Dewch i Feddwl Mathemateg (9 i 11 oed) Gwers 6 Siapiau Symudwyr

# Lesson Plan

Abstract |

Who knows what a crystal is? What is special about how it grows? A new type of crystal was discovered by a space expedition. It always starts in a square shape but can change to become a different quadrilateral shape. We need to work out the secret of exactly how the crystal changes its shape so we can predict what shapes it could turn into. |

Episode 1 |

IntroIntroduce the children to the square shaped aliens using a large pin board and an elastic band, or on an interactive whiteboard tool, by showing a 2 x 2 square on the top left of a 5 x 5 grid, labelled ABCD, and asking them to describe what they can see. Encourage them to focus on the position of the shape on the grid as well as the properties: Move point B one space to the right and tell the children that some crystals with this new shape have been seen. How could you describe how the shape has changed? What might the secret of the shape change be? Pairs discuss the questions, then feedback ideas, which are listed. Use questions eg. there? where? to play upon ambiguities that arise from initial descriptions, as the children need to struggle to explain their actions efficiently to see the need for using a common language. Establish that the shape can move one vertex horizontally or vertically in any direction, and this move can be more than one space, but that diagonal moves are not permitted. Ask the pupils to repeat the rules to you so that you can write them up on the board. For example: Reinforce by asking children what instruction they would give to change a given shape back to a square, and/or model an incorrect move and asking if it is permitted. |

Group DiscussionWorking in pairs, use a pin board or dotty paper to investigate how many different shapes the aliens could be if using the above rules. For each new shape you find, you must have a written description of how your shape changed. How will you record the move you have made for each alien? |

SharingSelected pairs to share their findings. Establish there are only three possibilities ie. these trapeziums in different orientations (one vertex, one move and one vertex two moves) How did you record the moves you did? Collate ideas on the board for comparison and agree a coding system. For example: • Use the A/B/C/D labels as above or label corners TL (top left) etc • Use V/H (for vertical/horizontal) or ↑/↓ • Use a number for distance. So a move might be B1V or TL2↓. Consider the systematic sequencing of the coding, so, is it best to always use the same order eg start point-distance-direction or is a random order acceptable? |

Episode 2 |

IntroA second and more advanced crystal has also been located. These crystals have been classified as level two crystals. Explore what this might mean by showing an oblong level two rectangle transposed over the original square and asking children to describe the change. They will recognise that two moves have been made (vertex B two moves right and vertex D two moves right) How could this alien change back to the square? Ask the pupils to write the rule for this second crystal. For example: |

Group DiscussionWork in pairs to investigate how many different shapes a level two alien can make. Record the moves made for each shape using the agreed coding system. (Some children will need to continue to use the pin boards, in which case a second elastic band of a different colour is useful, whilst most use several copies of Resource Sheet A.) |

SharingWhat different level two alien shapes did you find? Pairs feedback the different shapes and describe how they shifted, using the coding system. Identify shapes (children may be using 2D shape names, though not necessarily), which are the same, but in a different position (ie. translations). Children should recognise that in this system, the 2 x 2 square provides the starting point ie. the zero position. NB the focus for discussion here is not on finding all the possibilities, but checking the efficiency of the coding system they have developed. Have we found all possibilities? How can we be sure? Focus in on any use of a system to record the different possible moves. Some pupils may have listed these systematically, rather than relying on drawing alone. |

Episode 3 |

IntroA collection of crystals has been found, but these include new types which can make three, and even four, moves! The task for the scientists is to identify the crystals by working out the shifts they have made. Can we work out whether shapes have been made by level one/two/three/ or four crystals? Reinforce link to one/two/three/four moves from the original square shape. |

Group DiscussionChildren work in pairs to identify the crystals on Resource Sheet B, according to their level description, by working out how they have shifted. |

SharingFeedback findings by pairs of children giving instructions for transforming some of shapes on Resources Sheet B from the original square. Could you predict accurately which level the shape would be? How? Can you see any patterns? Prompt: What did you notice about the number of moves for shape 4 compared to shape 8? Will a bigger rectangle need more than 3 moves? Can you describe a link between the number of moves and the size of the oblong? |