Use proportional reasoning to make reasonable estimates
The Living Number Line
Description Students place cards labelled with fractional amounts on a large number line by equipartitioning. This physical number line, the living number line, is meant to grow throughout the year as subsequent units (i.e. fractions, percentages, decimals etc.) are placed. Students will use a variety of strategies to place cards appropriately, including relational and proportional thinking and knowledge of equivalency. 

Mathematics Research shows that the number line has greater longevity as a model than the circle model because it supports a deeper understanding of fractions (i.e., as a quantity represented by a number), and because it connects to representations that students need to understand in later mathematics (such as graphical representations). A circle model encourages an understanding of a fraction as a segment of a whole (e.g. piece of pizza), which is one way of seeing fractions, but does not help students connect to deeper and more sophisticated understandings. The use of a large number line allows students to better see connections between fractional amounts and to communicate their understanding. Accurately placing unit fractions on a number line involves significant spatial and proportional reasoning. 

Curriculum Connections Students will:


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Highlights of student thinking Students may:

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