Flag fractionisation

Warm-up: 2 truths, 1 lie

• Show the warm-up exercise image from the teacher’s slides (slide 2). Students use mini-whiteboards or their maths book to choose ‘True’ or ‘False’ and justify their answer using mathematical language.
• Expect responses such as - True because it is cut into four pieces; False because the parts don’t look the same. Rate the responses - gather or annotate some students’ answers. Have a class discussion as to what constitutes a quarter (four equal parts) and why this is quarters.
• Further questioning includes – What is the relationship between a quarter and a half?

Differentiation (extension): Can you prove it with concrete materials such as a piece of paper?

Differentiation (support): Similar diagram/discussion utilising halves instead of quarters.                                                                                                                                       

Classroom talk

• Conduct classroom talk with a ‘Notice/Wonder’: show students the flags of Thailand (left) and France (right) side by side (see teacher’s slides, slide 3).
• Ask students what they notice, and what they wonder about the flags. Direct the conversation towards mathematical language, including ‘vertical’, ‘horizontal’, ’fractions’, ’equal’, ’equivalent’ and ’thirds’.
• Share with students that today we will be investigating various flags from around the world.

(Optional: take a few minutes to research and discover the flags of the countries associated with students’ own heritage.)

Fractions of a flag student worksheet activity (15 mins)

• Distribute the Fractions of a flag student worksheet, which features flags of different countries. Ask students to find the fractions of different colours within each flag.
• Students work on the worksheet independently, investigating the fractional representations of these flags, including Italy, Germany, Austria, Jamaica, Panama, Australian Aboriginal, and Torres Strait Islander. (Note: Torres Strait Islander flag may look like it is thirds but is in fact halves/quarters.) See the Further information section for more background detail on some of these flags.
• Students can use estimation strategies for some of the more challenging flags.
• When students have done their investigation, ask the following.
  • ‘Which flags were easiest to find the fractions for each colour and why?’
  • ‘Which flags were hardest and why?’
  • ‘How did you figure out the fractions for the harder flags?’
  • ‘Why do you think the Australian flag isn’t included on the worksheet?’

 You may want to incorporate Aboriginal and Tores Strait Islander Histories and Cultures when discussing origins of Australian flags. Refer to Australian flags and maths.

Exploration of fractions through Asian flag design (15 mins)

• Distribute art supplies.
• Show students the Flags of Asia map (see teacher’s slides, slide 4). Explain that the flags have been distributed across two worksheets, and that students will receive a sheet showing half the flags.
• Distribute the Flags of Asia Worksheet and instruct students to select an Asian flag to redraw from their sheet using the 6 x 4 grid or blank rectangle (teachers can adjust the borders on the grid to suit their students).
• Students should represent fractions by colouring specific parts of the flag with different colours, so geometric designs are better suited, for instance, flags such as those from Cyprus or Saudi Arabia would not be a good choice for this activity.
• Emphasise the concept of numerator and denominator as students redraw their flags. For example, if they colour two out of four sections, explain that 2 is the numerator and 4 is the denominator.

Differentiation (support): for students experiencing difficulty, easier options include the flags of Indonesia, Japan, Armenia and Yemen.

Differentiation (mid): options include the flags of Laos, United Arab Emirates, Tajikistan and the State of Palestine.

Differentiation (extension): for students requiring a further challenge, options include the flags of Kuwait, Malaysia and Uzbekistan.

Paired ‘barrier’ activity (15 mins)

• When students have completed redrawing their chosen flag teacher removes the Flags of Asia map (slide 4).
• In pairs, students play a ‘barrier’ game using mathematical language to get their partner to redraw their chosen flag without looking at it. Students instruct their partner to complete this task again using a 6 x 4 grid or rectangle. See below for example for drawing the national flag of India:
  • Begin with a rectangular shape that is 6 x 4 (provided on reverse of worksheet).
  • Divide the rectangle into three equal horizontal stripes.
  • Colour the top stripe saffron, the middle one should be white, and the bottom stripe should be green.
  • Ensure that each stripe is one-third of the total height.
  • In the centre of the middle white stripe, draw a navy blue circle to represent the Ashoka Chakra.
  • The Ashoka Chakra should have 24 equally spaced spokes or lines radiating from the centre.
  • The flag from Nepal would not be a good choice for this activity.
• Gallery Walk: When students have redrawn their partner’s chosen flag, have students leave their flag on their desk and allow student to move about the room, looking at the various flags. Encourage discussions about the similarities and differences in their fractional representations.

Utilising number lines (10 mins)

• Provide students with number lines.
• Explain how they can use number lines to locate and represent unit fractions within their flag designs. For instance, if they coloured half of the flag, mark the number line accordingly.

Optional activity: Students design their own flag.

Differentiation (extension): ask open questions, for example, ‘What could your flag look like if   2 6  of it were blue?’

Differentiation (support): ask closed questions, for example, ‘I would like you to draw me a flag that is half blue, half red.’

• Summarise the lesson's key points.
• Invite students to reflect on what they've learned.
  • ‘What did you find most interesting about the various fractions in flags?’
  • ‘What do we know about numerators and denominators?’
  • ‘Do thirds always look the same? What makes fractions equal’?