Multiplicative thinking enables a wide range of real-world problems to be solved including scaling, proportions and rates of change, which are fundamental in fields such as science, economics, and engineering.
Multiplicative thinking involves understanding ‘times bigger’, ‘times smaller’, ‘times as many’ and ‘times fewer’ and using this thinking to explain relationships between place value, multiplication, division, fractions, factors, multiples and products.
By learning multiplicative thinking, students develop efficient mental strategies and meaningful forms of written computation to solve a wider range of problems.
The following concepts collectively form the foundation of multiplicative thinking in primary school:
equal groups (4 plates, each has 3 cakes. How many cakes altogether?)
rate (What is the average speed of a car that moves 10km in 13 minutes?)
scale factor (Reduce the size of the rhombus by two and a half times)
cartesian product (3 different shorts, 4 different shirts, how many outfits?)
ratio and proportion (the recipe feeds 4 people. Change it to feed 6 people)
percentages (20 marbles in a jar. 15% is how many marbles?)
Commencing in Kindergarten, there are five broad phases to understand how multiplicative thinking develops:
One-to-One Counting: Students can match an object to a number in order. During this phase students do not have a concept of a group and may think they will get a different count if the collection is rearranged or if they start in a different place.
Additive Composition: Students can use groups to count more efficiently. They understand that a group can be rearranged or counted in different ways and the quantity will not change.
Many-to-One Counting: Students can represent one group and count repetitions of the same group. At this phase students will use additive thinking and individually count groups and then add them together, known as double counting.
Multiplicative Relations: Students know that when one quantity changes, the other quantity will change by a consistent factor. They understand the structure of the multiplication and division algorithm.
Operating on the Operator: Students know that operators are special symbols that indicate a specific operation to be performed. They understand how to operate these symbols including the multiplication (x) and division (÷) symbols to solve more complex mathematical statements or equations.
Multiplicative thinking is part of the ACARA National Numeracy Learning Progression and NSW Mathematics Syllabus. It is a critical aspect of developing number sense and the ability to understand and apply algebra.
Multiplicative thinking is one of the big ideas of mathematics and is central to the learning of mathematics. It provides students with the conceptual knowledge to really understand maths.
creatingrounds.com/uploads/9/6/2/4/96240662/siemon_summary.pdf
Lorraine Jacob & Sue Willis The Development of Multiplicative Thinking in Young Children.
alearningplace.com.au/wp-content/uploads/2020/07/ Multiplicative-Thinking-Post-4.pdf
