Hi Teachers!

Angela Rogers, PhD


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  • Count
    Counting forwards and backwards in place value parts (e.g., 45, 55, 65 is counting using the unit ten). Bridging forwards and backwards over place value segments such as decuples and centuples (e.g., 995 and one more ten requires bridging forwards over hundreds to thousands).
  • Make/Represent
    Using the idea of grouping and re-grouping by tens to make, represent or identify the value of a number using a range of materials or manipulatives. These may be proportional (e.g., base-ten blocks), non-proportional (e.g. coloured counters) and be presented as canonical (e.g., 3 tens and 9 ones is 39) or non-canonical (e.g., 2 tens and 19 ones is 39) representations.
  • Rename
    Drawing on the ideas of grouping, regrouping and partitioning, rename numbers in multiple ways in terms of place value parts without the use of manipulatives ( e.g., 1 260 is equivalent to 126 tens or 12 hundreds and 6 tens or 1 thousand and 260 ones).
  • Compare/Order
    Compare numbers to determine which is larger or smaller using an understanding of the relationships between numbers. Compare numbers in a multiplicative manner, for example ten times larger than 54 is 540. Place numbers in descending or ascending order and locate numbers on empty, partially marked or complete number lines.
  • Name/Record
    Read and write or record a number in words and symbols (e.g., 75 is written as 'seventy-five'). Name the place value columns and round number to the nearest place value part.
  • Calculate
    Apply knowledge and understanding of the place value system when completing calculations using the four operations (e.g., 45 multiplied by ten is 45 tens, 45 plus 100 is 145, 120 divided by ten is 12, which is ten times smaller than 120)

Hierarchy of difficulty

The six aspects allow us to understand 'what to teach', but we need to know 'how to teach' this content. So, using the six aspects I was able to determine a hierarchy of difficulty within each aspect. That is, I discovered the content teachers should begin with and what they should move students onto in order to develop their knowledge in each aspect. This progression became known as the Stages of Place Value.

The progression highlights important implications for the teaching place value, namely the importance of the rename aspect and the irrelevance of the size of numbers.

The rename aspect of place value emerged as the most challenging and critical aspect for students, mostly because this relies on a deep understanding of composite units. This highlights the importance of focusing on this key aspect of place value in classroom instruction.

The progression also suggests that the difficulty of items is not related to the size of numbers involved, as commonly assumed in the literature. For example, students may find a two-digit rename item more difficult than reading or writing a four-digit number. This finding suggests that teachers need to be aware that each aspect of place value has its own inherent difficulties. This finding also has significant implications for the many curriculum documents and frameworks which suggest progression in place value in solely related to the size of numbers students are using.

The Zero Our Hero App presents the place value content in a hierarchical manner which is based on the four stages of difficulty I identified in my PhD. Once students have successfully completed Stage One, Stage Two will become unlocked and so on. This ensures all students are working at their individual point of need.


How can I use Zero in the classroom?


Sample Questions

Below I have included a sample of questions from the Zero Our Hero App to give you an idea of some of the content covered. The questions shown are all from Stage One. Remember there is much much more content covered in the App!