THE BIG 6 IN NUMBER
Multiplicative Thinking
When we ask students to ‘think multiplicatively’ we are asking them to think about numbers and collections in terms of multiplication and division. This starts right back in Kinder and Prep where students are asked to share things equally. This could simply be sharing out the pencils equally or sharing out a collection of counters to a group of students so that each student has the same amount. Students begin by thinking about multiples as repeated addition (e.g. 5 fours is 4 + 4 + 4 + 4 + 4) and then looking at these as groups (5 fours is 5 groups with 4 in each). The next progression is to look at these in terms of arrays and then regions.
Repeated Addition
Groups Of
Partitioning
Partitioning is developing the understanding of Fractions and Decimals. The concept of equal parts plays a large role in students being able to construct their own fraction models. Students begin to develop an understanding of fractions in Prep when they are learning to share amounts equally and then in Grade 1 where they explore partitioning a whole into equal parts. From here, the continued development of fractions continues throughout the curriculum for all grades in primary school.
Fractions are heavily linked to Multiplicative Thinking, in particular division which involves sharing or dividing things equally. There are five constructs of fractions: Part-whole fractions; Fractions as a measure; Fractions as division; Fractions as operators; and Fractions as ratios.
Part-whole Fractions
Fractions as a Measure
Fractions as Division
Fractions as Operators
Fractions as Ratios
Fractions are a complex part of the Mathematics curriculum. Once the foundational understandings of fractions have been consolidated students can then start exploring the different types of fractions (proper fractions, improper fractions and mixed fractions) and how fractions can be represented as decimals and percentages. This is where we can see the connection to Place Value and why it is important to gain a good understanding of the Place Value system.
Andrea Curran
Numeracy Coach