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10/08/2011
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Ma1 Using and applying mathematics

Generally odd and even

Handwritten example of sum of three even numbers, three odd numbers, an even number and an odd number, difference between an odd number and an even number.

Teacher's notes

  • Understands general statements.
  • Tries several examples and uses the results to complete a general statement.
  • Has support with creating examples and completing the first general statement.
  • Works independently with other statements.

Next steps

Investigate situations from which he can formulate his own 'rule' or general statement.

Wow fact-ors!

Handwritten note on finding out multiplication facts for ×2, ×4, ×5 and ×10 tables

Teacher's notes

  • Works independently.
  • Knows multiplication facts for ×2, ×4, ×5 and ×10 tables.
  • Uses these facts to derive other multiplication and division facts.
  • Factorises given numbers and counts the number of factors.
  • Understands definitions based on the number of factors a number has.
  • Uses definitions to identify which type of number he has factorised.

What the teacher knows about John's attainment in Ma1

When working on problems that involve finding 'how many ways…', John perseveres to find further solutions. In the 'Wow fact-ors!' investigation, he perseveres to find all factor pairs for each of the numbers. He is beginning to check his work, for example by making sure that his solution to a problem makes sense in the context of the problem. John talks about his work using familiar mathematical vocabulary appropriately. He refers to his written work when providing explanations. John demonstrates his reasoning, for example by completing generalisations about adding and subtracting odd and even numbers. When given incomplete generalisations, John works through appropriate examples, draws conclusions from them and completes the generalisation. He also uses definitions of prime and square numbers based on their numbers of factors. By finding the number of factors for given numbers, John is able to identify those which are prime or square.

Summarising John's attainment in Ma1

John understands a general statement and finds an example to match it, which is typical of performance at level 3. He needs more experience of a wider range of problems, with input on breaking into a problem and developing systematic approaches, to make further progress within level 3 and into level 4.