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A little while ago the CM Define It app featured the expression number line. When you think of the term number line, which other mathematical words spring to mind? What do you immediately connect with it? What other key ideas do you think will be connected to the term number line?
We’ve used the CM Framework to generate the following visualisation to help with these questions.
Figure 1. All the glossary entries in the CM Framework that are currently connected to the term number line. Two words are connected if they both occur as glossary links in the text of the same waypoint (piece of mathematical content), with the strength of the connection being the number of waypoints where this happens.
Does this match the words you thought about? Are there any surprises? Can you see any interesting conceptual trains of thought running through these semantic links?
For example, one intriguing connection is the term reflection. How could reflection be linked to the number line? The connection is mediated by the waypoint Extending the number line and relates to reflection via this student action:
“Recognise that negative numbers may be seen as a reflection of the natural numbers through a mirror placed at zero, perpendicular to the number line.
Know the implications for this in terms of positions as a 'distance from zero' in either the negative or positive direction."
Figure 2. A snapshot of the connection between the terms number line and reflection through the Extending the number line waypoint, including the underlying explanation for how the Extending the number line waypoint mediates the connection between the key terms.
Have you ever used a task or explanation of negative numbers that refers to this idea of reflecting a number line? You can tweet us @CambridgeMaths or reply in the comments below. Please also do sign up/continue to use the CM Define It app, which will help us develop our understanding of what makes useful as well as correct definitions for the words in our glossary.