Based on the principles of my original circling task (https://www.tes.com/teaching-resource/indices-circling-task-12117359), this task encourages students to think about what is going on with negative powers. In particular, it challenges popular misconceptions- such as negative powers giving negative answers- and forces students to simplify indices instead of working out the numerical values. There is also an extension at the bottom.
An activity for practicing means, medians, and modes from lists of numbers. The lists are chosen to address some misconceptions and tricksy problems- such as multiple modes, finding medians from an even number of figures, and means from numbers less than or equal to zero.
Below the grid are choices of rich, open extension questions for those that finish quickly.
The objective is simple- students need to find z. To do so, they will need to complete 25 algebraic substitutions in various forms (including some powers and roots). Plenty of practice with a competitive edge.
A rich activity to help students think about the meaning of indices and the index laws. Based on the numbers in index form, students should think about what the powers mean and use mathematical reasoning to deduce whether numbers are odd, even, square, or cube. There is also a short challenge to extend the thought processes.
Often the first stage of an iterations exam question asks students to rearrange an equation into the required form. This rich, high ceiling activity gives students the chance to practice this particular skill. Students can first rearrange the equation into any way they see fit (as long as it fits the ‘x=something’ format necessary for iterations), and then they can try to form the 8 versions given to them.
Good probing questions here might include “what do you think we should do first?” or “what do you think we should do last?” to encourage students to think in the way necessary to answer these exam questions.
An extension task asks students to investigate which versions could be used as iteration formulae (although this could be used as a follow-up activity instead of an extension, depending on the class).
A random right-angled triangle generator to create questions around Pythagoras’ Theorem. One length can be covered so students can calculate what would go there. Great for quick-fire mini whiteboard activities.
Lots of difficulty options to differentiate for audiences. Four categories:
All integer side lengths (i.e. Pythagorean triples)
All side lengths to 1 d.p.
And option to use smaller or bigger values in each category.