In school, classes have to progress at a certain rate that is set by the syllabus for that year. However, that rate might be too fast for any particular student which means that at some point it all gets a bit much and comprehension starts to fall away. A good example of this would be at pre-GCSE level when introducing a new subject like algebra while a student still doesn't have a firm grasp of fractions or powers (and the more challenging fractional powers). Rearranging and transforming equations implicitly relies on a good understanding of basic times tables, division (and therefore fractions) and how to cope with numbers raised to different powers.
Fractions are conceptually difficult because up till that point a student has got used to manipulating integers but a fraction seems very odd - it seems like two numbers, not one. In addition, the concepts of numerator and denominator are completely alien. Fractions will continue to be a challenge until the student finally understands that this strange looking pair of integers represents in fact, just a different kind of number. Conceptual aids like slices of cake or pizza, or marking fractions along a line can be helpful in this understanding, but it is of course also necessary to know how to do arithmetic with fractions.
Once the basic rules of how to add, subtract, multiply and divide fractions have been shown, it is simply a matter of practice until the process becomes second nature. Unfortunately there is often not enough time devoted to this practice in class due to the pressure to move on to new subjects and cover the syllabus.
Powers of numbers and fractional powers are particularly challenging. Practice with manipulating fractions and powers will help develop the skills and intuition needed for algebra.
Going through these kinds of problems in a private lesson can be time very well spent. Parents who are happy with fractions and powers can also help their children during homework by going through some problems together. To help pre-GCSE students and their parents, I have created a few worksheets for fractions and fractional powers that are freely available to download. Feel free to try them out. Practice makes perfect!
Fraction Worksheet 1
Fraction Worksheet 1 with answers
Fraction Worksheet 2
Fraction Worksheet 2 with answers
Fraction Worksheet 3
Fraction Worksheet 3 with answers
Fraction Worksheet 4
Fraction Worksheet 4 with answers
Fractional Powers Worksheets
Fractional Powers Worksheet 1
Fractional Powers Worksheet 1 with answers
Fractional Powers Worksheet 2
Fractional Powers Worksheet 2 with answers
Fractional Powers Worksheet 3
Fractional Powers Worksheet 3 with answers
Fractional Powers Worksheet 4
Fractional Powers Worksheet 4 with answers