Fruit fractions: Gardeners of fractions

Use the teacher's slides to support your teaching.

Warm-up challenge

Always, sometimes, never

• Show image from slide 1. Students work in a small group to justify whether a numerator is ‘always, sometimes or never’ smaller than the denominator. Groups present their answers to the class.
• Expect responses such as: Always because that is the only experience students have – introduce   54  pieces of pizza.

Differentiation (extension): Have the student list some examples.

Differentiation (support): Teacher to show/model examples for students.

Begin the lesson by sparking interest in Asian gardening and the concept of planting fruits in garden beds, connecting it to the students' everyday experiences of gardens. Share a brief Asian gardening anecdote or showcase images of various Asian garden fruits. (Show the example Planting Asian fruit trees, Asian fruits on slides 3, 4 and 5.)

• Distribute drawing paper or pre-made garden bed templates to students. Ask them to design an Asian-inspired garden bed consisting of 10 squares (2 X 5):

• Encourage creativity in the borders/outsides of their garden bed designs, drawing inspiration from the beauty of Asian gardens.
• Explain that they will be selecting and drawing different Asian fruits in their garden beds. Reshow images of unique Asian fruits (slides 3 and 4) to inspire their choices. Let each student choose one or more Asian fruits to include in their garden bed design.
• Let students know that each square in their garden bed represents a fraction of the whole garden. For instance, if they draw a dragon fruit in one square, it signifies   1 10 of the garden will be dedicated to dragon fruit, emphasising the concept of tenths.
• Have students draw their chosen Asian fruits in the squares of their garden beds, representing the fractions they discussed. For example, if they select lychees, they might draw 2 lychees in 2 squares, representing   210   or   1 5   of the garden bed is devoted to lychees.

Classroom talks: Fraction discussion

Gather the students to discuss what they've drawn and the fractions they used in their garden designs. Ask questions such as, ‘How much of your garden is dedicated to mangoes? How about durians?’ Ensure students understand that when combined, the fractions should equal 10 tenths – a whole garden.

Brain break

Which One Doesn’t Belong? (WODB)

• Host a discussion about which one of these fractions ‘doesn’t belong’. (Hint: any answer can be correct – the justification is the important part.) Expect answers such as,'  1 2 because all the rest are tenths,   1 10  because all the rest are half or more,   10 10   because all the rest are half or less or because in all the others the numerator is less than the denominator’. 

Explicit teaching: Decimal notation

• After the Asian garden bed fractional drawing activity, introduce the concept of decimal notation as an alternative way to represent fractions. For example,    1 10   can be written as 0.1 in decimal notation.
• Ask students to take their garden bed designs and represent the fractions they've drawn using decimal notation. For example,   2 10   if they had drawn for lychees, they should now represent it as 0.2 in one of the squares.
• Provide guidance to ensure students understand how to convert fractions into decimals and encourage them to annotate the decimal representations of their garden beds.
• Discuss their garden bed designs with decimal notations, asking questions like, ‘What is the decimal representation for the fraction    3 10   in your garden bed?’ Emphasise that the sum of all decimal fractions in their garden bed should equal 1.0, representing the entire garden.

Optional: Students use Excel (or Word tables) to re-create their own Asian garden in a digital version.

Differentiation (extension): Challenge students to work with a 10 X 10 grid, or alternatively a 10 X 2 grid; represent equivalent fractions; represent using hand-drawn arrays; link with other denominators, for instance, ‘Are any of your gardens more than half ‘x’ fruit?’

Differentiation (support): Students work with a garden plot 2 X 2 or only 2 different fruits.

Concrete, Representational, Abstract (CRA) model: This lesson moves from using representation when drawing the garden to abstract when writing the proportions of the different fruits as fractions and decimals.

Summarise the lesson's key points and invite students to reflect on what they've learned:

• ‘What do you now know about fractions, in particular tenths?’
• ‘Can you explain the difference between a numerator and a denominator?’
• ‘How are common and decimal fractions linked?’
• ‘How can you use fractions in everyday situations?’