female employee.

Introduction

     This Secondary 1 (~ grade 7) problem in introductory algebra is challenging due to the multitude of pieces of information and their interrelationships.  Using tables is a good strategy to help us organise the information.  

Strategy

     What we do is to fill up each piece of given information in the table first (shown in green below).  Once that is done, proceed to figure out the other blank cells of the table.  The more you do that, the more you would be able to figure out the rest, until you get the solution.

Solution

 Final Remark

     I hope you enjoyed this tip!

Heuristics Used

H02. Use a diagram / model

H03. Make a systematic list

H04. Look for pattern(s)

H05. Work backwards

H10. Simplify the problem

H11. Solve part of the problem

H13* Use Equation / write a Mathematical Sentence

Suitable Levels

* Lower Secondary Mathematics (Secondary 1)

* GCE ‘O’ Level “Elementary” Mathematics (revision)

* other syllabuses that involve ratios or algebra

[Pri20150330FBT] Open-ended Question on #Fractions

Question

Give a fraction with its value in between 2/5 and 1/2.  (Note: the denominator cannot be greater than 20)

Discussion

This is an open-ended question for primary (elementary) school, which ought to be easy because there are many possible answers and you just need to supply one that meets the requirements.  However, most people are used to closed-ended questions, which have only one correct answer.  This is what prompted a parent to pose this question on a parent-support forum on Facebook. 

Many people, including parents and even some private tutors, began to supply their answers to this question.  Much of the discussion clustered around the idea of the mid-point or the average of the two given numbers, namely ¹/₂ (²/₅ + ¹/₂) or  ⁹/₂₀, and why that gives an answer.

Then Dr Kho Tek Hong (retired curriculum specialist, the “father” of Singapore mathematics) chipped in.  He said that there are many possible answers e.g. ³/₇, ⁴/₉, ⁵/₁₁, ⁵/₁₂, ⁶/₁₃, etc.  He suggests that students be asked to justify their answers.  [ By the way, here is an interesting method to compare fractions. ]

And I thought that was a stroke of educational brilliance from The Guru!  It shows the spirit of the Singapore mathematics curriculum – to get students to think, to be open-minded, to use logic and to be able to communicate mathematically.  The Singapore curriculum is not meant to torture students, nor to get them to toil around a tortuous path around a high mountain seeking the elusive holy grail – although it often seems that way.  Teachers, tutors and parents would do well to help the learners it in the right spirit.  Mathematics is not always about calculations (although you need to do some calculation).  We also need to open our minds to multiple answers as well as to embrace various methods and concepts.