A problem which involves separating two jumbled series of numbers.
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Triangular numbers are those numbers that can be formed by counting the number of objects used in making a triangle.
1) Ask the children to make these triangles using Unifix cubes or other suitable equipment. They should note down the number of cubes it took to build each triangle.
2) Discuss the numbers of cubes needed and explain that the number of cubes in each triangle is called a triangular number.
3) Ask them to look for any patterns in their work. How many cubes do they need to add to the bottom of each triangle to make it larger?
4) Is there a way of predicting how many cubes will be needed to build each triangle? How many cubes would be needed to make a triangle which has a base of 100 cubes?
5) You could also try the above activity, using triangles which only have sides (i.e. no middles). What is significant about the numbers in this case?