What's It Worth?
Task 75 ... Years 2 - 8
SummaryValue Relations is an important component in developing fraction understanding. Essentially it is about parts making up a whole and assigning a value to either the part or the whole, in order to work out the other. The values in this case are about money, but they could easily be other decimals, fractions, or whole numbers. The triangles provided help some students work out the required values. They also offer spatial challenges in themselves because students are, in effect, asked to work out and record all the pentiamonds and hexiamonds.
IcebergA task is the tip of a learning iceberg. There is always more to a task than is recorded on the card.
The first question on the card is straightforward calculation. The pentiamond is worth 5 x 55¢ = $2·75. However even simple questions can be extended.
Three in a row
The value of $3.30 in Question 3 implies shapes made with 6 equilateral triangles at 55¢ each. These are the hexiamonds. The full set can be found by beginning with the four pentiamonds above and finding all the ways of adding one more triangle. There are 12 altogether, one of which is the Sphinx. Students may like to assign names to the others.
The shape in Question 4 uses nine equilateral triangles. Since this is an odd number, one of the triangles must somehow be in the 'middle' to maintain symmetry. Some solutions are:
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.
If you can make lots of triangles from card, or wood you can easily use this task as a whole class investigation. The easier way is probably using card and getting the students to cut the triangle pieces from copies. You can also create similar problems of your own based on square tiles which are common in classrooms, but triangles probably give more interesting shapes.
The Maths300 lesson uses the Sphinx as the shape for the lesson (cut-out master is included) and squares and triangles as the shapes for the software.
For more ideas and discussion about this investigation, open a new browser tab (or page) and visit Maths300 Lesson 99, What's It Worth, which also includes an Investigation Guide.
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 What's It Worth? task is an integral part of:
The What's It Worth? lesson is an integral part of: