These teaching activities also appear in the Misunderstandings and Good teaching sections of the drawer where they are preceded by additional important mathematical and pedagogical information to assist in your teaching. The activities include digital learning objects, the use of a variety of materials to model mathematical understandings, and games.
Students use a digital learning object to predict the written fraction that best describes part of a circle. Students then reconstruct both the symbolic fraction and the area model to check the prediction.
The digital learning objects provide contexts to help focus student thinking on the equality of parts, not just the number of parts.
Comparing non-unit fractions
The digital learning object provides a tool to help students develop strategies for comparing non-unit fractions.
Comparing unit fractions
The digital learning object supports students in making connections between the written unit fraction, a length representation of the fraction and the fraction’s position on the number line.
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.
Divide it up
Sharing-as-division problems may give a result with a remainder. In some contexts it makes sense to divide the remainder into equal parts (fractions) and continue the sharing process.
Students physically model problems that require them to cut the items into fractional parts to carry out the sharing process.
Two numbers are entered into a digital tool to construct a grid. Boxes on the grid are then shaded to represent fractions, and equivalent fractions determined.
The digital learning object illustrates the relationship between the part-whole model of a fraction and the value of the fraction, by representing its position on a number line.
Students fold strips of paper to create fractions then use the strips to build a fraction wall. The fraction wall facilitates comparison of fractions and the identification of equivalent fractions.
Fraction wall game
Students use dice to generate fractions that are coloured on an unlabelled fraction wall. Strategies develop for colouring equivalent fractions to fill the fraction wall.
Students can use a fraction wheel made from two paper plates to model fractions and build visualising skills.
Grids and jumps
Grids and number lines are used to model the addition and subtraction of fractions with related denominators, to connect with strategies for creating equivalent fractions.
Hit the apple
Using the digital learning object, students create a pair of fractions that add to one. There is a fraction bar representing each fraction and a vertical number line that monitors the progress towards the target of adding to one.
Students solve problems requiring the addition or subtraction of fractions with the same denominator, modelling with area diagrams and a number line. Students begin to realise the strategy of adding the numerators.
Pre-prepared squares, divided into equal parts using vertical (or horizontal) lines, are overlayed to create grids depicting smaller parts. This helps students to work with factors and multiples to find equivalent fractions.
Paper folding is an example of a practical activity that focusses students' attention on the need to create equal parts to represent fractions.
Part and wholes
Students develop strategies for working out the total number in a collection, given the number of items in the fractional part.
Reach the target
Supported by the digital learning object, students create a pair of fractions with related denominators that add to the target fraction.
Sense of size
One way to reduce the likelihood that students will blindly apply inappropriate procedures is to strengthen their sense of the size of fractions, particularly in relation to the whole.
Sequencing and counting
Students develop strategies for placing fractions on a number line in relation to other fractions and to whole numbers, up to 1 and beyond 1.