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Ma2 Number

This is a collection of work. Click through the chapters to see the full collection or download the attached standards file.

Place value

Drawing to showcase multiplication and division of integers

Teacher's notes

  • Uses multiplication and division by powers of 10, for example 10, 100, 1000, to make a target number, mostly correctly.
  • Explains the effect of multiplying and dividing integers and decimals by powers of 10 and sees patterns in the numbers she uses.
  • Understands the place value of digits, for example that the value of the 3 in 0.0032 is three thousandths.

Next steps

Use place value and known multiplication and division facts to find related facts, such as 320 = 40 × 8 = 400 × 0.8.

Reducing fractions

Illustration of fractions to determine other fractions having same values

Teacher's notes

  • Knows which fractions are more than or less than a half.
  • When prompted, converts fractions using a common denominator to order them more easily.
  • Recognises when fractions are in their simplest form.

Next steps

  • When ordering fractions, use common denominators more readily, to find equivalent fractions.
  • Use the lowest common multiple to obtain the common denominator, for example convert to tenths to compare one-fifth, one-half and four-tenths.

  • Order fractions with a wider range of denominators.

Sequences

Illustration of a table to determine pattern of a sequence of numbers

Teacher's notes

  • Creates a pattern using circles and squares.
  • Completes a table to record the numbers of circles and squares in the sequence.
  • Explains the pattern and predicts the numbers in the 50th and 100th term.
  • Independently finds a formula to calculate the number of squares and circles in the nth term.

Next steps

  • Use correct notation, for example 3 n for 3 × n.
  • In a similar investigation, choose own letters for variables and create own table to record results.

Real-life problems

Illustration of real life problems and a student's answer to the problems

Teacher's notes

  • Chooses and uses all four operations to solve word problems in a range of contexts.
  • When dividing, gives a remainder as a fraction or a decimal, or rounds appropriately.
  • Uses the grid method to multiply decimals such as 13 × £2.65.
  • Adds numbers with different numbers of decimal places, for example: 20 + 6 + 6 + 1.8 + 0.5 + 1.05 =.

Next steps

  • Check answers by using inverses and approximations.
  • Use a more efficient method to multiply decimals.

What the teacher knows about Louise's attainment in Ma2

Louise uses her understanding of place value to multiply and divide whole numbers and decimals by 10, 100 and 1000. She orders negative numbers in a context such as temperature. Louise understands prime numbers and uses her knowledge of multiples and divisibility rules to identify them. She rounds numbers to one and two decimal places if required. With prompting, Louise approximates and checks that answers are of an appropriate size.

Louise reduces a fraction to its simplest form by cancelling common factors. She recognises simple equivalences between fractions, decimals and percentages, for example three-tenths = 0.3 = 30%. She orders numbers with three decimal places, for example 0.345, 0.350, and 0.035. With some prompting, Louise orders fractions where the denominators are different.

Louise uses all four operations and understands the relationships between them. She uses the inverse operation to check her answers when prompted. She uses brackets in some number sentences to show which part needs to be calculated first and is beginning to express remainders as fractions and decimals.

Louise adds and subtracts small negative numbers in the context of temperature. She mentally calculates decimal complements to 10 or 100 (up to one decimal place), for example 62.3 + __ = 100. She multiplies a two-digit number by a single-digit number in her head, using partitioning and sometimes jottings; she uses her knowledge of tables and place value to multiply decimals, for example 0.6 × 7 = 4.2.

Louise solves word problems using symbols and diagrams to represent her work. She constructs simple formulae involving one operation and writes them using symbols, for example s = n × 3, to calculate the number of squares in the nth pattern of a sequence. She evaluates simple expressions by substituting numbers into them: for example, she finds the value of n if 3 × n = 60. She uses and interprets coordinates in all four quadrants.

Louise employs written methods to calculate using all four operations with decimals to two decimal places. Louise accurately adds numbers that do not have the same number of decimal places, but is not yet confident with subtraction. She multiplies and divides decimal numbers by a single digit. She uses short division for dividing three-digit numbers by single-digit numbers. Louise uses chunking for dividing three-digit numbers by two-digit numbers, but does not always choose the largest possible chunks. She uses long multiplication with a range of numbers.

Summarising Louise's attainment in Ma2

In Ma2 Louise is best described as working at the lower end of level 5. Her understanding of place value is sound. She is secure in using a range of mental methods of computation; she uses efficient written methods for addition, subtraction and multiplication and an expanded method for long division. She applies these methods to solving real-life problems involving all four operations with both integers and decimals to two decimal places. To progress further into level 5 she needs to develop a more secure understanding of fractions, ordering them when the denominators are different. She needs further work with formulae involving two operations.