# Place Value Essay

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Development of place value
Place value and the ten-base system are important foundations of later mathematical concepts. The development of these concepts takes years and is built upon pre-number and early number development. Therefore, the development of place value and understanding of the ten-base system needs to be understood in relation to early concepts.

Classifying and patterning are elements of pre-number development that need to be developed as part of numeracy. Classifying helps children distinguish what to count and forms a basis for comparison. Interviewing a student about their answer for a number line can highlight issues in classifying. For example, a student might experience confusion over whether to count dots or intervals
He demonstrated a lack of number sense for each of the line tasks. For question 5, I noted Boris counting by ones to 15 which indicated he had trouble estimating numbers based on place value (Appendix A). In addition, all number lines after this one were either counted by ones to the arrow or guessed far outside the acceptable ranges. According to Booker et al’s (2014) sequence of numeration, this may indicate he has not consolidated thinking in the tens or established place value with 2 digit numbers.

The partitioning of numbers in question 6 revealed he has developed some thinking in tens (Appendix B). However, Boris could not break the number down further than tens and ones, which might indicate a lack of practice in grouping. This is reinforced in early multiplicative thinking questions in which Boris was consistently using addition (Appendix C). Therefore, grouping has been established as an area of
According to Booker et al’s (2014) sequence, Boris has demonstrated a numeracy level between thinking in tens and developing place value for two digit numbers. This level is below the content descriptors for a Year Three; a student should be able to apply place value to partition, rearrange, recognize, model and represent numbers to 10,000 (ACARA, 2016). Therefore, it was determined that tutoring Boris should be aimed at this level to bolster his understanding of place value and trading up and down.

Initially, lessons were expected to reach a development sequence beyond 2 digit numbers. However, progress was slower than initially anticipated and targets were reevaluated regularly. For example, the three in a row playing board (Appendix ) continued to demonstrate a concern in his number sense. However, he also demonstrated increased fluency and understanding of place value and trading in other lessons. This was especially evident in pictorial representations of base-ten blocks in which Boris was able to subitise quantities quickly (Appendix ). This is likely because of his familiarity with them at

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