SOME SUGGESTIONS FOR CHILDREN
From a very early age children love making lines and towers in a wide variety of materials. These games contain many elements of mathematical discourse.
Numbers never ever finish. Matilde, 4.6 years
When children make a line, or tower, count the elements our loud using your finger to point to each one.
You can encourage the children to count with you, and compare different lines and towers with each other.
You can ask:
> “Which line or tower is longer/shorter, or higher/lower?”
> “Where can you see more pieces / fewer pieces?”
Suggest the children build a line/ tower that is higher/lower, shorter/ longer than another one. Or again, suggest they make a line or tower using a certain number of pieces, and then verify together if it has been made with the number you decided on.
Using different materials, such as small mosaic tiles, pebbles, and small bricks or blocks, sequences of lines can be made by progressively increasing the number of pieces by 1, 2, or 3 units.
Here again, pause and encourage reflection. For example you might ask:
> How many lines can we make with X number of pieces
> What if we make the first line with just one piece, and then progressively make each line one piece longer (+1 procedure).
Does the number of lines we were able to make with our number of pieces change?
For example: let’s say we have 10 pieces
line 1: 1 piece (total 1 piece)
line 2: 1 piece +1 (total 2 pieces)
line 3: 2 pieces +1 (total 3 pieces)
line 4: 3 pieces +1 (total 4 pieces)
If we add up all the pieces, using +1 for each line, we can make 4 lines.
How about if we use +2 pieces for each line? How many lines can we make?
In the same way we can make triangles and other geometrical shapes, either by forming outlines or by filling the shapes in.
> What other shapes could we make with these tiles/pebbles/blocks?
Certainly, playing together with the children, more ideas will arise, either from you or from the conversations you have together.
One thing to remember: when a tower made with four pieces falls over (invariably causing glee) children won't automatically assume the same number of pieces is now on the floor.
This suggestion is part of Playing with numbers