Why do this problem?
is an interesting way of practising addition and can be used to introduce children to the triangle numbers. It can also provide a context in which children can make mathematical predictions and justifications.
You could begin by using, for example, multilink cubes to represent the blocks. Show the children a red one and say that you could write an "A" on it. Then take two blue ones to write "B" on, then three yellows for "C". Ask the children how many blocks you have used altogether. How many would you have with the "D"s as well? How do they know? You could encourage them to talk to a partner and
use a mini-whiteboard or paper to jot down ideas. You can then set them off to work on the rest of the task.
You could use a plenary to talk about the different ways the children have worked on the problem - for example sharing different ways of recording. You might want to make a list of the totals on the board (1, 3, 6, 10, 15 etc) and ask the class whether they can see why these are triangle numbers. You could refer to square numbers to get them thinking, or draw patterns on the board.
What is the next letter of the alphabet?
How many bricks are needed for it?
How many bricks will that be altogether?
You could ask some children to predict how many blocks will have been used once, for example, the letter N has been used. How do they know? How about for the whole alphabet? Do they have any quick ways of working this out?
Using cubes to represent the blocks will help all children get started on this problem. When it comes to finding out why they are called triangle numbers, you could suggest that learners use squared paper and put the letters in the squares, for example:
Start like this: