This is a great, open ended, rich maths task which encourages students to understand connections - relationships - between many areas of maths.
a number machine,
for students to investigate… and hopefully come to the conclusion that all represent the same relationship in different ways. I’ve tried this a few times with Yr7, 8, 9 students and, although they start off slow and I keep my own input to a minimum, they usually get there and appreciate it all the more after a while. If the class is really struggling then you could use the suggestions for ways to investigate which are on slide 4. To extend this rich, open task students could create their own set of cards.
The file ‘Relationships’ is the main activity and the ‘LessonPlan’ goes with this. I suggest print out the main page for pairs of students as well as projecting from of class.
A subsequent activity / lesson could be students to complete the number machine, table, sentence and graph from the algebra. The file ‘Relationships2’ are the resources that you’ll need for this with the file ‘LessonPlan2’ as the lesson plan.
Tried and tested, and corrected(!), in the classroom many times. This download includes a pdf files as well as the original powerpoint and word files for easy editing.