Rich Learning Tasks

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How Many Units?
Questions to facilitate the learning
• How do you know that there are more possible units that it would take a lot of? How would you create them?
• How do you know that there are more possible units that it would take just a few of? How would you
create them?
• How was the unit you created to require a lot of units different from the one you created so that not so
many were needed?
Scaffolding the learning
• If you used a big unit, would a lot of them be needed to measure the line? Explain.
• How would you go about creating a unit that it would take 2 of to measure the line?
• How would you change that unit so that it would take more than 2 but fewer than 3 to measure the line?
Extending the learning
Students might attempt to create units to meet other conditions, e.g.:
It takes exactly 4 to measure the line.
It takes more than 1, but fewer than 2, to measure the line.
It takes exactly 2 more units than one of their previous choices to measure the line.
What’s the point of this task?
The purpose of this task is to reinforce understanding that it takes fewer large units or more smaller units
to measure a given length. At the same time, students have an opportunity to use visualisation skills to
estimate how many units long a particular length is. Informally, students are using early fractional thinking
when they estimate the unit size when just a few units fit.
The line being measured is neither horizontal nor vertical so that students become accustomed to
measuring lengths even when they are not straight across or straight up and down. Paper clips from which
to choose are not pre-determined; this puts more of the thinking in the hands of the student.
The phrases ‘a lot’ and ‘not so many’ were used to give latitude to students, so that they could come up
with different possibilities.
Measurement