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Objective: By the end of the lesson, students will be able to apply principles of order and symmetry to (a) order positive and negative numbers on and off the number line, and (b) write mathematical expressions comparing numbers using < and >.
- We can use the number line as a tool to order and compare integers.
- We can use the order principle to create expressions that compare numbers using > and <.
What Teachers Should Know
About the math. The number line is a useful resource for reasoning about relationships between integer values; in Figure A, for example, a student first placed three numbers on the line and then compared the values of the numbers with expressions like -5 < -4. Principles and definitions that support ordering and comparing integers on the number line include order, unit interval, multiunit interval, and symmetry. Notation for comparing integers includes > (greater than) and < (less than), and these symbols allow students to reflect on and communicate relationships between integer values.
About student understanding. When ordering negative integers, students may draw on their knowledge of positive integers and thus treat negatives as if they were positives, as illustrated in Figure B.
About the pedagogy. In this lesson, as illustrated in Figures A and B above, students use number line principles to place integers on open number lines, and then use their number line solutions as a resource for ordering and comparing integers. Students express comparisons with expressions that capture relationships of greater than and less than.