Multiplicative Thinking

“…the ability to work flexibly with the concepts, strategies and representations of multiplication (and division) as they occur in a wide range of contexts”

Multiplicative Thinking Micro Content

  1. Cyclical pattern of 100-10-1 is repeated from ones to thousands
  2. Cyclical pattern of 100-10-1 is repeated beyond 100s to millions
  3. Ten times multiplicative relationship exists between places
  4. The multiplicative relationship extends to numbers less than one, that is to the right of the decimal point
  5. There is symmetry in the place value number system based around the ones place so that the patter in naming wholes is reflected in naming decimals
  6. Double count by representing one group (e.g. hold up 4 fingers) and counting repetitions of that group, simultaneously keeping track of the number of groups and the number in each group
  7. The multiplicative relationship between quantities is expressed as ‘times as many’ and ‘how many times larger or smaller’ a number is than another number
  8. Numbers move a place each time they are multiplied or divided by 10
  9. Basic number facts to 10×10 are recalled and patterns in number facts are investigated
  10. Number facts can be extended by powers of 10
  11. Multiplicative situations can be represented as equal-groups problems, comparison problems, combinations (Cartesian) problems and area/array problems
  12. The multiplicative situation is understood (factor X factor = multiple) with the meanings of the terms clearly understood
  13. Multiplication arrays are used to visualise and represent multiplication situations
  14. Division and multiplication are known as the inverse of one another
  15. The communitive property of multiplication is understood and can be shown to be linked to arrays
  16. Partition division involves finding the size of each group and quotition division involves finding the number of groups and can be also expressed in terms of factors and multiple
  17. Quotition division can be considered in terms of fractions so that a quantity can be split by ‘halving’, ‘thirding’, ‘fifthing’ etc.
  18. Prime and composite numbers can be linked to multiplicative arrays – prime numbers can be made only with a single row array
  19. Distributive property of multiplication over addition is applied and shown by a multiplicative array
  20. Multiplicative arrays are linked to the concepts or area and volume
  21. Measurement units have the same multiplicative relationship as the Base 10 system
  22. Cartesian products can be represented symbolically and in tree diagrams