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Cut and find

Cut and find

Comparing and discussing concrete models of fractions can help students realise the significance of paying attention to whether the wholes are the same size or different sizes.

This activity focuses on halves and quarters but any fractions can be used.

Pose the question:

When is one-half larger than one-quarter?

and discuss possibilities as a class.

Prepare multiple copies of four paper shapes: a large and small circle, and a large and small square. The template of different shapes might be helpful.

Each student takes one of the four different paper shapes and:

  • folds the shape to make a fraction specified by the teacher
  • labels one of the equal parts with the appropriate unit fraction
  • cuts the labelled piece away from the whole.

Ensure that all possibilities are covered, i.e. small circles divided into halves, small circles divided into quarters, large circles divided into halves, large circles divided into quarters, small squares divided into halves, small squares divided into quarters, large squares divided into halves and large squares divided into quarters.

Students form groups and find someone with a labelled fraction piece that is:

  • the same unit fraction
    Is the other piece the same or different? Why?
  • a larger fraction
    How do you know that it is larger?
  • a smaller piece of paper
    Is the fraction the same or different? Why?
  • a different shaped piece
    Is the fraction the same or different? Why?

Each group prepares a poster to report several conclusions and explanations from their comparisons.

Yes

Yes

Name Class Section
Document Year 5: Compare and order common unit fractions and locate and represent them on a number line Infobox 3
Document Year 4: Investigate equivalent fractions used in contexts Infobox 3
Document Year 3: Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole Infobox 3
Document Source Infobox 3