Ma1 Using and applying mathematics

Pupil's handwritten work to solve a mathematical question.
The question reads 'Bipods and Tripods. Bipods have 2 legs and Tripods have 3 legs. I can see 23 legs altogether. There are at least two Bipods and at least two Tripods. How many could there be?' The pupil's writing says '23 legs'. This has been circled. They continue '20 divided by 3 equals tripods 21 equals 7 tripods 20 divided by 2 equals 10 bipods plus1 tripod 20 legs plus 3 legs equals 23 equals 2 tripods equals 6 legs equals 18 equals 3 tripods equals 9 legs 2 bipods equals 4 legs 4 tripods equals 12 legs 4 bipods equals 8 legs 5 tripods equals 15 legs So 5 tripods and 4 bipods equals 23 legs' This final answer has been annotated- the '5 tripods' with 'equals 15 legs' and the '4 bipods' with 'equals 8 legs'. There is a final note reading 'equals 23'.

Teacher’s notes

  • Finds a starting point, tries a few ideas to help understand the problem, then identifies key facts and operations to be used.
  • Approximates, then uses knowledge of tables to work out the number of legs on groups of Bipods and Tripods.
  • Finds a solution with only one Tripod then self-corrects his work to find one solution which satisfies the given criteria.
  • Explains his thinking orally and records it clearly.

Next steps

  • Develop a more systematic approach and organised way of recording.
  • Compare his solution with others in the class to find other possibilities.

What the teacher knows about David’s attainment in Ma1

When solving problems, David suggests ways to get started, choosing appropriate equipment to help him, for example coins or a 100-square. He independently carries out a simple investigation, sometimes using a systematic approach: for example, given a problem with a short list of clues, he follows them through, making sure each one is fulfilled. When faced with a more complicated problem he needs encouragement to continue, to read back and to check. He uses trial and improvement to find a solution that satisfies a set of two or three criteria.

David can discuss and explain his work, drawing on his mathematical knowledge and using appropriate language such as ‘multiply’, ‘double’, ‘halve’, ‘triple’. In his written work he records his thinking, often in an organised way. He can describe the methods and strategies he has used, for example: ‘I just used my times and divide to work out the answers. I know my three times table and my two times table facts.’