4 Arm Shapes
Task 154 ... Years 3 - 7
SummaryTiling patterns of various sorts can be found in many buildings, perhaps even in your school. The pattern used here is straightforward. The shape is an addition sign and the central tile is highlighted by a change of colour. The essence of the challenge is:
If I tell you any length for each arm can you tell me how many tiles are needed?This cameo has a From The Classroom section which shows unique ways of 'seeing' the generalisation that is the basis of the algebra in this problem.
4 Arm Shapes also appears on the Picture Puzzles Pattern & Algebra B menu where the problem is presented using one screen, two learners, concrete materials and a challenge.
IcebergA task is the tip of a learning iceberg. There is always more to a task than is recorded on the card.
The iceberg begins with the last challenge: Can you explain how you worked it out?
Extend further with questions such as:
Whole Class InvestigationTasks are an invitation for two students to work like a mathematician. Tasks can also be modified to become whole class investigations which model how a mathematician works.
To begin this lesson you will need a number of cards about 20cm square, one of which is different from the others. Hand out the cards and use a central floor or table space to invite the students to tile the area with the pattern above. Explain that the problem is:
If I tell you any length for each arm can you tell me how many tiles are needed?and more importantly:
Can you explain it to me in more than one way?Provide small tiles (or Poly Plug) to allow group exploration. Gather the students back at the floorboard model and invite them to use it to explain how they see the problem. Proceed further with questions such as those above.
It might help you to picture how this lesson could play out in your classroom as you watch two colleagues explore Teaching Craft with 4 Arm Shapes in this video on the You Tube channel of the Association of Teachers of Mathematics (ATM), UK, which can be accessed through Mathematics Centre Cube Tube.
For more ideas and discussion about this investigation, open a new browser tab (or page) and visit Maths300 Lesson 40, 4 Arm Shapes, which includes an Investigation Guide.
Visit 4 Arm Shapes in Menu Maths Pack A.
Is it in Maths With Attitude?Maths With Attitude is a set of hands-on learning kits available from Years 3-10 which structure the use of tasks and whole class investigations into a week by week planner.
The 4 Arm Shapes task is an integral part of:
The 4 Arm Shapes lesson is an integral part of:
4 Arm Shapes task is also included in the Task Centre Kit for Aboriginal Students.
From The Classroom
|My classrooms are usually with teachers because my work is 100% professional development. however, the great thing about my work is that the professional learning is often mine. I often use 4 Arm Shapes in algebra courses; it's seems so obvious and text-book like, but has so much more. In fact, at least four text book chapters are built into the one activity. I used it recently when working overseas and that's when I learnt a little more about how you could look at this problem.
|A teacher in one of my workshops at the ATM conference in England suggested that perhaps someone was ripping up an old courtyard to leave the four arm shape:
Johan Olsson, a teacher in training at one of my workshops at Högskolan Malmö, Sweden, used transformations to explain his way of seeing the algebra. Move the left and top arm as shown:
Algebra is concrete, visual and makes sense! This principle is explored further in the video Teaching Craft with 4 Arm Shapes, stored in Cube Tube.