The Learning Approach Behind Place Value Quest
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Place Value Quest is informed by established approaches to mathematics instruction. This page explains those ideas in plain language and links to the sources we drew on.
Concrete representations
Children start with objects they can move: cubes, rods of ten and flats of a hundred. In the game: your child drags blocks onto a mat and trades ten ones for one ten.
Visual representations
Pictures and diagrams — a place-value board, a number line — show the structure of a number without needing the objects. In the game: digits fly from the block columns onto a hundreds-tens-ones board.
Abstract notation
Written digits and symbols come last, once they stand for something the child has already seen. In the game: 100 + 30 + 9 = 139 appears only after the blocks and the board.
Connecting the three
The approach draws on the idea of moving from concrete representations to visual models to abstract notation, and of showing them together. In the game: the same number is shown as blocks, board, parts and words at once.
Guided practice and scaffolding
Support is given early and gradually removed. In the game: outlines show where blocks go at first; later they disappear, and hints become optional.
Feedback
Useful feedback explains why an answer is not right. In the game: common misunderstandings (such as 139 = 1 + 3 + 9, or ignoring zeros) each get their own explanation.
Retrieval and spaced review
Coming back to earlier ideas helps them stick. In the game: roughly a third of practice questions revisit earlier worlds.
Progressive difficulty
Challenge rises in small steps. In the game: number size grows gradually and adjusts to how your child is doing.
Research & further reading
- Assisting Students Struggling with Mathematics: Intervention in the Elementary Grades — Institute of Education Sciences, What Works Clearinghouse practice guide (2021). Includes a recommendation to use a well-chosen set of concrete and semi-concrete representations.
- Improving Mathematics in Key Stages 2 and 3 — Education Endowment Foundation guidance report (2017), including the use of manipulatives and representations.
- Five Big Ideas in Teaching for Mastery — NCETM, including representation and structure.
- National curriculum in England: mathematics programmes of study — Department for Education (statutory guidance), for where place value sits in primary school.
See how the game works in practice, or read about Place Value Quest.