Display the Number line tool with the relationship a=2n+2 already defined.
Take several suggestions and record them for everyone to see.
Choose one of the suggestions, for example, a = n+2.
Note : Avoid the correct one at this stage!
Invite a student to move n so that n=1.
Discuss with students why, although the rule a = n+2 was true when n = 0, as it is no longer true when n = 1.
Drag n to various positions on the line and build a table of values of n and a. For more able year 8 groups, include decimal and negative numbers.
Support students to establish that the actual relationship is a = 2n+2 and reveal the calculator to them to how the relationship was created. |
Would anyone like to suggest a relationship that might connect (or link) the values of n and a?
If the rule a = n+2 was true, what would you expect the value of a to become if we move n so that it equals one?
Do we think that the rule a = n+2 is true now? |
Set the task for students, which is to substitute different vales of n into expressions to determine which appear to give the same result, always, sometimes and never.
Choose the expressions to provoke discussion amongst students. |
What do you notice about your results?
Which expressions do you think could be equivalent? |
Use the Number line tool to test the students’ conjectures.
Invite students to suggest pairs of expressions.
Define the first expression as a and the second expression as b. |
If the expressions are equivalent, what will happen as we drag n along the line?
How can we check that they are equal if we can only see one of the points?
(Either reveal the values of a and b to show they are equal of switch off a or b from the Options menu)
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Use the Number line tool to confront and discuss the common misconception that 2n and n 2 are equivalent. |
How could we use the Number line tool to prove that n 2 and 2n are not equivalent, although they are equal when n = 0 and n = 2? |
