The purpose of this task is to engage students in using the order of operations and knowledge of squares, cubes and roots, to solve a problem.
The background knowledge and skills that need to be established before and/or during this task are outlined in the diagram below:
This task may be carried out with numerical exploration taking a 'guess and check' approach, or the student may be able to find ways of using their knowledge of number to form strategies for solution. The approach should be chosen in sympathy with their skills and depth of understanding.
The arithmetic approach (show more)
- The student is able form each of the numbers 1 through to 10, by combining cubes, squares and roots. The student may employ an approach of 'guess and check' to form and to amend solutions.
Prompts from the teacher could be:
- List the first ten squares and cubes as these numbers may be useful to you.
- Think about how each number you want as an answer can be written as a product/sum of three other numbers.
The conceptual approach (show more)
- The student is able form each of the numbers 1 through to 10, by combining cubes, squares and roots and is able to explain their strategy or strategies.