Problem Solving Lesson: Bryony’s Triangle (Fractions)

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Summary:

In this lesson, students watch the video of Bryony’s triangle, where she uses a piece of paper to make an origami flower. She poses the question of ‘What fraction is…’ to the viewers, which is a great mental maths / hands on way at looking at fractions for students. It allows them to create a flower and discuss their results with a partner. It’s ‘almost’ guaranteed to get them talking about maths at home too!

Australian Curriculum Links:

  • Year 7 – Multiply and divide fractions and decimals using efficient written strategies and digital technologies(ACMNA154)
  • Year 7 – Express one quantity as a fraction of another, with and without the use of digital technologies(ACMNA155)
  • Year 7 – Connect fractions, decimals and percentages and carry out simple conversions (ACMNA157)

Lesson:

Introduction:
  1. Hand out coloured paper and advise students that we are going to look at solving quite a tricky problem that involves fractions.
  2. Revise simple fractions using squares and triangles to show halves, quarters, eighths, sixteenths… etc (see a pattern…)
  3. Watch the video below and pause if it is going too quick for your students.
  4. Ask students to write down the question that Bryony asked them to answer and try and solve the problem.
  5. Advise that it would be even better if you could show what is happening with drawings/diagrams
Body:
  1. Rove students and discuss what they think is happening?
  2. Take your ipad/other recording device around and video/take photos of the students working out the problem. (Make sure you get a video of someone who solved it)
  3. Encourage students to verbalise their thoughts as they are trying to solve the problem (allows for greater retention of ideas and assists those who may be thinking differently)

Conclusion:

This is the greatest opportunity to discuss how the problem worked. The emphasis should be to get the students to explain what is happening, not for the teacher to tell.

  1. Ask students to come together as a whole group to discuss what they think happened.
  2. Now play the videos/show the pictures of what the pairs were doing. (allows for more than one possibility)
  3. Ask for any volunteers to explain what happened in the problem and how they went about solving the problem (don’t ask for the answer yet) and record it on the board. Students can copy down as well.
  4. Keep asking for ideas and record these on the board too.
  5. Now ask the students to rank what they thought was the most efficient method / accurate method to solve the problem (we’re still not after the answer yet)
  6. Collate a tally for the results of the most effective method / solution.
  7. Ask students if they can explain why they believe the  most popular method / solution was the best.
  8. Ask other students to explain as well.
  9. Now give the students the answer (1/512) and check against the solutions on the board. Discuss again.

 

Assessment:

  • Working out in books
  • Video / Photo Assessments
  • Anecdotal notes

Resources:

  • Paper Squares
  • Grey Lead Pencils
  • Bryony’s Triangle Video (Below)

 

 

 

Lesson created from an idea that was seen on http://nrich.maths.org/7392

 

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