Students struggle to see the point to remembering which law Associative or Distributive Law, and how do you even say Commutative (are you sure it isn't Communicative or Communitative?)
And the real point of empowering student with tool to do Algebraic Manipulations, is lost to repetitive matching exercises.
As Algebra becomes increasingly complicated understand in higher year levels what can (and can not) be done becomes more important.
Visual aids are very helpful (Mathisfun.com has some good visuals here) but to introduce more visual thinking and introduce some Art into Maths (STEAM instead of STEM), I challenged the students to develop some superheroes with the powers of relevant Algebraic Laws.
The students were given a piece of paper and some pencils, and as we described Algebraic Laws, they were to draw a super hero who demonstrated the law in some way. They had a lot of freedom to use creativity. A few students decided they wanted Sports Stars and others created Super Vehicles while some were happy just sticking with various super heroes.
We started with Commutative Law. We discussed the law, reviewed some visual representation. Some students quickly had ideas, others waited for my example, which swung across the screen... it was Commutative Chimp, from the example many students started creating.
I gave the students a few minutes to get started... long enough to get an idea down, but not to finish the 'pretty' drawings.
My second example came bounding across the screen; Distributive Dog.
This time I gave the students slightly less time. All the class had come up with interesting ideas and were very keen to show them off. I didn't want too much sharing (not yet!) so I continued on to our third and final law.. Associative Law.
Again description, then visual representation and finally a sneaky Agent Associative example.
The students were very keen to create attractive and accurate posters to describe their Super Heroes (or similar characters).
I set a timer for 8 minutes for students to see the time counting down and to manage completing their creations.
When the time ran out, I got students into groups of 3 (or less). Each group allocated a member to be A, B & C.
I explained that we were doing a sharing Gallery (like an Art Gallery). We got all the students to BluTack their posters, with one Wall for A, one for B and another for C.
As a class, we all started at "Wall A", we reviewed the posters and could discuss with the artists. Were there any Super Powers that were incorrect?
Did we really understand the Laws?
Really the Gallery was for checking understanding, but students were proud of what they created and we keen to share.
At the end of the sharing students were permitted to take their posters home (and many put them in their revision folder for future reference.)
In some ways it may have been better to give all of the laws upfront and let students free with them, but giving one at a time ensured focus and allowed each additional law to be a type of iteration for improvement.
I feel this was a good lesson to give students a creative outlet in Mathematics and differentiate learning for some students could repeat the teacher's examples while other could create truly new and innovative characters.