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A good story has a beginning middle and end as does a great maths lesson. In this practical workshop we will investigate ways to adapt a task to meet the needs of a diverse class. How can we both “lower the floor” and make it more complex. In the process we will explore ways to spark curiosity, empower student voice using #noticeandwonder, develop reasoning through estimation and build sense making.
Penta people, the Pentigles, always build their houses from five square rooms on one level
The houses can be designed in a variety of shapes,. A room must be joined to at least one other room by one wall.
How many different house plans can you create?
Resources: Printable template
Plan view
Lets name each house plan
See if you can find an alphabet letter for each house plan.
Rebuilding Penta Place
1. The first houses to be rebuilt are made by joining 3 plans together so they make a rectangle
Which plans can you join together to make a 3 X 5 rectangle?
Extending the rebuild
2. How many other sized rectangles can you make by fitting 3 plans together?
3. One of the Pentigle families would like to live in a square house. Design a house that is 5 X 5 for them
Thinking mathematically
Which of the pentigle house plans have the same area?
Which have the same perimeter?
Write 4 Yes No questions to classify each plan shape
Finding Patterns
Find the total area of all the house plans
How many different rectangles can you make/draw with the same area?
What patterns do you see ?
Record your findings in at least 2 different ways
Thinking Geometrically
Which house plans have line symmetry?
Which house plans have rotational symmetry?
Which ones tessellate?
Extend to the 3rd dimension
Which shapes fold to make an open box?
Using multilink cubes what shapes can you make with 5 cubes
What is volume of each?
What is surface area?
Isometric drawing - sketch on paper - side - front - top
Other tasks & sites
Dot to dot activities. Find the dots that are a given distance apart and join them to reveal a picture
Estimation 180.com improves students number sense and problem solving skills through estimation challenges
Open middle problems that have the same beginnings and multiple ways to get to the solution
Further Reading
Making Maths Moments that matter - download their short guidebook to "Spark Curiosity, Fuel Sense-Making and Ignite Your Teacher Moves! "
Nix the trix this free download is filled with alternatives to the tricks so prevalent in mathematics education and explains exactly why the tricks are so bad for understanding math
Best Evidence Synthesis Summary of key ideas for teaching mathematics
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