Table patterns go wild!

Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Table Patterns Go Wild! printable sheet

You might have made some times table patterns on hundred squares before. Some tables make vertical lines, some make diagonal lines and some make different patterns. Hundred squares are 10 by 10 grids, and in this problem we will call these '10 grids'.

Have a look at the 10 grids below.

Image
Table patterns go wild!



Which times tables made these patterns? Why?

We are going to look at the patterns made on square grids of other sizes, from 4 grids (a 4 by 4 grid) to 9 grids.

These are patterns on a 7, a 5, an 8 and a 6 grid:

Image
Table patterns go wild!

Which times tables made these patterns? Can you explain why they look like this?

Now it is time to do your own investigations. You can use grids drawn on squared paper or use this sheet of 10 grids.

Have a go at working out what makes vertical and diagonal lines on the different grids.

Can you make the checked pattern? What times table do you need to use on each grid?

Here are the top parts of some grids.

Can you identify which times table has been used to make each one?

Image
Table patterns go wild!



Here are some parts of various grids. This time we have not shown the edges of the grids. Can you identify which times tables on which grids could have been used to make these patterns?

Image
Table patterns go wild!

There may be more than one answer.