I am currently reading the book ‘making every maths lesson count’ by Emma McCrae. Open middle is mentioned in the book as a recommended website to use for practise.
I have blogged about meaningful practise before and the different elements that can make up meaningful practise such as arithmetic complexity, visual complexity, multiple steps and decoding. These 4 elements do not have to appear in one activity but should be incorporated into a lesson.
The topic of square numbers and roots was coming up with my year 7 class. A topic that they should be familiar with from primary school and because I had already covered square numbers with them during our sequences work. The objective of the lesson was to cover the square numbers from 1 to 225 and also the roots. I decided to create a worksheet that progressed through some different elements starting with basic questions on squares and roots building up to problem solving elements.
One of the tasks I chose to use was the following (this task is taken from open middle and can be found at: https://www.openmiddle.com/square-root-expression/ )
Square Root Expression
Directions: Use the digits 1 to 9, at most one time each, to fill in the boxes to make the following expression as close to 0 as possible.
This task made my students think about what they were doing and progresses on from simply regurgitating roots.
The task could be made easier by allowing the numbers 1 to 9 to be used more than once thus allowing for squares such as 121 and 144 to be used. Students could first of all think about the problem in this way and then progress onto only using the digits once.
Another task that I chose was below (again taken from open middle and can be found at https://www.openmiddle.com/perfect-squares/ )
Directions: Use the digits 1- 9, at most one time each, to fill in the boxes to make each expression evaluate to a perfect square number.
Extension/Challenge: What is the largest/smallest square number you can make? How many different perfect square numbers could be made?
The first part of this task can be completed without the students actually needing to calculate any values. For example, 18 x 9 x 2 will produce a square. This part of the task requires knowledge of square numbers and students understanding what squaring means. The extension then requires calculations and knowledge of square numbers along with the elements of trying to produce the largest and smallest squares.
My students engaged well with these tasks and I certainly think they fall within purposeful practise. I also think it was good for all my students in the room to feel challenged whilst all working on the same topic area.
I highly recommend looking at the open middle website and using their tasks where possible.