Tessellations Lesson Plan
Class 
Year 7 or 8 
Day 

Date 

Number of pupils 
25 
Start Time 
9:00 
End time 
10:00 
Topic
(including place in relation to previous and future lessons)
Previous lesson: on properties of regular polygons including number of sides and size of angles. Including group work so pupils will not need organising into tables for this lesson, just use the same ones. 5 groups of 5 pupils.
Future lessons:
 The shopping centre problem/ create a section of a beautiful wall poster for my classroom to explain tilings (emphasises on presentation and good explanations to appeal to other year 7 or 8's and the older pupils too!)
 Making polyhedra (quick search found this website: http://www.georgehart.com/virtualpolyhedra/classroom.html. Looks inspiring!).
National Curriculum References
(including key concepts, key processes and curriculum opportunities)
Pupil learning targets
To be shared:
Must: Find at least 3 tiling patterns.
Explain to a friend why the patterns you've found work, using maths words.
Should: Find 5 tiling patterns
Find patterns to explain why they work.
Could: Attempt the shopping centre problem.
Other learning targets:
Develop reasoning skills.
Personal Targets:
To ensure equal participation by each pupil in a group, and that noone is being left behind as the group moves forward.
Not to give information away  chose questions carefully to get them to tell me what is happening. Focus on helping them organise their thoughts and prompt to use the proper terminology to describe what they mean.
Resources:
Seating plan/group lists.
Whiteboard, pens and preprepared files.
Shapes precounted and divided into equal sized packs (one pack per table)
15x Semiregular tiling worksheets (one per pair)
15x shopping centre sheets (2 pages) (one each, not all will get that far)
Stack of lined and square paper (Can use either, offered to do lined for writing explanations, squared for drawing pictures)
Lesson Outline
Time 
Teacher Activity 
Pupil Activity /Actions/ Reactions (expected answers in brackets) 
9:00 
Have tessellation (of a relatively simple shape) projected on board before class arrives. Let pupils into classroom & quot;We've got some fun p rops to play with today, so be ready to work, quick! Don't need your books out, just your pencilcase." 
Should know where to sit from last lesson so will be relatively quick. Should be sufficiently interested. If take too long to settle class then skip parts of starter activity. Hopefully will be getting questions about the picture on the board which will draw in other pupils not settling down. 
STARTER 

9:05 [can be shortened] 
Here is a tessellation. Think about how you would describe it (allow 30secs). If answer is good but not sufficient ask someone else to build on it. 
Attention on the board. Take answers from approx 5 pupils (same shape repeated, no gaps in it, can be continued forever in all directions). 
[keep unless desperate for time] 
On whiteboard, have the triangle and hexagon picture with spare shapes at the side. 
What is different about this one? (2 different shapes) What rules are the same? (no gaps, can continue forever) Ask for volunteer to come up to the board and add some of the triangles/hexagons to the diagram. Ask someone else to explain how he knew where to put them. 
These are called semiregular tessellations 
Why do you think they were called that? (obvious!) 

Learning objectives screen. Leave up for rest of lesson, no need for pupils to copy down. 
Get pupils to read it (modify this: hard to stop them just ignoring it. Question the class on what they are?) 

9:15 
Instructions on the sheet, shapes in the pack, get started! 
4 volunteers to hand out first sheet, paper x2 and packs of shapes. 
To work on task without teacher intervention. Intervene only when a group is having trouble getting started : prompt them to start by creating the one on the sheet using the shapes handed out, then try to make a different one after that. 

9:20 [approx, monitor pupil's frustration levels] 
Emphasis importance of creating ways to describe what they are noticing and to record their findings (good and bad). 
Intervene with groups where workload is uneven  get all pupils involved. Only ask/answer vague or open ended questions, don't give anything away yet! 
9:30 
Monitor whole class 
Can give away some help now. For groups with several tiling patterns: how did they find them? Looking for signs of generalisation  expect pupils to explain a specific pattern. Can they give any rules for what will or won't tessellate? (angles sum to 360 at a point restricts choice > idea of looking at combinations of shapes around a vertex) Can you explain mathematically what you have found? For groups struggling to find patterns: Can they quickly show me what patterns they've tried already. What went wrong for (specific one/generalise to all of them)? How can this be avoided? Aim for them to discover looking around a vertex  lead in from "no gaps" idea in the starter if they don't bring it up themselves. For groups with all the tessellations: describe your findings mathematically. Be carefully to put a convincing argument together, write it on paper for me to take in. The best one will be typed up word for word to be used on a display about tessellations! (Next lesson  will get pupils to create an accompanying picture) 
For groups still only with few, come up with a way to describe what they are doing, can you use this rule to find another? (make sure they're on the right track so they don't fruitlessly stab in the dark) Once groups are happy with their convincing argument, start on the shopping centre problem. (To be continued next lesson) 

9:45 
PLENARY 

Class finish what they're doing, draw together to discuss findings. 
Get findings from each group, I pick a spokesperson from each group to give me one finding. Less interested in the tilings found, more interested in the maths behind it. Question to other members of the group (take volunteers): How did you figure that out? Can you show/explain why it works? If struggling, open the question to the rest of the class. 

Next lesson: those who started the shopping centre question, I expect you to explain the problem to the rest of the class. We'll be working on this. Also, I'll be picking the best reasoning to type up for a display. Next lesson someone gets to chose/make some semiregular tillings to accompany it. (A way to involve the weaker pupils?) 

End: Noone leaves until I have all the sheets and paper for each group stapled together with everyone's name on their group's work. 
Hands up when you've written everyone's names down, I'll come around with a stapler as you pack up. Dismissed as groups once work is stapled and in my hand. 
Prompts and Notes (possibly including whiteboard content)
Remember to check individual progress, not just group progress. Watch groups from afar to see interaction and division of tasks.
Language and Vocabulary
Tessellation, Semiregular tiling.
Triangle, square, hexagon.
Angle, vertex.
Differentiation Provision
(SEN, G&T, fast workers, slow workers)
G&T: The "convincing argument" must be very convincing: can ask them to add to it by looking over argument, finding a hole and asking them to plug it.
SEN: Early prompting to go in the correct direction. Put together on a table and stop there frequently as circulate classroom to help direct their thoughts. Depends on exact SEN: eg dyslexia provision is there is no need to write, only one copy needed per table.
Fast Workers: The Shopping Centre question.
Slow workers: Don't have to find all the tessellations.
Assessment Strategies
(how you will know if your learning targets have been made)
During lesson:
After lesson:
Homework
EDIT: I just came across this moreawesomethanaverage real life tesselation http://en.wikipedia.org/wiki/Tessellated_pavement
One comment
Jennifer Ingram
I really like this lesson plan – you have clearly thought about the task and the questioning to accompany the task. It might be worth adding to this as you go through more sessions, for example the assessment section is worth thinking about very carefully when you have completed the core and subject sessions on A4L.
06 Oct 2010, 22:24
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