Y6 Maths Masterclass 2008

Session 1 – Regular Polygons Incomputer suite

  • Make Name badges as pupils arrive.
  • Talk through Matchmania puzzles on board.
  • Demonstrate drawing regular polygons with turtle logo applet. What are the exterior angles? Why?
  • Fill in table showing exterior angles. Work out interior angles.
  • Then show Tessellating Polygons Investigation. Talk about regular tessellations. Why do some polygons tessellate?
  • Then they use GSP to investigate semi-regular tessellations and print out their results.
  • Finish with folding a regular pentagon/hexagon if time.
  • Show cake cutting puzzle clip for challenge.

Session 2 – The Fibonacci Sequence in maths room

  • Broken calculator puzzle as class arrive.
  • Talk about cake cutting puzzle. Any answers? Show video.
  • Go to stairs with whiteboard for recording. Complete stair climbing investigation. Encourage systematic approach.
  • Can anyone see a pattern in the numbers?
  • Now onto rabbits. Read from the Number Devil and show slides.
  • Show Fibonacci spiral video and then draw on squared paper using compasses.
  • Give brick wall problem as challenge.

Session 3 – Pascal’s Trianglein maths room

  • Talk through last week’s challenge. Link to Fibonacci sequence.
  • Find the words starter – Sand, Kites and Ghosts as pupils arrive. Encourage them to be systematic.
  • Then show binostat. Why do more balls end up in the middle?
  • They fill in The Binostat sheet. Use colours and make sure they don’t miss any. This should generate Pascal’s triangle.
  • Start writing the rows on blank triangle sheets. Can anyone see any patterns? They fill in rest of triangle. Check no mistakes.
  • Give out answers if necessary then look for patterns.
  • Now multiple colouring.
  • Give 12 days of Christmas problem as challenge.

Session 4 – The Platonic Solids in maths room

  • Look at last week’s challenge. Show location on Pascal’s triangle.
  • Explain what makes a Platonic Solid. They try to make platonic solids using Polydron shapes.
  • Show animated slides of 5 possible platonic solids.
  • Who knows about vertices, faces and edges? Count them up and fill in table.
  • Can we spot a pattern? Arrive at Euler’s theorem.
  • Extend onto making Archimedean Solids
  • Could also talk about Space Filling
  • Leave them with the Platonic Face Painting Solid.
  • Give them Maths Challenge Papers to do at home and email them with a list of sites relevant to the 4 lessons so far.

Session 5 – Quadrilaterals in computer suite

  • Play Back to Back to help develop terminology and accurate descriptions.
  • Investigate properties of quadrilaterals using GSP file. Fill in table.
  • Play Guess the Quadrilateral. 2 yes/no questions and then guess. What makes a good question?
  • Demonstrate the last biscuit game and give them this as a challenge.

Session 6 –Codes in maths room

  • Play last biscuit against each other. Then against computer. Who can explain their strategy.
  • Introduce Substitution Ciphers and give them simple one to solve.
  • Talk about different shifts. Give them Vigenere Square to solve the next one.
  • Introduce using letter frequency to solve a harder Caesar Cipher.
  • Give them order of frequency and harder example of passage to solve in groups. Prizes for winners. Hints available to help if necessary.
  • Could go onto another type of code – Bar Codes.
  • Some puzzles to take away as challenge.

Session 7 – Cubes and Cuboids in maths room

  • Talk through puzzles from last time.
  • In groups finding all the different pentominoes and then hexominoes.
  • Which of these will fold to make a cube?
  • Now Fly on cuboid video problem.
  • They work it out. Explain how the net can help with this answer.
  • Finish with making a folding cube net from card.

Session 8 – Topology and Paradoxes in compute suite

  • Square dissection puzzles to start
  • To start with, look at pencil caught in buttonhole problem and hands tied together problem.
  • Pass disc through hole that looks smaller. Removing waistcoat without jacket.
  • Talk about topology
  • Introduce the Mobius strip. Everyone makes one.
  • Ask class to colour in just one side of it. What happens? Talk about conveyer belt patent.
  • Now we will cut it lengthways. Prediction as to what will happen.
  • Now make another and cut one third of the way across this time.
  • 4 colour map problem.
  • Leave them with the disappearing square dissection online and which they can make themselves.
  • Email again with sites relevant to last 4 sessions and invite to JMC.