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Teaching Strategies for Comparing & Ordering Numbers

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  • 0:04 Inequality Symbols
  • 0:15 Less-Than Symbol
  • 0:40 Greater-Than Symbol
  • 1:00 Less-Than/Greater-Than…
  • 1:58 Comparing and Ordering Numbers
  • 4:27 Lesson Summary
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Lesson Transcript
Instructor: Matthew Bergstresser

Matthew has a Master of Arts degree in Physics Education

Learning about ordering and comparing numbers is a basis for understanding all other mathematics. In this lesson, we will explore memory devices and other strategies to teach students about the relationships between values.

Inequality Symbols

There are four inequality symbols that help us compare values. Let's explore each symbol and show how we can use memory devices to help students learn about them.

Less-Than Symbol

The word ''less-than'' begins with the letter ''L.'' You can tell your students that the less-than symbol looks like someone sat on a capital ''L'' and smashed it. Another way to remember this symbol is that the ''L'' in less-than can be opened to look like an alligator's mouth. You can explain that the alligator's mouth will always avoid the smaller number and open toward the larger number.

Greater-Than Symbol

An easy way to remember the greater-than symbol is to see if it looks like the smashed letter ''L.'' If it doesn't look like that, it must be the greater-than symbol. Remind students that the same alligator mouth rule applies when using this symbol to compare numbers: the mouth will always open toward the larger number.

Greater-than alligator
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Less-Than / Greater-Than-or-Equal-To

With the less-than-or-equal-to symbol and the greater-than-or-equal-to symbol, you can use a visual representation to show how these symbols physically combine the equal sign with the less-than and greater-than signs learned about just a moment ago, so that students can begin to understand how they work together. A way to help the students remember these symbols is to point out that ''less-than-or-equal-to'' consists of five words, and the symbol for this has five end-points. Looking at the symbol, ≤, the top arrow has three end-points: the start, the middle bend, and the end; additionally, the bottom line ends at two points. The same is true of the greater-than-or-equal-to symbol. Using a visual representation combined with this memory device will ensure students incorporate the prior knowledge on inequality symbols and expand it to grasp and remember these concepts.

Comparing and Ordering Numbers

The inequality symbols we just discussed are used to compare and order numbers. A number line, which uses points on a line that correspond with numbers, will really help to teach this skill because it provides a visual linear representation of greater and lesser values, allowing you not only illustrate number order, but also to show how inequality symbols work with those values.

Place a chip on a number to begin the discussion of numbers less-than or equal-to
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Another important tool for teaching about comparing and ordering numbers is showing how to convert between fraction and decimal form. That way, we can make values comparable to determine if they are of greater or lesser value. To teach how to turn a decimal into a fraction, we start with a place value chart of decimals.


Diagram 1. Place value chart for decimals
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The students need to write the decimal value in the place value chart, and the place of the last digit is the denominator of the fraction. The numbers in the decimal are then placed in the numerator. For example, in telling students to turn 0.441 into a fraction, the diagram on your screen (below) shows what they should enter in the chart.


Diagram 2. Putting values in the place value chart
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