*“…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**

- Cyclical pattern of 100-10-1 is repeated from ones to thousands
- Cyclical pattern of 100-10-1 is repeated beyond 100s to millions
- Ten times multiplicative relationship exists between places
- The multiplicative relationship extends to numbers less than one, that is to the right of the decimal point
- 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
- 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
- The multiplicative relationship between quantities is expressed as ‘times as many’ and ‘how many times larger or smaller’ a number is than another number
- Numbers move a place each time they are multiplied or divided by 10
- Basic number facts to 10×10 are recalled and patterns in number facts are investigated
- Number facts can be extended by powers of 10
- Multiplicative situations can be represented as equal-groups problems, comparison problems, combinations (Cartesian) problems and area/array problems
- The multiplicative situation is understood (factor X factor = multiple) with the meanings of the terms clearly understood
- Multiplication arrays are used to visualise and represent multiplication situations
- Division and multiplication are known as the inverse of one another
- The communitive property of multiplication is understood and can be shown to be linked to arrays
- 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
- Quotition division can be considered in terms of fractions so that a quantity can be split by ‘halving’, ‘thirding’, ‘fifthing’ etc.
- Prime and composite numbers can be linked to multiplicative arrays – prime numbers can be made only with a single row array
- Distributive property of multiplication over addition is applied and shown by a multiplicative array
- Multiplicative arrays are linked to the concepts or area and volume
- Measurement units have the same multiplicative relationship as the Base 10 system
- Cartesian products can be represented symbolically and in tree diagrams