Place Value And Decision-Making Model

Introduction
This report is about place value and how it should be approached based on the interview style diagnostic observations of year six student ‘Ariel’ and her knowledge and understanding of place value, including her ability to correctly use it with mathematical operations. The aim was to diagnose areas that required learning and offered improvement opportunities. The aim was to then support this with the development of a teaching plan. This was achieved by instructional activities through a series of tutoring sessions that worked towards refining her areas of knowledge and improvement, and then extend on those ideas. After completing the diagnostic test, the areas Ariel struggled most with were multiplicative thinking, partitioning,…show more content…
Modeling is the process of choosing and using appropriate mathematics and materials, apply them experiential situations, and analyse them for better understanding (“High School: Modeling | Common Core State Standards Initiative”, 2016). There are two kinds of modelling that can help understand place value especially when trying to progress understanding of larger numbers. The first is proportional modelling which is represented by units bearing the same size (Reys et al., 2012, p. 170). For example, the material used to represent the value of 10 is ten times the size of 1 unit. The second type of modelling is non-proportional modelling. This occurs when size relationships are not maintained and often differ, for example, money or coins (Reys et al., 2012, p. 170). These can help develop the relationship of place value through valuable trading practices (Reys et al., 2012, p.…show more content…
They are selected to support and enhance the lesson objective (Reys et al., 2012, p. 43). There are ungrouped materials that can be formed in to groups, for example, single beads or straws or anything that can be bundled into groups of say,10, or another amount. There are also pre-grouped materials that are already bundled to represent an amount. The use of ‘manipulative’ materials can be useful visual aids and assist children grasp concepts with a hands on approach, making it easier for a teacher to observe what a child is doing rather than thinking (Marshall