My granddaughter finished school a bit 'off colour' the other day and then was sick in the night. Her temperature was still a bit high in the morning, although she seemed to be picking up, so guess who got the call to look after her at home while mummy went to work.

When I arrived, apart from being shown where the food and the tea bags were and how to work the new control-everything-from-the-one-panel remote, I was presented with a list of possible activities for the day if needed. Mother and daughter had apparently discussed them in preparation for my arrival. One of the things on the list was 4 times tables.

The young lady had just started Year 3, so a reasonable expectation that she learn this set of facts to automatic recall level. A mathematician's work is certainly about investigating problems, but those investigations are going to be more efficiently tackled if key tools are available for instant use. So, as the day progressed we tried a few times - in between lots of other nice stuff. (I would have been happy to watch Moana for the umpteenth time.)

The first try was while munching Vegemite toast - no butter. Just asking a few to see what she knew. If she knew them she knew them. No problem. If she didn't, she tried to work them out. The process of working out seemed to be to start from one you know and count forward by ones. Understandable, but not really group counting and definitely not automatic response. Fifteen minutes and we had only worked on three or four.

Later we had another try when I found a laminated 0 - 100 chart. We used a marking pen to circle any she knew automatically when asked. Then she tried to fill in the gaps. My phone rang after we started this and by the time I finished the call - 3 minutes or so - she had circled every counting by 4 number from 0 to 100 (with only one slip up). So pattern was a tool she could use. We looked closer and she started to see the last digit pattern. That was enough though - we had been at it at least another 15 minutes.

However, not long after she asked if we could use 'that phone game we did before'. She meant the calculator game we had played with the calculator app on the phone. It's called 6 Times, but of course it can be 4 Times. It involves two people and two calculators. Both press 4 X then just one secretly presses another digit and =.

Player A shows their screen to Player B. Then Player B presses a *guessed* digit and they compare screens. This kept us occupied for a while but it was like pulling teeth because there was no way she was going to guess unless she was sure she was right. Mind you, there was a point where she said, "No, it can't be 31, that's an odd number." This was followed by the guess of 32, which turned out to be the same as on my screen. At this point I suggested she close her eyes and say '4 times 8 = 32' to herself three or four times to see if that would help her remember it. We tried that with a couple of others as well.

It was too wet to play outside, so we lined up some chairs and cushions in the longeroom and took some of the dolls for a trip to Sydney. During lunch - scrambled eggs on toast which we made together; she was clearly feeling better - I was thinking we hadn't really come too far with the automatic response. The back of mind was wondering what I was missing.

After lunch we looked at the activity list again. Having been to Sydney and back it was okay to do that. She chose the one that involved using her pad device. She showed me that she could go on line and log in to a site to do some maths. The software took her to some part where she had finished last time and I was fascinated with what happened next. A voice told her how to do a very particular type of maths exercise (not times tables), the screen wrote on itself, then she was given one to do ... and another ... and another ... and then ... this became like pulling teeth too.

I am certain she would have stopped well before getting her score out of 10 if I hadn't been sitting beside her encouraging her to get it over with.

For me it was almost the same as the way I was taught maths when I was at school, except I could see the teacher's face and all ten on the board at the same time and the teacher could see when I was bored witless. Technology has made such advances since then.

Then I had a thought. If we could go on line to this site, then we could also go to Mathematics Centre. So I headed for the Picture Puzzles (see **Link List** below) and the 2 & 4 Times Tables Torture:

These puzzles are designed as a timed game involving two people, but it was easy to adapt for one. We were told there were going to be 20 challenges, so on paper I wrote 1 to 20 with space for answers. I told Little One that she could use the timer on my phone to set any time for herself to work out the 20 answers. I watched as she rolled the timer around to 20 minutes, paused, then rolled it on to 30.

Then it was up to her. The slides were not in 'times tables order'. She studied each one as she chose it, wrote her answer and moved on to the next one. She didn't lose concentration. When she reached the big STOP sign on the screen she was momentarily surprised, then slapped her finger onto the timer to stop it. Nine minutes and a few seconds!

- Apart from the trip to Sydney this was more involvement (self-driven involvement in fact) than I had seen all day.
*Why?*
- What are the features offered by the Picture Puzzle that are likely to have captivated and absorbed her?

Any sensible grandparent would have stopped there, but that's not one of my characteristics. She seemed to know she had the 20 correct, but we hadn't really checked them. I encouraged her to show me how she did these ones:

The first had given trouble all day. She mostly worked out the 4 rows of 5 counting by ones, then sort of recognised that the 20 and 4 was like when she started at 4 x 5 because she knew it and then counted 4 more. Counting by ones was used to start with in the second one too, then all of a sudden, and with delight, she burst out with *'if that's 20 then it's 40'*. An 'aha' moment. Now it *was* time to stop. Besides, we heard mummy's car roll in.

The young one is still seeking automatic response. And I am still seeking ways to help her.

**Editor's Note:** This Picture Puzzle derives from a Calculating Changes activity. Members have access to the whole class investigation form of Times Tables Torture which includes a slide for each times table from 1 x 1 to 10 x 10. Teachers select the ones they want to use and make their own slide show. The slide show is first shown to the whole class as a timed challenge, then the discussion moves to *How do you know?* and *Can you check it another way?*