This problem solving activity has a geometry focus.
Ngawai and Tom make a peanut butter sandwich.
How can they share it fairly?
Can you find three different ways to cut the sandwich?
This problem is about finding equal parts of a whole. A whole can be described as a region or a unit. When there are two equal parts, each is a half. To succeed at this problem, students should have experiences of seeing and manipulating halves of different sized and shaped regions.
The cuts in this problem have to be made so that each piece is exactly the same as the other. You may need to simplify the problem, in the first instance, by imagining that the loaf of bread has a rectangular cross-section.
Encourage the students to find as many ways of solving this problem as they can.
Ngawai and Tom make a peanut butter sandwich. How can they share it fairly?
Can you find three different ways to cut the sandwich?
There are, in fact, an infinite number of solutions. As long as you cut or fold through the centre point of the rectangle the parts will be equal. Some examples of single cuts or folds are:
In order to see that all of these cuts do give equal parts, you could cut out the halves and put them one on top of the other, or use digital images with the level of transparency increased (e.g. on PowerPoint). This may require rotation in some cases. This may provide the opportunity to explore some of the transformation ideas from the Geometry Strand.
If the bread has a cross-section that consists of a rectangle with a semi-circle on top, then there is only one simple solution to the problem by making a vertical cut. There must be another solution by cutting parallel to the base of the rectangle (the side opposite the semi-circle) but it is extremely difficult to find the exact point to make this cut.
The solutions are dependent on the shape of the loaf.
If 4 students share one sandwich they will each get 1/4. Demonstrate different ways of dividing the sandwich picture into quarters.
If Ngawai and Tom share 8 lollies they will each get 4 lollies.
Model dividing an item with a circular region into halves and quarters. Demonstrate folding to find the centre and drawing straight lines.
Printed from https://meaningfulmaths.nt.edu.au/mmws/nz/resource/sandwiches at 8:55pm on the 26th February 2024