I am yet to meet a Maths teacher who doesn't love surds and yet it can take so so long for students to become confident with manipulating them that you can find yourself wondering just how you can keep the practice focussed but fresh.
When met with this problem earlier in the year I tried to think of ways that I could build on those skills they needed for simplifying surds whilst providing a purpose to ensure the practice didn't go stale.
For this first task it was about focussing on the importance of the 3. What conditions must the first box meet in order to end up with an integer coefficient of root 3?
The second part of this task is a subtle variation of the first but it creates a question. How does the change to the position of the 3 affect the possibilities for the empty boxes? What is the significance of the 3 being the coefficient of the surd?
Moving on to this final task which just provided students with one part of a multiplication and various constraints for the answer.
Students were able to practice manipulating surds whilst concentrating on a bigger problem. This purposeful practice is something I want to increase my use of in the classroom.
For a downloadable version of the two tasks seen above follow this link: https://drive.google.com/file/d/126G2c-UoW-4n_7Ch6_RnHPN-WVnSwy7N/view?usp=sharing