Task 178 ... Years 4 - 8
SummaryThis is one of several tasks that begin with an easily accessed concrete/visual pattern, but lead on to considerable algebraic possibilities. Students are asked to make triangle chains, similar to those used in engineering for strengthening structures. The main challenge in the problem is:
This cameo includes an Investigation Guide and a From The Classroom section which explains why a class of primary students developed a PowerPoint to 'teach the other teachers'.
Match Triangles 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: Explain your answer.
Extend further with questions such as:
Usually teachers prepare their own Investigation Guides but in this case two teachers have gone further. Jodi Wilson and Maria Antoniou, Mt. Eliza Secondary College, have prepared their own Guide and then offered it to colleagues through this cameo. We very much appreciate this form of sharing and encourage others to do the same.
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 convert this task to a whole class lesson with the purpose of addressing all the mathematics above while modelling what it means to work like a mathematician, you need plenty of pop sticks or an alternative such as straws cut to size. However, for a greater level of involvement, which is sensible management because it adds purpose to using the sticks before they are distributed, begin with each student quickly preparing a newspaper roll. Students bring this to a central floor space and a whole class model of the triangle chain is quickly constructed. Discussion and challenge begins here and the table top models are then used to explore and confirm hypotheses before returning to the public floorboard model for discussion and extension. (See From The Classroom below.)
Many teachers report that an added advantage of lessons like these is that when the next lesson is a related 'toolbox lesson', perhaps from a text book, students often comment that the ...stuff in the book is simple.
For more ideas and discussion about this investigation, open a new browser tab (or page) and visit Maths300 Lesson 164, Match Triangles.
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 Match Triangles task is an integral part of:
The Match Triangles lesson is an integral part of:
Match Triangles task is also included in the Task Centre Kit for Aboriginal Students.
From The Classroom
St. Monica's Primary School
Miss Collis called this an 'aha' moment and couldn't stop smiling and we felt successful.