Prime number investigation
Teacher's notes
- Finds examples and counter-examples to justify answer.
- Uses vocabulary accurately (prime number, sum of the digits) to explain and justify conclusion.
Next steps
Investigate and explain other number patterns.
Primes and squares
Teacher's notes
- Independently selects an appropriate method to record answers systematically.
- Identifies complex patterns and relationships: for example, states that one of the squares has to be a multiple (or factor) of 4, and the other has to be an odd square.
- Draws simple conclusions based on the investigation and gives an explanation of reasoning, supported by examples.
Next steps
- Justify methods (e.g. explain how systematic recording can be used to prove that all the possibilities have been found).
- Apply understanding of simple formulae and symbols to represent problems.
- Make predictions and relate them to conclusions.
Mobile phone investigation
Teacher's notes
- Discusses problem and possible approaches with a partner.
- Identifies and obtains necessary information to solve the problem, recognising the information that is important.
- Breaks a multi-step problem into simpler steps.
- Checks as he works, reviewing methods with his partner and correcting any errors.
- Chooses an appropriate, systematic way of recording findings and interprets results to draw simple conclusions.
Next steps
Develop use of diagrams and graphs to communicate results and conclusions (e.g. create a line graph to show the set-up cost and subsequent monthly expenses for each network).
What the teacher knows about Sachin's attainment in Ma1
Sachin independently interprets and solves problems in a range of mathematical contexts, applying existing knowledge and skills in a new context. He identifies and obtains the information required to solve a problem, deciding which information is important and which information is missing in order to solve the problem. He breaks down a problem or investigation into simpler steps when deciding how to approach a problem. Where appropriate he refers to previous work to support the development of problem-solving approaches. While working, he checks the reasonableness of his answers and reviews whether his approach is appropriate, making adaptations or corrections where necessary.
Sachin records his results and conclusions in a systematic way, using appropriate methods (e.g. a table, oral or written explanations). He gives detailed explanations to explain his solutions. He independently chooses precise and accurate mathematical vocabulary in his explanations and improves his explanations by redrafting them.
Sachin draws simple conclusions based on his mathematical investigations. He justifies his conclusions and supports his explanations with examples and counter-examples. He identifies complex sequences, patterns and relationships in his problem solving and investigations.
Summarising Sachin's attainment at Ma1
Sachin's attainment in Ma1 is best summarised as being securely at level 5. He independently solves mathematical investigations, recognising which information is important or which information is missing, and uses this to develop a line of enquiry. He breaks a problem down into simpler steps and confidently tries different approaches to reach a solution. Sachin draws conclusions based on his results and communicates his ideas using precise mathematical vocabulary. To progress further within this level, he needs to continue to use simple formulae and symbols to represent problems. He should represent his results in a wider variety of forms (e.g. graphs, diagrams). He also needs to make predictions at the start of his investigations and relate them to his conclusions. He is currently using and applying his mathematical skills from Ma2 and Ma3, but needs to develop this within Ma4, in particular when interpreting graphs and considering further questions to investigate.