Many years ago, I read about the co-authors of a handbook for mathematics teachers in primary schools warning readers not to use the sign “<” or “>” (because the symbols were removed from the primary school syllabus); instead, they suggested using phrases like “more than” and “less than.”

For example, teachers were to avoid setting questions in these formats:

34 is 6 > ☐
8 > 43 is ☐

Instead, they’d rephrase them as “34 is 6 more than ☐.” and “8 more than 43 is ☐.”

Similarly, they’d refrain from posing inequalities questions such as the following:

7 < ☐ is 15.
9 < 25 is ☐.

And also avoid problem sums like the one below:

What is the largest (or greatest) whole number that can be placed in the box to make the statement true? 8 + ☐ < 40

Why the Ban (with or without a Fine)?

Based on teachers’ feedback that young (or even older) schoolchildren are often confused about the similarity of the two symbols < and >, that’s likely a key why that prompted local curriculum math specialists in the “fine” city to ban these “unequal symbols” in primary school mathematics moons ago.

Inequality Metaphors from the Sunshine State

Over the years, to reduce the confusion between < and >, some elementary math authors have come up with some witty ways to help schoolchildren remember which is which.

For instance, students are often taught to see the symbols as hungry alligators or crocodiles with gaping mouths—these reptiles always want to eat the larger numbers, so the open mouth will always face this.

Observe that the < looks somewhat like a lopsided L, which reminds us that it denotes less than. Or, in any true statement, the large open mouth of the symbol is on the side of the greater quantity, and the small point is on the side of the lesser quantity.

No More Ban

Like last year’s repeal of Section 377A in pseudo-puritan Singapore, based on the CPDD’s Primary Mathematics Textbook 2A (2022), the inequality signs too are now free to roam the pages of any MOE-approved primary 2–6 textbooks and workbooks.

In the aftermath of zero ban on inequality signs, questions that involve comparing and ordering numbers would no longer be symbolically penalized or criminalized for using the “>” and “<” signs (until further notice).

Below are a sample of three “uninhibited” Singapore math primary two inequality questions:

Which sign will you use, > or <?
(a) 45 ☐ 42
(b) 81 ☐ 71
(c) 317 ☐ 407
(d) 734 ☐ 724

Fill in the boxes with ‘<’ or ‘>’.
(a) 35 ☐ 53
(b) 65 ☐ 62
(c) 79 ☐ 68

It’s not uncommon to see once-banned open-ended questions now gracing the pages of primary math textbooks, such as the following:

In 38 > 33 + ☐, what could the missing number be?

It looks like we’ve come some way in restoring the inequality signs in the (lower) primary school syllabus. Now that the mathematical resurrection of these symbols has taken place, does their confusion among schoolchildren still remain a concern for both teachers and parents?

An Inequality Quiz

Let’s end with a math quiz that tests our basic knowledge of inequalities.

1. How many types of inequalities in elementary school math are there?

2. Which metaphor(s) would you use to help children who are prone to mistake one inequality sign for another?

3. Name half a dozen math inequalities in real life that schoolchildren could relate to.

4. “An inequality is an equation that forbids the use of an equal sign.” True or False.

Symbolically yours

© Yan Kow Cheong, July 9, 2023.