Matthew was energetic and keen to solve the problems at hand. He adapted to my suggested techniques for multiplying numbers quickly in his head, and was able to produce faster answers. When I encouraged him to continue to write down all working, even when computing mentally, he was able to show me his working. He had a good recollection of the fractions techniques that we had previously covered, and with some reminders he was able to do most questions.

Matthew needed reminders to focus on the problems that I had set up, and to finish one problems before we moved on to the next. It is awesome that he is keen to come up with his own problems, but I encourage him to work with me to make sure that we don’t only focus on the content that he is already confident in. The main difficulties seem to arise when questions require multiple techniques that are not explicitly outlined. Matthew can often do each step, but we are practicing putting steps together to complete more complex problems.

Once I explained how to convert between equivalent fractions, Matthew picked it up quickly and was able to do examples. After a few examples and explanations, Matthew could define the independent variable and identify it, however he was having a bit more trouble with the dependent variable. We will continue to work on this. He was able to recognise that density was related to mass and volume, and could often determine which substance was more dense when I gave him worded scenarios. He is good at mental multiplication.

Matthew needs encouragement to stay on one problem at a time and to finish the problem at hand. We are working on seeing challenging problems as opportunities for brain growth rather than sources of distress, and accepting that we don't have to understand things the first time. We will continue to practise identifying independent and dependent variables. I am hoping to write a brief practise practical report as a learning activity with Matthew.

Matthew is gaining confidence working numerically. He can add and subtract numbers, and multiply and divide to a satisfactory level. He remembers important processes such as dividing fractions. His ability to apply such processes to more complex or worded questions is improving.

We are still working on active engagement and conveying mathematical definitions and processes. When I teach Matthew a definition and write it down on our working paper, I ask him to repeat it back to me, but he is often unsure. I think it would help if he would write down the definitions himself and explain them to me so that we could patch up any gaps in understanding. I have also been encouraging Matthew to have patience while we complete problems, but he often wants to switch problems midway when they get tricky. I will try to keep him engaged and boost his confidence as best as possible.

Matthew was able to persist throughout the lesson, even when tired. He was able to compute expressions quickly in his head. He read questions out loud and we worked on them step by step, acknowledging key information and drawing on our knowledge to work at the problems.

Matthew could use a small book to create key idea summaries. This would help him to create links between knowledge from different topics quickly and he could apply these links to more complex problems.